studies of laser beams propagating through turbulent atmospheres are important for many applications such as remote sensing , tracking , and long - distance optical communications .
 howerver , fully coherent laser beams are very sensitive to fluctuations of the atmospheric refractive index .
 the initially coherent laser beam acquires some properties of gaussian statistics in course of its propagation through the turbulence . as a result , the noise / signal ratio approaches unity for long - distance propagation .
 ( see , for example , refs.@xcite-@xcite ) .
 this unfavourable effect limits the performance of communication channels . to mitigate this negative effect
 the use of partially ( spatially ) coherent beams was proposed .
 the coherent laser beam can be transformed into a partially coherent beam by means of a phase diffuser placed near the exit aperture .
 this diffuser introduces an additional phase ( randomly varying in space and time ) to the wave front of the outgoing radiation .
 statistical characteristics of the random phase determine the initial transverse coherence length of the beam .
 it is shown in refs .
 @xcite,@xcite that a considerable decrease in the noise / signal ratio can occur under following conditions : ( i ) the ratio of the initial transverse coherence length , @xmath0 , to the beam radius , @xmath1 , should be essentially smaller than unity ; and ( ii ) the characteristic time of phase variations , @xmath2 , should be much smaller than the integration time , @xmath3 , of the detector .
 however , only limiting cases @xmath4 and @xmath5 have been considered in the literature .
 ( see , for example , refs .
 @xcite,@xcite and ref .
 @xcite , respectively ) .
 it is evident that the inequality @xmath6 can be easily satisfied by choosing a detector with very long integration time . at the same time
 , this kind of the detector can not distinguish different signals within the interval @xmath3 .
 this means that the resolution of the receiving system might become too low for the case of large @xmath3 . on the other hand
 , there is a technical restriction on phase diffusers : up to now their characteristic times , @xmath2 , are not smaller than @xmath7 . besides that , in some specific cases ( see , for example , ref .
 @xcite ) , the spectral broadening of laser radiation due to the phase diffuser ( @xmath8 ) may become unacceptably high .
 the factors mentioned above impose serious restrictions on the physical characteristics of phase diffusers which could be potentially useful for suppressing the intensity fluctuations .
 an adequate choice of diffusers may be facilitated if we know in detail the effect of finite - time phase variation , introduced by them , on the photon statistics . in this case
 , it is possible to control the performance of communication systems . in what follows , we will obtain theoretically the dependence of scintillation index on @xmath9 without any restrictions on the value of this ratio
 this is the main purpose of our paper .
 further analysis is based on the formalism developed in ref .
 @xcite and modified here to understand the case of finite - time dynamics of the phase diffuser .
 the detectors of the absorbed type do not sense the instantaneous intensity of electromagnetic waves @xmath10 .
 they sense the intensity averaged over some finite interval @xmath3 i.e. @xmath11 usually , the averaging time @xmath3 ( the integration time of the detector ) is much smaller than the characteristic time of the turbulence variation , @xmath12 , ( @xmath13 ) .
 therefore , the average value of the intensity can be obtained by further averaging of eq .
 [ one ] over many measurements corresponding various realizations of the refractive - index configurations .
 the scintillation index determining the mean - square fluctuations of the intensity is defined by @xmath14\bigg /\big
 < \bar{i}\big > ^2=
 \frac{\big < : \bar i(t ) ^2:\big>}{\big<\bar i \big>^2}-1,\ ] ] where the symbol @xmath15 indicates the normal ordering of the creation and annihilation operators which determine the intensity , @xmath10 .
 ( see more details in refs .
 @xcite,@xcite ) . the brackets @xmath16 indicate quantum - mechanical and atmospheric averagings .
 the intensity @xmath17 depends not only on @xmath18 , but also on the spatial variable @xmath19 . therefore , the detected intensity is the intensity @xmath20 averaged not only over @xmath18 as in eq .
 [ one ] , but also over the detector aperture . for simplicity , we will restrict ourselves to calculations of the intensity correlations for coinciding spatial points that correspond to `` small '' detector aperture .
 this simplification is quite reasonable for a long - distance propagation path of the beam .    in the case of quasimonochromatic light
 , we can choose @xmath20 in the form @xmath21 where @xmath22 and @xmath23 are the creation and annihilation operators of photons with momentum @xmath24 .
 they are given in the heisenberg representation .
 @xmath25 is the volume of the system .
 it follows from eqs .
 [ two],[three ] that @xmath26 can be obtained if one knows the average @xmath27 it is a complex problem to obtain this value for arbitrary turbulence strengths and propagation distances .
 nevertheless , the following qualitative reasoning can help to do this in the case of strong turbulence .
 we have mentioned that the laser light acquires the properties of gaussian statistics in the course of its propagation through the turbulent atmosphere . as a result , in the limit of infinitely long propagation path , @xmath28 , only
 diagonal " terms , i.e. terms with ( i ) @xmath29 or ( ii ) @xmath30 , @xmath31 contribute to the right part of eq . [ four ] . for large but still finite @xmath28
 , there exist small ranges of @xmath32 in case ( i ) and @xmath33 , @xmath34 in case ( ii ) contributing into the sum in eq .
 the presence of the mentioned regions is due to the two possible ways of correlating of four different waves ( see ref .
 @xcite ) which enter the right hand side of eq .
 [ four ] . as explained in ref .
 @xcite , the characteristic sizes of regions ( i ) and ( ii ) depend on the atmospheric broadening of beam radii as @xmath35 , thus decreasing with increasing @xmath28 . in the case of long - distance propagation , @xmath36 is much smaller than the component of photon wave - vectors perpendicular to the @xmath28 axis .
 the last quantity grows with @xmath28 as @xmath37 .
 ( see ref .
 @xcite ) . for this reason ,
 the overlapping of regions ( i ) and ( ii ) can be neglected . in this case
 eq . [ four ] can be rewritten in the convenient form : @xmath38 @xmath39 where the value @xmath40 , confining summation over @xmath41 , is chosen to be greater than @xmath42 but much smaller than the characteristic transverse wave vector of the photons ; this is consistent with the above explanations .
 the two terms in the right - hand side correspond to the two regions of four - wave correlations .
 the quantity @xmath43 entering the right side of eq . [ five ] is the operator of photon density in phase space ( the photon distribution function in @xmath44 space ) .
 it was used in refs . @xcite,@xcite and
 @xcite for the description of photon propagation in turbulent atmospheres . by analogy
 , we can define the two - time distribution function @xmath45 then eq . [ five ] can be rewritten in terms of the distribution functions as @xmath46    let us represent @xmath47 in the form @xmath48 .
 we assume that @xmath49 , as explained in the text after eq.[one ] . in this case
 the hamiltonian of photons in a turbulent atmosphere can be considered to be independent of time . as a result , both functions defined by eqs .
 [ six ] and [ seven ] satisfy the same kinetic equation , i.e.    @xmath50 @xmath51 where @xmath52 is the photon velocity , @xmath53 is a random force , caused by the turbulence .
 this force is equal to @xmath54 , where @xmath55 is the frequency of laser radiation .
 @xmath56 is the refractive index of the atmosphere .
 the general solution of the equation for @xmath48 can be written in the form @xmath57 where @xmath58 @xmath59 the functions @xmath60 and @xmath61 obey the equations of motion @xmath62 with the boundary conditions @xmath63 .
 the instant @xmath64 is equal to @xmath65 , where @xmath66 is the speed of light .
 @xmath64 is the time of the exit of photons from the source .
 this choice of @xmath64 makes it possible to neglect the influence of the turbulence on the initial values of operators @xmath67 ( their dependence on time is as in vacuum ) .
 the term for @xmath68 can be obtained from eq . [ twelve ] by putting @xmath69 . substituting both distribution functions into eq .
 [ eight ] , we obtain @xmath70 @xmath71 @xmath72:\big>,\ ] ] where @xmath73 and @xmath74 are solutions of eqs .
 [ twelve ] with the initial conditions @xmath63 and @xmath75 , respectively .
 the operators on the right side of eq . [ thirteen ] are related through matching conditions with the amplitudes of the exiting laser radiation ( see ref .
 @xcite ) by the relation @xmath76 where @xmath77 is the operator of the laser field which is assumed to be a single - mode field and the subscript ( @xmath78 ) means perpendicular to the @xmath28-axis component .
 the function @xmath79 describes the profile of the laser mode , which is assumed to be gaussian - type function [ @xmath80 .
 @xmath1 desribes the initial radius of the beam .    to account for the effect of the phase diffuser
 , a factor @xmath81 or @xmath82 should be inserted into the integrand of eq . [ fourteen ] .
 the quantity @xmath83 is the random phase introduced by the phase diffuser .
 a similar consideration is applicable to each of four photon operators entering both terms in square brackets of eq .
 [ thirteen ] .
 it can be easily seen that the factor @xmath84},\ ] ] describing the effect of phase screen on the beam , enters implicitly the integrand of eq .
 [ thirteen ] ( the indices @xmath78 are omitted here for the sake of brevity ) .
 there are integrations over variables @xmath85 as shown in eq .
 [ fourteen ] .
 furthermore , the brackets @xmath16 , which indicate averaging over different realizations of the atmosperic inhomogeneities , also indicate averaging over different states of the phase diffuser .
 as long as both types of averaging do not correlate , the factor ( [ fifteen ] ) entering eq .
 [ thirteen ] must be averaged over different instants , @xmath64 . to begin with ,
 let us consider the simplest case of two phase correlations @xmath86}\big > .\ ] ] it is evident that in the case @xmath87 , as shown schematically in fig .
 1 , the factor ( [ sixteen ] ) is sizable if only points @xmath19 and @xmath88 are close to one another .
 two curves correspond to different instants @xmath18 and @xmath89 . ]    therefore , the term given by eq .
 [ sixteen ] can be replaced by @xmath90 where @xmath91 is considered to be a gaussian random variable with the mean - square values given by @xmath92 ^ 2\rangle =   \langle [ \frac { \partial \varphi ( { \bf r},t_0)}{\partial y}]^2\rangle = 2\lambda _ c^{-2}$ ] , where @xmath93 is the correlation length of phase fluctuations . ( see fig.1 ) . as we see , in this case the effect of phase fluctuations can be described by the schell model @xcite-@xcite,@xcite-@xcite .    a somewhat more complex situation is for the average value of @xmath94 given by eq . [ fifteen ] .
 there is an effective phase correlation not only in the case of coincident times , but also for differing times . for @xmath95 , two different sets of coordinates contribute considerably to phase correlations .
 this can be described mathematically as @xmath96}\big > \approx \big < e^{i[\varphi ( { \bf r},t_0)-\varphi   ( { \bf r^\prime},t_0)]}\big > \times\ ] ] @xmath97}\big > + \big < e^{i[\varphi ( { \bf r},t_0)-\varphi   ( { \bf r^\prime _
 1},t_0+\tau ) ] } \big > \big < e^{i[\varphi ( { \bf r_1},t_0+\tau ) -\varphi   ( { \bf r^\prime } , t_0)]}\big > .\ ] ] repeating the arguments leading to eq .
 [ seventeen ] , we represent the difference in the last term @xmath98 as @xmath99 then , considering the random functions @xmath100 and @xmath101 as independent gaussian variables , we obtain a simple expression for @xmath102 . it is given by @xmath103}+ e^{-\lambda _ c^{-2}[({\bf r - r^\prime}_1)^2+({\bf r^\prime -r_1})^2]-2\nu^2\tau ^2},\ ] ] where @xmath104 ^ 2\rangle = 2\nu^2 $ ] .    as we see , the effect of the phase screen can be described by two parameters , @xmath93 and @xmath105 , which characterize the spatial and temporal coherence of the laser beam . in the limiting case , @xmath106 , the second term in eq .
 [ twenty ] vanishes and the problem is reduced to the case considered in refs .
 @xcite,@xcite . in the opposite case , @xmath107 , both terms in eq .
 [ twenty ] are important .
 this is shown in ref .
 @xcite . in
 what follows , we will see that these two limiting cases have physical interpretations where where @xmath108 ( slow detector ) and @xmath109 ( fast detector ) , respectively .
 there is a specific realization of the diffuser in which a random phase distribution moves across the beam .
 ( this situation can be modeled by a rotating transparent disk with large diameter and varying thickness . )
 the phase depends here on the only variable @xmath110 , i.e. @xmath111 where @xmath112 is the velocity of the drift .
 then we have @xmath113}+e^{-\lambda _ c^{-2}[({\bf r - r^\prime_1+v}\tau)^2+({\bf r^\prime -r_1+v}\tau)^2]}.\ ] ] comparing eqs .
 [ twenty ] and [ twtw ] , we see that the quantity , @xmath114 , stands for the characteristic parameter describing the efficiency of the phase diffuser .
 the criterion of  slow " detector requires @xmath115 .
 qualitatively , the two scenarios of phase variations , given by eqs . [ twenty ] and [ twtw ] , affect in a similar way the intensity fluctuations . in what follows
 , we consider the first of them as the simplest one .
 ( this is because the spatial and temporal variables in @xmath102 , given by eq . [
 twenty ] , are separable . )
 _ vs _ propagation distance @xmath28 in the case of `` slow '' detector : @xmath116 .
 the parameter @xmath117 indicates different initial coherence length . in the absence of phase diffuser @xmath118 ( solid line ) .
 @xmath119 is the conventional parameter describing a strength of the atmospheric turbulence . ]
 substituting the expressions for operators given by eq .
 [ fourteen ] with account for the phase factors @xmath120 and averaging over time as shown in eq .
 [ one ] , we obtain @xmath121 @xmath122\bigg > , \ ] ] where the notation @xmath16 after sums indicates averaging over different realizations of the atmospheric refractive index .
 the parameter @xmath123 describes the initial coherence length modified by the phase diffuser .
 other notations are defined by following relations @xmath124
 @xmath125 @xmath126 further calculations follow the scheme described in ref @xcite .
 2 illustrates the effect of the phase diffuser on scintillations in the limit of a  slow " detector ( @xmath127 ) .
 we can see a considerable decrease in @xmath128 caused by the phase diffuser . at the same time , the effect of the phase screen on @xmath128 becomes weaker for finite values of @xmath129 .
 moreover , comparing the two upper curves in fig .
 3 , we see the opposite effect : slow phase variations ( @xmath130 ) result in increased scintillations .
 there is a simple explanation for this phenomenon : the noise generated by the turbulence is complemented by the noise arising from the random phase screen .
 the integration time of the detector , @xmath3 , is not sufficiently large for averaging phase variations generated by the diffuser .
 the function , @xmath131 , has a very simple form in the two limits : ( i)@xmath132 , when @xmath133 ; and ( ii ) @xmath134 , when @xmath109 .
 then , in case ( i ) and for small values of the initial coherence [ @xmath135 , the asymptotic term for the scintillation index ( @xmath136 ) is given by @xmath137 the right - hand side of eq .
 [ twfo ] differs from analogous one in ref .
 @xcite by the value @xmath138 that is much less than unity but , nevertheless , can be comparable or even greater than @xmath139 .    in case ( ii )
 , the asymptotic value of @xmath26 is close to unity , coinciding with the results of refs . @xcite and @xcite .
 this agrees with well known behavior of the scintillation index to approach unity for any source distribution , provided the response time of the recording instrument is short compared with the source coherence time .
 ( see , for example , survey @xcite ) .
 a similar tendency can be seen in both figs . 3 and 4 : the curves with the smallest @xmath129 , used for numerical calculations ( @xmath130 ) , are close to the curves  without diffuser " in spite of the small initial coherence length [ @xmath140 .
 it can also be seen that all curves approach their asymptotic values very slowly .
 describing diffuser dynamics .
 the solid curve is calculated for @xmath118 ( without diffuser ) .
 other curves are for @xmath141 . ]    . ]
 it follows from our analysis that the scintillation index is very sensitive to the diffuser parameters , @xmath0 and @xmath142 , for long propagation paths .
 on the other hand , the characteristics of the irradience such as beam radius , @xmath143 , and angle - of - arrival spread , @xmath144 , do not depend on the presence of the phase diffuser for large values of @xmath28 . to see this , the following analysis is useful .
 the beam radius expressed in terms of the distribution function is given by @xmath145 straightforward calculations using eq .
 [ ten ] with @xmath69 ( see ref .
 @xcite ) result in the following explicit form : @xmath146 where @xmath147 and @xmath148 is the inner radius of turbulent eddies , which in our previous calculations was assumed to be equal @xmath149 m . as we see , the third term does not depend on the diffuser parameters and it dominates when @xmath150 .
 a similar situation holds for the angle - of - arrival spread , @xmath144 .
 ( this physical quantity is of great importance for the performance of communication systems based on frequency encoded information @xcite . )
 it is defined by the distribution function as @xmath151 simple calculations , which are very similar to those while obtaining @xmath152 , result in @xmath153 ^ 2=\frac 2{r_1 ^ 2q_0 ^ 2}+12tz-\frac { 4z^2}{q_0 ^ 4r^2}(r_1^{-2}+3tq_0 ^ 2z)^2.\ ] ] for long propagation paths ,
 . [ twei ] reduces to @xmath154 , which like @xmath152 does not depend on the diffuser parameters .
 as we see , for large distances @xmath28 , the quantities @xmath152 and @xmath144 do not depend on @xmath93 and @xmath105 .
 this contrasts with the case of the scintillation index .
 so pronounced differences can be explained by differences in the physical nature of these characteristics .
 it follows from eq .
 [ two ] that the functional , @xmath26 , is quadratic in the distribution function , @xmath155 .
 hence , four - wave correlations determine the value of scintillation index .
 the main effect of a phase diffuser on @xmath26 is to destroy correlations between waves exited at different times .
 ( see more explanations in ref .
 this is achieved at sufficiently small parameters @xmath93 and @xmath156 .
 in contrast , @xmath152 and @xmath144 depend on two wave - correlations , both waves being given at the same instant .
 therefore , the values of @xmath152 and @xmath144 do not depend on the rate of phase variations [ @xmath105 does not enter the factor ( [ seventeen ] ) describing the effect of phase diffuser ] .
 moreover , these quantities become independent of @xmath93 at long propagation paths because light scattering on atmospheric inhomogeneities prevails in this case .
 the plots in figs .
 3 anf 4 show that the finite - time effect is quite sizable even for very  slow " detectors ( @xmath157 ) .
 our paper makes it possible to estimate the actual utility of phase diffusers in several physical regimes .
 we have analyzed the effects of a diffuser on scintillations for the case of large - amplitude phase fluctuations .
 this specific case is very convenient for theoretial analysis because only two parameters are required to describe the effects of the diffuser .
 phase fluctuations may occur independently in space as well as in time .
 also , our formalism can be applied for the physical situation in which a spatially random phase distribution drifts across the beam .
 [ twtw ] . )
 our results show the importance of both parameters , @xmath93 and @xmath142 , on the ability of a phase diffuser to suppress scintillations .
 this work was carried out under the auspices of the national nuclear security administration of the u.s .
 department of energy at los alamos national laboratory under contract no .
 de - ac52 - 06na25396 .
 we thank onr for supporting this research .

Abstract:
the effect of a random phase diffuser on fluctuations of laser light ( scintillations ) is studied .
 not only spatial but also temporal phase variations introduced by the phase diffuser are analyzed .
 the explicit dependence of the scintillation index on finite - time phase variations is obtained for long propagation paths .
 it is shown that for large amplitudes of phase fluctuations , a finite - time effect decreases the ability of phase diffuser to suppress the scintillations .


the simulations we discuss here allowed us to obtain spectra of the shg response .
 we employed comsol multiphysics software ( www.comsol.com ) in order to perform simulations of the linear optical response as described in ref .
 @xcite . a unit cell containing a single sic pillar attached to the sic substrate
 was constructed , with floquet boundary conditions along the @xmath30-axis and periodic boundary conditions along the @xmath31-axis , perpendicular to the plane of incidence .
 a _ p_-polarized plane wave at frequency @xmath32 was launched towards the sic structure at an incident angle of 25@xmath33 .
 originating from the _ p_-polarised light source , the electric field @xmath34 inside the sic pillar and substrate was recorded .
 then , this electric field was translated into the nonlinear polarization @xmath16 , according to eq .
 ( 1 ) in the main manuscript . there , the following non - zero components of the nonlinear susceptibility were accounted for : @xmath14 , @xmath17 and @xmath18 .    as a next step , @xmath16 in the pillar and the substrate
 was regarded as the source of scattered electric field @xmath35 inside the unit cell .
 the shg output was then obtained by integrating the power flow through a _
 xy_-plane set above the substrate .
 sweeping the fundamental frequency and taking the dispersion of both linear and nonlinear sic susceptibilities from refs.@xcite , we calculated several shg spectra for samples with various periodicity of the pillars .
 we note that in these calculations , the input power density at fundamental frequency was kept constant , and the shg output power was normalized to the area of the _ xy_-plane @xmath36 . the results of the simulations presented in fig
 .  [ analysis ] in the main manuscript demonstrate a single pronounced peak corresponding to the excitation of the sphp monopole mode .
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Abstract:
we report on strong enhancement of mid - infrared second harmonic generation ( shg ) from sic nanopillars due to the resonant excitation of localized surface phonon - polaritons within the reststrahlen band .
 the magnitude of the shg peak at the monopole mode experiences a strong dependence on the resonant frequency beyond that described by the field localization degree and the dispersion of linear and nonlinear - optical sic properties . comparing the results for the identical nanostructures made of 4h and 6h sic polytypes
 , we demonstrate the interplay of localized surface phonon polaritons with zone - folded weak phonon modes of the anisotropic crystal . tuning the monopole mode in and out of the region where the zone - folded phonon is excited in 6h - sic , we observe a prominent increase of the already monopole - enhanced shg output when
 the two modes are coupled . envisioning this interplay as one of the showcase features of mid - infrared nonlinear nanophononics , we discuss its prospects for the effective engineering of nonlinear - optical materials with desired properties in the infrared spectral range .
 light localization in sub - wavelength volumes is a core of modern nanophotonics .
 conventional methods of achieving strong confinement of the electromagnetic fields extensively utilize unique properties of surface plasmons .
 a remarkable variety of objects and materials supporting these excitations ensures the key role of plasmonics in a broad range of applications @xcite .
 apart from unparalleled sensitivity of plasmonic structures to the optical properties of the environment , strong light localization facilitates nonlinear - optical effects @xcite .
 owing to the spectral tunability of the localized plasmon resonances and their sizeable nonlinearity , metallic nanostructures of different shapes and sizes have earned their place in nonlinear photonics .    despite obvious advantages of plasmon - based nanophotonics , metallic nanoobjects exhibit significant optical losses , which lower the quality factor of the localized surface plasmon modes .
 fast plasmon damping ( typically on the order of 10 fs ) due to ohmic losses @xcite thus inhibits nonlinear - optical conversion .
 an alternative , promising metal - free approach has been suggested , utilizing polar dielectrics such as sic @xcite or bn @xcite for high - quality light confinement in the mid - infrared ( ir ) . in these materials ,
 the subdiffractional confinement of electromagnetic radiation relies upon surface phonon polaritons ( sphp ) in the reststrahlen band : the electric polarization is created due to coherent oscillations of the ions instead of the electron or hole densities . due to the significantly longer scattering times associated with optical phonons
 as compared to surface plasmons , the lifetimes of sphps tend to be on the order of picoseconds , much longer than their plasmonic counterparts @xcite .
 in addition , due to energies associated with optical phonons , sphps with typical frequencies within the mid - ir ( @xmath0 ) to the thz domain hold high promise for spectroscopic and nanophotonic applications @xcite .    in this letter
 , we undertake a first step towards the largely unexplored domain of mid - ir nonlinear nanophononics .
 we study the nonlinear - optical response of localized sphps using nanostructures made of different polytypes of sic . using free electron laser ( fel ) radiation in the mid - ir spectral range @xcite
 , we probe second harmonic generation from rectangular arrays of sub - diffractional , cylindrical sic nanopillars .
 the shg yield in the reststrahlen band of sic demonstrates prominent enhancement at the wavelengths associated with the excitation of the sphp eigenmodes of the pillars . depending on both the size and the spatial periodicity of the pillars ,
 the shg - probed eigenmode exhibits a spectral shift accompanied with strong variations of the shg intensity . analyzing different sic polytypes
 , we demonstrate the interplay of the localized sphps with the zone - folded optical phonon modes .
 we further conclude that strong coupling of the two modes allows for a significant additional modulation of the sphp - enhanced shg output .
 the schematic of our experimental approach is outlined in fig .
 [ general],a .
 we employed a non - collinear shg configuration discussed elsewhere @xcite to perform spectroscopic shg measurements on square arrays of 1  @xmath1m - tall 4h - sic and 6h - sic pillars with the main axis of the arrays in the _ xz _ plane of incidence .
 the fundamental radiation incident at 28 and 62 degrees with respect to the normal to the sample surface was focused onto the sample with a peak fluence on the order of 10 mj/@xmath2 .
 both 4h and 6h - sic samples were c - cut so that the _ c_-axis of the crystals was parallel to the surface normal .
 typical shg and linear reflectivity spectra collected using the fel radiation for the two incident polarisations are presented in fig .
 [ general],b - e .
 there , the respective spectra of the bare substrate are shown for comparison .
 for _ p_-polarised fundamental radiation ( fig .
 [ general],d ) , the shg response features two pronounced peaks located at the zone - center frequencies of transverse and longitudinal optical phonons in sic @xcite , around 797 @xmath3 and 965 @xmath3 , respectively . the corresponding shg spectrum from the nanopillars demonstrate a much stronger shg signal at around 900 @xmath3 . due to the absence of this peak in the shg spectrum
 when the fundamental radiation is _
 s_-polarised , we attribute this shg feature to the excitation of the monopole sphp mode in the nanopillars @xcite .    in general ,
 the outgoing shg field @xmath4 is related to the incident electromagnetic fields @xmath5 via the so - called local field factors @xmath6 :    @xmath7    where @xmath8 is the nonlinear polarisation and @xmath9 is the nonlinear susceptibility tensor .
 the excitation of the sphp monopole mode leads to strong localization of the _ z_-projection of the fundamental electric field @xmath10 ( normal to the surface plane ) and thus a resonant enhancement of @xmath11 .
 the latter results in a pronounced increase of the shg output when the fundamental radiation is _ p_-polarised .
 however , the sphp dipole modes observed in the range of 920960  @xmath3 rely on the resonant enhancement of the in - plane electric fields described by the local field factors @xmath12 and thus can be excited with both _
 p_- and _ s_-polarised fundamental radiation .
 the total shg response is given by a vector sum of the terms on the right hand side of eq .
 ( 1 ) originating from various tensor components of the nonlinear susceptibility @xmath13 .
 as the strength of @xmath14 is the largest in this spectral range @xcite , the sphp monopole mode , with an enhancement of @xmath11 , naturally results in a higher shg output than the dipole modes .
 the results of the systematic studies of the shg response of various arrays of nanopillars are summarized in fig .
 [ shifts ] for the 4h - sic ( a , c ) and 6h - sic ( b , d ) samples .
 the panels ( a - b ) illustrate the evolution of the shg spectra upon varying pillar diameter @xmath15 .
 it is seen that upon decreasing @xmath15 , the sphp monopole - driven shg peak exhibits a clear redshift .
 remarkably , while the sphp monopole mode shifts in the range of about 890 - 910 @xmath3 , the shg enhancement factor associated with the excitation of the sphp monopole mode varies strongly with @xmath15 .
 the panels ( c - d ) offer a zoom - in into the evolution of the sphp monopole mode - driven shg for a large variety of nanopillar arrays , indicating that the variations of the shg enhancement are observed for both 4h and 6h samples .
 the dependences of the sphp monopole - driven shg output on the spectral position of the sphp monopole mode for the two sic polytypes are shown in fig .
 [ analysis],a with open symbols .
 = 1200 , 1100 and 1000 nm , respectively .
 , scaledwidth=47.0% ]        the strong dispersion in the sic reststrahlen band suggests that the observed spectral dependence of the shg enhancement could be captured in numerical simulations .
 we calculated shg response using both linear and nonlinear sic dispersion@xcite , the results of the simulation of the linear optical response@xcite , and nonlinear polarization @xmath16 from eq .
 ( 1 ) spatially integrated over the sic volume , with the following non - zero components of the nonlinear susceptibility : @xmath14 , @xmath17 and @xmath18 .
 the resultant shg spectra simulated with comsol multiphysics software ( www.comsol.com ) are shown in fig .
 [ analysis],b with full symbols .
 it is seen that the steep experimental dependence can not be quantitatively described within the simple model used in the calculations , which yields only a moderate increase of the shg output when the sphp monopole mode frequency is decreased .
 we note the work of carpetti _
 et al_. @xcite where the authors thoroughly examined plasmon - induced shg enhancement from arrays of au nanoparticles as a function of the inter - particle distance @xmath19 . in the regime of @xmath20 ( as it is in our case ) , the dependence of the shg output on @xmath19 was explained in terms of the changing filling factor ( and thus the associated number of active nanoemitters ) .
 for very small inter - particle gaps ( @xmath21 ) , a modulation of the shg output has been attributed to the modification of the electromagnetic field localization in the gaps @xcite .
 further , a large mismatch between the spatial period of the nanopillars @xmath22 and the resonant light wavelength @xmath23 rules out the excitation of propagating surface polaritons @xcite which are known to enhance the shg output @xcite .
 since all these effects are included in our simulations , we conclude that the origin of the observed shg enhancement is unrelated to the periodicity of the array .
 an alternative scenario for the observed trend could invoke modifications of the non - local shg contribution enhanced by a regular array structure .
 the importance of the non - local shg was already demonstrated in a number of subwavelength - separated plasmonic nanoobjects @xcite .
 the amplitude and phase of this non - local shg source depends on the electric field distribution , i.e. on both the pillar size @xmath15 and the periodicity @xmath24 .
 as such , the interference conditions between the shg sources vary for different samples , thus resulting in a strong modification of the shg output .
 further , the apparent difference in the shape of the resonant shg output for the 4h and 6h samples ( see fig .  [ shifts ] ) is related to the anisotropic nature of sic .
 the hexagonal sic polytypes are known to exhibit zone - folded weak modes in the reststrahlen region @xcite originating from particular stacking of the atomic layers along the _
 c_-axis of the crystal @xcite .
 these weakly ir - active zone - folded modes can be visualised in the reflectivity measurements at oblique incidence @xcite .
 although zone - folded modes exist in both 4h and 6h polytypes , different stacking of the sic atomic layers is responsible for them having different frequencies , as illustrated in fig .
 [ analysis],c - d .
 the additional periodicity in the crystal results in folding of the large brillouin zone thus modifying the phonon dispersion and making the excitation of phonons with non - zero wavevectors ( @xmath25 ) possible .
 it is seen in fig .
 [ analysis],d that the zone - folded mode in the 6h - sic polytype with the reduced wavevector @xmath26 @xmath27 can be excited in the range of @xmath28  @xmath3 which is close to the typical monopole sphp resonant frequency of the sic nanopillars discussed above .
 in particular , the interaction of the sphp and zone - folded mode which shifted the apparent spectral positions of the monopole sphp eigenmode in the linear response @xcite , is seen responsible for the complex structure of the resonant shg output in our experiments ( fig .
 [ shifts],d ) .
 the weak ir activity of the zone - folded modes is related to the large negative dielectric permittivity of sic in the reststrahlen band . as such , the out - of - plane component of the electromagnetic field @xmath10 remains small which inhibits the coupling of incident light to the zone - folded phonon mode .
 however , the excitation of the sphp monopole mode in the nanopillars drives a strong increase of @xmath10 , which facilitates the sphp monopole interaction with the zone - folded phonon ( fig .
 [ analysis],c ) .
 figure  [ analysis],a illustrates the effect of the zone - folded mode on the observed shg output .
 the open red squares ( 4h ) and blue circles ( 6h ) depict the shg intensity obtained at the sphp monopole ( resonant ) frequencies , and the dashed lines illustrate a clear correlation between the maximum shg output and the spectral position of the sphp monopole peak .
 similar trends are observed for the 4h and 6h - sic samples as long as the sphp monopole and the zone - folded mode are well - separated .
 when these two resonances start to overlap , an additional enhancement of the shg output produced at the sphp monopole resonance in 6h - sic samples is observed .
 moreover , the dependence of the shg signal at the frequency of the zone - folded mode @xmath29  @xmath3 ( green triangles ) exhibits a much faster increase when the two resonances are brought together ( dotted line ) , indicating an efficient interplay between the sphp monopole and the zone - folded mode .
 we note that the interaction of the localized sphp eigenmodes and the intrinsic excitations of the medium is a unique fingerprint of mid - ir nanophononics . indeed
 , surface plasmon excitations in metals rely on the free electron gas , which is essentially isotropic . as such , the shg output of plasmonic nanostructures is ( i ) largely determined by the metal of choice , usually au , ( ii ) exhibits only weak spectral dependence @xcite and ( iii ) is limited by robust phase relations in the likely case of multiple shg sources @xcite . on the contrary , the flexibility of the sphps is provided by the coupling of the surface phonon polariton excitations to the intrinsic bulk phonon modes . the latter can be engineered by designing artificial metamaterials based on hybrid multilayer structures @xcite , thus allowing for an effective control of their optical properties . to summarize ,
 we have observed shg output enhancement associated with the excitation of the sphp eigenmodes in an array of nanopillars grown from sic of different polytypes .
 the strongest shg output is associated with the excitation of the monopole sphp mode characterized by strong localization of the normal to surface projection of the electric field @xmath10 .
 the spectral positions of the shg peaks shift according to the geometric parameters of the nanophononic structures .
 we found a strong dependence of the magnitude of the shg enhancement on the resonant frequency .
 this experimentally observed dependence can not be quantitatively described by simply taking into account the sub - diffractional field localization and the dispersion of the linear and nonlinear optical properties of sic .
 further , we discuss the interplay of the sphps and the intrinsic crystalline anisotropy for an efficient nonlinear - optical conversion . this mechanism is supported by the shg spectral measurements on the 6h - sic nanopillars where excitation of the sphp monopole mode interacting with the weak zone - folded phonon resulted in an additional enhancement of the shg output .
 the presence of intrinsic resonances strongly alters the phase relations in their vicinity , providing a natural way for optimizing the shg response in a relatively narrow spectral range .
 our findings demonstrate high potential of mid - ir nonlinear nanophononics as a novel and promising platform for nonlinear optics and illustrate the rich opportunities it provides for efficient control over nonlinear - optical response .
 the authors thank g.  kichin and a.  kirilyuk ( radboud university nijmegen ) for stimulating discussions .
 s.a.m . acknowledges the office of naval research , the royal society , and the lee - lucas chair in physics . a.j.g . acknowledges financial support from the nrc / nrl postdoctoral fellowship program .
 funding for j.d.c . was provided by the office of naval research through the naval research laboratory s nanoscience institute .


with significant research efforts being directed to the development of neurocomputers based on the functionalities of the brain , a seismic shift is expected in the domain of computing based on the traditional von - neumann model .
 the @xmath0 @xcite , @xmath1 @xcite and the ibm @xmath2 @xcite are instances of recent flagship neuromorphic projects that aim to develop brain - inspired computing platforms suitable for recognition ( image , video , speech ) , classification and mining problems . while boolean computation is based on the sequential fetch , decode and execute cycles , such neuromorphic computing architectures are massively parallel and event - driven and are potentially appealing for pattern recognition tasks and cortical brain simulations
 to that end , researchers have proposed various nanoelectronic devices where the underlying device physics offer a mapping to the neuronal and synaptic operations performed in the brain . the main motivation behind the usage of such non - von neumann post - cmos technologies as neural and synaptic devices stems from the fact that the significant mismatch between the cmos transistors and the underlying neuroscience mechanisms result in significant area and energy overhead for a corresponding hardware implementation .
 a very popular instance is the simulation of a cat s brain on ibm s blue gene supercomputer where the power consumption was reported to be of the order of a few @xmath3 @xcite .
 while the power required to simulate the human brain will rise significantly as we proceed along the hierarchy in the animal kingdom , actual power consumption in the mammalian brain is just a few tens of watts .    in a neuromorphic computing platform
 , synapses form the pathways between neurons and their strength modulate the magnitude of the signal transmitted between the neurons .
 the exact mechanisms that underlie the `` learning '' or `` plasticity '' of such synaptic connections are still under debate .
 meanwhile , researchers have attempted to mimic several plasticity measurements observed in biological synapses in nanoelectronic devices like phase change memories @xcite , @xmath4 memristors @xcite and spintronic devices @xcite , etc .
 however , majority of the research have focused on non - volatile plasticity changes of the synapse in response to the spiking patterns of the neurons it connects corresponding to long - term plasticity @xcite and the volatility of human memory has been largely ignored . as a matter of fact , neuroscience studies performed in @xcite have demonstrated that synapses exhibit an inherent learning ability where they undergo volatile plasticity changes and ultimately undergo long - term plasticity conditionally based on the frequency of the incoming action potentials .
 such volatile or meta - stable synaptic plasticity mechanisms can lead to neuromorphic architectures where the synaptic memory can adapt itself to a changing environment since sections of the memory that have been not receiving frequent stimulus can be now erased and utilized to memorize more frequent information .
 hence , it is necessary to include such volatile memory transition functionalities in a neuromorphic chip in order to leverage from the computational power that such meta - stable synaptic plasticity mechanisms has to offer .
 [ drawing1 ] ( a ) demonstrates the biological process involved in such volatile synaptic plasticity changes . during the transmission of each action potential from the pre - neuron to the post - neuron through the synapse , an influx of ionic species like
 @xmath5 and @xmath6 causes the release of neurotransmitters from the pre- to the post - neuron .
 this results in temporary strengthening of the synaptic strength .
 however , in absence of the action potential , the ionic species concentration settles down to its equilibrium value and the synapse strength diminishes . this phenomenon is termed as short - term plasticity ( stp ) @xcite . however ,
 if the action potentials occur frequently , the concentration of the ions do not get enough time to settle down to the equilibrium concentration and this buildup of concentration eventually results in long - term strengthening of the synaptic junction .
 this phenomenon is termed as long - term potentiation ( ltp ) . while stp is a meta - stable state and lasts for a very small time duration
 , ltp is a stable synaptic state which can last for hours , days or even years @xcite .
 a similar discussion is valid for the case where there is a long - term reduction in synaptic strength with frequent stimulus and then the phenomenon is referred to as long - term depression ( ltd ) .
 such stp and ltp mechanisms have been often correlated to the short - term memory ( stm ) and long - term memory ( ltm ) models proposed by atkinson and shiffrin @xcite ( fig .
 [ drawing1](b ) ) .
 this psychological model partitions the human memory into an stm and an ltm . on the arrival of an input stimulus , information is first stored in the stm . however , upon frequent rehearsal , information gets transferred to the ltm . while the `` forgetting '' phenomena occurs at a fast rate in the stm , information can be stored for a much longer duration in the ltm .    in order to mimic such volatile synaptic plasticity mechanisms , a nanoelectronic device is required that is able to undergo meta - stable resistance transitions depending on the frequency of the input and also transition to a long - term stable resistance state on frequent stimulations .
 hence a competition between synaptic memory reinforcement or strengthening and memory loss is a crucial requirement for such nanoelectronic synapses . in the next section
 , we will describe the mapping of the magnetization dynamics of a nanomagnet to such volatile synaptic plasticity mechanisms observed in the brain .
 let us first describe the device structure and principle of operation of an mtj @xcite as shown in fig .
 [ drawing2](a ) .
 the device consists of two ferromagnetic layers separated by a tunneling oxide barrier ( tb ) .
 the magnetization of one of the layers is magnetically `` pinned '' and hence it is termed as the `` pinned '' layer ( pl ) .
 the magnetization of the other layer , denoted as the `` free layer '' ( fl ) , can be manipulated by an incoming spin current @xmath7 .
 the mtj structure exhibits two extreme stable conductive states  the low conductive `` anti - parallel '' orientation ( ap ) , where pl and fl magnetizations are oppositely directed and the high conductive `` parallel '' orientation ( p ) , where the magnetization of the two layers are in the same direction .
 let us consider that the initial state of the mtj synapse is in the low conductive ap state .
 considering the input stimulus ( current ) to flow from terminal t2 to terminal t1 , electrons will flow from terminal t1 to t2 and get spin - polarized by the pl of the mtj .
 subsequently , these spin - polarized electrons will try to orient the fl of the mtj `` parallel '' to the pl .
 it is worth noting here that the spin - polarization of incoming electrons in the mtj is analogous to the release of neurotransmitters in a biological synapse .
 the stp and ltp mechanisms exhibited in the mtj due to the spin - polarization of the incoming electrons can be explained by the energy profile of the fl of the mtj .
 let the angle between the fl magnetization , @xmath8 , and the pl magnetization , @xmath9 , be denoted by @xmath10 .
 the fl energy as a function of @xmath10 has been shown in fig .
 [ drawing2](a ) where the two energy minima points ( @xmath11 and @xmath12 ) are separated by the energy barrier , @xmath13 . during the transition from the ap state to the p state , the fl has to transition from @xmath12 to @xmath11 . upon the receipt of an input stimulus , the fl magnetization proceeds `` uphill '' along the energy profile ( from initial point 1 to point 2 in fig .
 [ drawing2](a ) ) .
 however , since point 2 is a meta - stable state , it starts going `` downhill '' to point 1 , once the stimulus is removed .
 if the input stimulus is not frequent enough , the fl will try to stabilize back to the ap state after each stimulus .
 however , if the stimulus is frequent , the fl will not get sufficient time to reach point 1 and ultimately will be able to overcome the energy barrier ( point 3 in fig .
 [ drawing2](a ) ) .
 it is worth noting here , that on crossing the energy barrier at @xmath14 , it becomes progressively difficult for the mtj to exhibit stp and switch back to the initial ap state .
 this is in agreement with the psychological model of human memory where it becomes progressively difficult for the memory to `` forget '' information during transition from stm to ltm .
 hence , once it has crossed the energy barrier , it starts transitioning from the stp to the ltp state ( point 4 in fig .
 [ drawing2](a ) ) .
 the stability of the mtj in the ltp state is dictated by the magnitude of the energy barrier .
 the lifetime of the ltp state is exponentially related to the energy barrier @xcite .
 for instance , for an energy barrier of @xmath15 used in this work , the ltp lifetime is @xmath16 hours while the lifetime can be extended to around @xmath17 years by engineering a barrier height of @xmath18 .
 the lifetime can be varied by varying the energy barrier , or equivalently , volume of the mtj .
 the stp - ltp behavior of the mtj can be also explained from the magnetization dynamics of the fl described by landau - lifshitz - gilbert ( llg ) equation with additional term to account for the spin momentum torque according to slonczewski @xcite , @xmath19 where , @xmath20 is the unit vector of fl magnetization , @xmath21 is the gyromagnetic ratio for electron , @xmath22 is gilberts damping ratio , @xmath23 is the effective magnetic field including the shape anisotropy field for elliptic disks calculated using @xcite , @xmath24 is the number of spins in free layer of volume @xmath25 ( @xmath26 is saturation magnetization and @xmath27 is bohr magneton ) , and @xmath28 is the spin current generated by the input stimulus @xmath29 ( @xmath30 is the spin - polarization efficiency of the pl ) . thermal noise is included by an additional thermal field @xcite , @xmath31 , where @xmath32 is a gaussian distribution with zero mean and unit standard deviation , @xmath33 is boltzmann constant , @xmath34 is the temperature and @xmath35 is the simulation time step .
 equation  [ llg ] can be reformulated by simple algebraic manipulations as , @xmath36 hence , in the presence of an input stimulus the magnetization of the fl starts changing due to integration of the input . however , in the absence of the input , it starts leaking back due to the first two terms in the rhs of the above equation .
 it is worth noting here that , like traditional semiconductor memories , magnitude and duration of the input stimulus will definitely have an impact on the stp - ltp transition of the synapse .
 however , frequency of the input is a critical factor in this scenario . even though the total flux through the device is same ,
 the synapse will conditionally change its state if the frequency of the input is high .
 we verified that this functionality is exhibited in mtjs by performing llg simulations ( including thermal noise ) .
 the conductance of the mtj as a function of @xmath10 can be described by , @xmath37 where , @xmath38 ( @xmath39 ) is the mtj conductance in the p ( ap ) orientation respectively . as shown in fig .
 [ drawing2](b ) , the mtj conductance undergoes meta - stable transitions ( stp ) and is not able to undergo ltp when the time interval of the input pulses is large ( @xmath40 ) .
 however , on frequent stimulations with time interval as @xmath41 , the device undergoes ltp transition incrementally .
 [ drawing2](b ) and ( c ) illustrates the competition between memory reinforcement and memory decay in an mtj structure that is crucial to implement stp and ltp in the synapse .
 we demonstrate simulation results to verify the stp and ltp mechanisms in an mtj synapse depending on the time interval between stimulations .
 the device simulation parameters were obtained from experimental measurements @xcite and have been shown in table i.    [ table ]    table i. device simulation parameters    [ cols="^,^ " , ]      +                the mtj was subjected to 10 stimulations , each stimulation being a current pulse of magnitude @xmath42 and @xmath43 in duration . as shown in fig .
 [ drawing3 ] , the probability of ltp transition and average device conductance at the end of each stimulation increases with decrease in the time interval between the stimulations .
 the dependence on stimulation time interval can be further characterized by measurements corresponding to paired - pulse facilitation ( ppf : synaptic plasticity increase when a second stimulus follows a previous similar stimulus ) and post - tetanic potentiation ( ptp : progressive synaptic plasticity increment when a large number of such stimuli are received successively ) @xcite .
 [ drawing4 ] depicts such ppf ( after 2nd stimulus ) and ptp ( after 10th stimulus ) measurements for the mtj synapse with variation in the stimulation interval .
 the measurements closely resemble measurements performed in frog neuromuscular junctions @xcite where ppf measurements revealed that there was a small synaptic conductivity increase when the stimulation rate was frequent enough while ptp measurements indicated ltp transition on frequent stimulations with a fast decay in synaptic conductivity on decrement in the stimulation rate .
 hence , stimulation rate indeed plays a critical role in the mtj synapse to determine the probability of ltp transition .
 the psychological model of stm and ltm utilizing such mtj synapses was further explored in a @xmath44 memory array .
 the array was stimulated by a binary image of the purdue university logo where a set of 5 pulses ( each of magnitude @xmath45 and @xmath46 in duration ) was applied for each on pixel .
 the snapshots of the conductance values of the memory array after each stimulus have been shown for two different stimulation intervals of @xmath47 and @xmath48 respectively .
 while the memory array attempts to remember the displayed image right after stimulation , it fails to transition to ltm for the case @xmath49 and the information is eventually lost @xmath50 after stimulation .
 however , information gets transferred to ltm progressively for @xmath51 .
 it is worth noting here , that the same amount of flux is transmitted through the mtj in both cases .
 the simulation not only provides a visual depiction of the temporal evolution of a large array of mtj conductances as a function of stimulus but also provides inspiration for the realization of adaptive neuromorphic systems exploiting the concepts of stm and ltm .
 readers interested in the practical implementation of such arrays of spintronic devices are referred to ref .
 the contributions of this work over state - of - the - art approaches may be summarized as follows .
 this is the first theoretical demonstration of stp and ltp mechanisms in an mtj synapse .
 we demonstrated the mapping of neurotransmitter release in a biological synapse to the spin polarization of electrons in an mtj and performed extensive simulations to illustrate the impact of stimulus frequency on the ltp probability in such an mtj structure .
 there have been recent proposals of other emerging devices that can exhibit such stp - ltp mechanisms like @xmath52 synapses @xcite and @xmath53 memristors @xcite .
 however , it is worth noting here , that input stimulus magnitudes are usually in the range of volts ( 1.3v in @xcite and 80mv in @xcite ) and stimulus durations are of the order of a few msecs ( 1ms in @xcite and 0.5s in @xcite ) .
 in contrast , similar mechanisms can be exhibited in mtj synapses at much lower energy consumption ( by stimulus magnitudes of a few hundred @xmath54 and duration of a few @xmath55 ) .
 we believe that this work will stimulate proof - of - concept experiments to realize such mtj synapses that can potentially pave the way for future ultra - low power intelligent neuromorphic systems capable of adaptive learning .
 the work was supported in part by , center for spintronic materials , interfaces , and novel architectures ( c - spin ) , a marco and darpa sponsored starnet center , by the semiconductor research corporation , the national science foundation , intel corporation and by the national security science and engineering faculty fellowship .
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Abstract:
synaptic memory is considered to be the main element responsible for learning and cognition in humans .
 although traditionally non - volatile long - term plasticity changes have been implemented in nanoelectronic synapses for neuromorphic applications , recent studies in neuroscience have revealed that biological synapses undergo meta - stable volatile strengthening followed by a long - term strengthening provided that the frequency of the input stimulus is sufficiently high .
 such `` memory strengthening '' and `` memory decay '' functionalities can potentially lead to adaptive neuromorphic architectures . in this paper , we demonstrate the close resemblance of the magnetization dynamics of a magnetic tunnel junction ( mtj ) to short - term plasticity and long - term potentiation observed in biological synapses . we illustrate that , in addition to the magnitude and duration of the input stimulus , frequency of the stimulus plays a critical role in determining long - term potentiation of the mtj .
 such mtj synaptic memory arrays can be utilized to create compact , ultra - fast and low power intelligent neural systems .


the segmentation process as a whole can be thought of as consisting of two tasks : recognition and delineation .
 recognition is to determine roughly `` where '' the object is and to distinguish it from other object - like entities .
 although delineation is the final step for defining the spatial extent of the object region / boundary in the image , an efficient recognition strategy is a key for successful delineation . in this study ,
 a novel , general method is introduced for object recognition to assist in segmentation ( delineation ) tasks .
 it exploits the pose relationship that can be encoded , via the concept of ball scale ( b - scale )  @xcite , between the binary training objects and their associated images .    as an alternative to the manual methods based on initial placement of the models by an expert  @xcite in the literature ,
 model based methods can be employed for recognition .
 for example , in @xcite , the position of an organ model ( such as liver ) is estimated by its histogram . in  @xcite ,
 generalized hough transform is succesfully extended to incorporate variability of shape for 2d segmentation problem .
 atlas based methods are also used to define initial position for a shape model . in  @xcite
 , affine registration is performed to align the data into an atlas to determine the initial position for a shape model of the knee cartilage .
 similarly , a popular particle filtering algorithm is used to detect the starting pose of models for both single and multi - object cases  @xcite . however , due to the large search space and numerous local minimas in most of these studies , conducting a global search on the entire image is not a feasible approach . in this paper
 , we investigate an approach of automatically recognizing objects in 3d images without performing elaborate searches or optimization .
 the proposed method consists of the following key ideas and components :    * 1 .
 model building : * after aligning image data from all @xmath0 subjects in the training set into a common coordinate system via 7-parameter affine registration , the live - wire algorithm  @xcite is used to segment @xmath1 different objects from @xmath0 subjects .
 segmented objects are used for the automatic extraction of landmarks in a slice - by - slice manner  @xcite . from the landmark information for all objects ,
 a model assembly @xmath2 is constructed .
 b - scale encoding : * the b - scale value at every voxel in an image helps to understand `` objectness '' of a given image without doing explicit segmentation . for each voxel ,
 the radius of the largest ball of homogeneous intensity is weighted by the intensity value of that particular voxel in order to incorporate appearance ( texture ) information into the object information ( called intensity weighted b - scale : @xmath3 ) so that a model of the correlations between shape and texture can be built . a simple and proper way of thresholding the b - scale image yields a few largest balls remaining in the image .
 these are used for the construction of the relationship between the segmented training objects and the corresponding images .
 the resulting images have a strong relationship with the actual delineated objects .
 relationship between @xmath2 and @xmath3 : * a principal component @xmath4 system is built via pca for the segmented objects in each image , and their mean @xmath5 system , denoted @xmath6 , is found over all training images .
 @xmath6 has an origin and three @xmath5 axes .
 similarly the mean @xmath5 system , denoted @xmath7 , for intensity weighted b - scale images @xmath8 is found .
 finally the transformation @xmath9 that maps @xmath7 to @xmath6 is found .
 given an image @xmath10 to be segmented , the main idea here is to use @xmath9 to facilitate a quick placement of @xmath2 in @xmath10 with a proper pose as indicated in step 4 below .    *
 hierarchical recognition : * for a given image @xmath10 , @xmath3 is obtained and its @xmath5 system , denoted @xmath11 is computed subsequently . assuming the relationship of @xmath11 to @xmath6 to be the same as of @xmath7 to @xmath6 , and assuming that @xmath6 offers the proper pose of @xmath2 in the training images , we use transformation @xmath9 and @xmath11 to determine the pose of @xmath2 in @xmath10 .
 this level of recognition is called coarse recognition . further refinement of the recognition can be done using the skin boundary object in the image with the requirement that a major portion of @xmath2 should lie inside the body region delimited by the skin boundary . moreover
 , a little search inside the skin boundary can be done for the fine tuning , however , since offered coarse recognition method gives high recognition rates , there is no need to do any elaborate searches .
 we will focus on the fine tuning of coarse recognition for future study .
 the finest level of recognition requires the actual delineation algorithm itself , which is a hybrid method in our case and called gc - asm ( synergistic integration of graph - cut and active shape model ) .
 this delineation algorithm is presented in a companion paper submitted to this symposium  @xcite .
 a convenient way of achieving incorporation of prior information automatically in computing systems is to create and use a flexible _ model _ to encode information such as the expected _ size _ , _ shape _ , _ appearance _ , and _ position _ of objects in an image  @xcite . among such information ,
 _ shape _ and _ appearance _ are two complementary but closely related attributes of biological structures in images , and hence they are often used to create statistical models . in particular , shape has been used both in high and low level image analysis tasks extensively , and it has been demonstrated that shape models ( such as active shape models ( asms ) ) can be quite powerful in compensating for misleading information due to noise , poor resolution , clutter , and occlusion in the images  @xcite .
 therefore , we use asm  @xcite to estimate population statistics from a set of examples ( training set ) . in order to guarantee 3d point correspondences required by asm
 , we build our statistical shape models combining semi - automatic methods : ( 1 ) manually selected anatomically correspondent slices by an expert , and ( 2 ) semi - automatic way of specifying key points on the shapes starting from the same anatomical locations .
 once step ( 1 ) is accomplished , the remaining problem turns into a problem of establishing point correspondence in 2d shapes , which is easily solved .
 it is extremely significant to choose correct correspondences so that a good representation of the modelled object results .
 although landmark correspondence is usually established manually by experts , it is time - consuming , prone to errors , and restricted to only 2d objects  @xcite .
 because of these limitations , a semi - automatic landmark tagging method , _ equal space landmarking _ , is used to establish correspondence between landmarks of each sample shape in our experiments .
 although this method is proposed for 2d objects , and equally spacing a fixed number of points for 3d objects is much more difficult , we use equal space landmarking technique in pseudo-3d manner where 3d object is annotated slice by slice .
 let @xmath12 be a single shape and assume that its finite dimensional representation after the landmarking consisting of @xmath13 landmark points with positions @xmath14 , where @xmath15 are cartesian coordinates of the @xmath16 point on the shape @xmath17 .
 equal space landmark tagging for points @xmath18 for @xmath19 on shape boundaries ( contours ) starts by selecting an initial point on each shape sample in training set and equally space a fixed number of points on each boundary automatically  @xcite . selecting the starting point
 has been done manually by annotating the same anatomical point for each shape in the training set .
 figure  [ img : landmarking_abd ] shows annotated landmarks for five different objects ( skin , liver , right kidney , left kidney , spleen ) in a ct slice of the abdominal region .
 note that different number of landmarks are used for different objects considering their size .    [ cols="^ " , ]
 \(1 ) the b - scale image of a given image captures object morphometric information without requiring explicit segmentation .
 b - scales constitute fundamental units of an image in terms of largest homogeneous balls situated at every voxel in the image .
 the b - scale concept has been previously used in object delineation , filtering and registration .
 our results suggest that their ability to capture object geography in conjunction with shape models may be useful in quick and simple yet accurate object recognition strategies .
 ( 2 ) the presented method is general and does not depend on exploiting the peculiar characteristics of the application situation .
 ( 3 ) the specificity of recognition increases dramatically as the number of objects in the model increases .
 ( 4 ) we emphasize that both modeling and testing procedures are carried out on the ct data sets that are part of the clinical pet / ct data routinely acquired in our hospital .
 the ct data set are thus of relatively poor ( spatial and contrast ) resolution compared to other ct - alone studies with or without contrast .
 we expect better performance if higher resolution ct data are employed in modeling or testing .
 this paper is published in spie medical imaging conference - 2010 .
 falcao , a.x . ,
 udupa , j.k . ,
 samarasekera , s. , sharma , s. , hirsch , b.e . , and lotufo , r.a . , 1998
 user - steered image segmentation paradigms : live wire and live lane . graph .
 models image process .
 60  ( 4 ) , pp .
 233260 .
 kokkinos , i. , maragos , p. , 2009 .
 synergy between object recognition and image segmentation using the expectation - maximization algorithm .
 ieee transactions on pattern analysis and machine intelligience , vol.31  ( 8) , pp.14861501 .
 brejl , m. , sonka , m. , 2000 .
 object localization and border detection criteria design in edge - based image segmentation : automated learning from examples .
 ieee transactions on medical imaging , vol.19  ( 10 ) , pp.973985 .
 fripp , j. , crozier , s. , warfield , s.k . ,
 ourselin , s. , 2005 .
 automatic initialisation of 3d deformable models for cartilage segmentation . in proceedings of digital image computing : techniques and applications , pp .

Abstract:
this paper investigates , using prior shape models and the concept of ball scale ( b - scale ) , ways of automatically recognizing objects in 3d images without performing elaborate searches or optimization .
 that is , the goal is to place the model in a single shot close to the right pose ( position , orientation , and scale ) in a given image so that the model boundaries fall in the close vicinity of object boundaries in the image .
 this is achieved via the following set of key ideas : ( a ) a semi - automatic way of constructing a multi - object shape model assembly .
 ( b ) a novel strategy of encoding , via b - scale , the pose relationship between objects in the training images and their intensity patterns captured in b - scale images . ( c )
 a hierarchical mechanism of positioning the model , in a one - shot way , in a given image from a knowledge of the learnt pose relationship and the b - scale image of the given image to be segmented .
 the evaluation results on a set of 20 routine clinical abdominal female and male ct data sets indicate the following : ( 1 ) incorporating a large number of objects improves the recognition accuracy dramatically .
 ( 2 ) the recognition algorithm can be thought as a hierarchical framework such that quick replacement of the model assembly is defined as coarse recognition and delineation itself is known as finest recognition .
 ( 3 ) scale yields useful information about the relationship between the model assembly and any given image such that the recognition results in a placement of the model close to the actual pose without doing any elaborate searches or optimization . ( 4 ) effective object recognition can make delineation most accurate .


I've seen this movie on several different occasions. I find one of the funniest things to do is to just watch the reactions of the different types of people who go to see it.

Type 1: OLD PEOPLE. A lot of old Japanese men and women go to this movie because they think it will be a honest-to-goodness samurai movie with lots of swordplay and medieval Japanese dialogue. As soon the two protagonists begin debating horror movies while inserting expletives almost randomly throughout their sentences, the old people walk out, usually disgusted.

Type 2: FILM SNOBS. These people think that just because a movie bears the label of "Independent" that it will automatically be a load of hard-to-follow, overemotional crap that may or may not be in English. Yet they see it anyway just to sing praises about it later so that people will think they are intelligent and cultured. They are really in for a surprise when they see this film. As soon as the blood begins to squirt exaggeratedly from anime-inspired sword battles or the over-the-top villain nonchalantly pegs a dog with his crossbow during a phone conversation, these people will be so dismayed, they will walk out. A few will stay just to see "how bad it will get" and later they'll rave about what a horrible film it was to their friends.

Type 3: PEOPLE EXPECTING TO SEE LIVE-ACTION ANIME OR MATRIX-LIKE SPECIAL EFFECTS. Sorry folks, the martial arts are pretty solid in the film, but director Yamasato really doesn't have the budget for that kind of thing.

Type 4: PEOPLE WITH NO EXPECTATIONS. These are the people who really enjoy the film. Whether they had only heard of Blood of the Samurai, picked it at random, or stumbled into the wrong theater in an alcoholic haze, these are the people who will laugh at all the jokes and appreciate the movie for what it ultimately is: ENTERTAINMENT. This movie was not made to enlighten or to provoke deep spiritual thought, it was meant (if I may borrow a line of dialogue from the film) to "really kick some ass." And that's what it does.

So depending on what type of person you are, you may or may not enjoy this film; however, if you appreciate the movie for what it is and can enjoy an excess of blood and acting, then go see this movie and make sure to bring your friends.


...would probably be the best word to describe this film (in my opinion). besides one great heck of a fan service for fan girls (well, that was redundant~), it was the story that blew me away. hurray for Takahisa Zeze and Gackt! and i know some people will disagree with me on this one, but it wasn't any of the big three actors (the guys that played Sho, son, and Kei) that gave the best performance (for me, anyway). it was Taro Yamamoto, boy #5 from battle Royale!

don't get me wrong, i like Hyde, i worship his voice, but the problem was that some of his scenes came a little bit 'off', but i loved that scene where he danced with the dead guy's body killing the other guys. and Gackt wasn't at all that bad too, i preferred how his character was kind of aloof from the start. nothing much i can say about my background on lee-Hom Wang, i won't pretend to know him, but he carried his own weight with the star-studded cast.

this movie paved the way for one of the best collaborations I've ever heard, Orenji No Taiyou (forgive my spelling if it's wrong). while the complete song lasts about nine minutes, you wouldn't notice the length because you'd be enjoying hearing Gackt and Hyde together.

anyway, this movie is a must-see not only for the fans (huge fan base~) but for those who enjoy sci-fi, futuristic movies, Asian-style.


It's very sad that Lucian Pintilie does not stop making movies. They get worse every time. Niki and Flo (2003) is a depressing stab at the camera. It's unfortunate that from the many movies that are made yearly in Romania , the worst of them get to be sent abroad ( e.g. Chicago International Film Festival). This movie without a plot , acting or script is a waste of time and money. Score: 0.02 out of 10.


Oh my God what the hell happened here?!! I'm not going to say this again but what sort of backward movie is this? The dubbing in this is way worst than the dubbing in "King Kong vs Godzilla",Linda Miller had to be the worst actress in it and the suits are really cheesy.Its about some villain called Dr.Who who gets henchmen to build a robot gorilla that has the same strength as King Kong but when this robot breaks down he builds another one and then tries to kidnap Kong.When he does(thats when Linda Miller gets annoying)he makes Kong his slave but everything goes wrong and King Kong escapes.Then Dr.Who sends the robot after him.

Later when I was watching the movie I got a headache when Linda Miller and the other clowns started moaning.As I sat through the misery of watching the DVD while it was playing I was hoping that the madness in the movie was going to end until the fight.The ending has to be a really bad one because they could've shown Kong back on his island fighting dinosaurs again.

Don't watch the movie under any circumstances or if you do... beware of the disappointment you will receive.


This movie is pretty cheesy, but I do give it credit for at least trying to provide some characterization for it's principles. There are some great moments in the film and the dialogue has some great moments as well.

The aerial assault sequence is perhaps the best part of the movie.

I guess I really like the idea of what lengths a veteran will go for a fellow veteran. Sure it's not all that well done, but the premise is not at all bad.

Tom


Initially I was put off renting this movie due to the jacket art for the DVD. In fact, this held true with friends of mine who didn't rent it due to the art and the mental image(s) it conjured of being a movie that held little or no interest to me (or to my friends). But, I rented and watched it and was truly amazed.

I agree with another user's comments that this movie is not for everyone due to the blatant sexual inferences, so it is definitely not something I'd want young children to watch (and doubt seriously if they would understand it anyway).

I enjoy movies like this whereby the character's personalities and who they are are genuinely defined in a no-nonsense, direct way with no teasers to indicate they will turn out bad. The acting done ... was it acting? Ricci and Jackson performed so well, I was drawn into this movie not even realizing they were acting. Same thing with the story ... may seem far-fetched somewhat, but it was done so very, very well. It reminded me of another movie with Mel Gibson, Tim, where each character had limitations, whether mental or circumstantial, so were well-defined.

I found much depth in this movie with the character's involved, so feel that everyone involved (from the cameramen to the actors) should be commended on a perfect fit/result. After viewing this movie, I had talked to a couple of friends who had a negative approach to watching it like I did, so after hearing my comments, they rented and watched it. They, too, were quite surprised at how good it was. It is too bad that the art on the jacket was done the way it was since it is a turn off. I can see now how the art applies, but I'd not heard of this movie before, and the art was my first impression ... art sells or destroys DVD sales/rentals.

These characters had more depth to them and good timing was allotted to give an audience like me time to absorb the "feel" for each. I felt I could trust the movie to flow well, and it did. So, with the jacket art aside, I would recommend watching this movie.


The novel WEAPON which serves as the basis for this atrocious piece of garbage is one of the best techno-thrillers to come down the pike in a long time.The character of SOLO, who is NOT supposed to look like a human, is a wonderful creation and it was simply awful to see him reduced to just another Terminator-clone with Mario Van Peebles horrendously trying to "act" like a robot. There is NOTHING worthwhile about this film.

Why does Hollywood insist on snapping up the rights to excellent novels and then butchering them? There are so many things wrong with SOLO that listing them seems as unfair as inviting a man with no legs to a brisk game of Hopscotch. Avoid this awful film and seek out the 2 novels by ROBERT MASON that feature the awesome character of SOLO. The books are WEAPON and an excellent sequel SOLO.But don't pay any attention to this awful dreck of a film.


El Padrino has just been released in Europe and is really kicking ass. This film with its great cast - Damian Chapa ( Blood in Blood Out ), Robert Wager, Jennifer Tilly, Robert Wagner and many more ) - is the best gangster movie since SCARFACE. A Film that everyone MUST SEE. 2 hours full of action with fantastic unbelievable stunt !!!!

GRACIAS JENNIFER !!!! We are eagerly waiting for part 2 !!!! Does anyone know if there will be one ? Keep up the good work !!! I loved it !!


In the literal sense....

Reminds you of those "cops-and-robber" or cowboys-indians" role-playing games you played with your 8 year old friends.

Tedious and un-inspired, the storyline was obviously written to make bad acting and dialogue seem as part of the plot, but all it does is showcase it. I cant believe John Badham let his name be associated with this piece of crap. This could have been done better by a high school film buff who had been given the camera lighting, filmstock and editing

Destined to be a time-filler on Sci-fi channel, when they've overused everything else from their library, and barely better than the paid programming shill downstream.


I am very surprised by the positive comments because there were four of us that saw this at one screening and we all walked out. We personally felt that it was painfully slow to watch and couldn't sit through the whole movie. And we really tried to stick with it. In particular, those in the group who really wanted to like it because of their personal experiences with sexual orientation alienation in the school years depicted didn't like or identify with it at all. :(

That said, it is great to see that this film really resonated with a lot of people here on the boards and with reviewers. That's the beauty of the subjective art form of film. :)


Battery and case arrived on time as expected, but the battery cover was cracked at the top, probably due to poor packaging in an envelope with bubble wrap. Will be asking for a replacement battery cover.

Edit: I spoke with Hyperion and they got back to me very quickly and have shipped me a new battery cover. Also, I know it's only been 1 day, but so far my battery has lasted 19 hours (with heavy use while I was awake) and is still going strong. 5 stars for awesome service and for the product performing as expected.


Works great


Love the size.  It cuts out quite a bit and doesn't get that loud.  Also, once I got it you look at the paperwork and it said the outside part is waterproof but basically the speaker is not.  So far, it still works.  Not great but better than nothing.  Oh, and it's CHEAP!


Used it in my car. Worked well for about a month. Afterwards like most AUX cables the sound started going out and had to move around the ends to try to get good sound out of them.


Working  as advertised


excellent very good product recommend


I did have to poke out the holes/slits of this guy once he (finally!) arrived because they had not been adequately punched out. But, that done, he does the job. It took a very long time to arrive, but it was so cheap that I couldn't ask for more really. Keeps my cord from becoming a total disaster in my bag, and it's a very cute and fashionable cat.


It is a neat little case, fits well everywhere. Can get a little dirty in white and I am not sure how long it will last but for the price its a great deal.


The bluetooth is awesome.  I use it to listen to my music and talk onthe phone.  Good sound and noise reduction.


Not as strong at OEM


From my grandfather Verus I learned good morals and the government


of my temper.


From the reputation and remembrance of my father, modesty and a manly


character.


From my mother, piety and beneficence, and abstinence, not only from


evil deeds, but even from evil thoughts; and further, simplicity in


my way of living, far removed from the habits of the rich.