Formation of optical vortices by light beams diffraction on holographically formed diffractive optical elements (DOE) in polymer-dispersed liquid crystals (PDLC) is theoretically described. The feature of investigated DOEs is in their special structure designed to convert the incident light fields into Bessel-like. Numerical simulations for the external electric field’s interaction on these DOEs are obtained. Its influence on the light beams conversion efficiency is studied. The possibility to create electrically controllable transformation elements in PDLCs is theoretically justified.
In this work the numerical simulations of the holographic formation of diffractive optical elements for the light beams conversion into Bessel-like ones in polymer-dispersed liquid crystals (PDLCs) are performed. Theoretical model for simulations is based on the solution of the kinetic equations of photopolymerization-diffusion processes of holograms recording in PDLCs by light beams with inhomogeneous amplitude and phase spatial distributions. Kinetics of spatial harmonics of refraction index changings are investigated and it is shown that during the recording process the spatial profile of diffractive optical element is changing from sinusoidal to inharmonic one. This process is also depends on the ratio of the diffusion and photopolymerization processes rates.
In this work a theoretical model of the holographic formation of the polarization diffractive optical elements for the
transformation of Gaussian light beams into Bessel-like ones in polymer-dispersed liquid crystals (PDLC) is developed.
The model is based on solving the equations of photo-induced Fredericks transition processes for polarization diffractive
elements formation by orthogonally polarized light beams with inhomogeneous amplitude and phase profiles. The results
of numerical simulation of the material’s dielectric tensor changing due to the structure’s formation process are presented
for various recording beams’ polarization states. Based on the results of numerical simulation, the ability to form the
diffractive optical elements for light beams transformation by the polarization holography methods is shown.
In this work we developed the analytical model of highly effective diffraction on holographic diffraction structures in polymer-stabilized liquid crystals (PSLC) under the impact of arbitrarily inhomogeneous external electric field. The exact self-consistent analytical solutions are obtained by solving the system of coupled–wave equations describing the diffraction process by Riemann’s method. They takes into account the electrically-induced phase mismatch changing’s inhomogeneity caused by the strong adhesion between liquid crystal molecules and bounding surfaces. According to the obtained relations, numerical simulation of the diffraction characteristics under the influence of external fields with different form of spatial inhomogeneity was made. The simulation results show qualitative compliance with the earlier obtained results.
In this work is we have developed the analytical models of holographic formation of polarization grating in polymerdispersed liquid crystals (PSLCs) by non-uniform recording field and its subsequent readout by uniform plane optical wave. The formation model is based on Jones formalism for recording field description and on equations of photoinduced Fredericks transition for description of dielectric tensor perturbations. The model of gratings readout is based on the system of coupled-wave equations solutions in the fixed-field approximation. Photo-induced absorption coefficient changing and the strong surface adhesion effects are taken into account. According to the obtained relations, numerical simulation of the spatial changing of the dielectric tensor was made for some forms of amplitude and phase non-uniformity of recording beams. For each complex of formation conditions the diffraction characteristics are also investigated numerically. The influence of recording field non-uniformity on grating’s diffraction characteristics is shown.
We present an analytical model of dynamics of three spatial harmonics of 2D spatial grating profiles with taking into consideration both record mechanisms (polymerization and components diffusion, absorption, interference pattern contrast. On the base of numerical simulation we examined an influence of these parameters on 2D spatial profile along grating vector and along thickness of a film.
Effects of spatiotemporal transformation of grating shape at nonlinear holographic recording in absorbent photopolymer have been investigated. We present an analytical model of dynamics of (N+1) spatial harmonics of spatial grating profiles with taking into consideration both record mechanisms (polymerization and components diffusion), absorption, interference pattern contrast and optional photopolymerization nonlinearity. Also we take into consideration so called additional gratings (AG) formed as a result of two waves mixing. On the base of numerical simulation we examined an influence of the material and record parameters on 2D spatial profiles of gratings.
In the work we suppose a mathematical model of 3-dimensional grating spatial profile formation in photopolymer material with light induced optical absorption at polymerization-diffusion processes of holographic recording of transmitted chirped grating. The model is based on kinetics equations of photopolymerisation and diffusion for the zero and the first spatial harmonics of refraction index grating. We have obtained analytical solution of the kinetics equations
describing the process of grating profiles transformation during the recording process. The main point of the numerical calculation presented in the paper was examination the possibilities to compensate the non uniformity of the chirped gratings profiles with the help of amplitude profiles of recording beams.
We present an analytical model of dynamics of three spatial harmonics of 2D spatial grating profiles with taking into consideration both record mechanisms (polymerization and components diffusion), absorption, interference pattern contrast. On the base of numerical simulation we examined an influence of these parameters on 2D spatial profile along grating vector and along thickness of a film
In this paper we present the model of record of 3-dimensional transmission and reflection gratings for 0.3<k<1 (k - exponent of intensity in photopolymerization equations) in photopolymers with a dye sensitizer. The numerical simulation of kinetics of transmission and reflection gratings record in this kind of photopolymers and its diffraction performances for optional value of k and contrast are carried out on the base of the model. The model also takes into consideration the following factors: polymerization and diffusion mechanisms of record, optical absorption, contrast of interference pattern, change of diffusion coefficients during record according polymerization level.
In this work the theoretical study of pulse string construction of holographic gratings in photopolymeric materials with light-induced optical attenuation has been carried out. The analytical model describing spatial-temporal transformation of holographic grating field during construction process is developed. The model has a view of recurrence relation and takes into consideration light-induced changing of optical attenuation and diffusion process. The results of numerical simulation on the base of the model are presented and include analysis of record stage, self-amplification stage and whole pulse string construction. The behavior of spatial profile and diffraction characteristics of constructed gratings are estimated with the help of numerical simulation. Fitting experiment and theoretical data has been made.
The researched photopolymer was made in Institute of Organic Chemistry of the Siberian Separation of the Russian Academy of Sciences (Novosibirsk).
The results of theoretical investigation of recording superimposed holographic gratings of transmitted type in optical absorbent photopolymeric materials are presented in the report. We consider the case of serial record of superimposed holographic gratings with angle multiplexing. The influence of photopolymer material parameters on diffraction effectiveness of superimposed holographic gratings is investigated in the work. It shows that the change of optical absorbent photopolymeric material during record may strongly change integrated diffraction characteristics or the recorded holographic gratings.
In this work the theoretical study of pulse string construction of holographic gratings in photopolymeric materials with light-induced optical attenuation has been carried out. The analytical model describing a spatial-temporal transformation of holographic grating field during construction process is developed. The model has a view of recurrence relation and takes into consideration light-induced changing of optical attenutation and diffusion processes. The results of numerical simulation on the base of the model are presented and include analysis of record stage, self-amplification stage and whole pulse string construction. The behavior of spatial profile and diffraction characteristics of constructed gratings are estimated with the help of numerical simulation. For calculation of selective properties we used perturbation technique.
In this work the theoretical study of pulse string construction of holographic gratings in photopolymeric materials with light-induced optical attenuation has been carried out. The analytical model describing spatial-temporal transformation of holographic grating field during construction process is developed. The model has a view of recurrence relation and takes into consideration light-induced changing of optical attenuation and diffusion processes. The results of numerical simulation on the base of the model are presented and include analysis of record stage, self-amplification stage and whole pulse string construction. The behavior of spatial profile and diffraction characteristics of constructed gratings are estimated with the help of numerical simulation. Fitting experiment and theoretical data has been made. The researched photopolymer was made in Institute of Organic Chemistry of the Siberian Separation of a Russian Academy of Sciences (Novosibirsk).
In this work the results of experimental investigations of holographic grating formation in photopolymer HPPM-633 are presented. On the base of fitting of experimental dependence of kinetics of diffraction efficiency with the theoretical one the photopolymer parameters are determined and presented. The photopolymer parameters such as diffusion coefficient and rate of their changing, optical absorption coefficient and rate of their changing, polymerization time, parameters defining contribution of photopolymerization and diffusion in change of refraction index, have been determined for other samples of photopolymer. On the base of model and numerical simulation it has been shown influence of experimental record conditions on diffraction efficiency, optimal record time, angle and wavelength selectivity of photopolymer gratings. The results obtained enable to define the optimal record time and direction of modification of photopolymer composition and external record parameters for achievement of diffraction characteristics predefined.
In this work the theoretical study of record of holographic gratings of transmitted and reflection type in photopolymeric materials with optical attenuation has been carried out. The analytical model describing spatial-temporal transformation of holographic grating field during record is developed. The model takes into consideration light-induced changing of optical attenuation. The results of numerical simulation on the base of the model are presented.
In this work we created analytical model of dynamics of nonlinear process of recording and reading the hologram in photopolymer media taking into account photoinduced absorption of photopolymer. The analytical model is based on the equations Lorentz-Lorenz and relations of the theory photopolymerization. Photoinduced absorption has been described with the help of the logarithmic function on the base of experimental data. Then experiments investigation was conducted. The record of the holograms was conducted under convergence angle 300 between laser beams. The data of experiment and the analytical model have allowed determining basic physical parameters of photopolymers. The researched photopolymer was made in Institute of Organic Chemistry of the Siberian Separation of a Russian Academy of Sciences (Novosibirsk).
In the report the results of theoretical investigation of recording superimposed holographic gratings with the help of angle multiplexing in optical-absorbent photopolymeric materials are presented. We consider the case of serial record of superimposed holographic gratings. In the model presented the photopolymerization and diffusion mechanisms of record, temporal changing of the diffusion coefficient, depletion of monomer and dye during record process have been taken into consideration.
In this work the theoretical study of record and postexpositional amplification of holographic gratings in photopolymeric materials with light-induced optical attenuation has been carried out. The analytical model describing spatial-temporal transformation of holographic grating field during record and postexpositional amplification is developed. The model takes into consideration light-induced changing of optical attenuation and diffusion processes. Light-induced optical attentuation has been described with the help of the logarithmic function on the base of experimental data. The results of numerical simulation on the base of the model are presented. The basic physical parameters of photopolymers have been described with the help of the experimental data and the analytical model.
The researched photopolymer was made in Institute of Organic Chemistry of the Siberian Separation of a Russian Academy of Sciences (Novosibirsk).
In this work we experimentally investigated dynamics of nonlinear process of record and reading of the hologram in photopolymer having photoinduced changing absorption. The record of the holograms was conducted under different angles between laser beams. The data of experiemnt have allowed to receive basic physical parameters of photopolymers on the base of the analytical model of recording processes. The researched photopolymer was made in Institute of Organic Chemistry of the Siberian Separation of a Russian Academy of Sciences.
In this work we created analytical model of dynamics of nonlinear process of record and reading of the hologram in photopolymer taking into account photoinduced absorption of photopolymer. The anlytical model is based on the equations Lorentz-Lorenz and relations of the theory photopolymerization. Photoinduced absorption has been described with the help of the logarithmic function on the base of experimental data
In this work we experimentally investigated dynamics of nonlinear process of record and reading of the hologram in photopolymer to a Gaussian beams of light. The analytical model of dynamics of record is based on the equations Lorentz- Lorenz and relations of the theory photopolymerization. The record of the holograms was conducted under different corners between bundles of light. The data of experiment have allowed to receive basic physical parameters of analytical model of a record of the holograms in photopolymer: characteristic time of polymerization, time of discussion and coefficient of monomer diffusion. The researched photopolymer was made in Institute of Organic Chemistry of the Siberian Separation of a Russian Academy of Sciences (Novosibirsk).
In this work we theoretically investigated the peculiarities of dynamics of hologram recording in photopolymer medium by short light pulses which space profiles are limited in two dimensions.The analytical model of dynamics of record is based on the equations Lorentz-Lorenz and relations of the radical photopolymerization theory. In the stage of readout the mathematical model have been considered as parametrical processes relatively time variable and involved the equations of light diffraction on holographic gratings with taking into account the diffraction effects connected with free propagation of light beams. The numerical simulation results of dynamics of holographic gratings recording and its readout by Gaussian light beams at various meanings of mathematical model parameters are presented.
The theoretical model of nonstationary diffraction on slant holographic gratings in photopolymer film is represented. The model is based on the analytical solutions of the interconnected equations of photopolymerization kinetics, diffusion of photopolymer composition components and light diffraction and describes the dynamical process of holograms reconstruction and its optical amplification. The peculiarities of the dynamics of amplitude-phase distributions and selective properties of slant gratings are discussed on the base of the numerical modeling results.
The theoretical investigation of the holographic grating pulse recording in the absorbing photopolymer materials is presented. The analytical models, describing the space-time transformation of holographic grating at the recording and the post-expositional amplification, have been obtained with taking into account the optical absorption and the diffusion processes. It is shown that the optical beams attenuation in the recording process leads to the spatial nonuniformity of index grating profile and its growth kinetics.
The investigations of hologram recording on a basis of photochemical polymerization reaction in polymer films have lead to creation the number of new holographic materials13. It is expected that their application will be realized in the nearest future. The performances of holographic recording useful for practice, such as sensitivity, maximum of diffraction efficiency (DE), storage, spatial resolution and other have been investigated in detail for this films4'5. But the question of mechanism of hologram formation, including the description of kinetic of photochemical and chemical stages of hologram recording is keeping open and discussed5'6. The holographic performances of HPPM-633 which consist of the light absorbing dye (Methylene Blue), initiator (triethanolamine - TEA), monomer (acrylamide -M), cross-linking monomer (hexamethylenbisacrylamide) and polymer binder (polyvinylalcohol) at He-Ne laser continuous recording were described7'8. In the preliminary investigation of hologram recording in HPPM-633 by the He-Ne laser pulses it was established that the DE about 1-5% appear at exposition time 0, 1 s with laser beam power density 0,05-0,1 W/cm2. The Fig. 1 illustrates the pulse hologram growth curves in HPPM633 , The phenomenon of hologram dark amplification (see Fig.2a,b) was observed in this experiment , That fact is in accordance with the mechanism of free-radical polymerization in HPPM. In this case the monomer polymerization in plasticizered polymer may expand independently after initial laser pulse action. It is interesting to know in which way the polymerization accrues at earlier stages. But the employment of pulse setup on the base of He-Ne laser does not allow to investigate the dark processes at time less then 0. 1 sec. To elucidate the material behaviour at the initial stages of the polymerization process immediately after excitation of the absorbing dye to the triplet state it is necessary to record the diffraction grating by laser pulse with durability about 108 sec. The DE growth of hologram under these conditions fall into nonsteady-state case of the polymerization. Thus we must to connect the hologram DE temporal dependence (DE(t)) with kinetic model of polymerization reactions in nonsteady-state case to have a possibility of the chemical interpretation of the obtained experimental date.
The theoretical investigation of the problem about the nonstationary recording of holograms in photopolymer media has been carried out. Analytical solutions have been found and analyzed with taking into account the radical polymerization process and diffusion processes of all components of photopolymer. The numerical results showing the kinetics of contributions of polymerization and diffusion processes at various grating periods are represented.It is shown that the kinetics of these contributions are characteristically different and depending from the grating period.
The theoretical investigation of the problem about the nonstationary amplification of holograms in photopolymer media has been carried out. Analytical solutions have been found and analyzed with taking into account the radical polymerization process and diffusion processes of all components of photopolymer for symmetrical and asymmetrical geometries of read out. The numerical results showing the kinetics of the hologram amplification, space-time transformation of the holographic gratings field, time evolution of the mismatch sensitivity of the amplification process are represented.
Mathematical model of nonstationary holograms recording in photopolymer materials has been developed. Analytical solution has been found with variation of kinetic coefficients such as medium viscosity, diffusion coefficient, break reaction parameter of polymeric chain in polymerization being taken into account. Numerical results show the importance of these variations in kinetic holograms recording. Postexpositionary amplification of holograms in this model is described too.
The theoretical investigation of the problem of the nonstationary process of holograms reconstruction in photopolymer media has been carried out. Analytical solutions have been found and analyzed taking into account the radical polymerization process and diffusion processes of all components of photopolymer for symmetrical geometry of read out. The numerical results showing the kinetics of the hologram reconstruction, space-time transformation of the holographic gratings field, time evolution of the mismatch sensitivity of the dynamic holograms reconstruction are represented.
Theoretical model of non-stationary process of self- amplification of weak holographic gratings in birefringence photorefractive crystals is submitted at two and one- frequency reading in view of multiwave and vector character of interactions. The analytical solutions of interconnected equations of record and diffraction are found. The effects of the spatial-time transformation of the grating and nonuniformity of the gain and also the dynamics of polarization and selective properties has been studied using numerical simulations at inter-mode and within-mode interaction geometries in optically active cubic crystals.
KEYWORDS: Crystals, 3D modeling, Adaptive optics, 3D image processing, Crystal optics, Acousto-optics, Laser crystals, Near field optics, Stereoscopy, Geometrical optics
The theoretical model of spectral filtration of noncoherent light imaging due to collinear and quasi collinear acousto- optic interaction (AOI) in 3D linear-nonuniform crystals is represented. The analytical solutions of the problem and space-spectral transfer functions are found. The theoretical estimation and numerical simulation of space-spectral selectivity and transformation 2D intensity profile of filtrated imaging are given. It was shown that 3D optical nonuniformity cause 2D spatial dependence of frequency- selective properties of quasicollinear AOI and also 2D nonuniformity of spatial transmission.
The theoretical 3D models for designing and developing acousto-optic components (modulators, deflectors) based on nonuniform crystals are represented. The influence of temperature induced 3D optical inhomogeneities on performance parameters of acousto-optic components including distortions of 2D amplitude-phase profiles and polarization parameters of light beams is discussed and illustrated by the analytical calculations and the detail numerical modeling results.
The results of investigations on acousto-optic interaction of quasimonochromatic fields in crystals are presented. Light diffraction in waveguide modulators have been considered, and light beam diffraction in thermo-disturbed crystals has been investigated.
The modern tendenci es i n the techni ques of acoustoopti c ( AO) data proceasing stinulate the technology development of the rnultichannel AO devices eleroental base, in the first turn nultichannel Bragg modulators' ' Z The demands made to them in the composition of the high-production signal and algebraic processors can be deVided into two groups. The demands of the large working band and the modulators high diffraction efficienty can be attributed to the first one. The realization of high indices on these parameters is based in the main on the technique achievements of the one channel AO modulators , progress i n worki ng out of whi ch i s defi ned by the successes in synthesizing of the new high effective AO materials, or achivernents in looking for the high effective cut-offs of the known crystals. The given criterion can be indicated by the value of AO quality coefficient M of the material for isotropic or anisotropic wide-band diffraction. Such important parameters as the admissible level of the interchannel coupling, the identity degree of the amplitude and phase-frequency channel characteri sti cs , quantity and densi ty of channel arrangement on the crystal can be attributed to the second group. The complex of these requl rements causes the more hard cri ten a i n selecting the material of the modulator sound wire and the AOl geometry, adding them by the physical parameters, playing the secondary role for one-channel modulators. To those in particular there have been attn buted the coeffi ci ents of the quadrati c acousti c ani sotropy showing the relative increasing or decreasing of the beam ( energetic) sound di vergence on compari son wi th the di ffracti on one. The value of these coefficients can greatly influence on the density of channel arangeroent in some cases. For example in widely used in acoustooptic mnodulators on TeO for slow shi fted waves near di recti on (11 0) the acoustic beam divergence forces in 50 times on comparison with the diffraction one. This circumstance limits essentially the use of the gi yen cut-off s TeO for building of the multichannel AO processor. In the given work we examine the main physical and technological aspects in the domain of development of wide-band multichannel microwave AO modulators of two different types: 1 - modulators on the crys— tal LiNJ on the base anisotropic AO interaction in YZ plane and the excitation of the acoustic waves on the crystal surface by the slotted transducer; 2 - isotropic modulators on the crystal TeO i-cut-ting with piezotransducer on the crystal LiNbO plates. The technology of the modulators with the surface excitation of the acoustic waves is more simple than the technology of the modulators with the plate or film transducer, but demands optimization of the interaction geometry with the joint calculation acoustooptical and piezoelectrical properties. the base of expression taking into account optical , acoustic and piezoelectrical anizotropy of the crystals by the numerical methods there have been analyzed the angular dependences of the AO quality coefficient M for isotropic and anisotropic geometries AO interaction in the crystal LiNW . There have been determined that the absolute maximum of the value M is achieved for the wide-band anisotropic light diffraction on the slow shifted waves of the IZ crystal plane. In the maximum M region the slow shifted waves possess the cross piezoactivity, moreover the coefficient of the electromechanical coupling L. for the given type of piezoactivity also reaches the absolute maxinum, that gives the possibility sufficiently effectively excite these waves on the crystal plane and develop simple from the technological point of view one channel and multi channel anisotropic microwave AO modulators. The analysis of the acoustooptical and acoustic anisotropy of the crystal TeO allows us to suppose that the most acceptable geometry of the AC interaction for building rnultichannel Bragg modulators correspond to the isotropic light diffraction on the longitudinal waves i n the di recti on ( 001 ) . This geometry is characteri zed by the peak anisotropy M relatively the acoustic wave deviation from the direction (001) in the sector 100 and by the small values of the quadratic acoustic anisotropy coefficients W.
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