Recording of holographic diffraction gratings in photopolymers: Theoretical modelling and real-time monitoring of grating growth

Abstract

Recording of holographic volume diffraction gratings in Du Pont's photopolymer HRS-150 is studied theoretically and experimentally. Particular attention is paid to the dynamics of the recording process. The temporal evolution of holographic gratings is monitored for a range of illumination intensities in two ways: (i) by means of a multiple-exposure approach when intensity profiles of recording beams are uniform, many holographic exposures are necessary and each exposure is carried out for a particular value of the total illumination intensity; (ii) by means of a single-exposure approach when intensity profiles of recording beams are strongly Gaussian and a volume grating with spatially distributed diffraction efficiency arises, depending on a local (average) value of the total illumination intensity. The second approach proves to be a useful tool providing us very quickly with qualitative information about the dynamics of the recording process while the first one, which is much more time-consuming, is more reliable for quantitative evaluations. The grating evolution is analysed theoretically by means of the well known photopolymerization-diffusion model. Discrepancies are found between the model and experimental results for low illumination intensities while qualitative agreement is found for higher intensities. For a given grating period, the discrepancies are interpreted in terms of insufficient change of the refractive index due to photopolymerization for low illumination intensities.     

基于光折变光栅的可调谐滤波方案及特性分析

在LiNbO3单模波导上利用双光束干涉可形成光折变波导光栅,针对粗波分复用系统提出了通过实时改变双光束之间的夹角进而改变光栅间距,实现可调谐滤波的方案.利用光折变动力学理论,得到光栅调谐时间在毫秒数量级.研究发现,适当提高光强和增加杂质掺杂浓度可提高衍射效率、减少光栅初次建立时间.基于耦合波理论的数值模拟结果表明,增大光栅长度能使衍射效率提高且带宽变小,而增加折射率调制度使衍射效率提高但同时带宽变宽.在折射率调制度为8×10-5,光栅长度大于12mm时,可获得91％以上的衍射效率和小于0.08 nm的带宽.     

Electro-optical investigations of holographic-polymer-dispersed ferroelectric liquid crystals

Uniform alignment of ferroelectric liquid-crystal domains encapsulated by a polymer binder was established through a holographic exposure process. The refractive index modulation in these thin films is modeled as a phase grating that can be electrically addressed to erase the optical diffractive properties. A phenomenological model is developed to take into account a distribution of domain sizes and an effective field that stabilizes the ferroelectric liquid-crystal domains. A diffraction model successfully predicts changes in normalized intensities for first-order diffraction with applied field. These gratings demonstrate microsecond-scale response and relaxation times for various grating pitch sizes between approximately 3 and approximately 12 microm.     

Static and dynamic two-wave mixing in GaAs

We studied the two-wave mixing anisotropic diffraction process in GaAs for demodulation of static and dynamic phase encoded signals. The static results quantitatively agreed with a previous theoretical model for cubic crystals. This model has been described explicitly for all beam polarizations and crystal rotation angles with respect to the plane of incidence. Dynamic phase modulation, in which the signal beam was phase modulated at frequency f(s) and the reference beam at f(r) = f(s) + Df, produced a signal at Df that was proportional to the difference between the static beam intensities with and without two-wave mixing under all conditions of polarization and crystal orientation studied. A significant dynamic output signal was produced even when only a shift in polarization but no energy transfer occurred as a result of the anisotropic two-wave mixing process. Therefore not only is the two-wave mixing gain important when the photorefractive effect is used for dynamic phase demodulation, but so are the polarization shifts occurring from the mixing process.     

Large two-beam coupling effect in poly(methylmethacrylate) doped with hemicyanine dye

Unexpected asymmetric energy exchange (two-beam coupling) between two writing beams in two-wave mixing experiments was observed in poly(methylmethacrylate) doped with hemicyanine dye. It was found that photobleaching of hemicyanine dyes was responsible for the formation of refractive index gratings. Instability of the laser-based optical system could be the cause of the phase shift between the interference pattern of the writing beams and the refractive index gratings, such a phase shift being a necessary condition for the two-beam coupling.     

Analytic steady-state solutions to dynamic grating envelope

Abstract

The photorefractive holographic recording is a dynamic grating formulation process, where the grating is induced by the interference modulation of two beams, and the energies of the beams are exchanged with each other owing to their interaction in the induced grating. The grating modulation envelope is a comprehensive analysis for holographic dynamic recording and non-destructive readout, but analytic solutions can only be obtained by simultaneously solving the materials equations and the coupled wave equations. In this paper, based on Kukhtarev's model and Moharam's field function exact steady-state analytic expressions for dynamic grating envelopes are deduced for any constant values of light modulation depth and light excitation efficiency. Thus their approximations for straight formulation instead of parametric formulation are then obtained. These steady-state analytic solutions to envelopes describe the dynamic holographic recording and readout more clearly and exactly.     

Erratum

Abstract

Results of a photon scanning tunnelling microscopy study of the plane diffraction grating with nickel stripes on a quartz substrate are reported. The ripples in the optical images with period of 600 nm have been observed when the plane of incidence of laser beam was perpendicular to the grooves of the grating. The interference patterns for the propagating modes in far field have been detected. They are supposed to be the result of Mie scattering of evanescent wave by the elements of the diffraction grating.     

Effect of Slab Interfaces on Diffraction of Visible Light by a Thick Volume Grating

Abstract

A theory of visible light diffraction by a volume grating is given for the case when reflection at slab interfaces cannot be neglected. A method of approximate solution of the second-order coupled-wave equations, applicable over a wide range of the grating vector orientation, is proposed. An appropriate boundary-value problem is discussed and solved in the two-wave approximation. The results are analytical and expressed in matrix notation suitable for both transmission and reflection diffraction gratings. Particular attention is given to the diffraction regime that arises in a slanted grating under the total internal reflection of the diffracted wave (TIRDW). Strong transmission anomalies occurring in the vicinity of the TIRDW threshold are established and analysed.     

Dependence of the refractive index grating in photorefractive barium titanate on intensity

The interference pattern of light waves creates a refractive index modulation in photorefractive media. This process is relatively well described by the theory (Kukhtarev equations) but deviations are found. Therefore, experimental methods are used in order to characterise the processes. The influence of the absolute intensity as well as the intensity ratio of the interfering waves on the refractive index modulation are studied in a two-wave mixing arrangement. Especially for the dependence on the absolute intensity the interesting relation Δn=f(I_abs)I_abs was found that is not predicted by the theory. Nevertheless, this experimental approximation can be used in calculations in order to minimise the error.     

Effects of fibre grating parameters on the spectral characteristics of cascaded long- and short-period gratings

Using coupled-mode theory combined with the transfer matrix method, this paper presents the impact of fibre grating parameters(grating period, grating length and average index modulation) and the separation between long-period fibre grating and fibre Bragg grating (FBG) on the reflection spectra of cascaded long-and short-period grating (CLBG). Two grating periods and two grating lengths have only impact on the two reflection peaks. The two resonance wavelengths shift towards the longer wavelength when the period of FBG decreases. Further, we study the sensing characteristics of coated CLBG. By analysing the relationship between the refractive index sensitivity and the thin film parameters (film refractive index and film thickness), the optimized parameters for the coated CLBG used as film sensor were obtained. Data simulation shows that the resolution of the refractive index of this coated CLBG film sensor is predicted to be 10^?6. This implies that the coated CLBG has an important application value in sensing and measurement field.     

测量薄膜折射率的光栅衍射干涉方法

根据光的干涉理论,讨论了条纹周期数对测量薄膜折射率不确定性的影响,推导出干涉条纹错位量与薄膜折射率和厚度的关系式。由此提出采用光栅衍射干涉测量薄膜折射率的方法和实验方案。实验表明:该方法的干涉条纹测量精度达λ/10~λ/20,薄膜折射率测量精度可达 0.01 以上。     

Sub-millisecond photorefractive two-wave coupling in Bi12TiO20 at 633 nm

Abstract

The unusually fast response of the two-wave mixing process in fibre-like Bi₁₂TiO₂₀ crystals on transient change of the external electric field was experimentally observed. Pulses of the amplification of the signal wave with a rise time of 0.2 ms and a width of 0.5 ms at a total input intensity of 6 mW mm^?2 are obtained when applying a rising or decreasing front of an external electric field to the crystal. The two-wave coupling without external field has a response time of 200 ms. A simple calculation based on the bandtransport model qualitatively explains the fast transient amplification but fails to explain the slow response without the electric field.     

Influences of Recording Geometry Parameters on Diffraction Efficiency in Bleached Silver Halide Transmission Holograms

Abstract

The experimental results of diffraction efficiency as a function of the geometrical disposition of recording beams in bleached silver halide transmission thick-holographic gratings are presented. Two variables have been used to relate these results with certain geometric parameters. These variables are spatial frequency and the slant angle of the interference fringes in the material. The experimental results obtained show that while maximum diffraction efficiency and refractive index modulation depend strongly on spatial frequency, they vary little with slant angle.     

On the efficient mixed amplitude and phase grating recording in vacuum deposited Disperse Red 1

We report on two-dimensional optical storage photochromic material made of Disperse Red 1 (DR1) thin film vacuum deposited on glass substrate. Holographic mixed amplitude and phase gratings were recorded in highly organized DR1 thin molecular films with 488 and 514.5 nm cw Ar⁺ laser light using degenerate two-wave mixing technique. Self-diffraction efficiency measured within Raman-Nath scattering limit reached 3.5%. The light scattering was mostly due to presence of periodic absorption changes (amplitude grating) as it was established from grating translation technique. Kinetics of grating recording was studied as a function of incident light intensity allowing to formulate the possible mechanism of grating build-up process in the studied film. Polarizing microscopic studies revealed the presence of light induced optical anisotropy possibly connected with heat-induced crystallization. Absorption grating profiles were analyzed in relation to exposure conditions.     

Low-power two-wave mixing in dry methylene-bluesensitized gelatin films

Abstract

Experimental observations of the power transfer effect between two writing beams in dry methylene-blue-sensitized gelatin films are presented. A low-power He-Ne laser is used for the realization of two-wave mixing. The influences of the writing angles and the polarization of the writing beams on the holographic enhancement coefficient, which shows the magnitude of the power transfer, are demonstrated. The diffraction efficiency was 0.4% and the holographic enhancement coefficient 0.16.     

Theoretical Analysis of Diffraction Efficiency of Photocarrier Grating

The diffraction efficiency of the photocarrier grating (PCG) has been theoretically analyzed. Firstly, the model of the PCG has been set up, and the distribution of the carrier concentration has been studied. Secondly, the change in refractive index produced by the photocarriers has been estimated. Finally, a rigorous coupled-wave analysis has been employed to investigate the diffraction efficiency of the PCG. The results show that when the angle between the two excitation lasers increases, the change of the refractive index decreases, leading to a weak grating. The optimal incident angle of the probe laser is dependent on the angle between the two excitation lasers, and the relation between these two angles for the higher diffraction efficiency of the +1st forward-diffracted wave has been found. In terms of diffraction efficiency, the optimal parameters have been estimated, and the feasibility of the PCG to be a forward-diffracted component has been confirmed.     

Effects of Arbitrary Phase Shift on the Higher-order Self-diffraction in Absorptive Photorefractive Medium

Abstract

Interactions between optical beams incident upon and two higher-order self-diffracted beams generated within an absorptive photorefractive material are investigated by solving a set of coupled differential equations. The medium is assumed to be free of linear and circular birefringence. Arbitrary phase shift between the light grating and the refractive index grating is considered. It is shown that under favourable conditions, a significant amount of power may be transferred to the newly generated waves. Investigated are the effects of phase shift, thickness and absorption of the crystal, coupling constant and off-Bragg parameter on energy transfer to the higher-order diffracted beams. It is shown that in the case of phase-shift other than π/2, higher-order self-diffracted beams can be generated on both sides of the input beams. Coupled wave equations are solved numerically by a fourth-order Runge-Kutta method and results are presented in graphical form. This analysis is valid for the near collinear interacting beam geometry, i.e. in the case of large grating spacing.     

Grating light reflection spectroscopy for determination of bulk refractive index and absorbance

An optical sensing technique is described and evaluated for sensitivity to changes in refractive index and absorbance of model sample matrices. A binary dielectric/metal transmission diffraction grating is placed in contact with a sample and utilized in reflection mode; thus, the light captured and analyzed does not pass through the sample. This particular condition creates thresholds at which a particular transmitted diffraction order is transformed from a traveling wave to an evanescent one. The positions of these thresholds depend upon the complex dielectric function of the sample, the period of the grating, and the wavelength and incident angle of light striking the grating. Experimental evidence directly supports the theoretical predictions regarding responses to both the real and imaginary portions of the refractive index: the reflection coefficient derivative wavelength peak position shifts linearly with changes in the real part of the refractive index, and the derivative peak amplitudes exhibit a square-root dependence on absorbance. Refractive index sensitivity to a series of ethanol/water solutions is demonstrated with detectable changes in index as small as 2 × 10(-)(6). Absorbance sensitivity is shown via the differentiation of methylene blue samples having equivalent 1 cm path length absorbances between 0.459 and 244 AU. In a single reflection measurement, GLRS offers a large dynamic range for absorbance detection, allows simultaneous determination of bulk refractive index in optically dense media, and provides a platform for performing continuous process analysis.     

Dynamics of photoinduced motions in azobenzene grafted polybutadienes

The goal of the investigations was to measure the dynamics of photoinduced motions in semicrystalline polybutadiene backbone based polymer grafted with various degree of mesogenic thiols. We studied the influence of the grafting degree of the azobenzene-containing side groups and the length of terminal oxyaliphatic substituent in the side groups on the dynamics of the laser holographic volume and surface gratings recording. Measurements were performed in a typical laser degenerate two-wave mixing experiment, in which light self-diffraction efficiency during holographic recording was monitored. Mathematical model for grating formation based on coupling of three gratings has been assumed to elaborate the obtained results. Theoretical estimations and experimental results have shown very good agreement.