Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings.     

Holographic imaging and interferometry with non-Bragg diffraction orders on volume and surface-relief gratings in lithium niobate and photo-thermoplastic materials

The recording of holographic volume and surface-relief gratings in a photorefractive crystal using a photo-thermoplastic (PTP) holographic camera with an image-bearing signal beam leads to the appearance of two Bragg and two or more non-Bragg diffracted beams that show the transformed images in each beam (rotation and angular amplification of images). Using this real-time mode of interferometry, the hologram is retrieved with a deformed object beam, resulting in the appearance of fringes with a proper phase shift in each of four diffracted beams. This one-shot (one-exposure) phase-shifting interferometry results in clarification of the object wave-front information (for example, from surface deformation) and solution of the sign ambiguity problem. This procedure demonstrates that high-resolution holographic imaging of the PTP holographic camera static deformations in the order of ～0.1?mm can be revealed on the diffusion reflection surface. In addition, it was demonstrated that using the PTP materials could achieve holographic recording and imaging through phase aberration, with the image appearing in the non-Bragg diffraction order.     

Formation of anisotropic diffraction gratings in a polymer-dispersed liquid crystal by polarization modulation using a spatial light modulator

Anisotropic diffraction gratings based on a holographic polymer-dispersed liquid crystal (HPDLC) are realized by interferometric exposure using a spatial light modulator (SLM). The SLM is used in the HPDLC grating formation for anisotropic holographic recordings of two-dimensional polarization states for an incident light beam. The diffraction efficiency for P-polarization and the distinctive ratio of diffraction efficiency in P-polarization to that in S-polarization increases with the signal level applied to the SLM. The resulting volume gratings exhibit diffraction efficiency of more than 60% and a distinctive ratio of diffraction over 100. The microscopic origin of the anisotropic property is investigated by an optical polarizing microscope. The novel characteristics of the anisotropic diffraction properties of HPDLC are applied to an image reconstruction technique.     

Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout

The diffraction properties of volume holographic gratings are studied when the gratings are illuminated by an ultrashort pulsed beam with different polarization states. The developed coupled wave theory of Kogelnik is used. Considering the dispersion effect of the grating media, solutions for the diffracted and transmitted intensities, diffraction efficiencies and the bandwidths of the gratings are given in transmission volume holographic gratings and reflection volume holographic gratings. The bandwidths of the gratings are reduced by the dispersion effect of the grating media. They also have different influences on the diffraction of an ultrashort pulsed beam with different polarization states. For different values of the ratio of the spectral bandwidth of the input pulse to that of the grating, the changes of the spectral and temporal distributions of the diffracted intensities, as well as the diffraction efficiencies of the gratings are shown.     

Interferometric fabrication of modulated submicrometer gratings in photoresist

Interferometric recording is applied to the fabrication of modulated submicrometer gratings in photoresist.High diffraction efficiency requires optimized recording conditions, which are obtained by the use of an on-axis continuous surface-relief grating for the generation of the object beam. The optimized phase function is copied into the resist layer by means of a self-aligned two-step recording process with an intermediate copy in a volume photopolymer hologram. As a result, we demonstrate high carrier frequency surface-relief off-axis fan-out gratings for illumination in transmission with visible light.     

Rectangular surface-relief transmission gratings with a very large first-order diffraction efficiency (~95%) for unpolarized light

Computer optimization shows that the first-order diffraction efficiency of a lossless-transmission surface-relief grating with a rectangular surface profile can be made very large (~95%) simultaneously for light of TE and TM polarizations incident near the Bragg angle by the proper choice of the fill factor. The case for visible light incident close to the Bragg angle on unslanted gratings with periodicities corresponding to Bragg angles of 30 degrees , 37.5 degrees , and 45 degrees is presented. The refractive index of the grating material was chosen in the range between 1.2 and 2.     

Preferential-order waveguide grating couplers: a comparative rigorous analysis using the finite-difference time-domain method

We rigorously analyze and compare preferential-order waveguide grating output couplers using the finite-difference time-domain method in the total-field/scattered-field formulation for TE and TM polarizations. Four kinds of preferential-order grating couplers are studied: volume holographic grating couplers, slanted parallelogrammic surface-relief grating couplers, double-corrugated surface-relief grating couplers, and reflecting-stack surface-relief grating couplers. The outcoupling efficiencies and branching ratios of the couplers, revealing their preferentiality, are calculated and compared with the rigorous coupled-wave analysis leaky-mode method. In addition, their performance is examined in terms of the main design parameters and the excitation wavelength.     

Apodizing holographic gratings for dual-wavelength operation of broad-area semiconductor lasers

Apodizing holographic gratings are designed to have a Gaussian reflectivity profile in the -1 order and a complementary reflectivity profile in the specular (0) order. They are obtained by the interference of two Gaussian beams on a glass plate covered with a photoresist. These gratings are intended to be used as the coupler of the external cavity of a broad-area semiconductor laser. When the grating is oriented to get the -1 order counterpropagating with respect to the incident beam, single-longitudinal- and single-lateral-mode operation is obtained. We report on the fabrication technique of an apodizing holographic grating designed to allow lasing on two wavelengths simultaneously, with a preselected wavelength separation. The results obtained with a commercial broad-area laser are presented.     

光刻胶灰化用于全息离子束刻蚀光栅制作

针对全息离子束刻蚀衍射光栅制作中,光刻胶光栅浮雕图形的制作是至关重要和困难的,引入O2反应离子刻蚀对光刻胶光栅进行灰化处理,给出光刻胶灰化技术在全息离子束刻蚀衍射光栅制作闪耀光栅、浅槽矩形位相光栅、自支撑透射光栅中的具体应用。实验结果表明,这一新工艺的突出优点是降低了苛刻的全息曝光、显影要求,使得光栅线条光滑、线空比和槽深可控。     

Optimum parallel-face slanted surface-relief gratings

Using a combination of rigorous coupled-wave analysis and simulated annealing, parallel-face slanted surface-relief gratings (PFSSRGs) are optimized. For substrate-mode optical interconnects, profiles are presented for both polymer and silicon PFSSRGs for both TE and TM polarizations at normal incidence with grating periods designed to give a 45 degrees output angle in the negative-first forward-diffracted order. The resulting diffraction efficiencies range from 70% to 99%, with a majority of the optimized profiles yielding over 90%. Optimized polymer profiles for TE and TM polarizations exhibit similar high diffraction efficiencies, but the TM profiles generally require greater groove depths. Silicon profiles optimized for TM polarization have greater diffraction efficiencies than those for TE polarization. Profiles that can feasibly be fabricated are identified, and sensitivities to groove depth, filling factor, slant angle, and incident angle are shown to be modest.     

Optimization of anisotropically etched silicon surface-relief gratings for substrate-mode optical interconnects

The optimum profiles of right-angle-face anisotropically etched silicon surface-relief gratings illuminated at normal incidence for substrate-mode optical interconnects are determined for TE, TM, and random linear (RL) polarizations. A simulated annealing algorithm in conjunction with the rigorous coupled-wave analysis is used. The optimum diffraction efficiencies of the -1 forward-diffracted order are 37.3%, 67.1%, and 51.2% for TE-, TM-, and RL-polarization-optimized profiles, respectively. Also, the sensitivities to grating thickness, slant angle, and incident angle of the optimized profiles are presented.     

Hologram recording in polyvinyl alcohol/acrylamide photopolymers by means of pulsed laser exposure

The variation in transmittance produced when a photopolymer is irradiated with a pulsed laser is analyzed and experimental results obtained when diffraction gratings are stored using pulsed exposure are presented. In either case, the influence of the energy of the irradiation pulse, the number of pulses, and the pulse repetition rate were studied. The photopolymer used was an acrylamide/polyvinyl alcohol dry film with a yellow eosin-thiethanol-amine mixture as a photoinitiator system. The recording of the gratings was performed by use of a holographic copying process. The samples were exposed and holograms recorded with a collimated beam from a frequency-doubled Nd:YAG (532 nm) Q-switched laser. Our initial results show that it is possible to obtain diffraction gratings with a diffraction efficiency of 60% and a refractive index modulation up to 2.8 x 10(-3). The energetic sensitivities achieved are close to those obtained with the same material and continuous irradiation without a preprocessing of the gratings.     

Three-dimensional analysis of subwavelength diffractive optical elements with the finite-difference time-domain method

We present a three-dimensional (3D) analysis of subwavelength diffractive optical elements (DOE's), using the finite-difference time-domain (FDTD) method. To this end we develop and apply efficient 3D FDTD methods that exploit DOE properties, such as symmetry. An axisymmetric method is validated experimentally and is used to validate the more general 3D method. Analyses of subwavelength gratings and lenses, both with and without rotational symmetry, are presented in addition to a 2 x 2 subwavelength focusing array generator.     

Comparison of beam propagation method and rigorous coupled-wave analysis for single and multiplexed volume gratings

Multiplexed holographic structures have been suggested to provide large capacity and parallel access as three-dimensional storage media. One of the most widely used techniques in the literature for analyzing such structures has been the coupled-wave analysis and its variations. Another approach that is becoming increasingly popular because of the ease with which it can be implemented is the beam propagation method (BPM). The BPM is quantitatively compared with the rigorous coupled-wave analysis for the cases of single and multiplexed gratings. Normal and off-normal incidence as well as TE and TM polarizations are considered for single (slanted and unslanted) and multiplexed gratings. It is shown that the BPM, even in its most rudimentary form, is a powerful and accurate calculational method that is especially suited for analyzing the many multiplexed grating diffraction problem.     

Control of morphology and diffraction efficiency of holographic gratings using siloxane-containing reactive diluent

Performance of holographic gratings, prepared by using epoxy-functionalized siloxane compound as a reactive diluent, was compared with that using N-vinylpyrrolidinone as a diluent in the presence of various contents of liquid crystal under different exposure beam intensity. Siloxane component strongly influenced the kinetics of polymerization, diffusion, and phase separation of the liquid crystalline compound, and high diffraction efficiency was obtained when 3-acryloxypropyltrimethoxysilane or 2-[(3,4-epoxycyclohexyl)ethyl]trimethoxysilane was used as a reactive diluent even at a very low concentration (10–25 wt%) of commercial liquid crystal mixture, E7 (Merk), in contrast to the case with N-vinylpyrrolidinone or benzyl glycidyl ether as the diluent without siloxane component.The phase-separated morphologies of gratings, such as spacing and surface topology, observed by SEM and AFM, were well controlled, and very regular and smooth morphologies were observed for the holographic gratings prepared with 3-acryloxypropyltrimethoxysilane and various contents of the liquid crystal.     

Polarisation response of mono-order concave diffraction gratings based on an elliptical Bragg reflector

The polarisation dependence of integrated concave diffraction gratings with extended metallic or dielectric elliptical Bragg reflectors was investigated. Equal grating efficiency of 99% for both polarisations was achieved for the dielectric configuration using finite-difference time-domain (FDTD) modelling, with a polarisation-dependent loss (PDL) of 0.07 dB.     

Broadband wide-angle polarization converter for LCD backlight

A novel polarization converter using reflective metallic gratings and a polarization beam splitter is introduced for LCD backlight illumination. These two optical elements form a polarization rotation resonator. Broadband and high optical efficiency of polarization conversion in the visible region is achieved through the resonance of the refracted light and the surface plasmon wave in metallic surface-relief gratings. For wide-angle illumination, the conversion efficiency with arbitrary incident angle is studied. This device can convert unpolarized light to linear polarization with over 85% efficiency.     

Application of holographic diffractive doublets as collimators for highly elliptical light beams edge emitted from diode lasers

Two schemes for collimation of diode laser light beams with high cross-sectional ellipticity by means of a doublet of holographic diffractive elements are proposed and designed; one of the schemes is realized and tested. In both the schemes the first element of the doublet collimates the beam in the plane of the longer axis of the ellipse, and the second element collimates it in the perpendicular plane. Each element simulates a cylindrical lens. The set-up with the focal line of the cylindrical beam oriented perpendicular to the meridional plane is realized experimentally. The elements are holographic surface-relief gratings recorded in photoresist. For recording, only homocentric diverging beams are used, which minimizes potential aberrations and optical dirt. The parameters of the elements are computed using four equations, including one equation for compensation of the aberration of the lowest order. The doublet is proposed for the He—Ne red wavelength. A collimated He—Ne laser beam is employed for quality testing of collimation in a reverse way, with this beam impinging upon the second element. Characteristics of an outgoing beam from the first element of the doublet are recorded with a charge-coupled device camera. Calculated spot diagrams are compared with cylindrical focal lines captured separately from both the elements.     

Effective grating theory for resonance domain surface-relief diffraction gratings

An effective grating model, which generalizes effective-medium theory to the case of resonance domain surface-relief gratings, is presented. In addition to the zero order, it takes into account the first diffraction order, which obeys the Bragg condition. Modeling the surface-relief grating as an effective grating with two diffraction orders provides closed-form analytical relationships between efficiency and grating parameters. The aspect ratio, the grating period, and the required incidence angle that would lead to high diffraction efficiencies are predicted for TE and TM polarization and verified by rigorous numerical calculations.     

The Properties of Holographic Overlap Gratings

The analysis of a holographic beam expander which can, under perfect lossless conditions, convert a plane input beam into a plane diffracted beam, with a specified diffraction efficiency and beam width expansion ratio, is presented. Using solutions of the coupled-wave differential equations of [2], the effects of average loss, and both constant and spatially dependent dephasing are studied. These solutions are also used to compare the properties of overlap gratings with Kogelnik's [1] results for infinite gratings, and to extend the analysis of [4] to lossy, dephased cases. The maximum possible diffraction efficiency of an absorption overlap grating is shown to depend on its shape and also to lie between the values for Kogelnik's reflection and transmission cases.