Pulse shaping properties of volume holographic gratings in anisotropic media

Based on a modified coupled wave theory, the pulse shaping properties of volume holographic gratings (VHGs) in anisotropic media VHGs are studied systematically. Taking photorefractive LiNbO(3) crystals as an example, the combined effect that the grating parameters, the dispersion and optical anisotropy of the crystal, the pulse width, and the polarization state of the input ultrashort pulsed beam (UPB) have on the pulse shaping properties are considered when the input UPB with arbitrary polarization state propagates through the VHG. Under the combined effect, the diffraction bandwidth, pulse profiles of the diffracted and transmitted pulsed beams, and the total diffraction efficiency are shown. The studies indicate that the properties of the shaping of the o and e components of the input UPB in the crystal are greatly different; this difference can be used for pulse shaping applications.     

Three-dimensional coupled wave study for finite-sized anisotropic volume holographic gratings under ultrashort pulsed beam readout

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously.     

Beam separator for high-order harmonic radiation in the 3-10 nm spectral region

We present the scheme of a beam separator for ultrashort high-order harmonic radiation below 10 nm. The system consists of a collimating mirror and two plane grazing-incidence gratings in compensated configuration. The first grating acts as the beam separator: it diffracts the extreme ultraviolet (XUV) light into the first order while reflecting the fundamental laser beam into the zero order. The diffracted light goes to a second grating that compensates both for the spectral dispersion and for the temporal broadening of the XUV ultrashort pulse caused by the diffraction at the first grating. The system can be designed for any wavelength in the 3-40 nm region. Since the gratings are operated at extreme grazing incidence, the area of the optical surface illuminated by the fundamental laser pulse is large, and therefore there is no risk of damage of the optical surfaces. The effects on the phase of the ultrashort pulse for narrowband applications are discussed.     

Spectrograph based on a single diffractive element for real-time measurement of circular dichroism

In this study, a novel and simple diffractive spectrographic method for real-time measurements of circular dichroism (CD) is considered from a theoretical and experimental approach. A demonstrator prototype of the CD spectrograph has been developed and its performance has been compared with a commercial phase-modulation CD spectrometer. The main element of the device is a polarization holographic grating, recorded in a thin photosensitive organic film, by two interfering opposite circularly polarized beams. A peculiarity of this grating is that the amplitude of the +1 (-1) order of diffraction is proportional to the right (left) circular polarization component of the incoming beam. Here we demonstrate that the CD spectrum of a specimen can be easily evaluated from the intensities of the diffracted beams. A white light beam passing through the specimen is diffracted from the grating and the intensities of the +/-1 orders of diffraction are measured. Due to the spectral selectivity of the grating, the CD at each wavelength can be evaluated at the same time using two linear array detectors.     

Polarization of holographic grating diffraction. I. General theory

The full polarization property of volume holographic grating diffraction is investigated theoretically. With a simple volume grating model, the diffracted fields and Mueller matrices are first derived from Maxwell's equations by using the Green's function algorithms. The formalism is derived for the general case that the diffraction beam and the grating wave vector are not in the plane of incidence, where s waves and p waves are not decoupled. The derived photon-momentum relations determine the Bragg angle selectivity. The parameters of diffraction strength related to the hologram-writing process and material are defined and are not necessarily small in general. The diffracted-beam profiles are analytically calculated by using the known grating shape function. This theory has provided a fundamental understanding of the polarization phenomena of a real holographic diffraction grating device. The derived algorithm would provide a simulation-analysis tool for the engineering design of real holographic beam combiner/splitter devices.     

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.     

Splitting of femtosecond laser pulses by using a Dammann grating and compensation gratings

When a Dammann grating is used to split a beam of femtosecond laser pulses into multiple equal-intensity beams, chromatic dispersion will occur in beams of each order of diffraction and with different scale of angular dispersion because the incident ultrashort pulse contains a broad range of spectral bandwidths. We propose a novel method in which the angular dispersion can be compensated by positioning an m-time-density grating to collimate the mth-order beam that has been split, producing an array of beams that are free of angular dispersion. The increased width of the compensated output pulses and the spectral walk-off effect are discussed. We have verified this approach theoretically and validated it through experiments. It should be highly interesting in practical applications of splitting femtosecond laser pulses for pulse-width measurement, pump-probe measurement, and micromachining at multiple points.     

Diffraction of optical communication Gaussian beams by volume gratings: comparison of simulations and experimental results

The diffraction effects induced by a thick holographic grating on the propagation of a finite Gaussian beam are theoretically analyzed by means of the coupled-wave theory and the beam propagation method. Distortion of the transmitted and diffracted beams is simulated as a function of the grating parameters. Theoretical results are verified by experimentation realized by use of LiNbO3 volume gratings read out by a 1550-nm Gaussian beam, typical of optical fiber communications. This analysis can be implemented as a useful tool to aid with the design of volume grating-based devices employed in optical communications.     

Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings

The total-field-scattered-field formulation of the finite-difference time-domain method (FDTD) is used to analyze the diffraction of finite incident beams by finite-number-of-periods holographic and surface-relief gratings. Both second-order and fourth-order FDTD formulations are used with various averaging schemes to treat permittivity discontinuities and a comparative study is made with alternative numerical methods. The diffraction efficiencies for gratings of several periods and various beam sizes, for both TE and TM polarization cases, are calculated and the FDTD results are compared with the finite-difference frequency-domain (FDFD) method results in the case of holographic gratings, and with the boundary element method results in the case of surface-relief gratings. Furthermore, the convergence of the FDTD results to the rigorous coupled-wave analysis results is investigated as the number of grating periods and the incident beam size increase.     

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.     

Photopolarimeter based on two gratings recorded in thin organic films

A photopolarimeter based on two different kinds of diffraction gratings (a two-grating photopolarimeter) has been developed for real-time measurements of the four elements of the Stokes vector. The main elements of the device are a pure polarization grating and an ordinary transmission grating, both recorded by means of holographic techniques in thin films of organic materials. The first one consists of a diffraction grating recorded by two interfering opposite circularly polarized beams in a Langmuir-Blodgett film of an azo-compound material. The second component is a grating recorded by two interfering parallel circularly polarized beams in a thin film of a photosensitive polymer. Both gratings offer long time stability and good diffraction efficiency. Four photodiodes collect the first-order diffracted beams from these gratings, the output signals of which are read through an analog-to-digital converter by a PC. The optical alignment of the device is easy and the calibration is realized in a one-step procedure.     

High-efficiency volume holograms recording on acrylamide and N,N′methylene-bis-acrylamide photopolymer with pulsed laser

In order to achieve a better understanding of the mechanisms of hologram formation and higher diffraction efficiencies in volume gratings stored in acrylamide based photopolymers, a crosslinker (N,N′methylene-bis-acrylamide) has been incorporated in the photopolymer to record holograms by pulsed laser exposure. The presence of this component increases the polymerization rate and refractive index modulation. The recording was performed using a holographic copying process. The original was a grating of 1000?lines/mm processed using silver halide sensitized gelatin. First, the effect of the pulse fluence was investigated. When the pulse fluence was optimized, the results obtained using the new composition of material were compared with those using the composition without a crosslinker. Using a pulsed laser at 532?nm the photopolymer without crosslinker presented diffraction efficiencies slightly less than 60%. On the other hand, when the crosslinker was introduced in the photopolymer composition, the diffraction efficiencies achieved were higher than 85%. The non-linearity of the material's response was also studied comparing the energetic sensitivity, diffraction efficiencies and index modulation of gratings recorded with pulsed and continuous laser exposure. This study was performed fitting the angular scan of each grating using Kogelnik's theory.     

Compensation of optical path lengths in extreme-ultraviolet and soft-x-ray monochromators for ultrafast pulses

The extraction of the spectrum corresponding to a single extreme-ultraviolet ultrashort pulse embedded in an extended spectrum may alter the duration of the pulse itself. This is due to the spectral filtering of optics and the differences in the optical path of the rays caused by ordinary diffraction when a grating is used. The basic mechanism that leads to the latter effect is the difference of one wavelength of the path length of two rays diffracted at the first order by nearby grating grooves. A study of these effects and some possible solutions obtained from using a pair of diffraction gratings is presented. The aim of this study is the selection without dispersion of one or more high-order laser harmonics produced by a pulse lasting a few femtoseconds and interacting with a gas jet.     

Stabilization of volume gratings recorded in polyvinyl alcohol-acrylamide photopolymers with diffraction efficiencies higher than 90%

Abstract

Obtaining holographic volume gratings with high diffraction efficiencies that can be used under white light has been a serious problem for the polyvinyl alcohol-acrylamide-based photopolymers developed by other researchers. In this paper we propose to eliminate the residual monomer in order to stabilize the holographic gratings. The residual dye and residual monomer are the main problems in achieving high diffraction efficiencies stable under white light. In order to polymerize the residual monomer we illuminate the gratings with coherent green light and incoherent white light and we heat the grating at 80°C for different times. We also study the conservation of gratings dried in critical conditions of humidity and temperature. After stabilization the diffraction efficiencies achieved were clearly higher than 90%.     

Three-dimensional converging-diverging Gaussian beam diffraction by a volume grating

The diffraction characteristics of a volume grating (VG) illuminated by a three-dimensional (3-D) converging-diverging Gaussian beam at conical incidence are investigated by applying 3-D finite-beam (FB) rigorous coupled-wave analysis (RCWA) based on the conventional 3-D RCWA in conjunction with two-dimensional plane-wave decomposition. The Gaussian beam is assumed to have an arbitrary incidence angle, an arbitrary azimuthal angle, and any linear polarization. The two cases with linear polarizations of the central beam of the Gaussian (E perpendicular K and H perpendicular K) are investigated. The diffraction efficiencies and the diffracted beam profiles for both unslanted VGs and slanted VGs (designed for substrate-mode optical interconnects) are presented. In general, the diffraction efficiencies of a converging-diverging spherical Gaussian beam diffracted by both unslanted VGs and slanted VGs increase and approach the central-beam results as the refractive-index modulation increases.     

Polarization-dependent diffraction efficiency of a photorefractive volume grating and suppression of this efficiency

In terms of refractive-index ellipsoid of a uniaxial crystal, the relationship between the diffraction efficiency of a volume grating and the polarization state of a readout beam is theoretically analyzed. The direction of a refractive light beam and the corresponding refractive-index modulation will both be changed by a variation of the polarization state. In the polarization state of the readout beam, which may lead to a strong variation in the diffraction efficiency of the volume grating. This kind of polarization-dependent diffraction efficiency of a volume grating in an anisotropic crystal is extremely disadvantageous for some applications. A method to suppress the polarization-dependent diffraction efficiency by use of double volume gratings is presented, and experiments with LiNbO3:Fe crystal are also demonstrated. The experimental results indicate that this method can well suppress the polarization-dependent diffraction efficiency of a volume grating. Furthermore, the diffraction properties of the double volume gratings are almost independent of the polarization state of the readout beam. The relative values of the diffraction peaks are calculated on the basis of the relationship between index modulation and the state of polarization. The experimental values are in good agreement with the theoretical analyses.     

Modeling and design of planar slanted volume holographic gratings for wavelength-division-multiplexing applications

Holographic gratings are modeled and designed for path-reversed substrate-guided-wave wavelength-division demultiplexing (WDDM) as a continuation of earlier research [Appl. Opt. 38, 3046 (1999)]. An efficient and practical method is developed to simulate the slanted volume holographic gratings. The trade-off between dispersion and the bandwidth of the holograms is analyzed. A 60 degrees (incident angle of the grating)/60 degrees (diffraction angle of the grating in air) grating structure is selected to demultiplex optical signals in the 1555-nm spectral region, and a 45 degrees /45 degrees grating structure is chosen for the spectral region near 800 nm. Experimental results are consistent with the simulation results for these two WDDM devices. A four-channel WDDM is also demonstrated at a center wavelength of 1555 nm and with a channel spacing of 2 nm.     

Secondary grating formation by readout at Bragg-null incidence

We show that when a dynamic hologram is read out by illumination at the Bragg nulls of a previously recorded grating the diffracted beam inside the medium can result in the recording of two secondary gratings that alter the final selectivity curve. This is confirmed experimentally. This effect can cause cross talk in hologram multiplexing that is stronger than interpage cross talk when a small number of holograms with high diffraction efficiencies are multiplexed.     

Polarization holographic gratings in side-chain azobenzene polyesters with linear and circular photoanisotropy

We investigate thin phase polarization holographic gratings recorded with two waves with orthogonal linear polarizations in materials in which illumination with linearly/circularly polarized light gives rise to linear/circular birefringence. The theoretical analysis shows that the presence of circular photoanisot-ropy changes significantly the diffraction characteristics of the gratings. The intensities of the waves diffracted in the +1 and -1 orders of diffraction and their ratio depend substantially on the reconstructing-wave polarization. Experiments with films of side-chain liquid-crystalline azobenzene polyester that is a photoanisotropic material of the considered type confirm the unusual polarization properties. It is shown that polarization holography may be used for real-time simultaneous measurement of photoinduced linear and circular birefringence.     

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.