Transmission, reflection, and absorption gratings in photorefractive polymers

Photorefractive polymers exhibit large refractive index changes when exposed to low power laser beams. When the optical excitation consists of two interfering coherent beams, the periodic light distribution produces a periodic refractive index modulation. The resulting index change produces a hologram in the volume of the polymer film. The hologram can be reconstructed by diffracting a third laser beam on the periodic index modulation. In contrast to many physical processes that can be used to generate a refractive index change, the photorefractive effect is fully reversible, meaning that the recorded holograms can be erased with a spatially uniform light beam. This reversibility makes photorefractive polymers suitable for real-time holographic applications. The mechanism that leads to the formation of a photorefractive index modulation involves the formation of an internal electric field through the absorption of light, the generation of carriers, their transport and trapping over macroscopic distances. The resulting electric field produces a refractive index change through orientational or non-linear optical effects. Due to the transport process, the index modulation amplitude is phase shifted with respect to the periodic light distribution produced by the interfering optical beams that generate the hologram. This phase shift enables the coherent energy transfer between two beams propagating in a thick photorefractive material. This property, referred to as two-beam coupling, is used to build optical amplifiers. Hence, photorefractive materials are also playing a role in imaging applications. Discovered and studied for several decades mainly in inorganic crystals and semiconductors, the photorefractive effect has not yet found wide spread commercial applications.

Large two-beam coupling gain with a low driving voltage and a small grating spacing was observed by use of a novel device structure in a photorefractive polymer with a low glass-transition temperature (Tg). A net gain (Γ−α)L close to 1 was observed for an external electric field of ∼40 V/μm and a grating spacing of 0.42 μm. The enhanced coupling strength was the result of optimized parameters and improved, effective electro-optical coefficient, phase shift, space-charge field, and effective interaction length compared with those of a conventional device structure. Moreover, mechanism for this enhancement of coupling strength was found to be applicable to typical efficient low-Tg polymeric materials.

The parallel stacked mirror (PSM) model of grating diffraction is extended to include a complex refractive index for the case of an unslanted reflection geometry at oblique incidence and for the σ-polarization. The well-known theoretical upper diffraction efficiency limit applicable to reflective absorption gratings described by Kogelnik's coupled-wave theory, is shown to be directly derivable from the PSM model. Analytical formulae for the diffraction efficiency of phase, absorption, and mixed harmonic-index gratings are compared with numerical computations using a rigorous coupled-wave description. A conventional truncated coupled-wave description, similar to Kogelnik's approach, is also derived from the harmonic-index rigorous coupled-wave equations by limiting the propagating modes to a signal and reference wave and by ignoring second-order derivatives. At low to moderate average loss the PSM theory is observed to provide a somewhat better fit to the rigorous coupled-wave calculations, and this is particularly evident for gratings that are dominated by phase modulation. As the average absorption coefficient is increased, all three models show the diffractive response sharpening around Bragg resonance and the characteristic sideband structure attenuating and then disappearing altogether, giving rise to a broader spectral behavior away from resonance. At high average loss, the truncated coupled-wave model is observed to very marginally outperform PSM. However, overall the PSM model is found to provide an exceedingly good description of the general mixed-phase-absorption unslanted reflection grating with finite average loss.

Calculated diffractive efficiencies in the visible spectral band from lossless planar holographic gratings are studied using the PSM and Kogelnik models of diffraction for the case of the σ-polarization. The results are numerically compared with rigorous coupled wave calculations over a wide parameter space covering both transmission and reflection geometries. For most reflection gratings, the PSM model is shown to consistently provide a marginally superior estimation of the diffractive efficiency. This is particularly evident in a clearly superior description of the diffractive sideband structure for most gratings, both in terms of angle and wavelength. For the transmission grating, the PSM model continues to provide a relatively good description of diffraction at low permittivity modulations and lower incidence angles with respect to the grating plane normal. However, overall Kogelnik's theory is shown to provide a somewhat superior estimation of diffractive efficiency and a clearly superior description of the diffractive side-band structure in the transmission case.

This paper presents the results obtained when holographic gratings were stored with a spatial frequency of 954 and 2663 lines/mm in transmission geometry and 4600 lines/mm in reflection geometry in a polyvinyl alcohol/acrylamide-based material. Photopolymers are materials that give good results at low frequencies, but their diffraction efficiency (DE) decreases at high frequencies. A chain transfer agent, 4,4'-azobis (4-cyanopentanoic acid) (ACPA) was incorporated in the material composition to improve spatial resolution. Furthermore, a curing process was applied to the stored gratings in order to maintain the DE stable over time. The DE and shrinkage for symmetric holographic transmission and reflection gratings were measured to evaluate their quality and quantify the improvement produced by ACPA.

The presented new type of interferometer combines the principle of two-beam interferometry and the technique of phase-shift keying of holographic gratings. On the basis of the phase-shift keying technique, the interferometer employs two different geometries for the recording and the readout process. Two holographic Bragg gratings are recorded in transmission geometry and simultaneously read out in reflection geometry using a tunable IR laser. Both gratings have the same grating period but a relative phase shift. The wavelength of the readout beam is fitted to the Bragg condition for the gratings. Using a tunable IR laser for the readout process, we can measure the spectral transfer function of both combined gratings. The shape of the measured transfer function is extremely sensitive to the phase shift between the two gratings. We demonstrate an application of this method by the measurement of refractive-index variations of gases due to pressure changes of the gases. The achieved resolution with respect to the measurement of phase shifts is approximately 1/40 pi. We present experimental investigations on two kinds of gas (an inert gas and a gas composition) as well as an efficient numerical approach to simulate the transfer function for Bragg gratings with a phase shift. Furthermore, we present a method to increase the resolution based on the controlled manipulation of the transfer function.

This study investigated the dynamic behavior of the first-order diffraction efficiency of gratings formed in polymer-dispersed liquid crystal (PDLC) films doped with a guest-host dye. PDLC films were fabricated using various LC-polymer mixing ratios, and written with various powers. Experimental results indicated that several peaks appeared in the curve of the first-order diffraction efficiency versus time. According to the light scattering study, we believe that the first peak was due to the superposition of density and absorption gratings. The density grating was associated with the spatially varied molecular weight of polymer molecules across the sample, and the absorption grating resulted from the spatially varied density of free electrons. The other peaks were caused by the superposition of the absorption and phase gratings. The phase grating was generated by the formation of a periodic structure of polymer-rich and LC-rich regions in the sample. This study also proposes a model to explain these experimental results. Moreover, the theory derived from this model correlates well with the experimental results, allowing us to determine the amplitude of the final grating.

In most derivations of the reflectivity of a photorefractive phase conjugator, the contributions from the transmission grating and reflection grating are assumed to be independent. This is in general not correct We show that within the undepleted pump approximation, the transmission and reflection gratings can couple through a grating formed by the two counter-propagating pump waves. We present a general linearized theory including this coupling and show that it significantly alters the response.

The development of a high-performance photorefractive polymer composite operating at 1550 nm is reported. We show 40% internal diffraction efficiency with response time of 35 ms and a net gain of 20cm−1 in four-wave mixing and two-beam coupling experiments, respectively. This is more than an order of magnitude improvement in the diffraction efficiency and net two beam coupling gain and two orders of magnitude in the response time than the previously reported photorefractive polymer operating at this technologically important wavelength. The improvement in photorefractive characteristics is accomplished by an enhanced orientation of the nonlinear optical chromophore in the present composite.

We have investigated photorefractive (PR) properties of a polymer composite with low glass-transition temperature (T g ) in a symmetric reflection geometry. A diffraction efficiency of more than 30% is observed in 105μm thick devices. In low T g photorefractive polymers, poling of the nonlinear optical chromophores at room temperature leads to birefringence in the material. The birefringence will alter the Bragg condition, as the propagation vectors for object and reference beams as well as the readout angle are influenced. We observed the Bragg-mismatch effect that caused a reduction in diffraction efficiency as the external field is increased. We have varied the angle of readout beam slightly at each bias field to get the highest efficiency.

We investigated the contribution of the absorption and phase gratings to the total diffraction efficiency of volume holographic gratings written in glass-like polymer recording materials based on poly(methyl methacrylate) and its thermostable derivative (copolymer with acrylic acid) with distributed phenanthrenequinone. The typical maximal diffraction efficiency was 0.5%-2.0% for the absorption grating and 22-32% for the phase grating. The modulation of the absorption coefficient varied between 10 cm(-1) and 100 cm(-1) and the modulation of the refractive index was about 10(-4)-10(-3).

Several techniques for determination of grating phase shifts relative to intensity grating have been developed by introducing artificial phase mismatch which includes by moving the nonlinear material, by phase shifting one of the two writing beams or by applying external electric fields.(1) In this work, we performed two kinds of experiment for two-wave energy couplings in a photopolymer film: (i) measurement of grating phase shifts of phase grating (PG) and absorption gratings (AG) by translation of the material along the grating wave vector K, (ii) experimental observation of quasi-periodic dynamic self-diffraction oscillations without introducing artificial phase mismatch.

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

We have derived the polarization dependent coupling constants for transmission and reflection gratings in degenerate four-wave mixing, measured phase-conjugate signals for various polarization conditions, and determined the relative contribution of the two gratings to the signal. The results obtained with cryptocyanine dissolved in methanol as the nonlinear medium show that the signal from transmission grating is 1.53–2.14 times larger than that from a reflection grating depending on the angle between the wave vectors of the forward pump beam and the probe beam.

Spatial resolutions of diffracted beams by photorefractive polymers are investigated in detail for applying the polymers to diffractive optical elements. The coupled wave equations for the four-wave mixing in photorefractive polymers and their solutions by applying the two-beam coupling approximation are derived taking the orientational enhancement effect into consideration. Characteristics of the diffraction efficiency of the polymers for the applied electric field, the incident angles of beams, the incident radiation intensity and the polarization are clarified. Furthermore, resolutions of diffracted images with the polymers are discussed by a numerical analysis from the viewpoint of the Bragg diffraction in a spatial frequency domain. An experiment with the TPD (tetra-phenyl-diphenyldiamine) acrylate based photorefractive polymers and the USAF test target is also performed to measure the spatial resolution of two-dimensional images diffracted by the polymer and to verify the calculated results. It is revealed that high resolution over 50 lp mm−1 can be obtained with sufficient diffraction efficiency in the case of the polymer thickness of several 10 µm.