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IEEE Journal of Quantum Electronics

Polarization dependence of phase-conjugate reflectivities in solid films containing randomly oriented saturable dyes

T. Sato, Shigeki Miyanaga

Published Jan 1, 1999• 3 citations
Publisher

Abstract

The properties of polarization-dependent phase-conjugate (PC) reflectivities by degenerate four-wave mixing in saturable-dye-doped films are investigated on the basis of a four-level model including an excited-state absorption. Numerical calculations are carried out by taking account of the effect of molecular orientation as well as of pump propagation under the assumption that optically anisotropic dye molecules are rigidly fixed in a solid matrix without any positional and orientational order, in which a PC wave can be generated even in the case of a probe wave perpendicularly polarized to pump waves. Two cases of the polarization state are employed, where the polarization direction of the probe wave is either parallel or perpendicular to that of the parallel linearly polarized pump waves. Numerically calculating the PC reflectivities as a function of the pump intensity, we show how the polarization properties of the PC-reflectivity curves depend on saturation parameters, and clarify the influences of the molecular orientational and the pump propagation effect. The numerical results are compared with the experimental results obtained by using eosin-Y-doped polyvinyl alcohol films as saturable absorbers.

DOI
10.1109/3.740739

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Polarization dependence of phase-conjugate reflectivity by degenerate four-wave mixing is clarified theoretically and experimentally in a saturable-dye-doped polymer film. 1. _INTRODUCTLON A dyedoped film in which optically anisotropic saturable dye molecules are rigidly fixed and are randomly oriented has been used as a nonlinear material which can generate a phase-conjugate (PC) wave by degenerate four-wave mixing13 (DFWM). Such a film can generate a PC wave which has the same polarization state as the probe wave even for a probe wave orthogonally polarized to two pump waves. Tompkin et. al. 4 showed that in such a phase conjugator the nearly perfect vectorial phase conjugation can be obtained at the pump intensity near the saturation intensity of the phase conjugator. In this work following the analysis of Tompkin et. al. 4 closed-form solutions for the PC reflectivities in the dye-doped film are derived for two states of the polarization: the probe wave is polarized parallel and perpendicular to the pump waves. Some experimental results are also demonstrated in an eosin-Y-doped poly-vinyl alcohol (PVA) film and are compared with the theoretical results. 2. POLARIZATION DEPENDENT PC REFLECTIVITIES Dye molecules are modeled as dipoles which are randomly and uniformly oriented and are rigidly fixed in a solid matrix. We assume that each dye molecule has only one component of transition dipole moments at a wavelength considered5. An induced dipole moment of each dye molecule by

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Studies on low power optical phase conjugation (OPC) in three saturable dyes, viz., eosin, erythrosin B, and rose bengal, embedded in two polymer films, viz., gelatin and polyvinyl alcohol, are presented. Experiments are performed using the 514.5 nm line of an argon-ion laser. Saturation intensities are determined from the transmission versus intensity plots, and triplet lifetimes are estimated from the phosphorescence decay curves. OPC experiments are performed, and the variation of OPC reflectivity with intensity and absorption length is studied. Experimental results are compared with the theory of degenerate four-wave mixing in absorbing media proposed by R. L. Abrams and R. C. Lind [Opt. Lett. 2(4), 94 (1 978)]. There is fair agreement between the theory and the experimental observations. The limitations in using these films for cw OPC applications are briefly discussed.

Optical Engineering•Jan 1, 1990•13 citations
The properties of polarization-dependent phase-conjugate (PC) reflectivities by degenerate four-wave mixing in saturable-dye-doped films are investigated on the basis of a four-level model including an excited-state absorption. Numerical calculations are carried out by taking account of the effect of molecular orientation as well as of pump propagation under the assumption that optically anisotropic dye molecules are rigidly fixed in a solid matrix without any positional and orientational order, in which a PC wave can be generated even in the case of a probe wave perpendicularly polarized to pump waves. Two cases of the polarization state are employed, where the polarization direction of the probe wave is either parallel or perpendicular to that of the parallel linearly polarized pump waves. Numerically calculating the PC reflectivities as a function of the pump intensity, we show how the polarization properties of the PC-reflectivity curves depend on saturation parameters, and clarify the influences of the molecular orientational and the pump propagation effect. The numerical results are compared with the experimental results obtained by using eosin-Y-doped polyvinyl alcohol films as saturable absorbers.
Polarization dependence of phase-conjugate reflectivity by degenerate four-wave mixing is clarified theoretically and experimentally in a saturable-dye-doped polymer film. 1. _INTRODUCTLON A dyedoped film in which optically anisotropic saturable dye molecules are rigidly fixed and are randomly oriented has been used as a nonlinear material which can generate a phase-conjugate (PC) wave by degenerate four-wave mixing13 (DFWM). Such a film can generate a PC wave which has the same polarization state as the probe wave even for a probe wave orthogonally polarized to two pump waves. Tompkin et. al. 4 showed that in such a phase conjugator the nearly perfect vectorial phase conjugation can be obtained at the pump intensity near the saturation intensity of the phase conjugator. In this work following the analysis of Tompkin et. al. 4 closed-form solutions for the PC reflectivities in the dye-doped film are derived for two states of the polarization: the probe wave is polarized parallel and perpendicular to the pump waves. Some experimental results are also demonstrated in an eosin-Y-doped poly-vinyl alcohol (PVA) film and are compared with the theoretical results. 2. POLARIZATION DEPENDENT PC REFLECTIVITIES Dye molecules are modeled as dipoles which are randomly and uniformly oriented and are rigidly fixed in a solid matrix. We assume that each dye molecule has only one component of transition dipole moments at a wavelength considered5. An induced dipole moment of each dye molecule by
Phase conjugation by degenerate four-wave mixing in a saturable absorbing medium with a relatively long-lived excited state is analyzed; the analytical results are compared with experimental results. We propose a four-level model and take into account the effects of both excited-state absorption and pump propagation to explain the experimental results, which could not be explained by the models proposed previously. The numerical result predicts that the value of the phase-conjugate reflectivity as a function of the pump intensity is maximum at a certain absorbance (as absorbance increases) that is dependent on the cross section of the excited-state absorption. The present analysis explains most observations in the experiment, which was performed with a saturable-dye-doped polymer film as the saturable absorbing medium.
Rigidly held molecules display nonlinear optical properties which differ substantially from the properties of isotropic absorbers.1 In particular, the absorption of a collection of randomly oriented, rigidly held molecules saturates differently for different polarization states. We show that the polarization properties of degenerate four-wave mixing in such a medium are dramatically modified by this polarization-dependent saturation. We predict theoretically that for linearly polarized pump waves and for an input intensity near the saturation intensity, degenerate four-wave mixing in this material system can lead directly to vector phase conjugation; that is, to the simultaneous reversal of the optical wavefront and conjugation of the polarization state of the incident optical field.2 We confirm these theoretical predictions through phase conjugation experiments using fluorescein doped boric acid glass as the material system, and we find that degenerate four-wave mixing leads to nearly perfect vector phase conjugation when pumped by linearly polarized pump waves for field strengths near the saturation intensity.
Optical phase conjugation through degenerate four-wave mixing is observed in 4-[4-(Dimethylamino)styryl]-1-docosyl pyridinium bromide (DASPB) dye-doped in Polymethyl methacrylate - metacrylic acid (PMMA-PA) polymer films under low-power, continuous-wave laser irradiation. A maximum phase conjugate efficiency of 0.42% has been obtained for probe beam intensity at 2.5 W/cm2. Phase conjugation is observed for both parallel- and orthogonally-polarized probe and pump beams. The maximum PC reflectivity is achieved when the angle between probe beam and forward pump beam is 8 degrees. The effects of dye concentration, inter beam angle between probe and forward pump beam on phase conjugation reflectivity are also studied. PC signal strength first increases and then decreases with time. PC reflectivity is also increased by increasing the intensity of the backward and forward pump beam. The polarization and intensity profile are verified to be preserved in the conjugate signal. The predominant phase conjugation signal is attributed due to the saturable absorption and two photon induced fluorescence property of the dye molecules.
The theory of polarised light phase conjugation (PC) in non-degenerate four-wave mixing in a resonant medium has been developed in the irreducible tensorial formalism. The theory is applied to a wave with any polarisation in a resonant medium with levels of arbitrary momentum in the absence of pump-induced saturation effects. The formula for the non-linear susceptibility of the medium has been found and it is shown that the change of the polarisation at PC is essentially connected with the relaxation of the atomic multipole momenta (population, orientation and alignment). Wave equations were investigated for different pump-wave polarisations and three different physical mechanisms of the PC are discussed. The influence of the different relaxation rates of the atomic multipole momenta on the PC reflectivity has been investigated. The spectral dependence of the reflectivity and the spectral ranges which depend on the wave polarisation are found. For motionless atoms with small momenta (J 1 = 1 / 2 to J 2 = 1 / 2 , J 1 =1 to J 2 =0), exact formulae for the non-linear susceptibility of the medium as a function of pump intensity were found. The spontaneous decay of higher level to the lower one was taken into account. Because of optical pumping, saturation effects can be shown at considerably smaller intensities than in the usual two-level system. The exact expressions for the PC reflectivity at different polarisations of the pump waves are given.
Studies on low power optical phase conjugation (OPC) in three saturable dyes, viz., eosin, erythrosin B, and rose bengal, embedded in two polymer films, viz., gelatin and polyvinyl alcohol, are presented. Experiments are performed using the 514.5 nm line of an argon-ion laser. Saturation intensities are determined from the transmission versus intensity plots, and triplet lifetimes are estimated from the phosphorescence decay curves. OPC experiments are performed, and the variation of OPC reflectivity with intensity and absorption length is studied. Experimental results are compared with the theory of degenerate four-wave mixing in absorbing media proposed by R. L. Abrams and R. C. Lind [Opt. Lett. 2(4), 94 (1 978)]. There is fair agreement between the theory and the experimental observations. The limitations in using these films for cw OPC applications are briefly discussed.