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Adaptive Optics

Properties of Resonant Two-Photon Processes in Photorefractive Media

Loukas Paraschis, Matthew C. Bashaw, Alice Liu, Lambertus Hesselink

Published Jan 1, 1996• 0 citations
Publisher

Abstract

Summary Holographic data storage systems [1] require sensitive optical materials that provide some means of nondestrective readout [2]. Among the number of techniques for nonvolatile readout available [2]. the sensitazation of a photorefractive medium by illumination at one wavelength, called gating, for writing at a second using a resonant two-photon process, constitutes the most versatile all-optical nondestructive method. Typically, this process consists of absorption of a photon at frequency ω1 to generate an intermediate excited state, followed by absorption of a second at ω2 to generate a free carrier [3, 4, 5]. Gating occurs for absorption of two photons at two different wavelengths. In the present work, we identify the critical physical characteristics of the processes that provide the simultaneous realization of true gating and writing sensitivity at a variety of frequencies, evaluate the refractive index perturbation and the response rate, and investigate the significance of the the intermediate state occupancy and the arisining nonlinear photorefractive behavior at its saturation regime.

DOI
10.1364/adop.1996.jtud.4

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Summary Holographic data storage systems [1] require sensitive optical materials that provide some means of nondestrective readout [2]. Among the number of techniques for nonvolatile readout available [2]. the sensitazation of a photorefractive medium by illumination at one wavelength, called gating, for writing at a second using a resonant two-photon process, constitutes the most versatile all-optical nondestructive method. Typically, this process consists of absorption of a photon at frequency ω1 to generate an intermediate excited state, followed by absorption of a second at ω2 to generate a free carrier [3, 4, 5]. Gating occurs for absorption of two photons at two different wavelengths. In the present work, we identify the critical physical characteristics of the processes that provide the simultaneous realization of true gating and writing sensitivity at a variety of frequencies, evaluate the refractive index perturbation and the response rate, and investigate the significance of the the intermediate state occupancy and the arisining nonlinear photorefractive behavior at its saturation regime.
Multiphoton excitation allows reversible photorefractive recording without the disadvantage of erasure during readout. The light intensity required for two-photon storage can be drastically reduced if two-step excitation via long†lived real intermediate states is used. Experimental results for LiNbO3:Cr3+ and LiTaO3:Cr3+ demonstrate the advantages of the two-step process. The energy and intensity requirements for optical two-step recording are within reach of presently available repetitively pulsed lasers.
Nondegenerate four-wave mixing (FWM) has been used for wavelength conversion of optical information.1 In such experiments, two beams F-P (frequency ω1) intersect in a nonlinear medium with a small crossing angle θ (≈ 10 mrad), while a third beam B {frequency ω2) is nearly counterpro- pagating to F [Fig. 1(a)]. This can be viewed as real-time holography with frequency conversion.1 However, the physics differ considerably when the medium is transparent at frequency ω1, as there is no optically induced grating. This occurs when FWM is based on resonant two-photon, ω1 + ω2, absorption (frequencies ω1 and ω2 being resonant with a cascade three-level system and ω1 coupling unpopulated excited states). One interesting feature is that the two-photon coherence is nearly Doppler-free and does not depend much on the θ angle.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
Two-photon transitions have provided the basis for numerous useful nonlinear interactions with radiation. In this paper we calculate the absorption and coupling coefficients for one-, two-, and three-wave mixing in two-photon homogeneously broadened media. The resulting field equations form the basis for understanding saturation spectroscopy, phase conjugation,1 and single-mode instabilities2 in lasers and optical bistability in two-photon media. We assume that the wave frequencies are not resonant with any intermediate state j and that the probe and conjugate waves cannot saturate the two-photon transition. This allows us to use the two-photon two-level model and to transfer much of our knowledge of the one-photon two-level systems to the two-photon case. Two major differences occur between the two models. First, dynamic Stark shifts of the active levels play an important role in generating asymmetric spectra and nonzero dispersion (≃ω s T1) at line center. Second, high pump intensities do not bleach the absorption coefficient at the Rabi sidebands.
Persistent spectral hole-burning (PHB) has been proposed as the essential element of a frequency domain optical storage system1 in which the frequency at which a hole is burned in an inhomogeneously broadened absorption line at low temperatures serves as an additional dimension for the storage of digital information. Essentially all of the mechanisms studied until recently have been single-photon mechanisms, i.e., the photoionduced change leading to hole-burning (writing) for a given center occurs with a certain fixed probability after the absorption of one photon. Such linear, monophotonic processes suffer from the drawback that the act of detecting holes (reading) can also produce changes in the absorption line. Recent modeling studies of the generalized single-photon process2 have shown that thousands to tens of thousands of reads can be obtained from single-photon mechanisms only when the material possesses high quantum efficiency and low absorption cross section. These restrictive requirements do not apply for photon-gated hole-burning mechanisms, i.e., those mechanisms for which hole-burning occurs only in the presence of an additional “gating” light source, because for these mechanisms, reading is performed in the absence of the gating light and is therefore nondestructive.