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Applied Physics Letters

Photorefractive waveguides and nonlinear mode coupling effects

Baruch Fischer, Mordechai Segev

Published Feb 20, 1989• 35 citations
Publisher

Abstract

Nonlinear photorefractive wave mixing in waveguides provides unusual intermode coupling effects which are independent of the overall light intensities. We present and demonstrate processes in which high-order modes of a guided beam are converted into the low modes (funnel-like) and vice versa (antifunnel-like). We also show capabilities of launching and amplifying a guided beam by pumping the waveguide laterally. Another use of polarization state conversion is discussed.

DOI
10.1063/1.100886

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Nonlinear photorefractive wave mixing in waveguides provides unusual intermode coupling effects which are independent of the overall light intensities. We present and demonstrate processes in which high-order modes of a guided beam are converted into the low modes (funnel-like) and vice versa (antifunnel-like). We also show capabilities of launching and amplifying a guided beam by pumping the waveguide laterally. Another use of polarization state conversion is discussed.
A slowing down of light pulses using backward-wave four-wave mixing is achieved in photorefractive crystals with different coupling strength. The delay and width of the output pulse are studied as a function of the input pulse width and pump intensity ratio for the amplified transmitted beam and for the phase-conjugated beam. The delay characteristics are compared with those of the two-beam coupling. It is demonstrated that the four-wave mixing process ensures a larger slowing down of short pulses (pulses with width shorter than the photorefractive response time) as compared to the photorefractive two-beam coupling scheme and guarantees the elimination of forerunners. The delay of long pulses in the four-wave mixing configuration is almost the same as the one that can be reached with two-beam coupling. The effect of absorption on the nonlinear shape transformation of the output pulses is discussed qualitatively.
Lithium niobate is a critical material extensively used in nonlinear optics. The recent development of nanophotonic lithium niobate devices further extends their importance with enhanced nonlinearity and scalability. However, the performance of nonlinear optical processes in lithium niobate is influenced by the photorefractive effect. In this work, we study the impact of the photorefractive effect on second-order nonlinear optical processes in nanophotonic lithium niobate waveguides. We simulate the parametric down-conversion for squeezed light generation and second-harmonic generation in nanophotonic lithium niobate waveguides, considering the photorefractive effect. The squeezing generation with parametric down-conversion only experiences a constant wavelength shift as the refractive index change remains constant. On the other hand, the second-harmonic generation spectrum is distorted, and a decrease in nonlinear efficiency is observed. This is because the strength of the photorefractive effect varies along the waveguide. We further show that the ideal efficiency of second-harmonic generation can be recovered by the adapted poling technique, where the phase matching condition change caused by the photorefractive effect is compensated by adjusting the poling period of lithium niobate waveguides. Eventually, we analyze the cascaded process of second-harmonic generation and parametric down-conversion for squeezed light generation, and show that squeezing level up to 17.6 dB can be realized using 10 mW power with current performance of nanophotonic lithium niobate devices.
We show that one can generate the time-reversed replica of an "input" monochromatic, image-bearing beam by coupling it into a waveguide where it interacts with counterpropagating multimode "pump" waves of the same frequency. The nonlinear electric polarization density that is third order in the propagating electric fields in the guide medium generates the replica by the process of "four-wave mixing." We show also that the input beam can serve simultaneously as its own pump beam. If the frequency ν of the backward pump beam is different from the frequency ω to of the input beam, then the "phase-conjugate" to the input is generated at the entrance plane to the guide, and this radiates a replica of the input field, magnified by\omega/\nu, back along the input beam. The pump power required per resolution element to phase-conjugate a beam in a waveguide is orders-of-magnitude less than for the corresponding process with free (unguided) waves interacting in an infinite medium. Unlike the requirements for free waves, the pump waves do not need to be well aligned or single-mode to produce high fidelity in the replication process. Neither does the guiding structure or enclosed medium have to be precise in dimension or uniformity; the main requirements on the guiding structure being that it not attenuate the waves too heavily. Formulas are derived for the replication efficiency and fidelity in the various guided configurations. We also show how the process can be used: 1) to make a narrowband optical filter with a large acceptance solid angle; 2) to perform image-frequency conversion; 3) to obtain Raman and two-photon spectra of small samples; and 4) to achieve broadband optical amplification. We examine the conditions under which phase conjugation and these applications can be performed at several frequencies simultaneously. Limitations placed by the power-dependence of propagation constants are derived.
A new use of gratings in nonlinear optics is presented, i.e., the realization of bistable components. The device studied here consist of grating couplers ruled on a Kerr nonlinear medium, which use the guided-wave resonance to increase the local field and thus the nonlinearities. The result is that they are intrinsic bistable optical systems with high-speed, low pumping thresholds, and geometry well adapted to optical integration. First, a linear electromagnetic study of the devices is presented. It follows optimizing the grating parameters in order to get the best coupling between the incident beam and the guided mode inside the corrugated waveguide. Then a graphical construction is given that demonstrates the bistable character of the system in nonlinear optics. Next a nonlinear analysis of the devices is rigorously derived from Maxwell equations. It states precisely the predictions of the graphical construction and allows comparison of the effectiveness of the guided-wave resonance with the surface plasmon resonance in order to reduce the threshold of bistability.
The generation of multi-photon quantum states in integrated waveguiding structures provides a route to the creation of quantum optical chips. In particular, the simultaneous generation of photons through spontaneous parametric down-conversion (SPDC) and their quantum walks in nonlinear waveguide arrays (WGAs) can be used to produce strongly spatially entangled biphoton states [1] with applications for quantum search algorithms [2]. Whereas up to now only arrays of single-mode nonlinear waveguides have been considered for SPDC, in general the waveguides may support several guided modes, which were demonstrated to strongly affect nonlinear wave mixing in the classical regime [3]. Here we show that using higher order modes for SPDC has a significant influence on the generated two-photon states and gives additional means to control them. In particular, we employ the symmetry of the modes to engineer effectively nonlocal photon pair generation by SPDC.