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Applied Physics Letters

Optical bistability in nonlocally nonlinear periodic structures

Gaetano Assanto, G. I. Stegeman

Published Jun 4, 1990• 24 citations
Publisher

Abstract

The transmission and reflection of electromagnetic guided waves by a periodic structure with a delocalized intensity-dependent nonlinearity was studied using a semianalytical approach. We show that such a nonlocal nonlinear distributed feedback grating can exhibit bistable and switching behaviors depending upon the input intensity and the detuning.

DOI
10.1063/1.102941

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The transmission and reflection of electromagnetic guided waves by a periodic structure with a delocalized intensity-dependent nonlinearity was studied using a semianalytical approach. We show that such a nonlocal nonlinear distributed feedback grating can exhibit bistable and switching behaviors depending upon the input intensity and the detuning.
In order to study optical bistability in a non-linear distributed feedback structure (NLDFB), we have generalized previous work. A mono-mode rectangular waveguide is chosen as the basic configuration for the device, although other guides could be considered. The grating, providing the passive feedback mechanism, has a geometry that can be arbitrarily chosen. Linear absorption is taken into account and the non-linearity is taken to be of the Kerr type. The effect of these three perturbations is treated using the Coupled Mode Theory and the Slowly Varying Envelope Approximation, including the radiation modes. Expressions for the coupling constants due to the three fundamental perturbations are derived and we show that new terms arise due to the interplay between the latter. Our model shows that an extra term, causing a shift of the Braggfrequency occurs in the equations. The analytical expressions are integrated numerically with the proper boundary conditions. Overall reflection and transmission properties of the device are displayed as a function of the intensity, the period of the grating, its length and several other device parameters.
The influence of the different parameters on the optical bistable behavior of a distributed feedback structure with an intensity-dependent refractive index is studied. Previous work is generalized toward two-dimensional waveguides, showing absorption. A general method is proposed to calculate the coupling coefficients up to a desired accuracy. This method is used to compare the feedback efficiency of sine, rectangular, and trapezoidal grating profiles. The numerical integration routine that was developed allows for the study of combinations of different nonlinear distributed feedback (NLDFB) structures. This is used to do a first investigation on the behavior of NLDFB devices with an aperiodic or nonperfect grating profile.>
The nonlinear phenomena of optical bistablity is investigated analytically in chalcogenide glass long period fiber grating. Using the basic sets of nonlinear coupled mode equation the expression for the transmittivity of grating has been derived under nonlinear Kerr regime. To examine the bistable charateristics of the grating, the operating wavelength is considerd slightly above the resonance wavelength of 1550 nm i.e. for off resonance condition where detuning parameter δ≠0. It is observed that the intensity of the transmitted wave increases with increasing input intensity and reaches its maximum value at particular intensity. On gradual reduction of the input intensity, the transmitted intensity does not retrace the same path, resulting in a hysteresis loop. This hysteresis loop shows that the LPFG supports the occurrence of optical bistability.
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.
One of the most interesting and applicable effects of nonlinear optics is optical bistability. This phenomenon is exhibited by certain resonant optical structures where it is possible to have two stable steady transmission states for the device, depending on the history of the input. Such a bistable device may be useful for optical computing elements as a result of its memory characteristics. Optical bistability behaviour is usually observed by inserting a nonlinear matter inside a Fabry–Perot interferometer. But in this study, it was shown that this can be achieved without the application of any optical resonator. Two laser beams were used to interact with the photorefractive media (doped PMMA polymer) which resulted in the bistability of the intensity of transmitted wave. Feedback was provided by a periodic grating created in the photorefractive polymer PMMA.