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Journal of Modern Optics

Effects of Taper in Nonlinear Distributed Feedback Gratings

Gaetano Assanto, Raymond Zanoni, G. I. Stegeman

Published Jun 1, 1988• 6 citations
Publisher

Abstract

The effects of taper in a nonlinear slab waveguide with a distributed feedback grating are studied. The role of taper in the operation of the bistable gate is analysed with regard to switching intensity and transmission for various detunings from the Bragg condition. A comparison is made between three different functional forms of taper, namely linear, quadratic and triangular, which could occur in the preparation of a working device.

DOI
10.1080/09500348814551011

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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.>

IEEE Journal of Quantum Electronics•Jun 1, 1990•11 citations
The effects of taper in a nonlinear slab waveguide with a distributed feedback grating are studied. The role of taper in the operation of the bistable gate is analysed with regard to switching intensity and transmission for various detunings from the Bragg condition. A comparison is made between three different functional forms of taper, namely linear, quadratic and triangular, which could occur in the preparation of a working device.
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.
Performance analysis of optical isolators based on the nonreciprocal property of optical bistability in tapered and chirped nonlinear Bragg grating (NLBG) has been carried out. The design method for detuning adjustment according to input power level and expected on-off ratio is also provided. The results display that, for tapered NLBG, the broad operation range and greater on-off ratio can be achieved by using larger taper slope; there exists an optimization range of chirp coefficient for chirped NLBG; the operation range boundary is shifted toward lower input power with the increased detuning; and the tapered NLBG is more preferable to obtain the larger on-off ratio and wider operation range simultaneously compared with chirped NLBG.
Bistability of an optical resonator with distributed Bragg-reflectors is analyzed by using the coupled-mode theory. Hysteresis and nonlinear properties are given as a function of the quantities characterizing the Kerr medium (the quadratic electrooptic coefficient n 2 and the length of the Kerr medium l ) and the propagation characteristics of the corrugated waveguide (the coupling coefficient k and the optical loss in the corrugated waveguide Γ). We show that the optical resonator with distributed Bragg-reflectors has a multi-valued transmission characteristic by the Kerr effect. From the numerical calculations, the up-switching and down-switching power intensities of bistable operation are estimated.
A simple numerical approach previously proposed for calculating the input-intensity dependence of the reflectivity and transmissivity of a nonlinear dielectric slab for incident plane electromagnetic waves is adopted for analyzing nonuniform nonlinear distributed feedback (NLDFB) structures. The method is first validated by checking with the analytic solution for the bistability characteristics of a strictly periodic, uniform NLDFB structure as well as the reported transmission characteristics of linear structures based on transfer matrix method calculation. The method is then applied to determine the transmission bistability characteristics of linearly tapered and linearly chirped NLDFB structures. The results are found to be different in some cases from those based on a generalized transfer matrix calculation in which the nonuniform structure is approximated by a set of strictly periodic, uniform segments.
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.>