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IEEE Journal of Quantum Electronics

Optical bistability in reflective fiber gratings

Chao‐Xiang Shi

Published Jan 1, 1995• 29 citations
Publisher

Abstract

Optical bistability in a nonlinearly reflective fiber grating through the mode coupling between the LP/sub 01/ and counter propagation LP/sub 02/ modes (i,e., the reflective LP/sub 01//spl rlhar2/LP/sub 02/ mode converter) is investigated by using the coupled-mode theory. Both the transmissive and the reflective properties of this nonlinear device are analyzed, which show that the output-versus-input relation exhibits the optical bistability. The switching power and the bistable hysteresis performances are also discussed. In addition, the comparison between the nonlinearly reflective mode converter (LP/sub 01//spl rlhar2/LP/sub 02/) and the nonlinear fiber Bragg grating reflector (i,e., the LP/sub 01/ and counter-propagation LP/sub 01/ modes) is also presented. It is shown that the former has much lower switching power than the latter.>

DOI
10.1109/3.469285

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IEEE Journal of Quantum Electronics•Jan 1, 1996•31 citations
Optical bistability in a nonlinearly reflective fiber grating through the mode coupling between the LP/sub 01/ and counter propagation LP/sub 02/ modes (i,e., the reflective LP/sub 01//spl rlhar2/LP/sub 02/ mode converter) is investigated by using the coupled-mode theory. Both the transmissive and the reflective properties of this nonlinear device are analyzed, which show that the output-versus-input relation exhibits the optical bistability. The switching power and the bistable hysteresis performances are also discussed. In addition, the comparison between the nonlinearly reflective mode converter (LP/sub 01//spl rlhar2/LP/sub 02/) and the nonlinear fiber Bragg grating reflector (i,e., the LP/sub 01/ and counter-propagation LP/sub 01/ modes) is also presented. It is shown that the former has much lower switching power than the latter.>
In this work, we studied the optical bistability of Fiber Bragg Grating (FBG) under nonlinear regime, considering three increasing and decreasing profiles of nonlinearity: linear, quadratic and exponential. We varied the nonlinearity range in each profile, and obtained different curves of bistability and reflectivity. We analyzed the powers [Formula: see text] and [Formula: see text], as well as the width of the photonic band gap ([Formula: see text] of each device under different nonlinearity profiles, and we observed the changes in reflectivity of the FBG. The power intensities [Formula: see text] and [Formula: see text] obtained for the bistability of decreasing profiles were lower than those obtained for the increasing profiles, and the values of [Formula: see text] were also lower in decreasing profiles, which is useful for optical switching applications.
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.
Based on the coupled mode theory, the bistability performance of nonlinear Bragg gratings is analyzed theoretically in terms of elliptic integration. The analytical expression describing the relation between the input intensity and the output intensity is presented. Consequently, the dependence of the bistability on the gratings inner parameters is investigated numerically. The results show that, the bistability performance of the nonlinear Bragg gratings depends not only on the product of the couple coefficient and the grating length but also on the couple coefficient and the gratings length respectively.
Using implicit Rungee-Kutta 4thorder method, we numerically report the optical bistablity and switching exhibited by a π-phase shifted nonlinear FBG with balanced gain and loss. Every control parameter which accounts for the variation in the hysteresis curve exhibited by the system is examined in detail. We begin with assessing the role of device length on the optical bistability and find that our system can exhibit switching at very short length of the fiber. Subsequently, the influence of coupling constant, detuning parameter and the nonlinearity on the switching power is also studied. The device exhibits switching at extremely low input intensities. Also, the effect of including the PT-symmetry on the switching characteristics of the device is investigated in brief.
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.
We present an analysis of the dynamic behavior of a nonlinear fiber ring resonator when an optical pulse with an arbitrary shape envelope is incident into it through a fiber directional coupler. The transient analysis is based on the extension of a well-known multiple-beam interference method to non-linear transmission problems. The steady-state analyses reported so far predict that the ring resonator exhibits reflection optical bistability in the input-output characteristics under appropriate conditions. But, our transient analysis shows that a nearly periodical oscillation of the transmitted power always takes place at a suitable initial detuning when the resonator has no loss or a small loss. It seems that the present instability is caused by the repetition of accumulation and release of the power in the ring resonator. We can obtain a bistable hysteresis loop by introducing a loss to the directional coupler. The dynamic behavior of bistability in a nonlinear fiber ring resonator with coupler loss is then investigated. It is found that a remarkable undershoot and overshoot occur in the switch-off curve and switch-on curve, respectively.