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IEEE Photonics Technology Letters

Nonlinear switching and pulse propagation in phase-shifted cubic quintic grating

Yosia Yosia, Shum Ping, Chao Lü

Published Nov 22, 2005• 11 citations
Publisher

Abstract

We investigate numerically the nonlinear switching characteristics and pulse propagation behavior in the phase-shifted cubic quintic grating (CQG). The continuous-wave nonlinear switching curve shows an interesting feature whereby two switching thresholds and consequently double bistability hysteresis are formed in a certain detuning window. We show the unique bistability (U-bistability) region close to the upper-switching threshold in each of the hysteresis, where the high state in U-bistability can be reached when input is coming from low to high with fast rise time. For medium peak intensity Gaussian pulse propagation in phase-shifted CQG, the full-width at half-maximum of the output pulse varies in upward parabolic manner as the peak intensity increases, whereas for high peak intensity Gaussian pulse propagation, the output pulse will experience distortion from the Gaussian shape because of the compression in its leading edge and broadening in its trailing edge concurrently.

DOI
10.1109/lpt.2005.858081

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We investigate numerically the nonlinear switching characteristics and pulse propagation behavior in the phase-shifted cubic quintic grating (CQG). The continuous-wave nonlinear switching curve shows an interesting feature whereby two switching thresholds and consequently double bistability hysteresis are formed in a certain detuning window. We show the unique bistability (U-bistability) region close to the upper-switching threshold in each of the hysteresis, where the high state in U-bistability can be reached when input is coming from low to high with fast rise time. For medium peak intensity Gaussian pulse propagation in phase-shifted CQG, the full-width at half-maximum of the output pulse varies in upward parabolic manner as the peak intensity increases, whereas for high peak intensity Gaussian pulse propagation, the output pulse will experience distortion from the Gaussian shape because of the compression in its leading edge and broadening in its trailing edge concurrently.
We show the Cross Phase Modulation (XPM) effect between CW probe that operates in bistability region and strong Gaussian pump in a Fiber Bragg Grating (FBG) by Implicit 4th Order Runge-Kutta Method. The XPM effect results in three unique nonlinear switching behaviors of the probe transmission depending on the pump peak intensity and its Full Width Half Maximum (FWHM) value. From this observation, we offer the FBG three potential nonlinear switching applications in all-optical signal processing domain as: a step-up all-optical switching, an all-optical inverter, and an all-optical limiter. The bistability threshold that determines the nonlinear switching behaviors of probe transmission after Gaussian pump injection is defined numerically and shown to be equivalent to the unstable state inside hysteresis loop.
In this paper, the numerical studies on optical-bistability phenomena in third-, fifth-, and seventh-order nonlinear periodic media are presented. By cross-phase modulation with strong Gaussian pump, the continuous-wave probe transmission that operates in bistability regime can be permanently switched from low to high and vice versa using the property of the unstable state. While there is only one hysteresis in the third-order nonlinear periodic media, double hysteresis are observed in the nonlinear-transmission characteristics of pi phase-shifted periodic media with third-fifth and third-fifth-seventh-order nonlinearities. In the context of double hysteresis, unique-bistability regime is defined where the high state can be reached as input comes from low to high with fast enough rise time such that the output rises above the unstable state during its transient. Finally, all-optical transistor operation is shown as a prominent application of optical bistability based on the unstable-state principle
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.
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.
In the last chapter, we examined the effect of cubic nonlinearity on selfrefraction of an optical beam. We have also seen that the presence of a quadratic nonlinearity can also contribute to change in the profile of a Gaussian beam in a crystal. In this chapter we will see how the effect of nonlinearity, alongwith the proper feedback, can give rise to optical bistability and hysteresis. This is not unexpected as hysteresis and bistability are also observed in nonlinear electronic circuits with feedback, such as in the Schmitt trigger, as well as in hybrid optical devices, such as an acoustooptic device with feedback (Banerjee and Poon, 1991). In what follows, we will examine two different types of optically bistable devices based on optical nonlinearities. The first is a nonlinear ring resonator comprising a two-level gain medium as the nonlinear element. We will treat both absorptive and dispersive bistability. Absorptive bistability is the case when the incident optical frequency is close to or equal to the transition frequency of the atoms from one level to another. In this case, the absorption coefficient becomes a nonlinear function of the incident intensity. On the other hand, if the frequencies are far apart, the medium behaves like a Kerr-type material and the system exhibits what is called dispersive bistability. In this case the material can be modeled by an effective n2 or v (3), meaning that the refractive index becomes a nonlinear function of the optical intensity. The second configurationwewill examine is a linear-nonlinear interface. In this case, the interface provides the feedback due to refractive index mismatch. In fact, the reflection coefficient (as well as the transmission coefficient) is modified due to the nonlinearity, which, as we shall see later, is responsible for demonstrating optical switching and bistability.