Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE photonics journal

On the Maxwell-Duffing Approach to Model Photonic Deflection Sensor

Abdel-Baset M.A. Ibrahim, P. K. Choudhury

Published Jul 4, 2013• 5 citations
Publisher

Abstract

This paper deals with the conceptualization of Maxwell-Duffing theory to model photonic deflection sensor along with functionality, which is based on the phenomena of optical bi- and multistabilities. The sensing system is considered to be consisting of Kerr nonlinear material along with suitably positioned mirrors. The efficacy of the approach is emphasized through a series of numerical simulations, and the reliability of the system is discussed. Effects due to system memory and periodicity in the optical bistability threshold have been demonstrated. It has been found that the approach provides a powerful tool to study optical bistability in resonating structures, particularly for materials with large third-nonlinearity and for operating frequencies near the natural resonance of the material.

DOI
10.1109/jphot.2013.2272318

Related papers

On the intrinsic optical bistability of a single Kerr nonlinear dielectric layer

Abdel-Baset M.A. Ibrahim

In this study, we investigate the optical bistability and multistability in a pure single Kerr nonlinear layer of dielectric material using the Maxwell-Duffing approach. We employ the Duffing anharmonic oscillator as an alternative constitutive relation to express the electric field as a nonlinear function of the induced polarization. Utilizing both the electromagnetic wave equation and the Duffing constitutive relation, we obtain a nonlinear polarization equation propagates through the nonlinear layer under the slowly varying envelope approximation. With the application of boundary conditions at both interfaces, expressions for the incident, reflected, and transmitted intensities of the light wave are obtained as nonlinear functions of the polarization and other controlling parameters. For realistic input parameters, our numerical results demonstrated the existence of an intrinsic optical bistability (IOB) in a pure single dielectric layer. Furthermore, the threshold value of the observed IOB depends essentially on the value Eth, i.e., the minimum value required to invoke the third-order nonlinearity inside the material. For operating frequency near the sharp resonance region, Eth was found to be ≈105 V/cm; this is equivalent to a threshold value of the optical intensity ≈1010 W/cm2. With the developments in THz sources, it is nowadays possible to observe this IOB experimentally by tuning the operating frequency near the sharp resonance region of the material. Steps to get the threshold value of Eth are also advised.

Journal of Applied Physics•May 8, 2015•5 citations

Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal

F. Y. Wang, Guixin Li, Hoi Lam Tam +2 more

The optical bistability and multistability in one-dimensional photonic crystal with the periodic metal-dielectric structure is investigated theoretically. In linear transmission, a structure with N periods will support N−1 resonant modes which correspond to the transmission peaks. Strong localized effect in these resonant modes is obtained. Optical bistability and multistability can be achieved when the incident wavelength is close to a resonance, which can be seen as an effect of the dynamic shifting of the wavelength of the resonant modes. It is found that the threshold for optical bistability in the periodic resonant structure is lower than the nonresonant metal-dielectric structure.

Applied Physics Letters•May 26, 2008•60 citations

Bistability of Nonlinear Photonic Crystal Microring Resonators

Tahereh Ahmadi Tameh, Babak Memarzadeh Isfahani, Nosrat Granpayeh +1 more

In this paper, two structures of nonlinear photonic crystal microring resonator have been analyzed by the flnite-difierence time-domain method and their optical bistability curves have been derived. In a modifled structure, by increasing the interaction of the lightwave and material, the optical bistability threshold is decreased to one third of that of flrst structure.

•Jan 1, 2009•3 citations

Optical Bistability from Ferroelectric Fabry-Perot Interferometer

Abdel-Baset M.A. Ibrahim, David Reginald Tilley, Junaidah Osman

We study the nonlinear optical bistability and multistability of a nonlinear ferroelectric (FE) Fabry-Perot (FP) interferometer assumed coated with partial dielectric mirrors on its interfaces. The FE material is considered to have an intensity-dependent refractive index where the third order nonlinear susceptibility χ ilmn (3) acts like Kerr coefficient. The nonlinear response of the FE medium is modeled by the Landau-Khalatnikov (LK) dynamical equation. Within a single frequency approximation, the nonlinear wave equation is written in terms of polarization P rather than the electric field E as the dependent variable. The resulting nonlinear polarization equation is numerically integrated across the FP film using the fourth order Runge-Kutta method. The behavior of the resulting polarization and transmission as a function of the field input intensity is investigated.

Ferroelectrics•Sep 4, 2007•7 citations

Nonlinear Prism Coupler: Approximate Theory and Comparison With Rigorous Analysis

Sergey A. Darmanyan, E. Popov, M. Nevière

A prism coupler filled with nonlinear Kerr-like material is studied theoretically. A simple, approximate analysis is developed to predict its behavior in both linear and nonlinear optics. In a wide range of incident amplitude magnitude, optical bistability and multistability are found. As far as field map not undergo drastic change, the simpler approximate theory is able to quantitatively analyze both prism couplers and waveguide in nonlinear optics and to study such effects as nonlinear phase shift, existence of nonlinear asymmetric modes in symmetric environments, bi-and multistability. The predictions of the analytical theory are compared with the results obtained via numerical integration of Maxwell equations and they agree quite well.

Journal of Electromagnetic Waves and Applications•Jan 1, 2000•2 citations

Modeling of nonlinear bistability with the FDTD method

T. Hruskovec, Zhizhang David Chen

Bistability due to the nonlinearity of an optical material has been studied recently and investigated for its potential high-speed all-optical signal-processing applications. As a result, accurate modeling techniques are required for design purposes. In this paper, the finite-difference time-domain (FDTD) method is applied to the modeling of optical bistability caused by the saturable Kerr effect of a GaAs–GaAlAs MQW-like material. A recursive finite-difference formulation for the saturable Kerr properties of the material is derived, and a physically realizable Fabry–Perot etalon is simulated. The numerical results demonstrate the effectiveness of the FDTD method for bistability modeling, and thus provide the foundations for further work and simulation of more complicated and realistic bistable structures. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 165–168, 1999.

Microwave and Optical Technology Letters•May 5, 1999•1 citation
This paper deals with the conceptualization of Maxwell-Duffing theory to model photonic deflection sensor along with functionality, which is based on the phenomena of optical bi- and multistabilities. The sensing system is considered to be consisting of Kerr nonlinear material along with suitably positioned mirrors. The efficacy of the approach is emphasized through a series of numerical simulations, and the reliability of the system is discussed. Effects due to system memory and periodicity in the optical bistability threshold have been demonstrated. It has been found that the approach provides a powerful tool to study optical bistability in resonating structures, particularly for materials with large third-nonlinearity and for operating frequencies near the natural resonance of the material.
In this study, we investigate the optical bistability and multistability in a pure single Kerr nonlinear layer of dielectric material using the Maxwell-Duffing approach. We employ the Duffing anharmonic oscillator as an alternative constitutive relation to express the electric field as a nonlinear function of the induced polarization. Utilizing both the electromagnetic wave equation and the Duffing constitutive relation, we obtain a nonlinear polarization equation propagates through the nonlinear layer under the slowly varying envelope approximation. With the application of boundary conditions at both interfaces, expressions for the incident, reflected, and transmitted intensities of the light wave are obtained as nonlinear functions of the polarization and other controlling parameters. For realistic input parameters, our numerical results demonstrated the existence of an intrinsic optical bistability (IOB) in a pure single dielectric layer. Furthermore, the threshold value of the observed IOB depends essentially on the value Eth, i.e., the minimum value required to invoke the third-order nonlinearity inside the material. For operating frequency near the sharp resonance region, Eth was found to be ≈105 V/cm; this is equivalent to a threshold value of the optical intensity ≈1010 W/cm2. With the developments in THz sources, it is nowadays possible to observe this IOB experimentally by tuning the operating frequency near the sharp resonance region of the material. Steps to get the threshold value of Eth are also advised.
The optical bistability and multistability in one-dimensional photonic crystal with the periodic metal-dielectric structure is investigated theoretically. In linear transmission, a structure with N periods will support N−1 resonant modes which correspond to the transmission peaks. Strong localized effect in these resonant modes is obtained. Optical bistability and multistability can be achieved when the incident wavelength is close to a resonance, which can be seen as an effect of the dynamic shifting of the wavelength of the resonant modes. It is found that the threshold for optical bistability in the periodic resonant structure is lower than the nonresonant metal-dielectric structure.
We study the nonlinear optical bistability and multistability of a nonlinear ferroelectric (FE) Fabry-Perot (FP) interferometer assumed coated with partial dielectric mirrors on its interfaces. The FE material is considered to have an intensity-dependent refractive index where the third order nonlinear susceptibility χ ilmn (3) acts like Kerr coefficient. The nonlinear response of the FE medium is modeled by the Landau-Khalatnikov (LK) dynamical equation. Within a single frequency approximation, the nonlinear wave equation is written in terms of polarization P rather than the electric field E as the dependent variable. The resulting nonlinear polarization equation is numerically integrated across the FP film using the fourth order Runge-Kutta method. The behavior of the resulting polarization and transmission as a function of the field input intensity is investigated.
A prism coupler filled with nonlinear Kerr-like material is studied theoretically. A simple, approximate analysis is developed to predict its behavior in both linear and nonlinear optics. In a wide range of incident amplitude magnitude, optical bistability and multistability are found. As far as field map not undergo drastic change, the simpler approximate theory is able to quantitatively analyze both prism couplers and waveguide in nonlinear optics and to study such effects as nonlinear phase shift, existence of nonlinear asymmetric modes in symmetric environments, bi-and multistability. The predictions of the analytical theory are compared with the results obtained via numerical integration of Maxwell equations and they agree quite well.
Bistability due to the nonlinearity of an optical material has been studied recently and investigated for its potential high-speed all-optical signal-processing applications. As a result, accurate modeling techniques are required for design purposes. In this paper, the finite-difference time-domain (FDTD) method is applied to the modeling of optical bistability caused by the saturable Kerr effect of a GaAs–GaAlAs MQW-like material. A recursive finite-difference formulation for the saturable Kerr properties of the material is derived, and a physically realizable Fabry–Perot etalon is simulated. The numerical results demonstrate the effectiveness of the FDTD method for bistability modeling, and thus provide the foundations for further work and simulation of more complicated and realistic bistable structures. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 165–168, 1999.