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arXiv:2005.13984 · Physical Review A

Optical bistability with bound states in the continuum in dielectric gratings

Дмитрий Н. Максимов, Andrey Bogdanov, Evgeny N. Bulgakov

Published Sep 11, 2020• 52 citations
arXivHTMLPDF

Abstract

We consider light scattering by dielectric gratings supporting optical bound states in the continuum. Due to the presence of instantaneous Kerr nonlinearity critical field enhancement in the spectral vicinity of the bound state triggers the effect of optical bistability. The onset of bistability is explained theoretically in the framework of the temporal coupled-mode theory. As the central result we cast the problem in the form of a single field-driven nonlinear oscillator. The theoretical results are verified in comparison with numerical simulations.

DOI
10.1103/physreva.102.033511

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We consider light scattering by dielectric gratings supporting optical bound states in the continuum. Due to the presence of instantaneous Kerr nonlinearity critical field enhancement in the spectral vicinity of the bound state triggers the effect of optical bistability. The onset of bistability is explained theoretically in the framework of the temporal coupled-mode theory. As the central result we cast the problem in the form of a single field-driven nonlinear oscillator. The theoretical results are verified in comparison with numerical simulations.
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.
We consider grating induced optical bistability (OB) arising from the resonant excitation of a given nonlinear guided mode. In that case it can be shown, using the coupled-mode formalismi(1), that in the whole bistable domain : a) the transverse field map of the resonantly excited nonlinear guided mode corresponds to that of the associated linear one which is known. b) the Kerr-type nonlinearity only modifies the longitudinal wavevector component. Thus the rigorous theory of diffraction(2), previously used to study grating-induced plane wave OB(3), can be replaced by a much more simple one which works as follows : i) determine the complex longitudinal wavevector component of the linear leaky guided mode p, βpL, through the solution of the associated linear homogeneous grating problem(2), ii) use the rigorous theory of diffraction in linear optics(2) to determine the in-coupling efficiency, tp, of the incident plane wave, iii) use the coupled-mode formalism to derive the analytical expression(4) of the complex nonlinear longitudinal wavevector component βpNL.
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.
Dynamical transient response and longitudinal spatial evolution of the first-order phase transition are presented for intrinsic optical bistability of a system of interacting spatially distributed, coherently driven two-level atoms. It is shown that a discontinuity in the nonlinear dielectric function is established internal to the medium due to transient response to a coherent, externally applied, time-dependent driving field, following the attainment of a critical value for the input intensity. If the externally applied field intensity reaches the steady state, beyond the critical value, the discontinuity of the nonlinear dielectric function in the medium reaches a stable stationary condition and forms a spatial boundary between states of high and low polarization in the medium. Thus it is shown that intrinsic optical bistability corresponds to a spatial as well as a temporal first-order phase transition in light-matter interactions, far from thermodynamic equilibrium, where the spatial boundary between different phases is established by transient dynamical response to the incident field.
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.