Nonlinear Fabry-Perot Resonator Research Articles

Optical limiter coatings towards reusable high irradiance shielding

Optical limiters (OLs) are systems designed to protect objects from high intensity irradiance above a set threshold. Often times, these OL systems are in the form of coatings and can be used to protect objects such as sensors, critical components, or human eyes. In this work, we report the successful development of a multilayer reflective OL coating system based on a non-linear Fabry-Perot resonator structure. The structure utilized distributed Bragg reflectors (DBRs) composed of silicon/silicon nitride and a boron nitride non-linear layer embedded in the resonant cavity. The coatings were fabricated via DC and RF magnetron sputtering and exhibited high reflectance (∼99%) over a 525 nm bandwidth with a single resonant transmission peak (∼7%). The optical limiters fabricated in this study exhibited a transmission drop-off when exposed to irradiances above ∼1000 kW/cm2 from a 1064 nm Nd:YAG laser, demonstrating an abrupt reduction in resonant transmission. Fabricated optical limiters also demonstrated multi-hit survivability, maintaining low transmittance (<0.4%) after numerous 3.6 ns laser pulse exposures. This multi-hit survivability and high reflectivity offers promising opportunities for improved protection against directed energy weapons. This study lays groundwork for future evaluation of the observed on/off mechanism, as well as further development of high laser damage threshold optical limiting thin films.

Optimized optical nonreciprocal transmission in defective one-dimensional photonic bandgap structures with weak asymmetry

A novel and compact one-dimensional (1D) geometry for optical nonreciprocal transmission was proposed in this paper. Different from previous designs with high spatial asymmetry, by simply introducing a few dielectric periods of (BA) and (AB) into a typical nonlinear Fabry–Perot resonator with symmetric Bragg mirrors (AB)ND(BA)N, excellent optical nonreciprocal transmission properties can be achieved in the optical communication wavelength range. The optimized structure can be generally expressed as: (AB)ND(BA)M(AB)L, where M=N+1, L=1; M=N+2, L=2; M=N+3, L=3;…… and N≥6. The relationship between the bistability and the local field distribution of the Kerr defect layer D and the optical nonreciprocal transmission of the whole 1D system was analyzed theoretically. The direction- and incident wavelength-dependent shift of defect mode are confirmed to be responsible for the optimized optical nonreciprocity. The proposed optimized structures (AB)6D(BA)8(AB)2 and (AB)7D(BA)8(AB)1 are shown to have advantages over previously reported 1D designs with wide unidirectional transmission range (UTR) width (>3.1nm), high transmission for the forward incidence (>88%) and low transmission for the backward incidence (<1.22%) at lower input intensity (10 MW/cm2) with fewer layers (33 layers). Interestingly, the asymmetry degree of the proposed structures can be as low as 11.12%, which is only 1/4 or less of that of previous designs. The effects of the incident angle and polarization on the nonreciprocal transmission properties were also discussed for practical applications. These results are of great importance to the design of high-performance optical nonreciprocal devices, such as all-optical diodes, isolators and limiters.

Self-induced light trapping in nonlinear Fabry–Perot resonators

In the framework of the coupled mode theory we consider light trapping between two off-channel resonators which serve as self-adjusted Fano mirrors due to the Kerr effect. By inserting an auxiliary nonlinear resonator between the mirrors we achieve self-tuning of phase shift between the mirrors. That allows for the light trapping for arbitrary distance between the mirrors.

Linear and nonlinear behaviors of light in a silicon ring resonator

We have investigated the nonlinear switching characteristics of an optical device using a double-coupler silicon ring resonator in the presence of the linear losses, the Kerr nonlinearity, two-photon absorption, free-carrier-induced absorption and dispersion, and thermo-optic, in which the general features of the nonlinear switching of the throughput and drop port signals are similar to a single-couple ring resonator and nonlinear Fabry–Perot resonator results, respectively. The interesting results of the double-coupler silicon ring resonator are the low switching power conditions and the linear amplification gain, in which the various applications can provide by controlling the input–output characteristic of silicon-based resonators, for instance, by controlling the coupling ratio, free-carrier lifetime, and input wavelength, which can provide the multiple applications for optical switches, logic gates, and memories. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:997–1000, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25948

Nonlinear switching in silicon-based ring resonators

In this paper, we analyzed and investigated the nonlinear switching characteristics of an optical device using a double-coupler silicon ring resonator in the presence of the linear losses, the Kerr nonlinearity, two-photon absorption, thermo-optic effects, free-carrier-induced absorption, and dispersion. Results obtained have shown that the general features of the nonlinear switching of the throughput and drop port signals are similar to a single-couple ring and nonlinear Fabry-Perot resonators, respectively. The interesting results of the double-coupler silicon ring resonator are the low switching power conditions and the linear amplification gain. The various applications can be provided by controlling the input-output of silicon-based resonators, for instance, by controlling the coupling ratio, free-carrier lifetime, and input wavelength, in which the multiple applications for optical switches, logic gates, and memories can be provided.

Enhanced terahertz bistability in a nonlinear Fabry-Perot resonator with n-type quantum wells.

The intrinsic bistable terahertz response of intersubband plasmons in wide n-type delta-doped quantum wells is predicted to be enhanced by a resonant Fabry-Perot cavity. With a simple low-Q resonator, the threshold for bistability is decreased by a factor of 2-3 compared with that for bare multiple quantum wells.

Finite-Difference Time-Domain Analysis on Nonlinear Fabry-Perot Resonator in Optical Waveguide Geometry

The finite-difference time-domain (FDTD) method is applied to investigate the characteristics of nonlinear Fabry-Perot (FP) resonators in optical waveguide geometries. Our treatment, which is the extension of Tran's method developed to analyse the characteristics of nonlinear photonic crystals, correctly reproduces analytical results on optical bistabilities of the FP resonator provided by Chen and Mills in 1987. It is found that the minimum power required for optical bistabilities is significantry decreased by adopting the optical waveguide geometry, compared with the case of Chen and Mills, i.e., a conventional nonlinear FP interferometer.

Photonic analog-to-digital conversion by use of nonlinear Fabry–Perot resonators

Spatially parallel analog-to-digital conversion is proposed with a nonlinear Fabry-Perot resonator used as a multifunctional photonic comparator based on the pulse circulation method. The transmissive output of the photonic comparator exhibits a binary signal of either 1 or 0, depending on whether the incident intensity is greater than or less than the switching intensity corresponding to the binary weight, respectively. The photonic comparator complimentarily reflects the incident light, either with or without subtraction of the binary weight, and returns the reflected light to the next-lower digit cycle. Starting at the most significant bit, the recursive circuit successively launches the binary-coded outputs. The analog-to-digital conversion numerically demonstrates up to 6-bit resolution without noticeable errors.

Effect of Material Response Time on Optical Bistability in Nonlinear Distributed Feedback Gratings

The dynamic behaviors of nonlinear periodic waveguides with a finite material response time have been investigated by numerically solving both the coupled-mode equations and Debye relaxation equation. When the response time of the nonlinearity is more than the transit time through the grating, a modulational instability is sufficiently suppressed and one can obtain optical bistability. Unlike a nonlinear Fabry-Perot resonator or ring resonators, overshoot in the transmission never takes place in the case of zero detuning. However, a relaxation (or damped) oscillation always takes place in the presence of detuning. It is also found that the switch-on time depends on the material response time and the switch-off time is almost independent of it.

Semiconductor saturable absorber mirrors as mode-locking device for femtosecond lasers: nonlinear Fabry–Perot resonator approach

We propose an analytical model for ultra-short pulse generation in CW solid-state lasers with semiconductor saturable absorber-based modulators, that regards such a modulator as a nonlinear Fabry–Perot interferometer. The ways to control ultrashort pulse parameters through the modulator's parameters are shown. A stability analysis of the solutions obtained is performed.

A diagrammatic method for analysis of GaAs and InP based optoelectronic devices

A modified version of the signal flow graphs method can be applied to reveal the topological structure of physical models describing the operation of optoelectronic devices based on heterostructures comprising AIIIBV semiconductor compounds. In particular, this kind of analysis is apt to reveal the presence of closed paths (feedback loops) in the causal make-up of the phenomena underlying function of the devices. The analytical apparatus associated with the diagrams affords a new formulation of criteria for the occurrence of such physical conditions as the bistability or the threshold behaviour. The approach is illustrated on the instances of injection semiconductor laser, nonlinear Fabry-Perot resonator, self-electro-optic effect device and semiconductor laser optical amplifier.

Selection rules for transverse-mode excitation in nonlinear ring and Fabry-Perot resonators

We establish that the energy transfer between transverse modes in nonlinear Fabry-Perot resonators with curved mirrors, having degenerate or nearly degenerate modes, is governed by selection rules. Although these rules are derived in a perturbative limit, assuming a thin medium centered in the resonator, we have found numerically and experimentally that they still account for the otherwise unexpected enhancement or suppression of certain modes in more realistic cases. The existence of selection rules constitutes a fundamental difference between standing wave and traveling wave cavities and therefore prevents, in principle, the possibility of describing experiments on transverse effects performed in Fabry-Perot cavities with (simpler) ring resonator models.

Analysis of Transient Optical Bistability and Stability in a Nonlinear Fiber Fabry-Perot Resonator Based on an Iterative Method

We perform a transient analysis, steady-state analysis, and linear stability analysis of a nonlinear Fabry-Perot resonator in order to examine the possibility of a fiber bistable device. We here develop two iterative methods for calculating the dynamics of the Fabry-Perot resonator containing a nonlinear medium with an instantaneous response time. The treatment of the counter-propagating field within the cavity is very important in estimating the nonlinear phase shift due to propagation. A trapezoid rule and midpoint rule are used here for the numerical integration. The iterative method using the trapezoid rule gives excellent agreement with the multiple-beam method developed by Bischofberger and Shen (Phys. Rev. A 19 (1979) 1169), which is more complicated than the proposed procedure. Unfortunately it is found that the midpoint approximation is numerically unstable. Assuming a conventional optical fiber, the switching power for optical bistability is less than 1 kW for a resonator length of 1-2 cm. On the basis of the iterative method, we perform a linear stability analysis to examine whether Ikeda instability affects bistable device application or not. The stability analysis shows that the instability threshold is two orders of magnitude larger than the switching power for optical bistability.

Optical bistability in an all-optical fiber nonlinear fabry-perot resonator with linear absorption

An all-optical fiber nonlinear Fabry-Perot resonator is proposed. The steady-state model for describing this resonator is developed. The transmission and refection bistabilities are shown numerically. Our results show that the bistability in this system is similar to that in a normal nonlinear Fabry-Perot etalon, except that the characteristics of the bistability can be changed not only by the cavity length but also by the phase shifts of the fiber loop mirrors.

Dynamic transmission properties of a nonlinear fiber ring resonator

We present a method for calculating the dynamic input–output characteristics of a nonlinear fiber ring resonator caused by a change in input intensity. It is based on an original method developed by Bischofberger and Shen [Phys. Rev. A 19, 1169 (1979)] to study a transient nonlinear Fabry–Perot resonator. We treat a double-coupler fiber ring resonator, in which two types of optical bistability (transmission bistability and reflection bistability) are available and present the illustrative numerical results for a few cavity parameters. This analysis will be useful for a future experimental verification of optical bistability in fiber ring resonators and for the design of fiber bistable devices.

Analysis of dynamic pattern formation in nonlinear Fabry-Perot resonators

We present a detailed analysis of transverse effects and pattern formation in bistable optical elements. The system we investigate consists of a Fabry-Perot resonator for the optical feedback element with a nematic liquid-crystal cell used as an optically nonlinear intracavity medium. On illumination with a cw-laser beam, the system causes the beam to break up into several individual spots, passing through several transitions before finally reaching a stationary state. We devise a theoretical model which is used as the basis for numerical simulations of the system. The simulation results are in good agreement with experiment. Finally, we characterize the principal instability of the system using a linear stability analysis of the theoretical model.

Maxwell equations in a nonlinear Kerr medium

In this paper we present an exact calculation of the transfer function associated with the nonlinear Fabry–Perot resonator. While our exact result cannot be evaluated in terms of elementary functions, it does permit us to obtain a number of simple approximate expressions of various orders of accuracy. In addition, our derivation yields criteria of validity for the approximate formulae. Our approach is to be compared with others in which approximations are introduced in the model itself, either through the equations or through the boundary conditions. Our lowest order approximate formula turns out to be identical, interestingly, with the result obtained from the slowly varying envelope approximation (SVEA). Thus, our validity criteria apply to the SVEA result, and predict well its domain of validity and its breakdown for short wavelengths and for very high intensities and nonlinearities. The simple higher order formulae we present provide improved estimations in such regimes.

Observation of Optical Freedericksz Transition in a Resonator

Abstract A nonlinear Fabry-Perotresonator (FPR) with a homeotropically aligned nematic liquid crystal (NLC) is experimentally investigated. Specific nonlinear optical features of this kind of FPR are connected with the threshold character of light beam orientational interaction with the NLC. Optical Freedericksz transition, bistability, power limiting and stabilization are realized for small radiation intensities. Transverse pattern formation and rich dynamics are observed.

Polarization induced switching and polarization bistability in non-linear Fabry-Perot resonators

The author aims at merging polarization optics and non-linear optics for non-linear Fabry-Perot cavities. The in-depth study shows, both from a stationary and a dynamical approach, that polarization modulation leads among others to a novel switching mechanism. Furthermore, in well defined circumstances, using e.g., anisotropic cavity materials, polarization optical bistability can occur. Aspects of the dynamics of these processes are highlighted and applications are suggested.

Drift instability and spatiotemporal dissipative structures in a nonlinear Fabry–Perot resonator under oblique incidence

By means of a simplified model we study the dynamics of transverse effects in the nonlinear Fabry–Perot resonator illuminated under both normal and oblique incidences. We show that oblique incidence leads to a new kind of instability characterized by the onset of periodic self-pulsing. On the basis of a simple linear stability analysis, we interpret this instability in terms of a drift of spatial dissipative structures.