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Baghdad Science Journal

Dynamic Response of a Nonlinear Fabry-Perot Etalon for Various Medium Response Times

Ali Hassan Khidhir

Published Mar 1, 2020• 1 citation

Abstract

In this work, the switching nonlinear dynamics of a Fabry-Perot etalon are studied. The method used to complete the solution of the differential equations for the nonlinear medium. The Debye relaxation equations solved numerically to predict the behavior of the cavity for modulated input power. The response of the cavity filled with materials of different response time is depicted. For a material with a response time equal to = 50 ns, the cavity switches after about (100 ns). Notice that there is always a finite time delay before the cavity switches. The switch up time is much longer than the cavity build-up time of the corresponding linear cavity which was found to be of the order of a few round-trip times. The slowing down of the cavity response occurs when the incident intensity is approximately equal to the critical switching intensity. This effect is called critical slowing down. As a result, the response of the cavity is much slower than what could be expected from the steady state analysis. The reflected intensity and the change in round-trip phase have similar dynamic response. In this research, the matlap programs are used to study the switching dynamics of a Fabry-Perot etalon.

DOI: 10.21123/bsj.2020.17.1.0120

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In this work, the switching nonlinear dynamics of a Fabry-Perot etalon are studied. The method used to complete the solution of the differential equations for the nonlinear medium. The Debye relaxation equations solved numerically to predict the behavior of the cavity for modulated input power. The response of the cavity filled with materials of different response time is depicted. For a material with a response time equal to = 50 ns, the cavity switches after about (100 ns). Notice that there is always a finite time delay before the cavity switches. The switch up time is much longer than the cavity build-up time of the corresponding linear cavity which was found to be of the order of a few round-trip times. The slowing down of the cavity response occurs when the incident intensity is approximately equal to the critical switching intensity. This effect is called critical slowing down. As a result, the response of the cavity is much slower than what could be expected from the steady state analysis. The reflected intensity and the change in round-trip phase have similar dynamic response. In this research, the matlap programs are used to study the switching dynamics of a Fabry-Perot etalon.

We have studied theoretically and experimentally the dynamic behavior of a nonlinear Fabry-Perot interferrometer filled with a Kerr medium. The Fabry-Perot responses ranging from extremely transient to quasi-steady-state in various modes of operation are considered. The experimental results are in excellent agreement with theory. It is shown that the quasi-steady-state operation requires not only a medium response time much smaller than the cavity round-trip time, but also a characteristic time of the input intensity variation several hundred times larger than the cavity round-trip time. Even in the quasi-steady-state limit, optical switching is often featured by overshoot and ringing after switching. The switching speed is limited by the cavity buildup time.

We develop equations for the dynamic response of the non-linear Fabry-Perot, including a finite material response time. Our model demonstrates overshoot switching for rapid onset signals. This phenomenon makes possible several new effects: switching below steady-state intensity values, output response determined by input onset characteristics, pulse trains transmitted in four distinct modes including alternate switching, and input phase switching up as well as down. Our model also exhibits critical slowing down which occurs, in general, at unstable equilibrium output intensities. Finally, we include coupled nonlinear cavities and analyze a three-mixror configuration which produces pulsed outputs for appropriate CW inputs.

The dynamic properties of a Fabry–Perot interferometer filled with a material exhibiting second-order dispersive nonlinearity are studied both theoretically and experimentally. The response of the medium is described by an intensity dependent phase constant as derived from self-action effects. Considering two relaxation times, that of the material and that of the cavity, the basic relations for the stability analysis and for the numerical calculations are obtained. Bistability and self-pulsing effects are predicted. Moreover, the transient behavior is characterized by anomalous switching properties like overshoot and alternate switching. The corresponding experiments performed on a nonlinear transmission line resonator confirm the theoretical results. In a final discussion, the relations to the field of nonlinear optics are outlined.

In this work, analytical study for simulating a Fabry-Perot bistable etalon (F-P cavity) filled with a dispersive optimized nonlinear optical material (Kerr type) such as semiconductors Indium Antimonide (InSb). Because of a trade off between the etalon finesse values and driving terms, an optimization procedures have been done on the InSb etalon/CO laser parameters, using critical switching irradiance (Ic) via simulation systems of optimization procedures of optical cavity. in order to achieve the minimum switching power and faster switching time, the optimization parameters of the finesse values and driving terms on optical bistability and switching dynamics must be studied. In addition, for different values of a cavity finesse (for example, F = 25 and 2.37) the switching intensity takes low values with a high finesse etalon compared to a high switching intensity with a low finesse etalon. So, the minimum switching power for a low finesse etalon is ⁓0.785mW, and is about 0.0785mW for a high finesse etalon. The driving term peak of a high finesse etalon becomes higher and the slowing down region becomes less, leading to a fast switching as compared with a slow switching in a low finesse etalon. So that, the minimum switching time was about 300ns for a low finesse etalon, and about 150ns for a high finesse etalon.

The analytical study of optical bistability is concerned in a fullyoptimized laser Fabry-Perot system. The related phenomena ofswitching dynamics and optimization procedure are also included.From the steady state of optical bistability equation can plot theincident intensity versus the round trip phase shift (φ) for differentvalues of dark mistuning 12,6,3,1.50 , o    or finesse (F= 1, 5, 20,100). In order to obtain different optical bistable loops. The inputoutputcharacteristic for a nonlinear Fabry-Perot etalon of a differentvalues of finesse (F) and using different initial detuning (φ0) are usedin this research. When the cavity finesse values increase, the switch-ON intensity increases for the same value of (φ0), because thebistable loop width increases with increasing the cavity finessevalues.