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Microwave and Optical Technology Letters

Ultra‐fast dynamic nonlinear mechanism of Fabry–Perot cavity with femtosecond pumping

Xueyang Shi, Yu Zhang, Xunya Jiang

Published Jun 2, 2022• 0 citations
Publisher

Abstract

Abstract We numerically investigate the ultrafast dynamic nonlinear mechanism of an Fabry‐Perot (FP) cavity with femtosecond (fs) pumping by the transmission change of an incident signal pulse. The nonlinear effect simulated by a two‐level system model can decrease the dielectric constant. Therefore, the temporally transmitted pulse is compressed owing to the faster phase velocity, and a sloped change in the transmission spectra is observed, which can be explained by the mechanism of pulse deformation. In addition, we stretched a certain part of the temporally transmitted pulse to further demonstrate the deformation of the pulse mechanism. This dynamic nonlinear mechanism based on the FP cavity can not only be used to design new optical devices with ultrafast response times, such as pulse modulators and passive amplifiers, but can also be easily constructed and integrated, which has great practical applications.

DOI
10.1002/mop.33275

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Abstract We numerically investigate the ultrafast dynamic nonlinear mechanism of an Fabry‐Perot (FP) cavity with femtosecond (fs) pumping by the transmission change of an incident signal pulse. The nonlinear effect simulated by a two‐level system model can decrease the dielectric constant. Therefore, the temporally transmitted pulse is compressed owing to the faster phase velocity, and a sloped change in the transmission spectra is observed, which can be explained by the mechanism of pulse deformation. In addition, we stretched a certain part of the temporally transmitted pulse to further demonstrate the deformation of the pulse mechanism. This dynamic nonlinear mechanism based on the FP cavity can not only be used to design new optical devices with ultrafast response times, such as pulse modulators and passive amplifiers, but can also be easily constructed and integrated, which has great practical applications.
We present a simple and intuitive model based on the impulse response of linear electrical systems for describing the propagation of optical pulses through a dynamic Fabry–Perot resonator whose refractive index changes with time. Our model shows that the adiabatic wavelength conversion process in resonators results from a scaling of the round-trip time with index changes. For pulses longer than the cavity round-trip time, we find that more energy can be transferred to the new wavelength when the input pulses are slightly detuned from the cavity resonance and the refractive index does not change too rapidly. In fact, the optimum duration of index changes scales with the photon lifetime of the resonator. We describe the evolution of the shape and spectrum of picosecond pulses inside a resonator under a variety of input conditions and with the magnitude and duration of index variations. We also apply our general theory to the case of pulses whose widths are shorter than the round-trip time and derive an analytical expression for the output field under quite general conditions. This analysis reveals a shifting of the spectral comb as well as compression of the temporal pulse train that depends on the both the magnitude and sign of the index change. Our results should find applications in the area of optical signal processing using resonant photonic structures.
We show that the temporal analog of a Fabry–Perot resonator (FPR) can be realized by using two moving temporal boundaries, formed by intense pump pulses inside a dispersive medium (such as an optical fiber). We analyze such FPRs using a transfer-matrix method, similar to that used for spatial structures containing multiple thin films. We consider a temporal slab formed using a single square-shape pump pulse and find that the resonance of such an FPR has transmission peaks whose quality ( Q ) factors decrease rapidly with an increasing velocity difference between the pump and probe pulses. We propose an improved design by using two pump pulses. We apply our transfer-matrix method to this design and show considerable improvement in the Q factors of various peaks. We also show that such FPRs can be realized in practice by using two short pump pulses that propagate as solitons inside a fiber. We verified the results of the transfer-matrix method by directly solving the pulse propagation equation with the split-step Fourier method.
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.
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.
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.