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.     

The transmission and bistability of a nonlinear quasioptical resonator in ESR-conditions in ruby

Due to rapid progress of the nonlinear optics it has become real to observe and use the phenomenon of optics bistability in such passive structure as a Fabry-Perot resonator filled (completely or partially) with a substance having nonlinear adsorbtion and refraction. The problem of the optic bistability of such resonance structures were discussed in [1,2].     

Cavity nonlinear optics at low photon numbers from collective atomic motion

We report on Kerr nonlinearity and dispersive optical bistability of a Fabry-Perot optical resonator due to the displacement of ultracold atoms trapped within. In the driven resonator, such collective motion is induced by optical forces acting upon up to 10(5) 87Rb atoms prepared in the lowest band of a one-dimensional intracavity optical lattice. The longevity of atomic motional coherence allows for strongly nonlinear optics at extremely low cavity photon numbers, as demonstrated by the observation of both branches of optical bistability at photon numbers below unity.     

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.     

非线性光纤环：2.掺铒光纤全纤光学双稳态实验

利用掺饵光纤和光纤定向耦合器组成全光纤谐振腔，在光学非线性条件下，实现了全纤光学双稳运转，实验双稳阈值与理论相符。     

Enhanced four-wave mixing in a high-finesse highly nonlinear fiber Fabry-Perot resonator

We have achieved a four-wave mixing process in a high-finesse highly nonlinear fiber Fabry-Perot resonator, where the amplified signal and idler were enhanced in transmission by 6 dB and 10 dB respectively comparing with those in a single fiber. We used a 6 m long low-loss Fabry-Perot resonator with two high-reflectivity fiber Bragg gratings written directly into a highly nonlinear fiber provided by Sumitomo Electric Inc., where the minimised intracavity loss resulted in the finesse in excess of 100. The resonator length was locked for 30 min by means of a modified Pound-Drever-Hall technique. The maximum intracavity power was increased by 14.3 dB by increasing the stimulated Brillouin scattering threshold with periodic phase modulation by a pseudo-random bit sequence, with length matching that of the cavity.     

Nonlinear Fabry-Perot resonator with a silicon photonic crystal waveguide

We derive an equation that describes the nonlinear operation of a Fabry-Perot resonator with a large group index waveguide. Specifically, a silicon photonic crystal microcavity with two-photon-excited free carrier nonlinearity and Kerr nonlinearity is assumed. The equation clearly explains the bistability of the device and the reduction of the required pump energy for a specific nonlinear phase shift at an appropriate phase detuning from the resonance. We present a simple procedure to predict the required optical pump energy for the modulation and the resulting modulation depth by use of the equation and the device parameters.     

Coupler-loss and coupling-coefficient-dependent bistability and instability in a fiber ring resonator

In this paper, we demonstrate the dynamic simulation of light traveling in a fiber ring resonator with a single coupler. Optical nonlinear phenomena including bistability, the Ikeda instability, bifurcation and chaos are studied. The Ikeda instability in ring resonator arises from the ring-cavity lifetime being much longer than the Kerr-effect response time of the fiber. The transmission curves of the bistability and the instability as function of the insertion losses (γ) and the coupling coefficients (κ) of the coupler are derived.     

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.     

On the finesse of a phase-conjugate Fabry-Perot resonator using nearly-degenerate four-wave mixing

We consider a Fabry-Perot cavity in which one of the mirrors is a phase-conjugate mirror (PCM) using near-degenerate four-wave mixing. We show that when taking pump depletion into account, the divergence in finesse of the resonator predicted by linear theories for a resonator round trip gain approaching unity is eliminated. The saturation of the finesse as a function of pump intensity leads to a new kind of bistability in the transmission characteristics of the system.     

Influence of nonlinear absorption effects on optical bistability in semiconductor ring resonators

We present a theoretical investigation of optical bistability in a nonlinear semiconductor ring resonator, by taking into account the two-photon absorption and the free-carrier absorption. By solving the intensity equation within the ring resonator, a parametric formulation is obtained for describing the bistability relation between the input and the output intensities. Numerical results show that the nonlinear absorption effects can affect the critical points and domain of the optical bistability.     

Optical bistability on a silicon chip

We demonstrate, for the first time to our knowledge, optical bistability on a highly integrated silicon device, using a 5-microm-radius ring resonator. The strong light-confinement nature of the resonator induces nonlinear optical response with low pump power. We show that the optical bistability allows all-optical functionalities, such as switching and memory with microsecond time response and a modulation depth of 10 dB, driven by pump power as low as 45 microW. Silicon optical bistability relies on a fast thermal nonlinear optical effect presenting a 500-kHz modulation bandwidth.     

FP腔中光驱动微悬臂的双稳效应的研究

研究了高灵敏度悬臂梁与光纤端面构筑的低精细度FP型光腔中光驱动的悬臂梁振动的双稳效应。通过改变输入到光腔内的激光功率,检测与之相应的悬臂梁的形变。在实验中发现悬臂梁的形变随激光功率的改变呈现非线性变化的关系,在激光功率增大到一定闽值时可以诱导产生光力双稳效应。通过改变光腔初始腔长成功实现了对产生光力双稳效应阈值的调节。     

Stability of nonlinear Fabry-Perot resonators

The stability of folded Fabry-Perot resonators is investigated for the case where the resonator contains a medium with a dispersive third-order nonlinearity. Positive-branch instabilities of Ikeda type are found, with thresholds comparable to optical bistability thresholds. In the unstable region, the internal field is apparently chaotic, though oscillatory behaviour is found in a special case.     

CdSSe玻璃在环形腔中的自振荡

两表面镀有高反射膜,自身形成F-P腔的CdSSe玻璃薄片置于环形腔中.在一定的输入光强参数下,反射光信号出现其有某种规律性的振荡.实验观测了作为输入光强函数的不同振荡模式.由于所用样品的光双稳回线宽阔,上下两支有较大的倾斜度,我们观察到较大数目的输出强度上升与下降台阶.简单的绝热模拟表明,自振荡的模式遵从Farey-tree结构.     

Nonlinearity penalties and benefits of light traveling in a fiber optic ring resonator

The nonlinearity properties of light traveling in a fiber optic ring resonator (FORR) are presented. The nonlinearity penalties suffering from Kerr effects and four-wave mixing nonlinear types including bistability, chaos and bifurcation are investigated. The advantages of the nonlinearity penalties including photon correlation, optical switching and information security using chaotic signals are also discussed. The obtained results have shown that the parameters of FORR can be changed, and thus the penalties of the nonlinear effects have shown the potential of using for some applications.     

Effect of the spectral half-width of the driving field on the bistability

The bistability behavior of a nonlinear absorbing medium inside a Fabry–Perot resonator driven by an external quasi-monochromatic field is studied. The driving field is considered to be of a Gaussian and Lorentzian spectral line profile. The effect of the spectral half-width on the bistability is discussed. The mathematical treatment is carried out through an interferometric point of view. The dependence of the driving intensity required to initiate bistability on the standing wave established inside the resonator is represented.     

Optical bistability in GaInAsP/InP coupled-circular resonator microlasers

Optical bistability is realized in GaInAsP/InP coupled-circular resonator microlasers, which are fabricated by planar technology. For a coupled-circular resonator microlaser with the radius of 20?μm and a 2?μm-wide bus waveguide, hysteresis loops are observed for the output power coupling into an optical fiber versus the cw injection current at room temperature. The laser output spectra of the upper and lower states of the hysteresis loop indicate that the bistability is related to mode competitions. The optical bistability can be explained as the mode competition between the symmetry and antisymmetry coupled modes relative to the bus waveguide.     

Enhanced bistability with the line-narrowed modes in a nonlinear modulated index Fabry-Perot cavity

We exploit the recently reported line narrowed modes [1] for observation of bistability in a nonlinear Fabry-Perot cavity with intracavity index modulation. We show that the frequency response of the structure exhibits larger bistability loops for the line narrowed modes.     

Investigation of Brillouin effects in small-core holey optical fiber: lasing and scattering

We demonstrate for what is believed to be the first time a Brillouin laser based on a holey fiber (HF). Using a simple Fabry-Perot resonator scheme containing a 73.5-m-long highly nonlinear HF with an effective area of 2.85 microm(2) , we obtain a threshold of 125 mW and a slope efficiency of ~70% . Stimulated and spontaneous Brillouin scattering effects are investigated in the HF, and we show that the high lasing threshold is due mainly to reduction of the effective gain coefficient caused by structural nonuniformity along the fiber length.