Instabilities in coupled photorefractive ring cavities and self-pumped phase conjugators

We investigate the temporal instabilities of mode intensities in two coupled unidirectional photorefractive ring resonators. The first resonator is driven by an external laser beam via photorefractive two-wave mixing. The internal oscillating beam is then employed to drive the second ring resonator. The second ring resonator provides a nonlinear loss mechanism for the coupled system. Complete spatial-temporal equations for describing the coupled system are derived and mean-field approximation is employed to simplify the transient analysis. The results of linear stability analysis indicate that the coupled system exhibits instability in the off-state and steady-state operation. The instability is explained in terms of competition between nonlinear gain and loss. The results are presented and discussed.Part II on Numerical Results will be published in a forthcoming issue of Applied Physics B     

Effect of photoconductivity and dielectric constant of the photorefractive materials on two-beam coupling gain and phase-shifts for a single unidirectional photorefractive ring resonator

Photoconductive dependence of two-beam coupling between the pump beam and the signal beam in photorefractive materials have been analyzed in case of non-degenerate wave mixing under the undepleted pump approximation method. During the two-wave mixing in photorefractive materials, steady state amplification of the signal beam and oscillation characteristics of a single unidirectional ring resonator has been studied. The domination of the two-beam coupling gain over the combined absorption and resonator losses such as Fresnel reflections from the crystal and imperfect mirrors builds up unidirectional oscillation. The buildup of such an oscillation leads to a saturation of the gain, which can be explained in terms of the photorefractive phase-shift. The existence of this phase-shift between the photorefractive index grating and the illumination intensity pattern, which is of characteristic of the photorefractive effect, leads to an energy transfer between the two beams. For a single unidirectional ring resonators, the effects of photoconductivity of the materials, two-beam energy coupling coefficient, dielectric constant, crystal thickness, and material's absorption coefficient on amplification of the two-beam coupling gain and photorefractive phase-shifts of the signal beam have also been studied in detail. It has been found that amplification of the signal beam and phase-shift can be enhanced by taking the photorefractive crystal having higher photoconductivity and lower dielectric constant, which improves performance of the resonators.     

Dependence of gain and phase-shift on crystal parameters and pump intensity in unidirectional photorefractive ring resonators

The steady-state amplification of light beam during two-wave mixing in photorefractive materials has been analysed in the strong nonlinear regime. The oscillation conditions for unidirectional ring resonator have been studied. The signal beam can be amplified in the presence of material absorption, provided the gain due to the beam coupling is large enough to overcome the cavity losses. Such amplification is responsible for the oscillations. The gain bandwidth is only a few Hz. In spite of such an extremely narrow bandwidth, unidirectional oscillation can be observed easily at any cavity length in ring resonators by using photorefractive crystals as the medium and this can be explained in terms of the photorefractive phase-shift. The presence of such a phase-shift allows the possibility of the non-reciprocal steady-state transfer of energy between the two light beams. Dependence of gain bandwidth on coupling constant, absorption coefficient of the material’s cavity length (crystal length) and modulation ratio have also been studied.      

Oscillation dependence of two-wave mixing gain for unidirectional ring resonator in photorefractive materials

Dependence of the coupling strength of two-wave mixing gain in photorefractive materials for the single unidirectional ring resonator on oscillation conditions has been analyzed in the strong nonlinear regime. In this regime, difference between the frequency of the pump beam and oscillating beam is proportional to the cavity-length detuning, which can be explained in terms of the photorefractive phase-shift. This phase-shift results due to slightly non-degenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for the steady-state oscillation. The presence of such a phase-shift allows the possibility of the nonreciprocal steady-state energy transfer between the pump and oscillating beams. If the gain due to the beam coupling is large enough to overcome the cavity losses then the signal beam is amplified in the presence of material absorption. Such amplification is responsible for the oscillations. For the single unidirectional ring resonator, the effects of cavity-length detuning, energy coupling coefficient, crystal thickness of the material, reflectivity of the cavity mirrors and material's absorption coefficient on the frequency and intensity of oscillations have also been studied in detail. It has been found that for the smaller value of absorption coefficient (α) of the photorefractive crystal, the unidirectional ring resonator can oscillate at almost any cavity-length detuning (ΔΓ) whereas for the larger value of α oscillation occurs only when the cavity-length detuning is limited to small region (around ΔΓ=0). But reverse of the case is found for energy coupling coefficient (γ₀).     

环形谐振腔频率响应特性研究

分析了方形环形谐振腔对S线偏光和P线偏光的频率响应特性,发现输入两个频率间隔相差很小的S线偏光和P线偏光都能引起环形谐振腔的谐振,其中S线偏光谐振峰频率特性更适于环形谐振腔的稳频。通过搭建环形谐振腔频率响应特性测试系统,从实验上验证了理论计算的正确性。对于环形谐振腔的稳频和调腔具有参考意义。     

Study of photoconductive and dielectric dependence of gain and phase-shift in the coupled unidirectional ring resonators based on non-degenerate wave-mixing in photorefractive materials

Photoconductive and dielectric dependence of gain and phase-shift in the coupled unidirectional photorefractive ring resonators (UPRR) have been analyzed for the case of non-degenerate two-wave mixing in photorefractive materials by employing the plane-wave approximation method. The effect of photoconductivity and dielectric constant of the coupled photorefractive crystals (A and B) on the gain and phase-shift in the coupled UPRR have also been studied in details. It has been found that for a given value of the photoconductivity of crystal B, the gain in the primary resonator can be enhanced by selecting lower value of frequency detuning of the same resonator and PR crystal A of higher photoconductivity in the coupled UPRR. But reverse of the case is found for the enhancement of phase-shift. Such enhancement of the gain and phase-shift in the primary resonator are responsible for build-up and non-reciprocal energy transfer between the modes of the internal oscillations, which greatly improves the performance of the coupled UPRR.     

光纤环形谐振腔的频率锁定及其特性

基于可调分束比的光纤分束器,制作了光纤环形谐振腔并通过调节分束比实现了对光纤环形谐振腔的欠耦合、临界耦合和过耦合的状态控制.实验测量了腔最小反射率与腔损耗之间的关系,获得光纤环形谐振腔的腔内衰减率为κ_0=2π×(1.60±0.03) MHz ,品质因子为Q=(1.10±0.02)×10.8.在此基础上,结合了压电陶瓷拉伸光纤以控制腔长和Pound-Drever-Hall锁频两大技术优势,克服了之前温度反馈控制等方法的反馈带宽窄、噪声大和稳定性差等问题,实现了对光纤环形谐振腔共振频率的快速、灵敏的控制和锁定.结果表明,锁频过程中相位调制功率与相位调制引起腔反射光的强度调制之间的关系为线性关系,进而通过降低相位调制信号的功率以减小相位调制对腔反射光强度调制的影响.当调制功率设定最低为–9 dBm时,光纤环形谐振腔仍能被稳定锁定.该光纤环形谐振腔为其与原子、金刚石色心等发光粒子相互作用的腔量子电动力学实验研究奠定了坚实的基础.     

Oscillation characteristics of a coupled unidirectional ring resonators with photorefractive crystals

For a coupled unidirectional photorefractive ring resonator (UPRR), the oscillation characteristics have been studied in details in terms of the photoconductive and dielectric constant of the photorefractive (PR) crystals under the assumption of the plane-wave approximation based on non-degenerate two-wave mixing in the photorefractive materials. It has been found that the steady oscillations are possible when the two resonators oscillate independently. Using the plane-wave approximation and steady state oscillation conditions, the effect of the frequency detuning, photoconductivity and dielectric constant of the PR crystals on the relative intensity and frequency of oscillation of the secondary resonator in the coupled UPRR have been studied. It has been found that the relative oscillation frequency of the secondary resonator could be enhanced by selecting PR crystal A of higher absorption strength relative to PR crystal B and the higher photoconductivity of the crystals B as compared to that of the crystal A. Due to the non-reciprocal energy transfer between the oscillating beams and the additional PR phase-shift in the PR crystals A and B, the magnitude of the relative oscillation frequency of the secondary resonator could be controlled by the absorption strength, dielectric constant and photoconductivity of the two crystals.     

Amplification of near-infrared light in a photorefractive ring resonator

We have demonstrated efficient amplification of near-infrared, 0.83-μm and 1.06-μm light, in a photorefractive ring resonator using Rh:BaTiO₃. The optical power oscillating inside the ring exceeded the pump power by a factor of up to 2.34. The sensitivity of a ring resonator to nanometer changes in its length was characterised using a piezo-mirror. Received: 30 November 2000 / Revised version: 24 January 2001 / Published online: 20 April 2001     

The effect of a high external electric field on a photorefractive ring phase conjugator

It is shown that a high external electric field often used to enhance the efficiency of photorefractive beam coupling and to decrease the photorefractive response time, may cause mode switching in photorefractive ring phase conjugator leading to a significant drop in the phase conjugate reflectivity.     

Minimization of the fluctuation in the signal beam intensity of a nonlinear optical medium with a transmission grating

Fluctuation in the intensity of the output signal beam of a photorefractive optical resonator can be reduced significantly by employing pump beam positive feedback. The fractional intensity transfer which is independent of time in the absence of fluctuation becomes time dependent in the presence of fluctuation of the optical wave-mixing process. The influence of various controlling parameters on the relative fluctuation of the output signal intensity has also been studied.     

Dynamic response of high-resolution ring resonator optical spectrometers to time-varying input signals

An analysis and experimental data of the time-dependent response of an all-fiber ring resonator in which the ring is illuminated by a phase modulated input beam are presented. The resonator is operated as a high-resolution optical-scanning spectrometer. Since the resolution limit is a function of the finesse and cavity-loop length, we will show that it is not possible to design a high-resolution ring resonator that will not produce a distorted output signal when the phase modulation rate is comparable to the response time of the ring.     

环形激光器反射镜相位延迟差测量方法研究

理论上推导出了环形激光器对Ｓ光和Ｐ光相位延迟差与其拍频峰对应的压电陶瓷电压差的关系式,分析了方形环形激光器对Ｓ光和Ｐ 光的频率响应特性,通过测量拍频峰电压差实现环形激光器反射镜相位延迟差测量。通过搭建环形激光器频率响应特性测试系统,从实验上验证了理论计算的正确性。结果表明,该方法测量误差小于１．５％,满足环形激光器反射镜相位延迟差测量要求。     

Design of a 2.5 THz submillimeter wave laser with optical pump beam guiding

A ring resonator design using the same set of mirrors for pump beam and submillimeter wave (SMMW) beam guiding is introduced. Optimal design is discussed on the example of a 2.5 THz methanol laser. It turns out that due to refocussing of the pump beam on the pinhole certain focal lengths of the focussing mirror, which mainly is responsible for the beam guiding, should be avoided. Diffraction losses and pinhole losses determine optimalg-parameters for which the pump beam guiding losses of the resonator are minimum, and optimal pump beam waist radii.The setup of an experimental laser with the optimized resonator and the experimental setup to measure laser performance are described, and results concerning laser output power, beam quality and efficiency are discussed.     

Conical parametric scattering of a single extraordinary beam in BaTiO3 crystal

In this paper, the parametric scattering of a single extraordinary polarized beam of laser in BaTiO₃ photorefractive crystal has been investigated experimentally and theoretically. The resulting pattern consists of beam fanning, isotropic ring, and anisotropic one. Among all parts of scattering pattern, isotropic ring has not been studied as much as beam fanning and anisotropic ring, and there still are some differences in reports about it. Therefore, the study has mainly focused on this part. In this experimental configuration, isotropic ring is just visible in positive angles although the other parts of parametric scattering pattern can be visible from behind and in front of the crystal. In addition to steady state pattern in forward and backward directions, its transient behavior with the rotation of crystal has been studied. The results of experiments have been analyzed carefully, and their theoretical explanations have been presented based on the standard theory of parametric scattering in photorefractive crystals. It has been shown that this configuration corresponds to the so called parametric B-process scattering.     

A Review of IR Transmitting,Hollow Waveguides

Abstract

An analysis and experimental data of the time-dependent response of an all-fiber ring resonator in which the ring is illuminated by a phase modulated input beam are presented. The resonator is operated as a high-resolution optical-scanning spectrometer. Since the resolution limit is a function of the finesse and cavity-loop length, we will show that it is not possible to design a high-resolution ring resonator that will not produce a distorted output signal when the phase modulation rate is comparable to the response time of the ring.     

A large-size SiO2 waveguide resonator used in integration optical gyroscope

We report on the resonance characteristics of a Si-based ring resonator model with the theory of multiple-beam interference. The resonator consists of a track pattern ring channel waveguides with radius of 2 cm, two input/output directional couplers and one ring resonator coupler. Using the wide angle finite-difference beam propagation method (WA-FDBPM), we presented optimal design of ring resonator and succeed in fabricating the ring resonator by Plasma Enhanced Chemical Vapor Deposition (PECVD) method. Observed from the resonance curve, finesse of 16.7 is measured. And a rate detection limit of 1.7°/h can be evaluated.     

Design of SMMW Laser Resonators with On-Axis Signal and Pump Beam Guiding in a Mirror Ring

A ring resonator design for optically pumped submillimeter wave (SMMW) lasers using the same set of four mirrors (including one focussing mirror) for pump beam and SMMW beam guiding is introduced.The optimum design is discussed on the example of a 2.523 THz methanol laser. It turns out that the focal length of the focussing mirror has to be adapted to the resonator perimeter. Eleven well suited focal length - resonator perimeter ratios, defining eleven standard resonator configurations, can be distinguished.The setup of an experimental laser with the optimized resonator and the experimental setup to measure laser performance are described, and results concerning laser output power, beam quality and efficiency are discussed.This paper is the extended version of the paper presented on the 23rd International Conference in Colchester [1] and continues a former article presented in this journal [2].     

A Differentiating Fiber-optic Ring Interferometer

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光折变振荡器中的模式巡游现象

在弱场条件下，给出了单向环形光折变振荡器的多模振荡方程．当模式处于非简并状态时，该方程可进一步化为Ｌｏｔｋａ-Ｖｏｌｔｅｒａ方程，从而反映出模式间的竞争现象；而当这些模式处于简并或准简并状态时，通过数值模拟发现由于模式间的相互作用加强，一定条件下引起了时空不稳定行为，例如横模间的周期巡游现象 关键词：