论文标题
非线性纤维KERR谐振器中的极化调节不稳定性
Polarization modulation instability in a nonlinear fiber Kerr resonator
论文作者
论文摘要
我们报告了非线性纤维KERR谐振器中极化调节不稳定性（PMI）的实验和数值观察。通过与腔内的两个主偏振模式相关的腔内场之间的相对相位，对此现象进行了分阶段匹配。我们的实验研究基于一个12米长的纤维环谐振器，其中插入极化控制器以精细控制腔内双折射的水平。根据双折射的量，发现通过PMI产生的时间模式是固定的或表现出倍增动力学的。实验结果与基于两种正交极化模式的Ikeda图的数值模拟非常吻合。我们的研究提供了对多模Kerr共振器中调制不稳定性控制的新见解。调制不稳定性（MI）是一种非线性现象，其特征是在强烈连续波（CW）激光束上定期扰动的指数增长和演变[1，2]。在非线性相匹配的参数过程的基础上，它与能量从狭窄的泵频率分量转移到泵周围对称排列的一对边带。在单通气光纤传播中，可以通过异常的组速度分散和Kerr非线性之间的平衡来自然相匹配[1，2]。相比之下，由于系统边界条件的至关重要的作用[3-5]，因此在被动KERR谐振器（例如纤维环腔）的背景下，可能会有更一般的相匹配条件。在这种情况下，已经研究了MI的各种配置，包括正常分散体制中的MI，MI通过双重或不连贯的驾驶，以及MI和FARADAY之间的竞争或周期倍加倍（P2）的不稳定性[6---12]。此外，在与单通繁殖的不同之处，KERR谐振器中的MI会导致固定周期性（Turing）模式的出现；现在，这种模式被理解为与颞腔孤子和微孔子光学频率梳密切相关[13---16]。众所周知，光的偏振分量之间的双折射和非线性耦合也有助于参数过程的相匹配。这导致极化MI（PMI）和矢量时间模式的出现[17-19]。在驱动的谐振器中，迄今为止，PMI仅在理论上进行了研究[20-22]，但是最近在微孔子中进行正交的双梳子产生的证明引起了对这一过程的重新兴趣[23]。在这封信中，我们报告了被动Kerr谐振器中对PMI的直接实验观察。我们的实验测试床基于正常的分散纤维环腔，该腔腔含有偏振控制器，用于调整腔内双折射。这种局部双折射会导致两个正交偏振模式之间的相对相位，这又影响了PMI侧带的频移。我们还发现，双向反射可以导致周期两倍（P2）动力学，其特征在于两个往返周期。我们的实验结果与基于迭代两组分数Ikeda图的理论预测和数值模拟非常吻合。实验设置显示在图1（a）中。它由L = 12米长的无源纤维环腔组成，细节约为27，主要是由Spun纤维建造的。为了避免与标量MI的竞争[2]，我们建立了一个腔腔，其群估计为2 = 47 PS 2 /km，这一值足够大，足以忽略三阶分散。同样，使用旋转纤维（几乎各向同性）避免了极化成分之间的群速不匹配。此外，为了防止任何其他弯曲引起的双折射的来源，纤维被仔细地偏离伪造，并直接在我们的实验板上缠绕，直径较大。我们估计这会导致双折射$δ$ n不超过10-8 [24]，这在我们的研究中可以忽略。
We report on the experimental and numerical observation of polarization modulation instability (PMI) in a nonlinear fiber Kerr resonator. This phenomenon is phased-matched through the relative phase detuning between the intracavity fields associated with the two principal polarization modes of the cavity. Our experimental investigation is based on a 12-m long fiber ring resonator in which a polarization controller is inserted to finely control the level of intra-cavity birefringence. Depending on the amount of birefringence, the temporal patterns generated via PMI are found to be either stationary or to exhibit a period-doubled dynamics. Experimental results are in good agreement with numerical simulations based on an Ikeda map for the two orthogonally polarized modes. Our study provides new insights into the control of modulation instability in multimode Kerr resonators. Modulation instability (MI) is a nonlinear phenomenon characterized by the exponential growth and evolution of periodic perturbations on top of an intense continuous-wave (cw) laser beam [1, 2]. Underpinned by a nonlinearly phase-matched parametric process, it is associated with a transfer of energy from a narrow pump frequency component to a pair of sidebands arranged symmetrically around the pump. In single-pass optical fiber propagation, MI can be naturally phase-matched through a balance between anomalous group-velocity dispersion and Kerr nonlinearity [1, 2]. In contrast, more general phase-matching conditions are possible in the context of passive Kerr resonators, such as fiber ring cavities, because of the crucial role played by the systems' boundary conditions [3-5]. Various configurations of MI have been investigated in that context, including MI in the normal dispersion regime, MI via bichromatic or incoherent driving, as well as competition between MI and Faraday or period-doubled (P2) instabilities [6--12]. Moreover, at variance with single-pass propagation, MI in Kerr resonators can lead to the emergence of stationary periodic (Turing) patterns; such patterns are now understood to be intimately related to temporal cavity solitons and microresonator optical frequency combs [13--16]. Birefringence, and nonlinear coupling between the polarization components of light, is also known to contribute to the phase-matching of parametric processes. This leads to polarization MI (PMI) and the emergence of vector temporal patterns [17-19]. In driven resonators, PMI has only been investigated theoretically so far [20-22], but recent demonstrations of orthogonally-polarized dual comb generation in microresonators are sparking a renewed interest in this process [23]. In this Letter, we report on the direct experimental observation of PMI in a passive Kerr resonator. Our experimental test-bed is based on a normally dispersive fiber ring cavity that incorporates a polarization controller for adjustment of the intra-cavity birefringence. This localized birefringence gives rise to a relative phase detuning between the two orthogonal polarization modes of the cavity, which in turn affects the frequency shift of the PMI sidebands. We also find that birefringence can lead to period-doubled (P2) dynamics, characterized by a two round-trip cycle. Our experimental results are in good agreement with theoretical predictions and numerical simulations based on an iterative two-component Ikeda map. The experimental setup is displayed in Fig. 1(a). It consists of a L = 12-m long passive fiber ring cavity with a finesse F of about 27, mainly built out of spun fiber. To avoid competition with scalar MI [2], we have built a cavity with normal group-velocity dispersion estimated to 2 = 47 ps 2 /km, a value large enough to neglect third-order dispersion. Also, the use of a spun fiber (nearly isotropic) avoids group-velocity mismatch between the polarization components. Additionally, to prevent any additional source of bending-induced birefringence, the fiber was carefully off-spooled and wound directly on our experimental board with a large 50-cm diameter. We estimate that this causes a birefringence $Δ$n no greater than 10 --8 [24], which can be neglected in our study.
