Statistical PT-symmetric lasing in an optical fiber network

PT-symmetry in optics is a condition whereby the real and imaginary parts of the refractive index across a photonic structure are deliberately balanced. This balance can lead to a host of novel optical phenomena, such as unidirectional invisibility, loss-induced lasing, single-mode lasing from multimode resonators, and non-reciprocal effects in conjunction with nonlinearities. Because PT-symmetry has been thought of as fragile, experimental realizations to date have been usually restricted to on-chip micro-devices. Here, we demonstrate that certain features of PT-symmetry are sufficiently robust to survive the statistical fluctuations associated with a macroscopic optical cavity. We construct optical-fiber-based coupled-cavities in excess of a kilometer in length (the free spectral range is less than 0.8 fm) with balanced gain and loss in two sub-cavities and examine the lasing dynamics. In such a macroscopic system, fluctuations can lead to a cavity-detuning exceeding the free spectral range. Nevertheless, by varying the gain-loss contrast, we observe that both the lasing threshold and the growth of the laser power follow the predicted behavior of a stable PT-symmetric structure. Furthermore, a statistical symmetry-breaking point is observed upon varying the cavity loss. These findings indicate that PT-symmetry is a more robust optical phenomenon than previously expected, and points to potential applications in optical fiber networks and fiber lasers.Comment: Submitted to Nature Communications, Pages 1-19: Main manuscript; Pages 20-38: Supplementary material

Nonlinear reversal of PT symmetric phase transition in a system of coupled semiconductor micro-ring resonators

A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linear PT-symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states still retain the structural form of the corresponding linear eigenvectors expected above and below the phase transition point. The conclusions of our analysis are in agreement with experimental data.Comment: 9 pages, 8 figure

Integrable nonlinear parity-time symmetric optical oscillator

The nonlinear dynamics of a balanced parity-time symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain-thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time symmetric systems. Unlike other saturable parity time symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.Comment: 6 pages, 5 figures, accepted for publicatio

Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion

We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate—irrespective of initial conditions. Moreover, numerical simulations suggest that this mechanism can still persist in the presence of nonlinear effects. We further show that this robust process can be harnessed to realize an optical omnipolarizer: a configuration that generates a desired polarization output regardless of the input polarization state, while from the opposite direction it always produces the counterpart eigenstate.United States. Army Research Office. Institute for Soldier Nanotechnologies (Grant W911NF-13-D-0001)United States-Israel Binational Science Foundation (Grant 2013508

Pt-Symmetric Micro-Resonators: High Sensitivity At Exceptional Points

Enhanced sensitivity is demonstrated in PT-symmetric coupled micro-resonator arrangements biased at an exceptional point. The spectral response of such a system is shown to follow a square root dependence on externally introduced perturbations. OCIS codes: 140.3948 (Microcavity devices), 280.3420 (Laser sensors), 140.3560 (Lasers, ring) Exceptional points (EPs) represent degeneracies in parameter space, where both eigenvalues and eigenvectors of a non-Hermitian operator tend to coalesce [1]. Recently, the properties associated with such singularities have been utilized in optics to introduce a number of new functionalities that are not readily attainable in conventional Hermitian systems [2,3]. Among various optical structures, parity-Time (PT) symmetric arrangements provide an excellent platform for the experimental realization of exceptional points [4]. Along these lines, single mode lasing in PTsymmetric coupled microring lasers has been demonstrated by exploiting the abrupt phase transitions at EPs [5,6]. An important feature of this class of non-Hermitian arrangements is an extreme sensitivity to external perturbations when operated close to their exceptional points. While this behavior has been proposed as a means to increase the responsivity of optical micro-resonator [7,8], this enhancement is yet to be experimentally demonstrated. In this study, we report on the observation of enhanced sensitivity associated with a PT-symmetric coupled cavity configuration biased at an EP. We show that the system response has a square root dependence on the applied perturbation that can be further boosted by increasing the coupling strength between the resonators

Pt-Symmetric Micro-Resonators: High Sensitivity At Exceptional Points

Enhanced sensitivity is demonstrated in PT-symmetric coupled micro-resonator arrangements biased at an exceptional point. The spectral response of such a system is shown to follow a square root dependence on externally introduced perturbations

Universal Entropie Response Of Nonlinear Multimode Optical Systems

We show that the mode occupancies in nonlinear multimode optical systems follow a universal behavior that tends to maximize the system\u27s entropy at steady-state. This thermodynamic response occurs irrespective of the type of nonlinearities involved