Loss-induced suppression and revival of lasing

Abstract

†These authors contributed equally to this work.Controlling and reversing the effects of loss are major challenges in optical systems. For lasers losses need to be overcome by a sufficient amount of gain to reach the lasing threshold. We show how to turn losses into gain by steering the parameters of a system to the vicinity of an exceptional point (EP), which occurs when the eigenvalues and the corresponding eigenstates of a system coalesce. In our system of coupled microresonators, EPs are manifested as the lossinduced suppression and revival of lasing. Below a critical value, adding loss annihilates an existing Raman laser. Beyond this critical threshold, lasing recovers despite the increasing loss, in stark contrast to what would be expected from conventional laser theory. Our results exemplify the counterintuitive features of EPs and present an innovative method for reversing the effect of loss.2 Dissipation is ubiquitous in nature; the states of essentially all physical systems thus have a finite decay time. A proper description of this situation requires a departure from conventional Hermitian models with real eigenvalues and orthogonal eigenstates to non-Hermitian models featuring complex eigenvalues and nonorthogonal eigenstates (1,2,3). When tuning the parameters of such a dissipative system, its complex eigenvalues and the corresponding eigenstates may coalesce, giving rise to a non-Hermitian degeneracy, also called an Exceptional Point (EP) (4). The presence of such an EP has a dramatic effect on the system, leading to nontrivial physics with interesting counterintuitive features such as "resonance trapping" (5), a mode exchange when encircling an EP (6), and a singular topology in the parameter landscape (7). These characteristics can control the flow of light in optical devices with both loss and gain.In particular, waveguides having parity-time symmetry (8), where loss and gain are balanced, have attracted enormous attention (9,10), with effects such as loss-induced transparency (11), unidirectional invisibility (12), and reflectionless scattering (13,14) having been already observed.Theoretical work indicates that EPs give rise to many more intriguing effects when they occur near the lasing regime; for example, enhancement of the laser linewidth (15,16), fast selfpulsations (15), and a pump-induced lasing death (17). Realizing such anomalous phenomena, however, requires moving from waveguides to resonators, which can trap and amplify light resonantly beyond the lasing threshold. With the availability of such devices (18,19), we discuss here the most counterintuitive aspect that close to an EP lasing should be inducible solely by adding loss to a resonator.Our experimental system (20) consists of two directly-coupled silica whispering-gallery-mode resonators (WGMRs) μR 1 and μR 2 , each coupled to a different fiber-taper WG1 and WG2 ( Fig. 1A and sec. S1). The resonance frequencies of the WGMRs were tuned to be the same via thermo-optic effect, and a controllable coupling strength κ was achieve...

Constant-intensity waves and their modulation instability in non-Hermitian potentials

“…Such non-Hermitian potential regions 4,5 , which serve as sources and sinks for waves, respectively, can give rise to novel wave effects that are impossible to realize with conventional, Hermitian potentials. Examples of this kind, which were meanwhile also realized in the experiment [6][7][8][9][10] , are the unidirectional invisibility of a gain-loss potential 11 , devices that can simultaneously act as laser and as a perfect absorber [12][13][14] and resonant structures with unusual features like non-reciprocal light transmission 10 or loss-induced lasing [15][16][17] . In particular, systems with a so-called parity-time (PT ) symmetry 18 , where gain and loss are carefully balanced, have recently attracted enormous interest in the context of nonHermitian photonics [19][20][21][22][23][24] .…”

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

“…Since it is not easy to achieve PT symmetry experimentally, several ways have been proposed to avoid the use of gain in a system. For example, a system with asymmetric loss is equivalent to a PT -symmetric system with a background of uniform loss, and so no gain is required to achieve an EP [3,[21][22][23][24]. In a system with many coupled modes, the emergence of multiple EPs and their interactions can occur under system parameter variation [25][26][27].…”

“…The extension of Hermitian Hamiltonians to non-Hermitian ones can be achieved mathematically by various ways, such as by introducing a complex potential or adding asymmetric losses to the system [2,3]. It is also recognized that if the complex potential has parity-time (PT ) symmetry, the system will possess real eigenvalues at small non-Hermiticity, and when the non-Hermiticity is sufficiently large, the system will experience a phase transition at an exceptional point (EP).…”

Eigenvalue dynamics in the presence of nonuniform gain and loss

“…After a critical amount of loss is added, further increases in the absorption also increases the total transmission through the waveguide pair. Likewise, reversed pump dependence can be observed in laser systems consisting of two coupled cavities [18][19][20]25]. First, one of these cavities is pumped such that the total system begins to lase.…”

“…The conditions presented here vastly expand the design space for observing these effects. We also show that a similarly broad class of systems exhibit a loss-induced narrowing of the density of states.Recently, the study of parity-time (PT ) symmetric optical systems has highlighted the importance of exploring non-Hermitian systems with patterned gain and loss [1][2][3][4][5][6][7][8][9][10][11], and has led to the discovery of a remarkable array of phenomena, such as loss-induced transmission in waveguides [12], unidirectional transport behavior [13][14][15][16][17], reversed pump dependence in lasers [18][19][20], and band flattening in periodic structures [4,[21][22][23][24]. These effects are leading to new possibilities for constructing on-chip integrated photonic circuits for the manipulation of light.…”