## Abstract

Effective manipulation of cavity resonant modes is crucial for emission control in laser physics and applications. Using the concept of parity-time symmetry to exploit the interplay between gain and loss (i.e., light amplification and absorption), we demonstrate a parity-time symmetry–breaking laser with resonant modes that can be controlled at will. In contrast to conventional ring cavity lasers with multiple competing modes, our parity-time microring laser exhibits intrinsic single-mode lasing regardless of the gain spectral bandwidth. Thresholdless parity-time symmetry breaking due to the rotationally symmetric structure leads to stable single-mode operation with the selective whispering-gallery mode order. Exploration of parity-time symmetry in laser physics may open a door to next-generation optoelectronic devices for optical communications and computing.

## Compensating optical loss for laser gain

Optical loss is thought to be detrimental to the operation of a laser, typically resulting in poor beam quality, multimode emission, and low efficiencies. Now results that take their cue from theoretical ideas of parity-time symmetry and implement them into the design of coupled laser components show that loss and gain can actually work together. Feng *et al.* and Hodaei *et al.* designed laser systems based on microring cavities to carefully control the amount of loss and gain within each component. The interplay between the loss and gain resulted in enhanced and cleaner emission from their lasers.

Laser cavities support a large number of closely spaced modes because their dimensions are typically much larger than an optical wavelength. As a result, the outputs from such lasers are subject to random fluctuations and instabilities because of mode competition for limited gain. During recent decades, effective mode manipulation and selection strategies have been intensively explored to achieve single-mode operation with both spatial and spectral controllability—a requirement for enhanced laser performance with higher monochromaticity, less mode competition, and better beam quality. Obtaining single-mode operation depends on sufficiently modulated gain and loss, but such modulation is impeded by factors such as inhomogeneous gain saturation. Several approaches have been developed that make use of an additional cavity for the intracavity feedback (*1*), distributed feedback gratings (*2*), an enlarged free spectral range through mode size reduction (*3*, *4*), or spatially varied optical pumping (*5*). However, these approaches are applicable to specific configurations; what is desired is a general design concept with flexible control of cavity modes.

Recent explorations of parity-time (PT) symmetry offer an opportunity to advance laser science by strategically manipulating gain and loss in order to control light transport. PT symmetry was initially proposed in quantum mechanics as an alternative criterion for non-Hermitian Hamiltonians that possesses a real eigenspectrum (*6*). Because of the equivalence between the Schrödinger equation in quantum mechanics and the electromagnetic wave equation, optics has become an ideal platform for studying the fundamentals of PT symmetry (*7*–*16*), with non-Hermiticity denoted by optical gain and loss. An intriguing PT phase transition has been demonstrated (*11*, *12*), enabling unique optical phenomena such as unidirectional light transport (*13*–*15*) and novel devices including low-power optical diodes (*16*). The strategic modulation of gain and loss in the PT symmetry–breaking condition can fundamentally broaden optical science at both semiclassical and quantum levels (*17*–*23*).

Using the PT symmetry–breaking concept, we delicately manipulated the gain and loss of a microring resonator and observed single-mode laser oscillation of a whispering-gallery mode (WGM). We exploited the continuous rotational symmetry of the microring structure to facilitate unique thresholdless PT symmetry breaking. This thresholdless PT symmetry breaking was valid only for the desired WGM order and enabled two energy-degenerate modes—the non-oscillating loss mode and the oscillating gain mode—whereas all other WGM modes experienced balanced gain/loss modulation and thus remained below the lasing threshold, leading to single-mode lasing.

The PT-synthetic microring resonator was designed with 500-nm-thick InGaAsP multiple quantum wells (MQWs) on an InP substrate (Fig. 1A). InGaAsP MQWs have a high material gain coefficient (>1000 cm^{−1}) around 1500 nm (*24*). The gain/loss modulation, satisfying an exact PT symmetry operation, was periodically introduced using additional Cr-Ge structures on top of the InGaAsP MQW along the azimuthal direction (ϕ):
(1)where *n*′′ denotes the index modulation in only the imaginary part; *m* is the azimuthal order of the desired WGM in the microring; and *l* = 0, 1, 2, …, 2*m* – 1 divides the microring into 2*m* periods (i.e., 4*m* sections of gain and loss in total). The PT modulation is designed using bilayers on top of the gain material that introduces loss and exactly reverses the sign of the imaginary part of the local modal index while maintaining the same real part (in practice, the deposition of Cr/Ge also slightly modifies the real part on the order of 0.01%). The wave numbers of the eigenmodes in our PT microring resonator are β = β_{0} ± *i*κ*n*′′, where β_{0} is the intrinsic wave number of the WGM without gain or loss, and κ denotes the coupling between the clockwise and counterclockwise traveling waves through PT modulation in the microring resonator (*25*) (see supplementary text). Evolution of PT symmetry of the *m* = 53 WGM in the microring resonator as a function of imaginary part–index modulation can be seen from the corresponding complex eigenspectra (Fig. 1, B and C). Two WGMs are energy-degenerate at the same resonant eigenfrequency, but their modal wave numbers are complex conjugates of each other, corresponding to PT symmetry breaking with a simultaneous coexistence of lasing and absorption eigenmodes.

The microring resonator goes into the PT-broken phase with a bifurcation in the imaginary spectrum even if the strength of gain/loss modulation is infinitesimal. This thresholdless feature in our PT phase transition is attributable to the continuous rotational symmetry associated with the desired WGM order in the absence of a real-index modulation (see supplementary text and fig. S1). This feature is distinct from the previously studied coupled PT waveguide systems, including the recently developed coupled gain/loss WGM resonators (*16*, *23*). In those systems, there are no continuous symmetries, such that PT symmetry breaking requires a finite strength of the gain/loss modulation (*20*). Although our design is based on a linear model by assuming a steady lasing state with a certain gain coefficient of InGaAsP (*3*, *4*, *19*, *21*, *26*), it is worth noting that lasing itself is an intrinsic nonlinear process. However, this thresholdless PT symmetry breaking in our system is robust against optical nonlinearity and its induced PT phase transition (*10*). In the experiment, a slight deviation from the desired perfectly balanced gain/loss modulation is possible, but the thresholdless PT symmetry–breaking feature is still preserved (see supplementary text and fig. S2).

Figure 2, A and B, shows the modal intensity distribution of the lasing and absorption modes in the PT microring resonator with 15 nm of Cr and 40 nm of Ge on top (corresponding to the InGaAsP MQW material gain coefficient of 800 cm^{−1} for the presumed ideal balanced gain/loss modulation). In the lasing mode, electric fields are confined mainly in the amplification sections, exhibiting a net modal gain coefficient of 268 cm^{−1}, whereas the absorption mode is loss-dominant with electric fields mainly under the Cr/Ge sections, with a loss coefficient of –268 cm^{−1}. Their eigenfrequencies are energy-degenerate but their gain/loss coefficients are opposite one another, consistent with the features of PT symmetry breaking. For other WGMs, for instance *m* = 54, electric fields in both energy-degenerate WGMs are uniformly distributed in gain and loss regimes. As a result, gain and loss are averaged out, creating modal wave numbers without net gain or loss (simulations show both modes have a similarly small loss coefficient of about –8 cm^{−1}) (Fig. 2, C and D). In this case, WGMs fall into the PT symmetric phase for the nondesired azimuthal orders (see supplementary text). It is therefore clear that only the lasing mode at the desired order contains a positive effective gain coefficient above the lasing threshold, enabling single-mode lasing. All other WGMs are suppressed by the intentionally introduced loss from the PT modulation. This unique single-mode operation is valid even with an arbitrarily wide gain spectrum because of its stringent mode selectivity, which is inherently different from the conventional single-mode microring lasers that use real-index coupling and modulation to achieve the mode splitting in eigenfrequencies and are limited by the bandwidth of the gain media (*27*, *28*).

The PT microring laser with Cr/Ge modulations (Fig. 3A) was fabricated using overlay electron beam lithography and plasma etching. Under optical pumping with a femtosecond laser (see supplementary text and fig. S3), a broad photoluminescence emission around 1500 nm was first observed at low pump power densities. As the pump power was increased, the transition to amplified spontaneous emission and full laser oscillation was clearly observed from the rapidly increasing spectral purity of the cavity mode (Fig. 3B). At higher pumping intensities well above the lasing threshold, the single-mode lasing peak is seen at the wavelength of 1513 nm, confirming our theoretical prediction of the single WGM lasing operation of the PT microring laser. The lasing linewidth is about 1.7 nm around the transparency pump power, corresponding to a quality factor of about 890 that is limited by the surface roughness of the sample. In Fig. 3C, the light-light curve corresponding to single-mode emission clearly shows a slope change corresponding to a lasing threshold at peak pump power density of about 600 MW cm^{−2}. The lasing mode (*m* = 53) in the PT-broken phase emerges above the lasing threshold, creating pronounced single-mode lasing with an extinction ratio of more than 14 dB, whereas other WGMs are all below the lasing threshold and are strongly suppressed.

For comparison, a control sample of a WGM laser was fabricated consisting of the same-sized InGaAsP/InP microring resonator without additional Cr/Ge index modulation. As expected, we observed a typical multimode lasing spectrum with different WGM azimuthal orders distributed over the gain spectral region (Fig. 4A). Relative to the PT microring laser, it can be seen that under a similar pumping condition, the resonance peak for the same azimuthal order of *m* = 53 well matches the single-mode lasing of the PT ring resonator at a wavelength of 1513 nm (Fig. 4B). The power efficiency and the lasing threshold are also similar because the introduced loss in the PT microring laser minimally affects the desired lasing mode. We also fabricated an additional PT microring laser with a different azimuthal PT modulation for the order of *m* = 55. Its lasing emission at 1467 nm (Fig. 4B) also agrees well with the multimode lasing spectrum of the conventional WGM laser for the same azimuthal order (Fig. 4A). It is evident that instead of altering the WGM in the microring resonator, the introduced PT gain/loss modulation selects the lasing WGM in the PT-broken phase over a broad spectral band. By changing the desired azimuthal order of the structured PT modulation, the single-mode lasing frequency can be efficiently selected. Although we demonstrated lasing for only two WGM orders, this mode selection concept is general and in principle valid for arbitrary gain spectra. In applications, the demonstrated stable single-mode lasing can be efficiently routed, using a bus waveguide through the evanescent ring-waveguide coupling, to photonic integrated circuits for on-chip signal amplification and processing.

We have demonstrated a PT microring laser by delicate exploitation of optical loss and gain. Such a microring laser is intrinsically single-mode regardless of the gain spectral bandwidth. This is because the continuous rotational symmetry of PT modulation enables the thresholdless PT symmetry breaking only for the desired mode. More important, our PT laser demonstration is a major step toward unique photonic devices such as a PT-symmetric laser-absorber that coincides lasing and anti-lasing [i.e., coherent perfect absorption (*29*, *30*)] simultaneously.