Parity-time-symmetric coupled microring lasers operating around an exceptional point

Abstract

The behavior of a parity-time (PT) symmetric coupled microring system is studied when operating in the vicinity of an exceptional point. Using the abrupt phase transition around this point, stable single-mode lasing is demonstrated in spectrally multi-moded micro-ring arrangements.The notion of PT-symmetry was first introduced within the context of mathematical physics [1]. It generally implies that even nonHermitian systems can support entirely real spectra, provided their corresponding Hamiltonians commute with the parity-time (PT) operator. In recent years, several studies have shown that PT symmetric structures can be readily realized in photonic arrangements by exploiting the mathematical isomorphism between the quantum-mechanical Schrödinger equation and the paraxial wave equation of optics [2][3][4][5][6][7]. In this regard, a necessary albeit not sufficient condition for optical PT symmetry to hold is that the refractive index distribution involved should respect the following relationship * (− ) = ( ). In other words, the real part of the complex refractive index profile associated with a photonic PT symmetric structure must be an even function of position, while its imaginary component representing gain or loss must have an odd distribution.By virtue of their non-Hermiticity, PT-symmetric arrangements are capable of supporting exceptional points in their parameter space. Exceptional points, also known as non-Hermitian degeneracies, typically occur in non-conservative physical systems. At these points, the eigenvectors as well as their associated eigenvalues coalesce, resulting in an abrupt phase transition that dramatically changes the behavior of the system [8]. In optical settings, such degeneracies can arise from the interplay of gain and loss in the underlying design. A multitude of recent theoretical and experimental studies has shown different ways of how the presence of exceptional or phase-transition points can be fruitfully utilized to attain new behavior and functionality in non-Hermitian photonic systems, including those respecting PT symmetry [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Thus far, this methodology has been explored in a number of laser studies where a lower threshold and an inverse pump dependence of the output power have been investigated [18][19][20][21][22][23][24]. Lately, the selective breaking of PT symmetry has also been considered for laser mode management applications [23,24]. In particular, in [24], a PT symmetric double ring configuration was proposed as a promising avenue to enforce single longitudinal mode operation in inherently multi-moded semiconductor micro-cavities. This type of system is comprised of two identical ring resonators, where one provides gain while its counterpart is subjected to an appropriate amount of loss.In this work, our goal is to experimentally characterize the behavior of a parity-time symmetric photonic molecule around the exceptional point. We start with developing a mathematical model for a coupled cavity arrangement sh...

Single mode lasing in transversely multi‐moded PT‐symmetric microring resonators

“…Despite having a non‐Hermitian representation, such a system may still support an entirely real spectrum. While originally developed in the context of quantum mechanics , such notions have lately attracted considerable attention in different areas of optics such as photonic lattices, microresonators, gratings, and lasers . In optical settings, a structure is PT symmetric if the real part of the refractive index is an even function of position, whereas the imaginary component (representing gain and loss) exhibits an odd profile.…”

“…The PT‐symmetry is achieved using a coupled microring system in which the pump power is selectively withheld from one of the cavities. In such settings, the net differential gain associated with the spectral envelope of the line shape function is systematically enhanced – a direct byproduct of the existence of a non‐Hermitian exceptional point . Exceptional points have been also shown to reverse the dependence of lasing threshold on pump power .…”

An integrated parity-time symmetric wavelength-tunable single-mode microring laser

“…The first approach is to use optical feedback in a cavity to achieve single-mode operation456; the second is to enhance mode confinement by reducing the mode size in a laser cavity to achieve single-mode operation789; the third is to shape the spatial profile of a pump light to a laser cavity to achieve mode selection10; and the fourth approach is to use parity-time (PT) symmetry111213141516 to implement mode selection. The last approach has been an active topic and has been heavily researched recently1718192021.…”

“…In the fourth approach, mode selection is achieved based on PT symmetry by manipulating the interplay between gain and loss in a laser cavity1718192021. In a coupled arrangement with two identical microring resonators one is experiencing gain, whereas the other is experiencing an equal-magnitude loss, to form a PT-symmetry situation.…”

“…Therefore, the desired mode can be controlled for single-mode operation in an inherently multi-mode microring laser18. The breaking of the PT-symmetry condition provides a simple and effective solution to achieve single-mode lasing by allowing the desired mode to have a higher gain, while suppressing other modes1718192021. In refs 18, 19, a single-mode lasing was demonstrated with an enhanced mode discrimination by using the exceptional points in a PT-symmetric coupled ring resonator structure20.…”