Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators

Abstract

Compound-photonic structures with gain and loss 1 provide a powerful platform for testing various theoretical proposals on non-Hermitian parity-time-symmetric quantum mechanics 2-5 and initiate new possibilities for shaping optical beams and pulses beyond conservative structures. Such structures can be designed as optical analogues of complex parity-timesymmetric potentials with real spectra. However, the beam dynamics can exhibit unique features distinct from conservative systems due to non-trivial wave interference and phase-transition effects. Here, we experimentally realize paritytime-symmetric optics on a chip at the 1,550 nm wavelength in two directly coupled high-Q silica-microtoroid resonators with balanced effective gain and loss. With this composite system, we further implement switchable optical isolation with a non-reciprocal isolation ratio from 28 dB to 18 dB, by breaking time-reversal symmetry with gain-saturated nonlinearity in a large parameter-tunable space. Of importance, our scheme opens a door towards synthesizing novel microscale photonic structures for potential applications in optical isolators, on-chip light control and optical communications.One of the most fundamental postulates in canonical quantum mechanics, formulated by Dirac and von Neumann, mandates that the Hermiticity of each operator be directly associated with a physical observable. As such, the spectrum of a self-adjoint operator is ensured to be real and the total probability (or unitary evolution) is conserved. In 1998, however, Bender and colleagues 2 discovered a wide class of complex non-Hermitian Hamiltonians that can possess entirely real spectra below a certain phase-transition point, provided they satisfy combined parity-time (PT) symmetry. This counterintuitive discovery immediately aroused extensive theoretical interest in extending canonical quantum theory by including non-Hermitian but PT-symmetric operators 2-5 . For instance, a PT-symmetric Hamiltonian operator may contain a complex potential V(x) subject to a spatial-symmetry constraint V(x) ¼ V*(2x). One of the most striking properties of a PT-symmetric operator stems from the appearance of a sharp, symmetrybreaking transition once a non-Hermitian operator crosses a certain critical threshold 2-5 . On crossing that 'exceptional point', the spectrum ceases to be real and starts to become complex. This transition signifies the appearance of a spontaneous PT symmetry breaking from the exact-to the broken-PT phase. Despite much fundamental theoretical success in the development of PT-symmetric quantum mechanics, an experimental observation of pseudo-Hermiticity remains elusive and very challenging in real physical settings. Thanks to the formal equivalence between the quantum-mechanical Schrödinger equation and the paraxial optical diffraction equation, complex PT-symmetric potentials can be easily achieved in optics by spatially modulating the refractive index with properly placed gain and loss in a balanced manner 1 . This analogy immediately spurred theoretica...

Metawaveguide for Asymmetric Interferometric Light-Light Switching

“…Attractive physical phenomena including phase transitions and exceptional points are emulated with photonics, consequently, leading to novel effective manipulation of cavity lasing modes [21][22][23][24][25][26] and unidirectional light transport [27][28][29][30][31][32]. Here, we will show a unique metawaveguide of potential for on-demand control of interferometric light-light switching can be realized through non-Hermitian metamaterial explorations.…”

Unidirectional reflectionless light propagation at exceptional points

“…The constructed PT-symmetric optical structures with balanced gain and loss can lead to a range of extraordinary phenomena, including novel beam refraction [14,15], power oscillation [16,17], loss-induced transparency [18], nonreciprocal nonlinear light transmission [17,19,20], perfect absorption [21][22][23], teleportation [24], optical switching [25], optical tunneling [26], mode conversion [27], super scattering [28], and various other novel nonlinear effects [29][30][31]. In addition, there has been significant progress in using PT-symmetric periodic optical structures to attain unidirectional light reflectionlessness [12,13].…”

Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system

“…Extra imaginary potentials induce many unusual features even in certain simple or trivial systems, which include quantum phase transition occurred in a finite system [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], unidirectional propagation and anomalous transport [4,[21][22][23][24][25][26][27][28], invisible defects [29][30][31], coherent absorption [32] and self sustained emission [33][34][35][36][37], lossinduced revival of lasing [38], as well as laser-mode selection [39,40]. Most of these phenomena are related to the critical behaviours near exceptional or spectral singularity points.…”