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A Hamiltonian H satisfies parity-time (PT) symmetry if it commutes with combination of parity operator P and time-reversal operator T, i.e., HPT=PTH. Currently, PT symmetric H is widely incarnated by symmetric refractive index profile n(x)=n(-x) and anti-symmetric gain and loss profile g(x)=-g(-x) in optical systems. Its eigenvalue can spontaneously transit from real to imaginary eigenvalues as |g(x)| increases, identified as PT symmetric or PT broken phase. This peculiarity has been utilized for inducing asymmetric mode coupling to achieve directional light transport [1], low-power optical diode [2], etc. However, all these structures can not be used for any nonreciprocal devices since their modes can always find pathways to scatter back to the input under symmetric scattering matrix [3]. Here, we introduce a magnetic-free dynamic modulation of gain and loss profile in an on-chip micro-ring resonator to break reciprocity. Applying a moving grating of alternating gain and loss along the azimuthal direction of the ring, the original degeneracy between clockwise whispering gallery mode (WGM) and the counter-clockwise one will be removed in the PT broken phase. With that, two laser emission of different frequencies can be simultaneously extracted by a bus waveguide to each end, respectively, where the frequency detuning is controlled by the modulation. Benefit from the PT symmetry of the system, the lasing threshold can be tailored by the strength of dynamic modulation. Our study pointed out a new viable way for on-chip integration of lasing sources which can generate and separate different emission frequencies simultaneously.
[1]. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by p t-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[2]. H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional nonlinear pt-symmetric optical structures,” Phys. Rev. A 82, 043803 (2010).
[3]. S. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popovic, M. Vanwolleghem, D. Jalas et al., “Comment on ”nonreciprocal light propagation in a silicon photonic circuit”,” science 335, 38–38 (2012).
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