Observation of parity-time symmetry in microwave photonics

Symmetry plays a crucial role in explorations of the laws of nature. Parity-time (PT) symmetry phenomena can lead to entirely real spectra in non-Hermitian systems, which attracts considerable attention in the fields of optics and electronics because these phenomena provide a new tool for the manipulation of oscillation modes and non-reciprocal signal transmission. A potential new field of application is microwave photonics, an interdisciplinary field in which the interaction between microwaves and optical signals is exploited. In this article, we report the experimental use of PT symmetry in an optoelectronic oscillator (OEO), a key microwave photonics system that can generate single-frequency sinusoidal signals with high spectral purity. PT symmetry is theoretically analyzed and experimentally observed in an OEO with two mutually coupled active oscillation cavities via a precise manipulation of the interplay between gain and loss in the two oscillation cavities. Stable single-frequency microwave oscillation is achieved without using any optical/electrical filters for oscillation mode selection, which is an indispensable requirement in traditional OEOs. This observation opens new avenues for signal generation and processing based on the PT symmetry principle in microwave photonics.Microwave photonics: exploiting PT symmetryParity-time (PT) symmetry, a fundamental concept that has been widely explored in quantum mechanics and optics, has now been observed and put to good use in microwave photonics. Yanzhong Liu and coworkers from Beijing and Valencia built and theoretically simulated a dual-loop optoelectronic oscillator (OEO)—a device used to convert laser energy into a radiowave or microwave signal. By adjusting the level of gain and loss in the two loops it was possible to switch the system between different phases of PT symmetry and generate a pure single-mode output at 4.0703 GHz without the need for a RF filter. Furthermore, the output was found to have very low phase noise and strong side-mode suppression. The result suggests that PT symmetry may find rich applications in microwave photonics.

[1]  Tunable parity-time-symmetric microring lasers , 2015, 2015 Conference on Lasers and Electro-Optics (CLEO).

[2]  Shanhui Fan,et al.  Parity–time-symmetric whispering-gallery microcavities , 2013, Nature Physics.

[3]  J. G. Muga,et al.  Physical realization of -symmetric potential scattering in a planar slab waveguide , 2005, 1706.04056.

[4]  B. M. Fulk.  MATH , 1992 .

[5]  Jianping Yao,et al.  An integrated parity-time symmetric wavelength-tunable single-mode microring laser , 2017, Nature Communications.

[6]  Shachar Klaiman,et al.  Visualization of branch points in PT-symmetric waveguides. , 2008, Physical review letters.

[7]  L. Maleki,et al.  Optoelectronic microwave oscillator , 1996 .

[8]  H. Haus.  Waves and fields in optoelectronics , 1983 .

[9]  M. Berry,et al.  Optical lattices with PT symmetry are not transparent , 2008 .

[10]  Li Ge,et al.  Nonlinear modal interactions in parity-time (PT) symmetric lasers , 2016, Scientific Reports.

[11]  L. Maleki,et al.  Multiloop optoelectronic oscillator , 2000, IEEE Journal of Quantum Electronics.

[12]  Li Ge,et al.  Non-Hermitian photonics based on parity–time symmetry , 2017 .

[13]  Shilong Pan,et al.  Full-duty triangular pulse generation based on a polarization-multiplexing dual-drive Mach-Zehnder modulator. , 2016, Optics express.

[14]  Li Ge,et al.  Pump-induced exceptional points in lasers. , 2011, Physical review letters.

[15]  Tao Wang,et al.  Raman lasing and Fano lineshapes in a packaged fiber-coupled whispering-gallery-mode microresonator , 2016 .

[16]  M. Segev,et al.  Observation of parity–time symmetry in optics , 2010 .

[17]  D. Christodoulides,et al.  Parity-time–symmetric microring lasers , 2014, Science.

[18]  Tsampikos Kottos,et al.  Experimental study of active LRC circuits with PT symmetries , 2011, 1109.2913.

[19]  Z. Musslimani,et al.  Theory of coupled optical PT-symmetric structures. , 2007, Optics letters.

[20]  R. El-Ganainy,et al.  Symmetry in optics and photonics: a group theory approach. , 2017, Science bulletin.

[21]  Z. Musslimani,et al.  Beam dynamics in PT symmetric optical lattices. , 2008, Physical review letters.

[22]  G. Strasser,et al.  Reversing the pump dependence of a laser at an exceptional point , 2014, Nature Communications.

[23]  Lan Yang,et al.  Dynamic Fano-like resonances in erbium-doped whispering-gallery-mode microresonators , 2014 .

[24]  Lan Yang,et al.  Ultrasensitive detection of mode splitting in active optical microcavities , 2010, 1007.0385.

[25]  Liang Hao,et al.  Observation of a fast evolution in a parity-time-symmetric system , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[26]  Lan Yang,et al.  On-chip Single Nanoparticle Detection and Sizing by Mode Splitting in an Ultra-high-Q Microresonator , 2009 .

[27]  H. Yamazaki,et al.  PDM-QPSK Modulator With a Hybrid Configuration of Silica PLCs and LiNbO$_{3}$ Phase Modulators , 2011, Journal of Lightwave Technology.

[28]  Ş. Özdemir,et al.  Gain competition induced mode evolution and resonance control in erbium-doped whispering-gallery microresonators. , 2016, Optics express.

[29]  Nikolay I. Zheludev,et al.  Controlling light-with-light without nonlinearity , 2012, Light: Science & Applications.

[30]  Stefano Longhi,et al.  PT-symmetric laser absorber , 2010, 1008.5298.

[31]  C. Bender,et al.  Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry , 1997, physics/9712001.

[32]  Lan Yang,et al.  On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh- Q microresonator , 2010 .

[33]  S. Longhi.  Quantum‐optical analogies using photonic structures , 2009 .

[34]  Dorje C Brody,et al.  Faster than Hermitian quantum mechanics. , 2007, Physical review letters.

[35]  Philipp Ambichl,et al.  Wave propagation through disordered media without backscattering and intensity variations , 2017, Light, science & applications.

[36]  Limin Tong,et al.  Single whispering-gallery mode lasing in polymer bottle microresonators via spatial pump engineering , 2017, Light: Science & Applications.

[37]  Z. Musslimani,et al.  Optical Solitons in PT Periodic Potentials , 2008 .

[38]  Nelson,et al.  Localization Transitions in Non-Hermitian Quantum Mechanics. , 1996, Physical review letters.

[39]  Matthias Heinrich,et al.  Single mode lasing in transversely multi-moded PT-symmetric microring resonators , 2016 .

[40]  S. Longhi.  Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip. , 2017, Science bulletin.

[41]  Yidong Chong,et al.  Time-Reversed Lasing and Interferometric Control of Absorption , 2011, Science.

[42]  Li Ge,et al.  PT-symmetry breaking and laser-absorber modes in optical scattering systems. , 2010, Physical review letters.

[43]  Jianping Yao,et al.  A Wideband Frequency Tunable Optoelectronic Oscillator Incorporating a Tunable Microwave Photonic Filter Based on Phase-Modulation to Intensity-Modulation Conversion Using a Phase-Shifted Fiber Bragg Grating , 2012, IEEE Transactions on Microwave Theory and Techniques.

[44]  Shiyue Hua,et al.  Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators , 2014, Nature Photonics.

[45]  Hui Cao,et al.  Coherent perfect absorbers: Time-reversed lasers , 2010, CLEO/QELS: 2010 Laser Science to Photonic Applications.