Nonlinear modal interactions in parity-time (PT) symmetric lasers

Parity-time symmetric lasers have attracted considerable attention lately due to their promising applications and intriguing properties, such as free spectral range doubling and single-mode lasing. In this work we discuss nonlinear modal interactions in these laser systems under steady state conditions, and we demonstrate that several gain clamping scenarios can occur for lasing operation in the -symmetric and -broken phases. In particular, we show that, depending on the system’s design and the external pump profile, its operation in the nonlinear regime falls into two different categories: in one the system is frozen in the phase space as the applied gain increases, while in the other the system is pulled towards its exceptional point. These features are first illustrated by a coupled mode formalism and later verified by employing the Steady-state Ab-initio Laser Theory (SALT). Our findings shine light on the robustness of single-mode operation against saturation nonlinearity in -symmetric lasers.

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

[2]  Hakan E. Tureci,et al.  Self-consistent multimode lasing theory for complex or random lasing media (17 pages) , 2006 .

[3]  R. El-Ganainy,et al.  Optical solitons in PT periodic potentials , 2008, 2008 Conference on Lasers and Electro-Optics and 2008 Conference on Quantum Electronics and Laser Science.

[4]  Y. Wang,et al.  Single-mode laser by parity-time symmetry breaking , 2014, Science.

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

[6]  Alexander Cerjan,et al.  Steady-state ab initio laser theory for complex gain media. , 2014, Optics express.

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

[8]  H J Korsch,et al.  Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer. , 2008, Physical review letters.

[9]  University of Central Florida,et al.  Unidirectional nonlinear PT-symmetric optical structures , 2010, 1005.5189.

[10]  Li Ge,et al.  Unconventional modes in lasers with spatially varying gain and loss , 2011, 1106.3051.

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

[12]  Li Ge,et al.  Quantitative verification of ab initio self-consistent laser theory. , 2008, Optics express.

[13]  U. Peschel,et al.  Parity–time synthetic photonic lattices , 2012, Nature.

[14]  A. Mostafazadeh.  Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies. , 2009, Physical review letters.

[15]  M. Berry.  Physics of Nonhermitian Degeneracies , 2004 .

[16]  Patrick Dorey,et al.  The ODE/IM Correspondence and PT -Symmetric Quantum Mechanics , 2002, hep-th/0201108.

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

[18]  B. M. Fulk.  MATH , 1992 .

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

[20]  W. Heiss,et al.  Exceptional points of non-Hermitian operators , 2003, quant-ph/0304152.

[21]  Li Ge,et al.  Parity-Time Symmetry Breaking beyond One Dimension: the Role of Degeneracy , 2014 .

[22]  Li Ge,et al.  Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures , 2011, 1112.5167.

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

[24]  Li Ge,et al.  Parity-Time Symmetry in a Flat Band System , 2015, 1507.08986.

[25]  Stefan Rotter,et al.  Strong Interactions in Multimode Random Lasers , 2008, Science.

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

[27]  Songky Moon,et al.  Observation of an exceptional point in a chaotic optical microcavity. , 2009, Physical review letters.

[28]  Li Ge,et al.  Exceptional points and lasing self-termination in photonic molecules , 2014, 1404.1242.

[29]  R. Morandotti,et al.  Observation of PT-symmetry breaking in complex optical potentials. , 2009, Physical review letters.

[30]  Ian J. Spalding,et al.  Laser physics , 1977, Nature.

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

[32]  Jan Wiersig,et al.  Asymmetric scattering and nonorthogonal mode patterns in optical microspirals , 2008, 0810.1584.

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

[34]  Mordechai Segev,et al.  Nonlinearly induced PT transition in photonic systems. , 2013, Physical review letters.

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

[36]  Acknowledgements , 1992, Experimental Gerontology.

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

[38]  Dorje C Brody,et al.  Complex extension of quantum mechanics. , 2002, Physical review letters.

[39]  Ingrid Rotter,et al.  Dynamics of quantum systems embedded in a continuum , 2003 .

[40]  H. Harney,et al.  Experimental observation of the topological structure of exceptional points. , 2001, Physical review letters.

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

[42]  Hui Cao,et al.  Unidirectional invisibility induced by PT-symmetric periodic structures. , 2011, Physical review letters.

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

[44]  Yeshaiahu Fainman,et al.  Nonreciprocal Light Propagation in a Silicon Photonic Circuit , 2011, Science.

[45]  Demetrios N. Christodoulides,et al.  Nonlinear reversal of the PT -symmetric phase transition in a system of coupled semiconductor microring resonators , 2015, 1510.03936.

[46]  Li Ge,et al.  Steady-state ab initio laser theory : generalizations and analytic results , 2010, 1008.0628.