Demetrios N. Christodoulides

Incoherent Solitons: Self-Trapping of Weakly Correlated Wavepackets

Incoherent Solitons are self-trapped wave-packets upon which the phase distribution is random. In this chapter we describe this new area of science, from the first observation of solitons made of light from an incandescent light bulb, to the recent discoveries of pattern formation and modulation instabilities in weakly-correlated nonlinear wave systems.

Discrete solitons in nonlinear zigzag optical waveguide arrays with tailored diffraction properties

We show that the discrete diffraction properties of a nonlinear optical zigzag waveguide array can be significantly modified, by exploiting the topological arrangement of the lattice itself. This introduces extended interactions (beyond nearest-neighbors), which, in turn, affect the lattice dispersion relation within the Brillouin zone. As a result, we demonstrate that new families of discrete soliton solutions are possible which are stable over a wide range of parameters. Our method opens new opportunities for diffraction management that can be employed to generate low power spatial discrete optical solitons.

Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope (Conference Presentation)

A new scheme for ultrasensitive laser gyroscopes that utilizes the physics of exceptional points will be presented. By exploiting the properties of such non-Hermitian degeneracies, we show that the rotation-induced frequency splitting becomes proportional to the square root of the gyration speed (√𝛀)- thus enhancing the sensitivity to low angular rotations by orders of magnitudes. In addition, at its maximum sensitivity limit, the measurable spectral splitting is independent of the radius of the rings involved. Our work paves the way towards a new class of ultrasensitive miniature ring laser gyroscopes on chip.

Higher-order exceptional points in photonic systems (Conference Presentation)

Student contribution: In recent years, non-Hermitian degeneracies, also known as exceptional points (EPs), have emerged as a new paradigm for engineering the response of optical systems. This class of degeneracies represents points in parameter space where the eigenvalues and their corresponding eigenvectors simultaneously coalesce [1,2]. Among the large set of non-conservative photonic systems, parity-time (PT) symmetric arrangements are of particular interest since they provide an excellent platform to study the physics and properties of non-Hermitian degeneracies [3,4]. So far, the abrupt nature of the phase transitions at EPs has led to a number of new functionalities such as loss-induced transparency [5], unidirectional invisibility [6,7], and single mode lasing [8-11]. In addition, it has been suggested that the bifurcation properties associated with second-order exceptional points can be utilized to achieve enhanced sensitivity in micro-resonator arrangements [11]. Of interest is to use even higher-order exceptional points that in principle could further amplify the effect of perturbations. While such higher-order singularities have been theoretically studied in a number of recent works [13,14], their experimental realization in the optical domain has so far remained out of reach. In this paper, for the first time, we show the emergence of third order exceptional points in ternary parity-time-symmetric coupled resonator lasers by judiciously designing the gain/loss distribution and coupling strengths following a recursive bosonic quantization procedure. Subsequently, the nature of the third order exceptional point is confirmed through the cubic root response of this ternary system to external perturbations. Our work may pave the way towards the utilization of higher order exceptional points in designing ultrasensitive photonic arrangements. References [1] W. D. Heiss, J. of Phys. A: Mathematical and Theoretical 45, 444016 (2012). [2] N. Moiseyev, Non-Hermitian Quantum Mechanics. (Cambridge University Press, 2011). [3] K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 103904 (2008). [4] C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010). [5] A. Guo et al., Phys. Rev. Lett. 103, 093902 (2009). [6] B. Peng et al., Nat. Phys. 10, 394 (2015). [7] A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012). [7] M. Miri, P. Likamwa, D. N. Christodoulides, Opt. Lett. 37, 764 (2012) [8] H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Science 346, 975 (2014). [9] L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, X. Zhang, Science 346, 972 (2014). [11] H. Hodaei et al., Laser & Photon. Rev. 10, 494 (2016). [12] J. Wiersig, Phys. Rev. Lett. 112, 203901 (2014). [13] G. Demange, and E.-M. Graefe, J. Phys. Math. Theor. 45, 25303 (2012). [14] M.H. Teimourpour, R. El-Ganainy, A. Eisfeld, A .Szameit, D.N. Christodoulides, Phys. Rev. A 90, 053817 (2014).

Soliton Transitions in Waveguide Arrays

It is theoretically demonstrated that interband and Rabi soliton transitions are possible in waveguide arrays. Such transitions can take place in optical lattices when the cell is periodically modulated along the propagation direction.

Spatio-Temporal Reallocation and Evolution Patterns of Interacting Beams in Nonlinear Bi-Dispersive Media

Beam interactions in nonlinear bi-dispersive media are studied and the spatio-temporal reallocation of beams is investigated, in order to transform an initial space separation of beams to a certain time separation.

Pulse Compression Using Nonlinear Waveguide Arrays

We demonstrate that high fidelity compression is possible when normally dispersive waveguide arrays are used together with gratings or other programmable phase filters. The performance of this scheme is assessed in AlGaAs array systems.

Discrete solitons/soliton-trains in two-dimensional photonic lattices induced with partially-coherent light

We demonstrate the formation of 2D discrete solitons/soliton-trains in a photonic-lattice induced with partially-coherent light, along with a clear transition from discrete-diffraction to discrete-soliton in the periodic lattice.

Clustering in weakly correlated wavef ronts

We observe the spontaneous clustering of solitons in partially coherent wavefronts during the final stages of pattern formation initiated by modulation instability and noise. Experiments are conducted in biased photorefractives and corroborated by numerical simulations.