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 , 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 . 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.
 W. D. Heiss, J. of Phys. A: Mathematical and Theoretical 45, 444016 (2012).
 N. Moiseyev, Non-Hermitian Quantum Mechanics. (Cambridge University Press, 2011).
 K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 103904 (2008).
 C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
 A. Guo et al., Phys. Rev. Lett. 103, 093902 (2009).
 B. Peng et al., Nat. Phys. 10, 394 (2015).
 A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
 M. Miri, P. Likamwa, D. N. Christodoulides, Opt. Lett. 37, 764 (2012)
 H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Science 346, 975 (2014).
 L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, X. Zhang, Science 346, 972 (2014).
 H. Hodaei et al., Laser & Photon. Rev. 10, 494 (2016).
 J. Wiersig, Phys. Rev. Lett. 112, 203901 (2014).
 G. Demange, and E.-M. Graefe, J. Phys. Math. Theor. 45, 25303 (2012).
 M.H. Teimourpour, R. El-Ganainy, A. Eisfeld, A .Szameit, D.N. Christodoulides, Phys. Rev. A 90, 053817 (2014).
In recent years, the concept of parity-time (PT) symmetry has received considerable attention in the field of optics and photonics. In PT-symmetric arrangements, the interaction between gain/loss-contrast and coupling leads to the formation of exceptional points in parameter space. At these junctures, not only the eigenvalues but also the eigenvectors tend to merge, resulting in a sudden reduction of the dimensionality of the eigen-space. Consequently, in the vicinity of such points, the eigenfrequencies are strongly affected by external perturbationsas the system regains its original dimensionality. This unique behavior can be utilized to fundamentally enhance the sensitivity of micro-resonators. Here, we experimentally investigate this effect in integrated semiconductor PT-symmetric microring lasers that are biased at exceptional points. Using this arrangement, we demonstrate >10- fold enhancement in sensitivity. Our results also show that unlike standard microcavities, the parity-time symmetric system responds to the square-root of the perturbation. Our work provides a new avenue for enhancing the sensitivity of optical integrated sensors.
We study both theoretically and experimentally the cross-correlation function of single-ringed Laguerre-Gaussian (LG) beams, which allows us to determinate the topological charge of the beam by performing power measure-ments only. We employ a superposition of two exact copies of the original LG beam whose centroids are displaced from each other. The behaviour of the auto-correlation is studied as a function of the displacement between these two copies of the beam for different topological charges. Our results indicate that the auto-correlation is described by a polynomial function of the displacement parameter, and the number of zeros of this polynomial maintains a one to one correspondence with the topological charge. A detailed description of the experiment to perform these measurements is also provided, our experimental findings are in excellent agreement with the theory. This technique offers an alternative for measuring the content of orbital angular momentum in a beam without the need of a camera.
The study of open quantum billiards has gained popularity in the last decades, including different common and
uncommon geometries such as the circular and stadium billiards. We study the electromagnetic scattering of a
linearly polarized electric field in the elliptic quantum billiard with hyperbolic channels. We analyze the effect
of different parameters on the scattering in a billiard configuration obtained by displacing both channels by the
same angle. We observed that for the configuration proposed in this work the polarization of the electric field is
An analysis of the diffraction of plane waves by an apodized finite-radius circular spiral phase plate (SPP)
with integer and fractional topological charge and with variable transmission coefficients inside and outside of
the plate edge is presented. We introduce a sinusoidal apodization function at the edge of the plate to allow
for a continuous transition between the transmission coefficients, and between the spiral and uniform phase
distributions inside and outside of the plate edge. The interference between the light crossing the SPP and the
light which undergoes no phase alteration at the aperture plane, and the presence of an apodization at the edge
of the plate, cause some interesting phenomena previously unobserved in this widely known problem.