We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.

We present measurements of transmission and reflection spectra of a microwave photonic crystal composed of 874 metallic cylinders arranged in a triangular lattice. The spectra show clear evidence of a Dirac point, a characteristic of a spectrum of relativistic massless fermions. In fact, Dirac points are a peculiar property of the electronic band structure of graphene, whose properties consequently can be described by the relativistic Dirac equation. In the vicinity of the Dirac point, the measured reflection spectra resemble those obtained by conductance measurements in scanning tunneling microscopy of graphene flakes. PACS numbers: 42.70.Qs, 73.22.Pr, 42.25.Fx Graphene is a monolayer of carbon atoms arranged in a honeycomb lattice [1,2]. Due to its peculiar electronic properties this carbon allotrope recently attracted a lot of attention in condensed matter physics. The conduction and the valence band of the electronic energy in graphene form conically shaped valleys that touch each other at the corners of the Brillouin zone [3]. As a consequence, close to these touch points the energy of the electron depends linearly on its quasi-momentum vector. This linear dispersion relation implies an energy independent velocity, and the related wave equation is the Dirac equation [4]. Thus, although the Fermi velocity is typically 300 times smaller than that of light, the energy spectrum of the electrons in graphene is similar to that of massless relativistic fermions [4][5][6][7]. However, graphene with its Dirac spectrum is not an exception. Photonic crystals, an optical analogue of ordinary crystals, possess similar particular properties [8,9]. The unusual transmission properties near a Dirac point predicted in [9] were observed experimentally both in sonic and in microwave photonic crystals [10,11].The photonic crystal considered in the present work is two-dimensional and composed of rows of metallic cylinders which are arranged to form the triangular lattice schematically shown in the left part of Fig. 1. Electromagnetic waves propagating in such a periodic structure exhibit a dispersion relation with a band structure similar to the electronic band structure in a solid. That for the triangular lattice of metallic cylinders with radius R = 0.25a, where a is the lattice constant, is shown on the right part of Fig. 1. It was obtained by solving numerically the Helmholtz equation with the finite difference method [12]. In this so-called band diagram the frequency f is plotted as function of the quasi momentum components (k x , k y ) for the first two propagating modes. Around the corners of the first Brillouin zone the bands have the shape of cones and the band structure resembles that of the electronic energy in graphene [2,5]. In fact FIG. 1: (Color online) Left: Triangular lattice of metallic cylinders. The arrows indicate the two different directions ΓM and ΓK in the triangular lattice; the radius R of the metallic cylinders equals R = 0.25a, where a is the lattice constant. Right: The plot of the numerically dete...

The invention of lasers 60 years ago is one of the greatest breakthroughs in modern optics. Throughout the years, lasers have enabled major scientific and technological advancements, and have been exploited in numerous applications due to their advantages such as high brightness and high coherence. However, the high spatial coherence of laser illumination is not always desirable, as it can cause adverse artifacts such as speckle noise in imaging applications. To reduce the spatial coherence of a laser, novel cavity geometries and alternative feedback mechanisms have been developed. By tailoring the spatial and spectral properties of cavity resonances, the number of lasing modes, the emission profiles and the coherence properties can be controlled. This technical review presents an overview of such unconventional, complex lasers, with a focus on their spatial coherence properties. Laser coherence control not only provides an efficient means for eliminating coherent artifacts, but also enables new applications.

Random numbers are widely used for information security, cryptography, stochastic modeling, and quantum simulations. Key technical challenges for physical random number generation are speed and scalability. We demonstrate a method for ultrafast generation of hundreds of random bit streams in parallel with a single laser diode. Spatiotemporal interference of many lasing modes in a specially designed cavity is introduced as a scheme for greatly accelerated random bit generation. Spontaneous emission, caused by quantum fluctuations, produces stochastic noise that makes the bit streams unpredictable. We achieve a total bit rate of 250 terabits per second with off-line postprocessing, which is more than two orders of magnitude higher than the current postprocessing record. Our approach is robust, compact, and energy-efficient, with potential applications in secure communication and high-performance computation.