Vishwa Pal

Measurement of the coupling constant in a two-frequency VECSEL

We measure the coupling constant between the two perpendicularly polarized eigenstates of a two-frequency Vertical External Cavity Surface Emitting Laser (VECSEL). This measurement is performed for different values of the transverse spatial separation between the two perpendicularly polarized modes. The consequences of these measurements on the two-frequency operation of such class-A semiconductor lasers are discussed.

Intensity noise correlations in a two-frequency VECSEL.

We present an experimental and theoretical study of the intensity noise correlation between the two orthogonally polarized modes in a dual frequency Vertical External Cavity Surface Emitting Laser (VECSEL). The dependence of the noise correlation spectra on the non-linear coupling between the two orthogonally polarized modes is put into evidence. Our results show that for small coupling the noise correlation amplitude and phase spectra remain nearly flat (around -6 dB and 0° respectively) within the frequency range of our interest (from 100 kHz to 100 MHz). But for higher values of the coupling constant the low frequency behaviors (below 1-2 MHz) of the correlation amplitude and phase spectra are drastically changed, whereas above this cut-off frequency (1-2 MHz) the correlation spectra are almost independent of coupling strength. The theoretical model is based on the assumptions that the only source of noise in the frequency range of our interest for the two modes are pump noises, which are white noises of equal amplitude but partially correlated.

Manipulating the spatial coherence of a laser source.

An efficient method for controlling the spatial coherence has previously been demonstrated in a modified degenerate cavity laser. There, the degree of spatial coherence was controlled by changing the size of a circular aperture mask placed inside the cavity. In this paper, we extend the method and perform general manipulation of the spatial coherence properties of the laser, by resorting to more sophisticated intra-cavity masks. As predicted from the Van Cittert Zernike theorem, the spatial coherence is shown to depend on the geometry of the masks. This is demonstrated with different mask geometries: a variable slit which enables independent control of spatial coherence properties in one coordinate axis without affecting those in the other; a double aperture, an annular ring and a circular aperture array which generate spatial coherence functional forms of cosine, Bessel and comb, respectively.

Conversion of out-of-phase to in-phase order in coupled laser arrays with second harmonics

A novel method for converting an array of out-of-phase lasers into one of in-phase lasers that can be tightly focused is presented. The method exploits second harmonic generation and can be adapted for different laser arrays geometries. Experimental and calculated results, presented for negatively coupled lasers formed in a square, honeycomb, and triangular geometries are in good agreement.

Optical phase dynamics in mutually coupled diode laser systems exhibiting power synchronization

We probe the physical mechanism behind the known phenomenon of power synchronization of two diode lasers that are mutually coupled via their delayed optical fields. In a diode laser, the amplitude and the phase of the optical field are coupled by the so-called linewidth enhancement factor, α. In this work, we explore the role of optical phases of the electric fields in amplitude (and hence power) synchronization through α in such mutually delay-coupled diode laser systems. Our numerical results show that the synchronization of optical phases drives the powers of lasers to synchronized death regimes. We also find that as α varies for different diode lasers, the system goes through a sequence of in-phase amplitude-death states. Within the windows between successive amplitude-death regions, the cross-correlation between the field amplitudes exhibits a universal power-law behaviour with respect to α.

Observing Dissipative Topological Defects with Coupled Lasers

Topological defects have been observed and studied in a wide range of systems, such as cosmology, spin systems, cold atoms, and optics, as they are quenched across a phase transition into an ordered state. These defects limit the coherence of the system and its ability to approach a fully ordered state, so revealing their origin and control is becoming an increasingly important field of research. We observe dissipative topological defects in a one-dimensional ring of phased-locked lasers, and show how their formation is related to the Kibble-Zurek mechanism and is governed in a universal manner by two competing time scales. The ratio between these two time scales depends on the system parameters, and thus offers the possibility of enabling the system to dissipate to a fully ordered, defect-free state that can be exploited for solving hard computational problems in various fields.Topologically protected defects have been observed and studied in a wide range of fields, such as cosmology, spin systems, cold atoms and optics as they are quenched across a phase transition into an ordered state. Revealing their origin and control is becoming increasingly important field of research, as they limit the coherence of the system and its ability to approach a fully ordered state. Here, we present dissipative topological defects in a 1-D ring network of phaselocked lasers, and show how their formation is related to the Kibble-Zurek mechanism and is governed in a universal manner by two competing time scales of the lasers, namely the phase locking time and synchronization time of their amplitude fluctuations. The ratio between these two time scales depends on the system parameters such as gain and coupling strength, and thus offers the possibility to control the probability of topological defects in the system. Enabling the system to dissipate to the fully ordered, defect-free state can be exploited for solving hard combinatorial optimization problems in various fields. As opposed to unitary systems where quenching is obtained via external cooling mostly through the edges, our dissipative system is kept strictly uniform even for fast quenches. INTRODUCTION Topological defects have been extensively studied in cosmology, spin systems and optics [1]. Their origin and scaling behavior was first explained by Kibble-Zurek (KZ) mechanism [2, 3], which was experimentally studied in various systems, such as atomic gases [4-9], nonlinear optics [10], and condensed matter systems [11-13]. Due to complexity and experimental limitations, these systems do not fulfil the exact KZ mechanism, and only deal with limited aspects [5, 11, 14, 15]. The formation of defects in the Zurek’s approach relies on the notion of competing time scales in the system, and the density of defects follows a power-law behavior with respect to the rate at which the phase transition is crossed [13]. The topologically protected defects may prevent the system from reaching a globally stable state with spontaneous symmetry breaking and long range ordering [8]. In most of these works the phase transition into an ordered state was crossed by cooling the system from the outside, whereby the external cooling rate determined the density of defects. For the most interesting regime of fast cooling, it is hard to maintain uniformity over the entire system [4]. Here we present and characterize a new mechanism to form topological defects without external cooling in a dissipative system of coupled laser network [16-18]. In coupled lasers and polaritons networks, losses depend on the relative phase between all oscillators [18-21]. This provides dissipative coupling [20] that can drive the system to a stable steady state phased-locked solution with minimal loss that can be directly mapped to the ground state of the classical XY spin Hamiltonian [18, 19, 21]. However, when the dissipative dynamics is highly over-damped [22] and occurs on a complex landscape, the system fails to reach the globally stable solution and gets stuck in local minima. For a 1-D system on a closed ring, such local minima are topological defects [8], characterized by a non-zero phase circulated over the ring that must be an integer multiple of 2π (winding number or topological charge) [23]. The degeneracy of the co-existing degenerate

Phase locking of even and odd number of lasers on a ring geometry: effects of topological-charge

The effects of topological charge on phase locking an array of coupled lasers are presented. This is done with even and odd number of lasers arranged on a ring geometry. With an even number of lasers the topological-charge effect is negligible, whereas with an odd number of lasers the topological-charge effect is clearly detected. Experimental and calculated results show how the topological charge effects degrade the quality of the phase locking, and how they can be removed. Our results shed further light on the frustration and also the quality of phase locking of coupled laser arrays.

Observation of noise phase locking in a single-frequency VECSEL.

We present an experimental observation of phase locking effects in the intensity noise spectrum of a semiconductor laser. These noise correlations are created in the medium by coherent carrier-population oscillations induced by the beatnote between the lasing and non-lasing modes of the laser. This phase locking leads to a modification of the intensity noise profile at around the cavity free-spectral-range value. The noise correlations are evidenced by varying the relative phase shift between the laser mode and the non-lasing adjacent side modes.

Rapid and efficient formation of propagation invariant shaped laser beams

A rapid and efficient all-optical method for forming propagation invariant shaped beams by exploiting the optical feedback of a laser cavity is presented. The method is based on the modified degenerate cavity laser (MDCL), which is a highly incoherent cavity laser. The MDCL has a very large number of degrees of freedom (320,000 modes in our system) that can be coupled and controlled, and allows direct access to both the real space and Fourier space of the laser beam. By inserting amplitude masks into the cavity, constraints can be imposed on the laser in order to obtain minimal loss solutions that would optimally lead to a superposition of Bessel-Gauss beams forming a desired shaped beam. The resulting beam maintains its transverse intensity distribution for relatively long propagation distances.

Teaching an old laser new tricks: Solving the inverse scattering problem rapidly

Inverse scattering problems, namely reconstructing the structures of objects from their scattered intensity distributions occur in many fields of science and technology[1], such as tomographic imaging, seismology, single shot X-ray scattering[2] and imaging. Solving the inverse scattering problem where all the phase information is lost, is generally very difficult. The difficulty is alleviated by resorting to some a priori knowledge such as the boundaries within which the object lies (compact support), sparsity or other spatial features. Then it is possible to reconstruct the object using iterative algorithms, such as the well-known Gerchberg-Saxton algorithm. Unfortunately, the algorithms are time consuming and do not always converge to the right solution even with advanced computational resources.