Laguerre-Gaussian Modes and the Wigner Transform

Recent developments in laser physics have called renewed attention to Laguerre-Gaussian (LG) beams of paraxial light. In this paper we consider the corresponding LG modes for the two-dimensional harmonic oscillator, which appear in the transversal plane at the laser beam's waist. We see how they arise as Wigner transforms of Hermite-Gaussian modes, and we proceed to find a closed form for their own Wigner transforms, providing an alternative to the methods of Simon and Agarwal. Our main observation is that the Wigner transform intertwines the creation and annihilation operators for the two classes of modes.Comment: 12 pages, minor corrections; submitted, Journal of Modern Optic

The Laser

The laser is an oscillator of light using an amplification process based on stimulated emission from atoms in an optical resonator. Laser light has a narrow spectral width and a high degree of spatial coherence. Laser beams are highly directional and can be focused into a tiny spot. Pulsed lasers produce ultrashort light pulses with ultrahigh peak power. Since its invention in 1960, the laser has enabled many scientific discoveries and has been at the core of a plethora of light-based technologies. It is truly a light fantastic

Hermite Coherent States for Quadratic Refractive Index Optical Media

Producción CientíficaLadder and shift operators are determined for the set of Hermite–Gaussian modes associated with an optical medium with quadratic refractive index profile. These operators allow to establish irreducible representations of the su(1, 1) and su(2) algebras. Glauber coherent states, as well as su(1, 1) and su(2) generalized coherent states, were constructed as solutions of differential equations admitting separation of variables. The dynamics of these coherent states along the optical axis is also evaluated.MINECO grant MTM2014-57129-C2-1-P and Junta de Castilla y Leon grant VA057U16

Solving the riddle of codon usage preferences: a test for translational selection

Translational selection is responsible for the unequal usage of synonymous codons in protein coding genes in a wide variety of organisms. It is one of the most subtle and pervasive forces of molecular evolution, yet, establishing the underlying causes for its idiosyncratic behaviour across living kingdoms has proven elusive to researchers over the past 20 years. In this study, a statistical model for measuring translational selection in any given genome is developed, and the test is applied to 126 fully sequenced genomes, ranging from archaea to eukaryotes. It is shown that tRNA gene redundancy and genome size are interacting forces that ultimately determine the action of translational selection, and that an optimal genome size exists for which this kind of selection is maximal. Accordingly, genome size also presents upper and lower boundaries beyond which selection on codon usage is not possible. We propose a model where the coevolution of genome size and tRNA genes explains the observed patterns in translational selection in all living organisms. This model finally unifies our understanding of codon usage across prokaryotes and eukaryotes. Helicobacter pylori, Saccharomyces cerevisiae and Homo sapiens are codon usage paradigms that can be better understood under the proposed model

Frame dragging with optical vortices

General Relativistic calculations in the linear regime have been made for electromagnetic beams of radiation known as optical vortices. These exotic beams of light carry a physical quantity known as optical orbital angular momentum (OAM). It is found that when a massive spinning neutral particle is placed along the optical axis, a phenomenon known as inertial frame dragging occurs. Our results are compared with those found previously for a ring laser and an order of magnitude estimate of the laser intensity needed for a precession frequency of 1 Hz is given for these "steady" beams of light.Comment: 13 pages, 2 figure

Optical Detection of Ultrasound by Two-Wave Mixing in Photorefractive Semiconductor Crystals Under Applied Field

The optical detection of transient surface motion has many practical applications which include, in particular, the vibration monitoring of engineering structures (aircraft, power plants,...) and the detection of ultrasound produced by piezoelectric transducer or by pulse laser excitation. This last application where ultrasound is generated and detected by lasers, presents many advantages over conventional piezoelectric based methods. First, laser-ultrasonics is a remote sensing technique. Consequently it can be used, for example, for inspecting hot materials and products moving on a production line. Second, surfaces of complex shapes can also very easily be probed. For many applications, these advantages compensate the usually lower sensitivity of the laser-based technique compared to piezoelectric transduction

Giant Superfluorescent Bursts from a Semiconductor Magnetoplasma

Currently, considerable resurgent interest exists in the concept of superradiance (SR), i.e., accelerated relaxation of excited dipoles due to cooperative spontaneous emission, first proposed by Dicke in 1954. Recent authors have discussed SR in diverse contexts, including cavity quantum electrodynamics, quantum phase transitions, and plasmonics. At the heart of these various experiments lies the coherent coupling of constituent particles to each other via their radiation field that cooperatively governs the dynamics of the whole system. In the most exciting form of SR, called superfluorescence (SF), macroscopic coherence spontaneously builds up out of an initially incoherent ensemble of excited dipoles and then decays abruptly. Here, we demonstrate the emergence of this photon-mediated, cooperative, many-body state in a very unlikely system: an ultradense electron-hole plasma in a semiconductor. We observe intense, delayed pulses, or bursts, of coherent radiation from highly photo-excited semiconductor quantum wells with a concomitant sudden decrease in population from total inversion to zero. Unlike previously reported SF in atomic and molecular systems that occur on nanosecond time scales, these intense SF bursts have picosecond pulse-widths and are delayed in time by tens of picoseconds with respect to the excitation pulse. They appear only at sufficiently high excitation powers and magnetic fields and sufficiently low temperatures - where various interactions causing decoherence are suppressed. We present theoretical simulations based on the relaxation and recombination dynamics of ultrahigh-density electron-hole pairs in a quantizing magnetic field, which successfully capture the salient features of the experimental observations.Comment: 21 pages, 4 figure

Laguerre-Gaussian wave propagation in parabolic media

We report a new set of Laguerre-Gaussian wave-packets that propagate with periodical self-focusing and finite beam width in weakly guiding inhomogeneous media. These wave-packets are solutions to the paraxial form of the wave equation for a medium with parabolic refractive index. The beam width is defined as a solution of the Ermakov equation associated to the harmonic oscillator, so its amplitude is modulated by the strength of the medium inhomogeneity. The conventional Laguerre-Gaussian modes, available for homogenous media, are recovered as a particular case.Comment: 11 pages, 5 figure

Regeneration limit of classical Shannon capacity

Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit -the upper bound of regeneration efficiency -is derived