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Register a new userModulation Instability and Pattern Formation in Spatially Incoherent Light Beams
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We present the first experimental observation of modulation instability of partially spatially incoherent light beams in non-instantaneous nonlinear media. We show that even in such a nonlinear partially coherent system (of weakly-correlated particles) patterns can form spontaneously. Incoherent MI occurs above a specific threshold that depends on the beams coherence properties (correlation distance), and leads to a periodic train of one-dimensional (1D) filaments. At a higher value of nonlinearity, incoherent MI displays a two-dimensional (2D) instability and leads to self-ordered arrays of light spots.
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A phenomenological model for spectral broadening of incoherent light in silica fibers via self-phase modulation and dispersion is presented, aiming at providing a qualitative and readily accessible description of incoherent light spectral broadening. In this model, the incoherent light is approximated by a cosine power-modulated light with modulation parameters depending on the coherent time and the dispersion in fibers. A simple and practical method for spectral broadening predictions is given and demonstrated by both the straightforward NLSE-based numerical modeling and series of experiments including narrowband and broadband incoherent light in passive fibers and fiber amplifiers.
We derive analytical expressions for the coherence in the onset of modulation instability, in excellent agreement with thorough numerical simulations. As usual, we start by a linear perturbation analysis, where broadband noise is added to a continuous wave (CW) pump; then, we investigate the effect of adding a deterministic seed to the CW pump, a case of singular interest as it is commonly encountered in parametric amplification schemes. Results for the dependence of coherence on parameters such as fiber type, pump power, propagated distance, seed signal-to-noise ratio are presented. Finally, we show the importance of including higher-order linear and nonlinear dispersion when dealing with generation in longer wavelength regions (mid IR). We believe these results to be of relevance when applied to the analysis of the coherence properties of supercontinua generated from CW pumps.
While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to asses the amount and quality of information inside a noisy optical channel. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations. Some of these approaches are limited to a certain alphabet, while others tend to fall short when considering optical beams with non-trivial structure, such as Hermite-Gauss, Laguerre-Gauss and other modes with non-trivial structure. Here, we propose a new definition of classical Shannon information via the Wigner distribution function, while respecting the Heisenberg inequality. Following this definition, we calculate the amount of information in a Gaussian, Hermite-Gaussian, and Laguerre-Gaussian laser modes in juxtaposition and experimentally validate it by reconstruction of the Wigner distribution function from the intensity distribution of structured laser beams. We experimentally demonstrate the technique that allows to infer field structure of the laser beams in singular optics to assess the amount of contained information. Given the generality, this approach of defining information via analyzing the beam complexity is applicable to laser modes of any topology that can be described by well-behaved functions. Classical Shannon information defined in this way is detached from a particular alphabet, i.e. communication scheme, and scales with the structural complexity of the system. Such a synergy between the Wigner distribution function encompassing the information in both real and reciprocal space, and information being a measure of disorder, can contribute into future coherent detection algorithms and remote sensing.
In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a waves constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole new class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study, for the first time, the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.
Several applications, such as optical tweezers and atom guiding, benefit from techniques that allow the engineering of optical fields spatial profiles, in particular their longitudinal intensity patterns. In cylindrical coordinates, methods such as Frozen Waves allow an advanced control of beams characteristics, but in Cartesian coordinates there is no analogous technique. Since Cartesian beams may also be useful for applications, we develop here a method to modulate on-demand the longitudinal intensity pattern of any (initially) unidimensional Cartesian beam with concentrated wavevector spectrum, thus encompassing all paraxial unidimensional beams. To this end, we write the total beam as a product of two unidimensional beams and explore the degree of freedom provided by the additional Cartesian coordinate. While in the plane where this coordinate is zero the chosen unidimensional beam keeps its structure with the additional desired intensity modulation, a sinusoidal-like oscillation appears in the direction of this variable and creates a spot whose size is tunable. Examples with Gaussian and Airy beams are presented and their corresponding experimental demonstrations are performed to show the validity of the method.
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