We studied numerically 1000 nm, 1 ps pulse width propagation in a PT-symmetric nonlinear directional coupler in the form of dual-core photonic crystal fiber. The base material of the fiber is phosphate glass, while gain and loss channels are implemented by ytterbium-based and copper-based doping, respectively. The propagation models were based on coupled generalized nonlinear Schrödinger equations solved with the Split-Step method: 1) extended model including coupling coefficient dispersion, self-steepening nonlinearity and its spectral dependence, stimulated Raman contribution, cross-phase modulation and Gaussian-like gain and loss coefficient frequency function; 2) simplified model with second-order dispersion term, linear coupling and first-order nonlinearity. We predicted two states of light propagation: 1) linear pulse energy oscillation between gain and loss channels (PT-symmetry state) at 100 pJ; 2) retention of the pulse in the excited gain channel (broken PT-symmetry) at 445 pJ. The presented results open perspective on the demonstration of fiber-based all-optical switching devices.
Supercontinuum generation (SG) in fused silica photonic crystal fibers (PCFs) having a core infiltrated with liquid benzene is analyzed. Three PCF designs, with dimensions and chromatic dispersion optimized for SG using off-the-shelf femtosecond pulse lasers (1560 nm, 90 ps), are proposed. F1 fiber with lattice constant Λ = 1.5 μm and linear filling factor f = 0.45 has all-normal dispersion and offers SG in the 700- to 2000-nm band at relative power levels within 15 dB when pumped with 3 nJ pulses. F2 fiber (Λ = 1.5 μm, f = 0.6) enables SG in an anomalous dispersion regime, covering 600 to 2600 nm spectral range at relative power levels within 30 dB when pumped with low-energy pulses (1 nJ). The F3 fiber (Λ = 2.5 μm, f = 0.6) also exhibits mostly anomalous dispersion and makes possible SG in a very broad 600 to 3500 nm range at relative power levels within 30 dB when pumped with 2 nJ pulses.
We present the study of the dynamics of a two-ring waveguide structure with space-dependent coupling, linear gain and nonlinear absorption; the system that can be implemented in polariton condensates, optical waveguides and nanocavities. We find that due to the modulation instability, it is possible to observe several complex nonlinear phenomena, including spontaneous symmetry breaking, stable inhomogeneous states, oscillating states (limit cycle) and even chaotic dynamics. We compare two systems of coupled rings, with one and two symmetrically located coupling centres.
Nanostructured GRIN components are optical elements which can have arbitrary refractive index profile while retaining flat-parallel entry and exit facets. They are composed of more than 9000 individually placed glass subwavelength rods made of two types of glass with different refractive indices. They are developed using a standard stack-and-draw method used for fibre drawing. The refractive index profile of the nanostructured GRIN element can be described by the effective refractive index theory when the diameter of the individual rods are sufficiently smaller than the wavelength. In this paper we show that use of glasses designed for high diffusion and high temperatures during drawing process allows to develop parabolic nanostructured GRIN microlenses with rod diameter larger than wavelength. In particular, we have developed a GRIN microlens with diameter of 115 μm composed of 115 rods on diagonal. Our GRIN microlens has a length of 200 μm and a working distance equal to 1.05 mm, with focal spot of 8.5 μm measured for the 658 nm wavelength. We experimentally verified its imaging properties. Image resolution higher than 3.25 μm was measured.
We study optical properties of gradient index vortex masks based on an effective medium approach. We consider masks with single charge developed using two types of nanorods made of thermally matched low and high refractive index glasses. Optical performance of generated vortices are analyzed in terms of glass refractive index difference and spatial dimension of the components. A fabricated vortex mask has been combined with single mode optical fiber. Optical performance of the resulting fiber integrated vortex mask is characterized and discussed.
We study optical properties of the gradient index vortices obtained using effective medium approach. Vorteces with charge +1 has been was developed using two types of nanorods made of thermally matched low and high refractive index glasses. Their optical properties of vortices are analyzed in the context of glass refractive index and size of the components. Consequently vortex has been integrated with single mode optical fiber and such a system is analyzed.
In this paper we present a numerical study on the optimization of dispersion of a photonic crystal fiber infiltrated with water-ethanol mixtures. The advantage of such an approach stems from the fact that the dependence of the refractive index on temperature is larger in liquids than in solid materials. Here, we examine photonic crystal fibers with a regular, hexagonal lattice and with various geometrical and material parameters, such as different number of rings of holes, various lattice constants and the size of core and air-holes. Additionally, for the optimized structure with flat dispersion characteristics, we analyze the influence of temperature and concentration of the ethanol solution on the dispersion characteristic and the zero dispersion wavelength shift of the fundamental mode.
We present a numerical study of the dispersion characteristic modification in a nonlinear photonic crystal fibre (PCF) infiltrated with organic solvents. The PCF is made of PBG08 glass and was developed in the stack-and-draw process. The PBG08 glass has a high refractive index (n < 2.0), high nonlinear refractive index (n2 = 4.3×10−19 m2/W) and good rheological properties that allow for thermal processing of the glass without crystallization. In the numerical study 18 different solvents were used. The dispersion, mode area, and losses characteristics were calculated. The zero dispersion wavelength (ZDW) of the fibre can be shifted towards longer wavelengths by approx. 150 nm by using Nitrobenzene as infiltrating liquid and by a smaller value using other liquids. At the same time the mode area of the fundamental mode increases by approx. 5 to 15% depending on the wavelength considered. The confinement losses increase significantly for six analysed liquids by a few orders of magnitude up to 102 dB/m. Our approach allows to combine high nonlinearities of the soft glass with the possibility to tune zero dispersion wavelength to the desired value.
We present an experimental and theoretical study of the nonlinear propagation of 90 fs laser pulses at 800 nm in bulk fused silica. An unexpected behavior of the off-axis emission for pulse energy corresponding to the supercontinuum generation threshold has been discovered. Our model, based on 3D Nonlinear Schrodinger Equation, well explains the observed nonlinear dynamics. For the first time we experimentally confirm that the onset of the supercontinuum generation is inevitably accompanied by the pulse collapse in transverse dimensions.
In this paper we treat two and three dimensional light bullets by somewhat different methods. In both cases stability is achieved for some parameters. In the first case we propose a scheme for stabilizing spatiotemporal solitons (STS) in media with cubic self-focusing nonlinearity and "dispersion management", i.e., a layered structure inducing periodically alternating normal and anomalous group-velocity dispersion . We develop a variational approximation for the STS, and verify results by direct simulations. A stability region for the 2D (two-dimensional) STS is identified. A new stable object, in the form of a periodically oscillating bound state of two subpulses, is also found. We go on to also demonstrate a possibility to stabilize fully three-dimensional spatiotemporal solitons ("light bullets") in the same self-focusing Kerr media by means of a combination of dispersion management in the longitudinal direction and periodic modulation of the refractive index in one of the transverse directions. Assuming the usual model based on the paraxial nonlinear Schrodinger equation for the local amplitude of the electromagnetic field, the analysis relies upon the variational approximation. A predicted stability area is identified in the model's parameter space.
We present angularly resolved spectra of 65 fs laser pulses at 800 nm after propagation through bulk fused silica. For the first time we report angular dependence of the spectrum after propagation in a solid sample far from resonances. Reproducible spectral and spatial effects have been observed for pulse powers several times above critical power for self-focusing.
We have studied, theoretically and experimentally, nonlinear propagation of 90 fs laser pulses at 800 nm in bulk fused silica samples. For the first time, we present comparisons between numerically simulated and experimentally measured angle-resolved, far-field spectra for such pulses. They are in good agreement for pulse powers up to, approximately, critical power for self focusing.
A new equation for self-focusing of extremely focused intense pulses is derived. This method can be generalized to derive propagation equations for intense focused pulses to all orders of diffraction and dispersion with nonlinearity present, including the self-consistent derivation of nonlinear derivative coupling terms. This generalizes both the previously formulation of linear optical pulse propagation to the nonlinear propagation regime, and the cw nonlinear regime to the pulsed regime by including temporal characteristics of the pulse. Here we present the results for isotropic Kerr-type nonlinear media.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. FEC has already been exploited to produce a matter-wave `laser' leading to the threshold of a new field of physics: nonlinear atom optics. Recently the first experiment in nonlinear atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schrodinger equation (also called the Gross-Pitaevskii equation), to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. BEC has already been exploited to produce a matter-wave 'laser' atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schroedinger equation, to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation, and particle number conservation in four-wave mixing of matter waves.
We have developed a method to precisely propagate short optical pulses through dispersive media with a self-focusing (chi) (3) Kerr-type nonlinear polarization. Above the critical cw self-focusing power, onset of pulse splitting into pulselets separated in time occurs, and for a certain regime of parameters a cyclic series of pulse splitting and pulse recombination occurs for diffraction length smaller than dispersion length. At higher power, another threshold for non-cyclic temporal and spatial pulse splitting is manifest. Self-steepening and self-frequency shifting affect pulse propagation too. We use our formulation to calculate the dynamics of collisions of two pulses in nonlinear optical media, and show how the collision can give rise to pulse splitting. We also investigate the effects of saturation of the nonlinearity on the phenomenon of pulse splitting and pulse collision dynamics.
We analyze propagation of ultra-short light pulses in transparent, dispersive, nonlinear media. A general formula for a femtosecond wavepacket evolution in birefringent materials is presented and applied to specific problems. Theoretical and experimental results for wavepacket distortion by lenses, wavepacket rotation in birefringent media, group velocity matching in sum frequency generation, and ultra-short pulse propagation in birefringent crystals are presented. Splitting of femtosecond wavepackets in dispersive Kerr media is also discussed.
We develop a method to precisely propagate short optical pulses through dispersive media with a cubic self-focusing nonlinear polarization. We show that above the critical cw self-focusing power, onset of pulse splitting into pulselets separated in time occurs, and for a certain regime of parameters a cyclic series of pulse splitting (into pulselets separated in time) and pulse recombination occurs for diffraction length smaller than dispersion length. At higher power, another threshold for non-cyclic temporal and spatial pulse splitting is manifest. The physics of these phenomena are described and delineated. We then incorporate self-steepening and self-frequency shifting. These effects can significantly affect pulse propagation dynamics, both in the normal but especially in the anomalous dispersion regimes. The nature of the dynamics is significantly different in the two regimes.
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