We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with self-focusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Lévy indexes, combined with saturable nonlinearity, supports two-dimensional symmetric, antisymmetric and asymmetric solitons, where the asymmetric solitons emerge by way of symmetry breaking bifurcation. Different scenarios of bifurcations emerge with the change of stability the branches of asymmetric solitons split off the branches of unstable symmetric solitons with the increase of soliton power and form a supercritical type bifurcation for self-focusing saturable nonlinearity; the branches of asymmetric solitons bifurcates from the branches of unstable antisymmetric solitons for self-defocusing saturable nonlinearity, featuring a convex shape of the bifurcation loops an antisymmetric soliton loses its stability via a supercritical bifurcation, which is followed by a reverse bifurcation that restores the stability of the symmetric soliton. Furthermore, we found a scheme of restoration or destruction the symmetry of the antisymmetric solitons by controlling the fractional diffraction in the case of self-defocusing saturable nonlinearity.A new metric for imaging systems, the volumetric imaging efficiency (VIE), is introduced. It compares the compactness and capacity of an imager against fundamental limits imposed by diffraction. Two models are proposed for this fundamental limit based on an idealized thin-lens and the optical volume required to form diffraction-limited images. The VIE is computed for 2,871 lens designs and plotted as a function of FOV; this quantifies the challenge of creating compact, wide FOV lenses. We identify an empirical limit to the VIE given by VIE 100x increase in VIE.Semiconductor lasers (SLs) show relaxation oscillation (RO) due to the cavity damping rate being higher than the carrier damping rate. The presence of RO in SLs contributes to abundant complex dynamics when the laser is perturbed by external optical feedback (EOF). In this work, the influence of feedback optical phase on the relaxation oscillation frequency (ROF) in an SL is investigated both theoretically and experimentally. By numerically solving the well-known Lang Kobayashi equations, the relationship between the ROF and feedback optical phase was obtained, which shows ROF is in a sinusoidal manner with respect to the feedback optical phase under weak feedback strength. A simplified mathematic expression for ROF was derived to describe such a sinusoidal relationship. Potential sensing applications can be developed based on the relationship. As an example, a new method of measuring linewidth enhancement factor of an SL was presented. Finally, an experimental setup was built and experiments were carried out to verify the relationship and the measurement method for linewidth enhancement factor.In this letter, a distributed optical fiber hydrophone (DOFH) based on Φ-OTDR is demonstrated and tested in the field. The specially designed sensitized optical cable with sensitivity up to -146 dB rad/µPa/m is introduced, and an array signal processing model for DOFH is constructed to analyze the equivalence and specificity of the distributed array of acoustic sensors. In the field test, a 104-meter-long optical cable and a Φ-OTDR system based on heterodyne coherent detection (Het Φ-OTDR) is utilized, and underwater acoustic signal spatial spectrum estimation, beamforming and motion trajectory tracking with high accuracy can be realized. As far as we know, this is the first report on the field trial of DOFH based on Φ-OTDR. The DOFH has the potential to achieve an array range of tens of kilometers, with elements spaced up to the meter level and flexible configuration, which has a broad application prospect for marine acoustic detection.We theoretically and numerically study the effects of thermal noise on pulses in backwards stimulated Brillouin scattering (SBS). Using a combination of stochastic calculus and numerical methods, we derive a theoretical model that can be used to quantitatively predict noise measurements. We study how the optical pulse configuration, including the input powers of the pump and Stokes fields, pulse durations and interaction time, affects the noise in the output Stokes field. We investigate the effects on the noise of the optical loss and waveguide length, and we find that the signal-to-noise ratio can be significantly improved, or reduced, for specific combinations of waveguide properties and pulse parameters.We experimentally verified the enhanced nonlinear tolerance of probabilistic shaping (PS) 64QAM super symbol (SUP) transmission over both dispersion uncompensated and compensated standard single mode fiber (SSMF) links. https://www.selleckchem.com/products/cadd522.html PS-64QAM with SUP is found to provide ∼0.51- and ∼1.6-dB gains in OSNR over PS-64QAM with traditional probabilistic amplitude shaping, after ∼1000-km uncompensated and 320-km compensated links, respectively.The yield of a large-area ultra-thin display panel depends on the realization of designed thickness of multilayer films of all pixels. Measuring the thicknesses of multilayer films of a single pixel is crucial to the accurate manufacture. However, the thinnest layer is reaching the sub-20nm level, and different layers feature remarkable divergence in thickness with similar optical constants. This turns to a key obstruction to the thickness characterization by optical spectroscopy. Based on the tiny differences in absorptivity, a fast method for measuring the film thickness in a single pixel is proposed which combines the layer number reducing model and micro-area differential reflectance spectroscopy. The lower layers can be considered as semi-infinite in the corresponding spectral range whose thickness is infinite in the fitting algorithm. Hence, the thickness of the upper layer is fitted in a simplified layer structure. For demonstration, a multilayer silicon microstructure in a single pixel, p-Si/a-Si/n-Si (10nm/950nm/50nm) on complex substrate, is measured.
We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with self-focusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Lévy indexes, combined with saturable nonlinearity, supports two-dimensional symmetric, antisymmetric and asymmetric solitons, where the asymmetric solitons emerge by way of symmetry breaking bifurcation. Different scenarios of bifurcations emerge with the change of stability the branches of asymmetric solitons split off the branches of unstable symmetric solitons with the increase of soliton power and form a supercritical type bifurcation for self-focusing saturable nonlinearity; the branches of asymmetric solitons bifurcates from the branches of unstable antisymmetric solitons for self-defocusing saturable nonlinearity, featuring a convex shape of the bifurcation loops an antisymmetric soliton loses its stability via a supercritical bifurcation, which is followed by a reverse bifurcation that restores the stability of the symmetric soliton. Furthermore, we found a scheme of restoration or destruction the symmetry of the antisymmetric solitons by controlling the fractional diffraction in the case of self-defocusing saturable nonlinearity.A new metric for imaging systems, the volumetric imaging efficiency (VIE), is introduced. It compares the compactness and capacity of an imager against fundamental limits imposed by diffraction. Two models are proposed for this fundamental limit based on an idealized thin-lens and the optical volume required to form diffraction-limited images. The VIE is computed for 2,871 lens designs and plotted as a function of FOV; this quantifies the challenge of creating compact, wide FOV lenses. We identify an empirical limit to the VIE given by VIE 100x increase in VIE.Semiconductor lasers (SLs) show relaxation oscillation (RO) due to the cavity damping rate being higher than the carrier damping rate. The presence of RO in SLs contributes to abundant complex dynamics when the laser is perturbed by external optical feedback (EOF). In this work, the influence of feedback optical phase on the relaxation oscillation frequency (ROF) in an SL is investigated both theoretically and experimentally. By numerically solving the well-known Lang Kobayashi equations, the relationship between the ROF and feedback optical phase was obtained, which shows ROF is in a sinusoidal manner with respect to the feedback optical phase under weak feedback strength. A simplified mathematic expression for ROF was derived to describe such a sinusoidal relationship. Potential sensing applications can be developed based on the relationship. As an example, a new method of measuring linewidth enhancement factor of an SL was presented. Finally, an experimental setup was built and experiments were carried out to verify the relationship and the measurement method for linewidth enhancement factor.In this letter, a distributed optical fiber hydrophone (DOFH) based on Φ-OTDR is demonstrated and tested in the field. The specially designed sensitized optical cable with sensitivity up to -146 dB rad/µPa/m is introduced, and an array signal processing model for DOFH is constructed to analyze the equivalence and specificity of the distributed array of acoustic sensors. In the field test, a 104-meter-long optical cable and a Φ-OTDR system based on heterodyne coherent detection (Het Φ-OTDR) is utilized, and underwater acoustic signal spatial spectrum estimation, beamforming and motion trajectory tracking with high accuracy can be realized. As far as we know, this is the first report on the field trial of DOFH based on Φ-OTDR. The DOFH has the potential to achieve an array range of tens of kilometers, with elements spaced up to the meter level and flexible configuration, which has a broad application prospect for marine acoustic detection.We theoretically and numerically study the effects of thermal noise on pulses in backwards stimulated Brillouin scattering (SBS). Using a combination of stochastic calculus and numerical methods, we derive a theoretical model that can be used to quantitatively predict noise measurements. We study how the optical pulse configuration, including the input powers of the pump and Stokes fields, pulse durations and interaction time, affects the noise in the output Stokes field. We investigate the effects on the noise of the optical loss and waveguide length, and we find that the signal-to-noise ratio can be significantly improved, or reduced, for specific combinations of waveguide properties and pulse parameters.We experimentally verified the enhanced nonlinear tolerance of probabilistic shaping (PS) 64QAM super symbol (SUP) transmission over both dispersion uncompensated and compensated standard single mode fiber (SSMF) links. https://www.selleckchem.com/products/cadd522.html PS-64QAM with SUP is found to provide ∼0.51- and ∼1.6-dB gains in OSNR over PS-64QAM with traditional probabilistic amplitude shaping, after ∼1000-km uncompensated and 320-km compensated links, respectively.The yield of a large-area ultra-thin display panel depends on the realization of designed thickness of multilayer films of all pixels. Measuring the thicknesses of multilayer films of a single pixel is crucial to the accurate manufacture. However, the thinnest layer is reaching the sub-20nm level, and different layers feature remarkable divergence in thickness with similar optical constants. This turns to a key obstruction to the thickness characterization by optical spectroscopy. Based on the tiny differences in absorptivity, a fast method for measuring the film thickness in a single pixel is proposed which combines the layer number reducing model and micro-area differential reflectance spectroscopy. The lower layers can be considered as semi-infinite in the corresponding spectral range whose thickness is infinite in the fitting algorithm. Hence, the thickness of the upper layer is fitted in a simplified layer structure. For demonstration, a multilayer silicon microstructure in a single pixel, p-Si/a-Si/n-Si (10nm/950nm/50nm) on complex substrate, is measured.
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