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The Rayleigh–Taylor instability at the weakly nonlinear (WN) stage in spherical geometry is studied by numerical simulation. The mode coupling processes are revealed. The results are consistent with the WN model based on parameter expansion, while higher order effects are found to be non-negligible. For Legendre mode perturbation Pn(cosθ), the nonlinear saturation amplitude (NSA) of the fundamental mode decreases with the mode number n. When n is large, the spherical NSA is lower than the corresponding planar one. However, for large n, the planar NSA can be recovered by applying Fourier transformation to the bubble/spike near the equator and calculating the NSA of the converted trigonometric harmonic. [ABSTRACT FROM AUTHOR]

We present an optical encryption scheme for hyperspectral images using an improved binary tree structure (IBTS) and phase-truncated discrete multiple-parameter fractional Fourier transform (PTdmpFrFT). In the IBTS, the encryption modules based on the phase-truncated fractional Fourier transform represented the branch nodes, while the hyperspectral bands of the plain images were considered as leaf nodes. All pairs of bands were encoded into intermediate data using the IBTS, with subsequent encryption into asymmetric ciphertexts using the PTdmpFrFT. The proposed approach generated different pairs of bands with different secret keys, and encryption and decryption paths. Compared with state-of-the-art optical hyperspectral encryption methods, our approach not only achieved superior encryption security but also reduced the computation and storage requirements of the encrypted data. The original hyperspectral image information could be successfully decrypted only when using all the correct keys. Numerical simulations were performed to verify the performance of the proposed method. [ABSTRACT FROM AUTHOR]

A novel approach for producing sidelobe-free optical vortices is proposed, for the first time, utilizing object-oriented computer generated holograms (CGH). By conjugate-symmetrically extending the complex amplitude of any desired optical vortices prior to performing the discrete Fourier transform, the resulting real-valued number profile is encoded into an object-oriented CGH without having conventional forked-shaped fringes. On the basis of the CGH generated, use is first made of numerical simulations to reconstruct optical vortices with spiral phase profiles. Detailed experimental measurements employing a computer-controlled spatial light modulator and extensive numerical simulations are undertaken to verify the proposed technique. Excellent agreements between numerical simulations and experimental measurements are observed. Results show that optical vortices with a single primary intensity ring are generated without the occurrence of any sidelobes in the periphery for absolute values of topological charges as large as 20. [ABSTRACT FROM AUTHOR]

The stability of ion velocity distributions in magnetized plasmas is studied under conditions where the plasma has an E0 × B/B2-drift with respect to a neutral background. Charge–exchange collisions can give rise to velocity distributions having the form of a ring or a loss-cone that can become linearly unstable. Sometimes the distributions have distorted forms and a stability analysis is not straightforward. Numerical simulations offer the most convenient method of a stability analysis in such cases. By numerical simulations using a particle-in-cell code that includes collisional interactions we demonstrate the formation of such velocity distributions and study the instabilities associated with them. We observe the saturation of the linear instability by quasi-linear velocity space diffusion. The parameter dependence of the instability conditions is illustrated by examples. The results are relevant for explaining some of the low frequency oscillations observed in the lower parts of the Earth's ionosphere (E- and F-regions), where collisions with neutrals are abundant. The results are important for laboratory experiments as well. [ABSTRACT FROM AUTHOR]

We consider quantum learning machines-quantum computers that modify themselves in order to improve their performance in some way-that are trained to perform certain classical task, i.e. to execute a function that takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machines in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the kth root of NOT (NOT = logical negation), with k = 2m and mϵℕ. The reason for this speed-up is that the classical machine requires memory of size log k = m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k. [ABSTRACT FROM AUTHOR]

An exact calculation of the Voigt spectral line profile in spectroscopy has been derived using the Fourier transform method. The analytical formula we calculated is a real function, rather than a complex function as has been previously discussed, because the imaginary part will be zero in our calculation. The analytical formula is very convenient in practical applications. The relationship of the half width of the Voigt profile, the Gaussian profile and the Lorentzian profile is also discussed. Through analysis using a computer simulation, we find that the formula we calculated is in good agreement with the experimental result. [ABSTRACT FROM AUTHOR]

We have studied a femtosecond (fs) ultrafast all-optical photonic crystal (PhC) switch, and a new dynamic mechanism of the interplay between nonlinearity and Bragg scattering is revealed. Almost all phenomena observed in the experiments are reproduced in our numerical simulations. Completely different from the traditional band-gap shift mechanism, we propose a new dynamic mechanism that can explain the considerable increase of transmission and almost all other complex transmission behaviors of the switch. First, the fs-level ultrashort-lifetime nonlinearity generated by the fs pumping pulse, which cannot generate a band-gap shift, only causes a sudden phase change on the signal field that is still inside the PhC. Second, such a phase change can partially destroy the destructive interference of Bragg scattering, which is the physical reason for the low transmission in the photonic gap of the PhC. The study by Fourier transform of the temporally transmitted field can clearly support our new explanation. New phenomena, such as the larger than unity sum of transmission and reflection, are predicted. The new dynamic mechanism could be widely used in other systems as a new method to amplify nonlinear effects, or as a detector for ultrafast (femto- or attosecond) electronic processes. [ABSTRACT FROM AUTHOR]

We present a generalized theory for describing encryption and decryption by using the double random phase encoding (DRPE) technique under the framework of the Collins diffraction transform formalism. The theory covers to a variety of diffraction domain which includes the Fourier domain (conventional 4f-optical processor), the Fresnel domain and the fractional Fourier transform (FRFT) domain. From the theoretical basis developed in this work, we present novel optical DRPE systems such as Gaussian imaging DRPE, inverse operation DRPE and Fresnel diffraction DRPE systems, which are plausible to implement. It is shown that the maximum number of degrees of freedom (or independent design parameters) of proposed DRPE system increases four times, when compared with the conventional 4f-optical system, which guarantee much more secure encryption and decryption. [ABSTRACT FROM AUTHOR]

We propose and implement a wide-field vibrational phase contrast detection to obtain imaging of imaginary components of third-order nonlinear susceptibility in a coherent anti-Stokes Raman scattering (CARS) microscope with full suppression of the non-resonant background. This technique is based on the unique ability of recovering the phase of the generated CARS signal based on holographic recording. By capturing the phase distributions of the generated CARS field from the sample and from the environment under resonant illumination, we demonstrate the retrieval of imaginary components in the CARS microscope and achieve background free coherent Raman imaging. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel method to achieve super-resolution imaging by utilizing shifting media based on the transformation optics theory. According to the effective medium theory, the homogenous but anisotropic shifting media can be simply replaced by only two kinds of homogenous and isotropic materials in an alternating layered structure. In addition, another scheme of the symmetrical trapezoidal shifting media shells with layered isotropic materials is proposed to realize the super-resolution imaging. Finite element simulations have been performed to prove these ideas. [ABSTRACT FROM AUTHOR]