Relations between chirp transform and Fresnel diffraction,Wigner distribution function and a fast algorithm for chirp transform

Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional- order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.

The Wigner distribution function of a super Lorentz–Gauss SLG_(11) beam through a paraxial ABCD optical system

An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.

A new finite-dimensional thermal coherent state and its Wigner distribution function

This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.

The Wigner function and phase properties of superposition of two coherent states with the vacuum state

This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the Wigner function. Phase probability distribution and phase variance are calculated. Special cases of the constructed superposition states are presented. The results show that depending on the vacuum state coefficient γ and the coherent state coefficient a, it can generate a variety of nonclassical states.

Wigner function and the entanglement of a quantized Bessel-Gaussian vortex state of a quantized radiation field

A new kind of quantum non-Gaussian state with a vortex structure, termed a Bessel-Gaussian vortex state, is constructed, which is an eigenstate of the sum of squared annihilation operators a2 ＋ b2. The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality. It is also found that a quantized vortex state is always in entanglement. And a scheme for generating such quantized vortex states is proposed.

Nonclassicality of photon-modulated atomic coherent states in the Schwinger bosonic realization

We theoretically introduce two new photon-modulated atomic coherent states(ACSs)via using the Schwinger bosonic representation of the angular momentum operators(the sequential operations J±n)on an ACS,and investigate their nonclassicality using the Wigner distribution,photon number distribution,and entanglement entropy.It is found that photonmodulated ACSs possess more stronger nonclassicality than the original ACS in certain regions ofτ,the nonclassicality enhances with increasing number n of the operations J±and the operation J+(-)n enhances the entanglement in the region of small(large)τ.

Nonclassicality of photon-modulated spin coherent states in the Holstein-Primakoff realization

Two new photon-modulated spin coherent states(SCSs)are introduced by operating the spin ladder operators J±on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution,second-order correlation function,photocount distribution and negativity of Wigner distribution.Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials.Compared with the ordinary SCS,the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j,which means that the nonclassicality can be enhanced by selecting suitable parameters.

Influence of tube voltage and current on in-line phase contrast imaging using a microfocus x-ray source

In-line x-ray phase contrast imaging has attracted much attention due to two major advantages： its effectiveness in imaging weakly absorbing materials, and the simplicity of its facilities. In this paper a comprehensive theory based on Wigner distribution developed by Wu and Liu [Med. Phys. 31 2378-2384 （2004）] is reviewed. The influence of x-ray source and detector on the image is discussed. Experiments using a microfocus x-ray source and a CCD detector are conducted, which show the role of two key factors on imaging： the tube voltage and tube current. High tube current and moderate tube voltage are suggested for imaging.

Decoherence of elliptical states in phase space

The effects of decoherence on elliptical states which concern the quantum superposition of N coherent states on an ellipse in the a plane are studied. The characteristic decoherence times are determined. The evolutions of the Wigner functions associated with these states are investigated theoretically and the losses of nonclassicality as a result of decoherence are discussed. The result shows that the decoherence of elliptical states is slower than circular states relying on the number of coherent states and the amplitude, and the constructed states have a higher resilience to losses.

Decoherence of a Damped Anisotropic Harmonic Oscillator under Magnetic Field Effects in a Two-Dimensional Noncommutative Phase-Space

In this paper, decoherence of a damped anisotropic harmonic oscillator in the presence of a magnetic field is studied in the framework of the Lindblad theory of open quantum systems in noncommutative phase-space. General fundamental conditions that should follow our quantum mechanical diffusion coefficients appearing in the master equation are kindly derived. From the master equation, the expressions of density operator, the Wigner distribution function, the expectation and variance with respect to coordinates and momenta are obtained. Based on these quantities, the total energy of the system is evaluated and simulations show its dependency to phase-space structure and its improvement due to noncommutativity effects and the environmental temperature as well. In addition, we also evaluate the decoherence time scale and show that it increases with noncommutativity phase-space effects as compared to the commutative case. It turns out from simulations that this time scale is significantly improved under magnetic field effects.

A New Approach for the DFT NIST Test Applicable for Non-Stationary Input Sequences

The National Institute of Standards and Technology (NIST) document is a list of fifteen tests for estimating the probability of signal randomness degree. Test number six in the NIST document is the Discrete Fourier Transform (DFT) test suitable for stationary incoming sequences. But, for cases where the input sequence is not stationary, the DFT test provides inaccurate results. For these cases, test number seven and eight (the Non-overlapping Template Matching Test and the Overlapping Template Matching Test) of the NIST document were designed to classify those non-stationary sequences. But, even with test number seven and eight of the NIST document, the results are not always accurate. Thus, the NIST test does not give a proper answer for the non-stationary input sequence case. In this paper, we offer a new algorithm or test, which may replace the NIST tests number six, seven and eight. The proposed test is applicable also for non-stationary sequences and supplies more accurate results than the existing tests (NIST tests number six, seven and eight), for non-stationary sequences. The new proposed test is based on the Wigner function and on the Generalized Gaussian Distribution (GGD). In addition, this new proposed algorithm alarms and indicates on suspicious places of cyclic sections in the tested sequence. Thus, it gives us the option to repair or to remove the suspicious places of cyclic sections (this part is beyond the scope of this paper), so that after that, the repaired or the shortened sequence (original sequence with removed sections) will result as a sequence with high probability of random degree.

An application of matching pursuit time-frequency decomposition method using multi-wavelet dictionaries

In the time-frequency analysis of seismic signals, the matching pursuit algorithm is an effective tool for non-stationary signals, and has high time-frequency resolution and a transient structure with local self-adaption. We expand the time-frequency dictionary library with Ricker, Morlet, and mixed phase seismic wavelets, to make the method more suitable for seismic signal time-frequency decomposition. In this paper, we demonstrated the algorithm theory using synthetic seismic data, and tested the method using synthetic data with 25% noise. We compared the matching pursuit results of the time-frequency dictionaries. The results indicated that the dictionary which matched the signal characteristics better would obtain better results, and can reflect the information of seismic data effectively.

Quantum statistical properties of photon-added spin coherent states

The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state.

On the Spectral Distribution of Gaussian Random Matrices

We consider the empirical spectral distribution （ESD） of a random matrix from the Gaussian Unitary Ensemble. Based on the Plancherel-Rotaeh approximation formula for Hermite polynomials, we prove that the expected empirical spectral distribution converges at the rate of O（n^-1） to the Wigner distribution function uniformly on every compact intervals [u,v] within the limiting support （-1, 1）. Furthermore, the variance of the ESD for such an interval is proved to be （πn）^-2 logn asymptotically which surprisingly enough, does not depend on the details （e.g. length or location） of the interval, This property allows us to determine completely the covariance function between the values of the ESD on two intervals.

Multifunctional interleaved geometric-phase dielectric metasurfaces

Shared-aperture technology for multifunctional planar systems,performing several simultaneous tasks,was first introduced in the field of radar antennas.In photonics,effective control of the electromagnetic response can be achieved by a geometric-phase mechanism implemented within a metasurface,enabling spin-controlled phase modulation.The synthesis of the shared-aperture and geometric-phase concepts facilitates the generation of multifunctional metasurfaces.Here shared-aperture geometric-phase metasurfaces were realized via the interleaving of sparse antenna sub-arrays,forming Si-based devices consisting of multiplexed geometric-phase profiles.We study the performance limitations of interleaved nanoantenna arrays by means of a Wigner phasespace distribution to establish the ultimate information capacity of a metasurface-based photonic system.Within these limitations,we present multifunctional spin-dependent dielectric metasurfaces,and demonstrate multiple-beam technology for optical rotation sensing.We also demonstrate the possibility of achieving complete real-time control and measurement of the fundamental,intrinsic properties of light,including frequency,polarization and orbital angular momentum.

Time-energy analysis of the photoionization process in a double-XUV pulse combined with a few-cycle IR field

We calculate the time-energy distribution(TED)and ionization time distribution(ITD)of photoelectrons emitted by a doubleextreme-ultraviolet(XUV)pulse and a two-color XUV-IR pulse using the Wigner distribution-like function based on the strong field approximation.For a double-XUV pulse,besides two identical broad distributions generated by two XUV pulses,many interference fringes resulting from the interference between electrons generated,respectively,by two pulses appear in the TED.After adding an IR field,the TED intuitively exhibits the effect of the IR field on the electron dynamics.The ITDs during two XUV pulses are no longer the same and show the different changes for the different two-color fields,the origin of which is attributed to the change of the electric field induced by the IR field.Our analysis shows that the emission time of electrons ionized during two XUV pulses mainly depends on the electric field of the combined XUV pulse and IR pulse.

Statistical properties of quantum spectra in nuclei

Some aspects of quantum chaos in a finite system have been studied based on the analysis of statistical behavior of quantum spectra in nuclei.The experiment data show the transition from order to chaos with increasing excitation energy in spherical nuclei.The dependence of the order to chaos transition on nuclear deformation and nuclear rotating is described.The influence of pairing effect on the order to chaos transition is also discussed.Some important experiment phenomena in nuclear physics have been understood from the point of view of the interplay between order and chaos.

WHT-Based Detection and Parameter Estimation of a Single LFM Interference Signal in Spread Spectrum Systems

A method is presented for the detection and parameter estimation of a single Linear Frequency Modulation (LFM) signal in spread spectrum systems based on Wigner Hough Transform (WHT) , followed by the theoretical analysis. A simulation result is given to show the effectiveness of this method.