Method for extracting angle-domain common image gathers in Kirchhoff beam migration

Kirchhoff beam migration is a simplified Gaussian beam migration,which omits the dynamic information and can calculate multi-arrival traveltime,so it is a high-precision and fast seismic imaging method.In the imaging process,extracting common image gathers can be used for velocity analysis,improving the accuracy of modeling and imaging quality.Compared with the conventional common image gathers extracting methods,the angle-domain common image gathers extracting method can avoid the artifacts caused by multi-arrival seismic waves.The authors present a new method of extracting common image gathers in angle-domain from Kirchhoff beam migration and verify the method by numerical calculations.

Generalization and propagation of spiraling Bessel beams with a helical axicon

A generalized type of spiral Bessel beam has been demonstrated by using a spatially displaced helical axicon （HA）. The topological charge of the spiraling Bessel beams is determined by the order of the input Laguerre Gaussian （LG） beam and the topological charge of the HA. The obtained spiraling Bessel beams have an LG type of modulation along their propagation direction and exhibit annihilation-reconstruction properties. Theoretical analysis is presented, including that of the stability, propagation distance, topological charge, and spiraling dynamic characteristics. The mathematical and numerical results show that the propagation distance and helical revolution of the spiraling Bessel beams can be controlled through choosing appropriate radius of the HA.

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

Transversal reverse transformation of anomalous hollow beams in strongly isotropic nonlocal media

Based on the nonlocal nonlinear Schr6dinger equation, the propagation properties of anomalous hollow beams in strongly isotropic nonlocal media are investigated. The analytical expressions of the beam propagation, the on-axis intensity and the beam width are obt.ained. The results show that the evolution of the beam is periodical and the input power is the most important parameter. The input power determines the variation of the period. Furthermore, it is found that there exists a critical input power in the x direction and in the y direction separately when the initial beam widths in the two transversal directions are unequal. The beam width remains invariant in the corresponding transversal direction when the input power equals the critical power in one of the transversal directions. Selecting a properinput power, the beam can be broadened or compressed in the two transversal directions at the same time, In particular, the beam can be broadened （compressed） in one transversal direction, whereas in the other transversal direction, it is compressed （broadened）, i.e., the transversal reverse transformation.

Artificial boundary conditions for Euler–Bernoulli beam equation

In a semi-discretized Euler-Bernoulli beam equa- tion, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial boundary treat- ments. With the discrete equation regarded as an atomic lattice with a three-atom potential, two accurate artificial boundary conditions are first derived here. Reflection co- efficient and numerical tests illustrate the capability of the proposed methods. In particular, the time history treatment gives an exact boundary condition, yet with sensitivity to nu- merical implementations. The ALEX （almost EXact） bound- ary condition is numerically more effective.

Propagation properties of off-axis Hermite-cosh-Gaussian beam combinations through a first-order optical system

Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite-cosh-Gaussian （HChG） beam combinations with rectangular symmetry passing through a paraxial first-order optical system are derived, and corresponding numerical examples are given and analysed. The resulting beam quality is discussed in terms of power in the bucket （PIB）. The study suggests that the resulting beam cannot keep the initial intensity shape during the propagation and the beam quality for coherent mode is not always better than that for incoherent mode. Reviewing the numerical simulations of Gaussian, Hermite-Gaussian （HG） and cosh- Gaussian （ChG） beam combinations indicates that the Hermite polynomial exerts a chief influence on the irradiance profile of composite beam and far field power concentration.

M2-factor of high-power laser beams through a multi-apertured ABCD optical system

Based on the generalized truncated second-order moments,an approximate analytical formula of the beam propagation factor M^2 of high-power laser beams passing through the optical system with multiple hard-edged apertures is deduced.Numerical examples of the beams passing through an aperture-spatial filter are enclosed,and the influences of amplitude modulations(AMs)and phase fluctuations(PFs)on the beam propagation quality of high-power laser beams passing through the multi-apertured ABCD optical system are considered and discussed.It is shown that PFs are able to degrade the beam propagation quality of laser beams more than AMs when the high-power laser beams passing through the aperture-spatial filter,furthermore,one or two aperture-lens optical systems configured appropriate aperture parameters are both able to upgrade the beam propagation quality of high-power laser beams.The M2 factor of Gaussian beam passing through the multi-aperture optical system is a special case in this paper.

M^2 factor of four-petal Gaussian beam

Based on the second-order moments, this paper derives an analytical expression of the M^2 factor of four-petal Gaussian beam. The results show that the M^2 factor is only determined by the beam order n. The corresponding numerical calculations are also given. As the beam order increases, the augment of M^2 factor is disciplinary. As the expression of M^2 factor is expressed in series form and becomes more complicated, a new concise formula of M^2 factor is also presented by using curve fitting of numerical calculations. When 3 ≤ n ≤ 200, the maximum error rate of fitting formula will not exceed 2.6% and the average error rate is 0.28%. This research is helpful to the applications of four-petal Gaussian beam.

Hollow Gaussian beams in strongly nonlocal nonlinear media

The propagation of hollow Gaussian beams in strongly nonlocal nonlinear media is studied in detail. Two analytical expressions are derived. For hollow Gaussian beams, the intensity distribution always evolves periodically. However the second-order moment beam width can keep invariant during propagation if the input power is equal to the critical power. The interaction of two hollow Gaussian beams and the vortical hollow Gaussian beams are also discussed. The vortical hollow Gaussian beams with an appropriate topological charge can keep their shapes invariant during propagation.

Propagation of Partially Coherent Elegant Hermite-Cosh-Gaussian Beam in Non-Kolmogorov Turbulence

Based on the extended Huygens-Fresnel integral, analytical propagation expressions for the rms beam width and angular of partially coherent elegant Hermite cosh Caussian beam （EHChCB） in non-Kolmogorov turbulence are derived. The effects of exponent value, inner and outer scales of non-Kolmogorov turbulence on partially coherent EFIChGB are investigated quantitatively.

Semi-vectorial analysis of a compact wavelength demultiplexer based on the tapered multimode interference coupler

Based on a parabolically tapered multimode interference （MMI） coupler with a deep-etched SiO2/SiON rib waveguide, a compact wavelength demultiplexer operating at 1.30 and 1.55 μm wavelengths is proposed and analysed by using three-dimensional semi-vectorial finite-difference beam propagation method （3D-SV-FD-BPM）. The results show that a MMI section of 330.0 μm in length, which is only 76% length of a straight MMI coupler, is achieved with the contrasts of 42.3 and 39.2dB in quasi-TE mode, and 38.4 and 37.8dB in quasi-TM mode at wavelengths 1.30 and 1.55μm, respectively, and the insertion losses below 0.2dB at both wavelengths and in both polarization states, The alternating direction implicit algorithm with the Crank-Nicholson scheme is applied to the discretization of the 3D-SV-FD-BPM formulation along the longitudinal direction. Moreover, a modified FD scheme is constructed to approximate the resulting equations along the transverse directions, in which the discontinuities of the derivatives of magnetic field components Hy and Hx along the vertical and horizontal interfaces, respectively, are involved.

Theoretical investigation of band-gap and mode characteristics of anti-resonance guiding photonic crystal fibres

With the full-vector plane-wave method （FVPWM） and the full-vector beam propagation method （FVBPM）, the dependences of the band-gap and mode characteristics on material index and cladding structure parameter in anti- resonance guiding photonic crystal fibres （ARGPCFs） are sufficiently analysed. An ARGPCF operating in the near- infrared wavelength is shown. The influences of the high index cylinders, glass interstitial apexes and silica structure on the characteristics of band-gaps and modes are deeply investigated. The equivalent planar waveguide theory is used for analysing such an ARGPCF filled by the isotropic materials, and the resonance and the anti-resonance characteristics r：~n h~ w~｜] r^r~dlrtpd

Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length

A new polarization rotator based on the silica photonic crystal fiber is proposed. The proposed polarization rotator photonic crystal fiber （PR-PCF） possesses a triangle jigsaw-shape core region. The full-vector finite-element method is used to analyze the phenomenon of polarization conversion between the quasi-TE and quasi-TM modes. Numerical simulations show that the wavelengths of 1.31 μm and 1.55 μm are converted with a nearly 100% polarization conversion ratio with their matched coupling length and has a relatively strong realistic fabrication tolerance - 100 nm on the y axis and 50 nm on the x axis. The full vectorial finite difference beam propagation method is used to confirm the performance of the proposed PR-PCF.

Effect of interstitial air holes on Bragg gratings in photonic crystal fibre with a Ge-doped core

The effect of interstitial air holes on Bragg gratings in photonic crystal fibre （PCF） with a Ge-doped core is numerically investigated by using the beam propagation method （BPM）. It is shown that the interstitial air holes （IAHs） can make Bragg resonance wavelength λB shift a little towards short wavelengths and increase λB -λ1 （the wavelength spacing between the main peak with Bragg resonance wavelength λB and the first side peak with wavelength λ1） and the coupling coefficient κ of Bragg resonance. Moreover, when the ratio of air hole diameter （d） to pitch （∧）, d/∧, is small, IAHs can suppress the cladding mode resonance. When d/∧ is large, IAHs increase the number of mode that could strongly interact with the fundamental mode. By comparing the transmission spectral characteristics of PCF-based fibre Bragg grating （FBG） with IAHs with those without IAHs at the same air-filling fraction, it is clarified that the change of transmission spectral characteristics of PCF-based FBG with IAHs is not due to a simple change in air-filling fraction. It is also closely related to the distribution of interstitial air holes.

The Notched Filtering Characteristics of Stratified Volume Holographic Grating

Utilizing the tool of beam propagation method (BPM) to calculate the zeroth order diffraction beam intensity, we find SVHG displays notched diffraction response as a function of the readout wavelength. Using the method of SA and considering the variance of refractive index as the readout wavelength changes, a practiced notch filter can be designed and the period of the filter is discussed.

Design of novel three port optical gates scheme for the integration of large optical cavity electroabsorption modulators and evanescently-coupled photodiodes

This paper presents a novel scheme to monolithically integrate an evanescently-coupled uni-travelling carrier photodiode with a planar short multimode waveguide structure and a large optical cavity electroabsorption modulator based on a multimode waveguide structure. By simulation, both electroabsorption modulator and photodiode show excellent optical performances. The device can be fabricated with conventional photolithography, reactive ion etching, and chemical wet etching.

Elliptical Gaussian solitons in synthetic nonlocal nonliear media

This paper studies analytically and numerically the dynamics of two-dimensional elliptical Gaussian solitons in a ＂double-self-focusing＂ synthetic nonlocal media featuring elliptical and circular Gaussian response with different degrees of nonlocality. Based on the variational approach, it obtains the approximately analytical solution of such Gaussian elliptical solitons. It also computes the stability of the solitons by numerical simulations.

High-performance evanescently-coupled uni-traveling-carrier photodiodes

A new evanescently-coupled uni-traveling-carrier photodiode （EC-UTC PD） based on a multimode diluted waveguide （MDW） structure is fabricated, analysed and characterized. Optical and electrical characteristics of the device are investigated. The excellent characteristics are demonstrated such as a responsivity of 0.36 A/W, a bandwidth of 11.5 GHz and a small-signal 1-dB compression current greater than 18 mA at 10 GHz. The saturation current is significantly improved compared with those of similar evanescently-coupled pin photodiodes. The radio frequency （RF） bandwidth can be further improved by eliminating RF losses induced by the cables, the probe and the bias tee between the photodiode and the spectrum analyzer.

Three-dimensional beam propagation method based on the variable transformed Galerkin's method

A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.

Bessel–Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence

We model the effects of weak fluctuations on the probability densities and normalized powers of vortex models for the Bessel–Gauss photon beam with fractional topological charge in the paraxial non-Kolmogorov turbulence channel. We find that probability density of signal vortex models is a function of deviation from the center of the photon beam, and the farther away from the beam center it is, the smaller the probability density is. For fractional topological charge, the average probability densities of signal/crosstalk vortex modes oscillate along the beam radius except the half-integer order. As the beam waist of the photon source grows, the average probability density of signal and crosstalk vortex modes grow together. Moreover, the peak of the average probability density of crosstalk vortex modes shifts outward from the beam center as the beam waist gets larger. The results also show that the smaller index of non-Kolmogorov turbulence and the smaller generalized refractive-index structure parameter may lead to the higher average probability densities of signal vortex modes and lower average probability densities of crosstalk vortex modes. Lower-coherence radius or beam waist can give rise to less reduction of the normalized powers of the signal vortex modes, which is opposite to the normalized powers of crosstalk vortex modes.