Lineshape and polarization mode dispersion of waves diffracted by apodized and chirped fiber Bragg gratings in reflection

The amplitude and phase of a light wave propagating in an apodized and chirped Bragg grating is given by the superposition of two orthogonal coupled wave functions that are the solution of a non-linear Riccati equation. An analytical solution, in the form of an integral transform, that predicts the amplitude, phase, and intensity profile of the light diffracted by grating, in which the local Bragg wavelength is asymmetric, and the forward and counter propagating modes are non-degenerate is presented. For even apodization and odd chirp the lineshape has an asymmetrical Gaussian form the result of mixing of the real and imaginary components of the apodized grating wave function. The effect of chirping is to shift the resonance wavelength, increase the grating bandwidth and polarization mode dispersion. The dependence of linewidth and dispersion on parameters that alter apodization and chirp after fabrication, is also discussed.     

Line profile of the Q01(1) vibrational resonance in H2 in the zone of dicke narrowing

A new method of high resolution non-linear spectroscopy based on the detection of the anti-Stokes intensity arising from a resonant four-photon coherent interaction is applied to the determination of the line profile of the Raman resonance Q₀₁(1) in hydrogen gas. The real part as well as the imaginary part of the non-linear Raman susceptibility has been observed in a thermodynamical condition for the gas in which the Dicke narrowing process and the dephasing collision-broadening effect determine competitively the shape of the resonance line.     

The slope of the proton-proton scattering amplitude at t = 0

A dispersion relation for the slope of a crossing symmetric amplitude is derived and applied in pp scattering at high energies and at t = 0. The crossing symmetric amplitude is extracted from the pp amplitude with reasonable assumptions on the crossing antisymmetric part. It is found that the slope of the imaginary part is almost equal to the slope of the modulus. The derivative of the real part is much smaller than that of the imaginary part and shows a zero at NAL energies.     

Method for computing the intensity distribution in the image plane of an aberration-free lens with allowance for the wave properties of light

For the Gaussian model of a lens, a Green-function-based method is proposed to compute the intensity distribution in the lens image plane. The method is used to accomplish several test tasks, which include the simulation of the image of a square area, the diffraction by an infinitely long slit, the focusing of a convergent wave with a Gaussian amplitude profile in the focal waist region, and the image of a surface representing an analog of a diffraction grating. After a suitable modification, the method can serve for simulating the propagation of light waves within a real lens and for solving other applied problems.     

Electric-field-controlled two-dimensional Raman-Nath diffraction from paraelectric potassium lithium tantalate niobate

Electric-field-controlled two-dimensional Raman-Nath diffraction has been realized using a photorefractive diffraction grating. The grating was produced by two-wave coupling (at a wavelength of 632.8 nm) at small incidence angles using a potassium lithium tantalate niobate single crystal. Results for the Raman-Nath diffraction from the g₄₄ grating are presented, in which the externally applied field is perpendicular to both the grating vector and the wave vector of the incident beam. Two pairs of coherent beams were used to record the grating for two-dimensional Raman-Nath diffraction. The wave vector and the polarization of one pair lay in the (x, z) plane, and those of the other pair lay in the (y, z) plane. The influence of the applied electric field was studied, and the results show that the intensity of the Raman-Nath diffraction could be controlled by the direction and intensity of the applied field.     

Effect of absorption on light scattering by agglomerated debris particles

We study the influence of material absorption on light scattering by agglomerated debris particles whose sizes are comparable with the wavelength. We find that the angular profile of linear polarization is extremely sensitive to the imaginary part of refractive index, and there are some unique features that may assist in the retrieval of physical properties of particles using remote-sensing techniques. Most notably, the position of the positive polarization maximum α_max changes monotonically with the imaginary part of refractive index, allowing it to be used to characterize this property. In addition, the amplitude of the negative polarization branch (NPB) is significantly greater for dielectric particles than for non-dielectric particles. It disappears in the transition region between dielectric and conducting particles before reappearing as the imaginary part of the refractive index is increased further. Further increasing the imaginary part of the refractive index may see the NPB disappearing and reappearing in quasi-periodic fashion. This recurrent NPB has a much smaller amplitude than that of dielectric particles. This suggests that the cometary circumnuclear haloes, which have significant NPBs, cannot contain significant quantities of absorbing particles. In addition, combined observations suggest that the polarization maximum of circumnuclear haloes are relatively small P_max～12%, and occur at relatively small phase angles α_max～60°, which is also consistent with dielectric particles.     

Effects of cross-correlation between the real and imaginary parts of the quantum noise in a two-mode saturation laser system

A two-mode saturation laser model with cross-correlation between the real and imaginary parts of the quantum noise is considered. The laser intensity Langevin equation and corresponding Fokker-Planck equation are derived by the phase-locking method. The effects of the cross-correlation strength λ between the real and imaginary parts of quantum noise and the cavity decay constant K on the steady-state intensity distribution Q(I₁,I₂), the mean light intensity 〈I〉, the normalization autocorrelation λ₁₁(0) and cross correlation λ₁₂(0) are studied by numerical calculation. The results show that as λ increases the Qs(I₁,I₂) show two extrema, and λ almost does not affect the 〈I〉, λ₁₁(0) and λ₁₂(0) when the laser system is operated far above threshold. Nevertheless, when the laser system is operated at and below threshold, λ makes the curves of Qs(I₁,I₂) have the higher peak and drop faster. Furthermore, it enhances the deviation of λ₁₁(0) and λ₁₂(0) and lessens the mean light intensity 〈I〉 when the laser system is operated at and below threshold.     

An application of dispersion relations to Kaon-nucleon scattering

In this paper we have made predictions for the invariant KN and $\text{K}$N scattering amplitudes in the kinematical region q_lab < 15 GeV/c and 0 >; t > -0.7 (GeV/c)².We have performed a direct fit to medium and high-energy data using a parametrization where the imaginary part of the amplitudes for energies above the phase-shift region is identical with the imaginary part of a Regge-pole amplitude, and the real part of the amplitudes has been obtained from a dispersion relation.The s-channel helicity amplitudes are compared with their counterparts in pion-nucleon scattering and other reactions. Exact exchange degeneracy can not be verified.Also the real part of the amplitudes are compared with the real part of phase-shift solutions. There is a qualitative agreement between these two real parts even though they differ in detail.     

Single Folding Optical Potential for Elastic Scattering of Protons from <Superscript>14</Superscript>N and <Superscript>16</Superscript>O in a Wide Range of Energies

Available experimental data for protons elastically scattered from ¹⁴N and ¹⁶O target nuclei are reanalyzed within the framework of single folding optical potential (SFOP) model. In this model, the real part of the potential is derived on the basis of single folding potential. The renormalization factor N _r is extracted for the two aforementioned nuclear systems. Theoretical calculations fairly reproduce the experimental data in the whole angular range. Energy dependence of real and imaginary volume integrals as well as reaction cross sections are discussed.     

The optical potential for vector-polarized deuterons of 52 MeV

The vector analysing power for elastic scattering of 52 MeV polarized deuterons was measured for ¹²C, ¹⁶O, ²⁰Ne, ²⁸Si, ³²S, ⁴⁰Ar, ⁵⁸Ni, ⁹⁰Zr and ¹⁹⁷Au. The data were analysed together with previously measured differential cross sections in the framework of the optical model. Best-fit and average optical-model parameters were obtained both for surface and volume absorption. Fits with surface absorption are superior to those with volume absorption, especially for heavier nuclei. Typical parameters of the spin-orbit part of the best-fit optical potentials are found to be V_s.o. ～- 5.5 MeV, r_s.o. ～- 1.15 fm and a_s.o. ～- 0.4 fm, and there is no evidence for an imaginary component. The volume integrals and rms radii of real, imaginary and l · s potentials show a smooth mass dependence and differ insignificantly for different sets of potentials.     

Stochastic resonance in a gain--noise model of a single-mode laser driven by pump noise and quantum noise with cross-correlation between real and imaginary parts under direct signal modulation

Stochastic resonance (SR) is studied in a gain--noise model of a single-mode laser driven by a coloured pump noise and a quantum noise with cross-correlation between real and imaginary parts under a direct signal modulation. By using a linear approximation method, we find that the SR appears during the variation of signal-to-noise ratio (SNR) separately with the pump noise self-correlation time \tau , the noise correlation coefficient between the real part and the imaginary part of the quantum noise \lambda_q , the attenuation coefficient \gamma and the deterministic steady-state intensity I_0 . In addition, it is found that the SR can be characterized not only by the dependence of SNR on the noise variables of \tau and \lambda_q, but also by the dependence of SNR on the laser system variables of \gamma and I₀. Thus our investigation extends the characteristic quantity of SR proposed before.     

Improved performance of complex gain-coupled DFB laser by using tapered grating structure

In this paper, theoretical analysis of antireflection complex gain coupled distributed feedback lasers (CGC-DFB) with tapered grating structure has been presented. Two types of gratings, convex and concave tapered grating with longitudinal variable depth, in active layer have been proposed. Evaluation of flatness parameter variation above threshold condition shows that concave tapered grating improves the stability of CGC-DFB laser against spatial hole burning (SHB) effect. The dependencies of output power, side mode suppression ratio (SMSR) and oscillation wavelength of CGC-DFB laser on convex and concave grating parameters have been studied. Both convex and concave tapered grating CGC-DFB structures have higher output power than conventional CGC-DFB lasers with uniform grating. It is found that, concave tapered grating structure with parameters p ₀?=?15?nm and a ₀?=?0.7 nm has minimum flatness parameter, stable lasing wavelength and flat SMSR profile as a function of current. Theoretical calculation model is based on the numerical solution of coupled wave equations and carrier rate equation by using transfer matrix method. In numerical calculation SHB effect has been assumed.     

Strain profile reconstruction of fiber Bragg grating with gradient using chaos genetic algorithm and modified transfer matrix formulation

In this paper, a new heuristic approach based on chaos genetic algorithm and modified transfer matrix method is presented to demodulate the fiber Bragg grating strain sensors. To facilitate accurate calculation of the grating reflected intensity spectrum, the modified transfer matrix approach is applied. The motivation for using the spline smooth function scheme is to provide nice approximation of strain profiles from a scattered data set and overcome the difficulty of calculating the strain gradients in local period function of the modified T-matrix formulation for the piecewise constant strain field assumption. The chaos genetic algorithm is developed to improve the performance of GA and optimize the data of control nodes of the spline smooth function, and more valuably, the reconstructed strain profile is continuous with discretionary spatial resolution. The proposed method is verified through numerical example reconstructions of Bragg grating sensor simulated strain profile cases.     

High energy pion photoproduction amplitudes from fixed-t dispersion relations and duality

Contributions to the high energy imaginary parts of the charged and neutral pion photoproduction amplitudes from degenerate ? and A₂ exchanges and ω and B exchanges are parametrized similarly to the dual absorptive model. These contributions together with the imaginary parts of the amplitudes found at low energies from partial-wave analyses are then used to evaluate the high energy real parts of the photoproduction amplitudes from fixed-t dispersion relations. A fit is made to data on pion photoproduction at 3.4 and 16 GeV incident photon energies, for momentum transfers up to ?1(GeV/c)². It is shown that much of the data is reproduced both qualitatively and quantitatively by our model. The high energy imaginary parts of the photoproduction amplitudes given by the fit are shown to be in accord with their average low energy behaviour.     

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions ¹⁶O on nuclei at an energy of E ～ 100 MeV per nucleon.     

Phase shift analysis of pion-4He scattering by optimal polynomial expansion

A novel method of phase shift analysis for the scattering of charged pion from⁴He nuclei is proposed. The nuclear amplitudef _N (ϑ) has been parametrized in terms of a polynomial expansion in a conformally mapped variable, which is obtained by optimally exploiting the analytic property off _N . The method exhibits a significant reduction in the number of free parameters required for the fixed energy phase shift analysis of the differential cross-section data. The nuclear amplitude thus constructed is then used to obtain phase shifts and inelastic parameters of all possible orders. Reliable values of the real and imaginary parts of the forward amplitude are also obtained.     

Optical testing of ultrasonic phase gratings using a Fresnel diffraction method

A simple optical method is proposed for studying the Raman-Nath parameter of plane, sinusoidal, ultrasonic beams. The Fresnel diffraction field of a continuous ultrasonic grating illuminated by a collimated laser beam is measured by a photodetector placed mid-way between the self-image planes of the grating. Measurement of the amplitude of the fundamental of the output signal enables the absolute determination of the depth of phase modulation. A comparison of the proposed method with the techniques discussed in the literature is presented.     

Asymptotics and zeros of the imaginary part of the elastic scattering amplitude

The s-channel unitarity condition for the imaginary part of the hadronic elastic scattering amplitude outside the diffraction peak is studied within different assumptions about the behavior of its real part. The integral equation for the imaginary part is derived with the asymptotical expression for the real part inserted in the unitarity condition. The conclusions about the asymptotical approach to the black disk limit and possible zeros of the imaginary part of the amplitude are obtained. Their relation to the present day experiments is discussed.