Surface sum-frequency generation from chiral medium by elliptically polarized light beyond plane-wave approximation and coplanar geometry of incidence

2022 ◽  
Author(s):  
Kirill Grigoriev ◽  
Vladimir Makarov
Keyword(s):  
Nonlinear Response ◽  
Order Approximation ◽  
Polarized Light ◽  
Surface Heterogeneity ◽  
Chiral Medium ◽  
Near Surface ◽  
Sum Frequency ◽  
Arbitrary Amplitude ◽  
First Order Approximation ◽  
Light Beams

Abstract Aiming to study the nonlinear response of the surface of isotropic chiral medium, we obtained analytical expression relating the transverse amplitudes of the spatial Fourier-spectra of two incident arbitrary polarized fundamental beams and one signal reflected beam at the sum-frequency within the first-order approximation by their divergence angles. The calculations, carried out in paraxial approximation, simultaneously take into account the spatial dispersion of the bulk of the medium, its near-surface heterogeneity and the transverse finiteness of the three interacting light beams with arbitrary amplitude profiles and orientation in space. A special compact form for the final formulas was found, which makes use of effective nonlinear transformation tensors, the components of which are solely determined by the geometry of incidence of the beams and the material constants of the medium. A possibility of ``switching off'' the certain mechanisms of nonlinear response by choosing the specific polarization states of the incident beams is discussed.

SURVEILLANCE, TRACKING, AND MODEL CORRELATION OF THE SPILL FROM THE TANKER BURMAH AGATE

1981 ◽  
Vol 1981 (1) ◽  
pp. 147-152
Author(s):  
Frank J. Kelly ◽  
Roy W. Hann ◽  
Harry N. Young
Keyword(s):  
Order Approximation ◽  
Meteorological Data ◽  
Department Of Energy ◽  
Disposal Site ◽  
San Jose ◽  
Near Surface ◽  
Oil Transport ◽  
Strategic Petroleum Reserve ◽  
First Order Approximation ◽  
Model Correlation

ABSTRACT The trajectory of the oil spilled from the tanker Burmah Agate passed through the extensively instrumented area of the U.S. Department of Energy Strategic Petroleum Reserve Brine Disposal Site off Freeport, Texas. Because of the potential impact of the spill on the 3-year baseline study, a major effort was made to monitor the slick movement, obtain samples, and collect and process oceanographic and meteorological data. Daily reconnaissance flights were made by the authors to obtain VOR position fixes of oil patches and document them with 35mm and color video cameras. The orientation, centroid position, and velocity of the initial impulse of oil from the collision, which was tracked as far as San Jose Island, Texas, have been computed for the first 9 days. These results, as well as daily summaries are presented. Continuous measurements of near-surface currents at locations 6.5 and 11.5 nautical miles off Freeport, Texas and wind velocity at the 6.5-nautical mile location were also recorded, which provide a unique opportunity to correlate the oil movement with the traditional first-order approximation for oil transport. Good agreement between actual and predicted movements is found for the longshore component of motion, whereas the cross-shelf movement is not well predicted. The presence of a weak frontal zone in the coastal waters is suggested as a possible complicating factor.

Improved first-order approximation of eigenvalues and eigenvectors

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1721-1727
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane ◽  
Robin S. Langley
Keyword(s):  
Order Approximation ◽  
Eigenvalues And Eigenvectors ◽  
First Order ◽  
First Order Approximation

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

FIRST-ORDER APPROXIMATION OF THE NUMBER-PROJECTED SO(2N) TAMM-DANCOFF EQUATION AND ITS REDUCTION BY THE SCHUR FUNCTION

1999 ◽  
Vol 08 (05) ◽  
pp. 461-483
Author(s):  
SEIYA NISHIYAMA
Keyword(s):  
Wave Function ◽  
Order Approximation ◽  
Approximate Equation ◽  
Variation Principle ◽  
Schur Function ◽  
Soliton Theory ◽  
First Order ◽  
Fermion Systems ◽  
Group Manifold ◽  
First Order Approximation

First-order approximation of the number-projected (NP) SO(2N) Tamm-Dancoff (TD) equation is developed to describe ground and excited states of superconducting fermion systems. We start from an NP Hartree-Bogoliubov (HB) wave function. The NP SO(2N) TD expansion is generated by quasi-particle pair excitations from the degenerate geminals in the number-projected HB wave function. The Schrödinger equation is cast into the NP SO(2N) TD equation by the variation principle. We approximate it up to first order. This approximate equation is reduced to a simpler form by the Schur function of group characters which has a close connection with the soliton theory on the group manifold.

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