Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to...
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Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution from the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.
Diffraction-scattering calculations for perturbed optical cavity resonators and their relation to optical cavity decay-time measurements are discussed.
Diffraction-scattering calculations for perturbed optical cavity resonators and their relation to optical cavity decay-time measurements are discussed.
A method is reported for bringing about more rapid and complete convergence of the equations that implement the minimum-negativity constraint. The method utilizes an improved spatial function constructed by leaving th...
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A method is reported for bringing about more rapid and complete convergence of the equations that implement the minimum-negativity constraint. The method utilizes an improved spatial function constructed by leaving the negative values intact and replacing the positive values with the differences between their values for the present and previous iteration. (This difference is found to converge after several iterations.) The advantage of this new spatial function is that convergence may be obtained for recalcitrant data using fast approximate procedures requiring the FFT. Several improvements were made in restoring inverse-filtered data. One is to impose an upper bound constraint (in the form of a tapered window) on the Fourier spectrum most degraded by noise and other errors. This provides stability, and the window can be used on the starting estimate and all succeeding iterations. Errors in the low frequency spectrum (below the cutoff radius) are determined and corrected by a slight modification of the restoration procedure described in this paper. Results are shown for simulated CO2 interferograms, experimental interferometer data, and experimental IRAS data.
Stimulated-emission pumping spectra were recorded for many pure bending levels [(0, 2, 0)–(0, 34, 0)] and bend–symmetric-stretch combination levels [(1, 0, 0)–(1, 8, 0) and (3, 4, 0)–(3, 8, 0)] in the X ˜ 1 Σ g ...
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Stimulated-emission pumping spectra were recorded for many pure bending levels [(0, 2, 0)–(0, 34, 0)] and bend–symmetric-stretch combination levels [(1, 0, 0)–(1, 8, 0) and (3, 4, 0)–(3, 8, 0)] in the X ˜ 1 Σ g + state of C 3 following excitation of transitions in the A ˜ 1 Π u − X ˜ 1 Σ g + band system. Rotational levels to J = 16 were probed and, because of strong mixing of vibrational angular momentum components, levels with l up to 8 were observed. A rotational analysis was carried out by means of a simple rigid-rotor harmonic-oscillator model for a linear molecule. An adequate fit was obtained, showing that all these vibrational levels could be described by a linear average geometry even though the bending vibration is known to be of extremely large amplitude. B υ was found to increase strongly with υ 2 and to decrease with excitation in ν 1 . Interpretation of the physical meaning of the resulting parameters is difficult, however, since the vibrational potential is not well described by a harmonic oscillator.
We present a many-electron, many-photon (MEMP) nonperturbative theory of nonlinear static and dynamic polarizabilities of polyelectronic atoms and molecules. The time-dependent, dynamic polarization is treated as a fr...
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We present a many-electron, many-photon (MEMP) nonperturbative theory of nonlinear static and dynamic polarizabilities of polyelectronic atoms and molecules. The time-dependent, dynamic polarization is treated as a frequency-dependent problem with the Floquet assumption that the computed quantities are averaged over a cycle. The MEMP theory defines a non-Hermitian problem whose efficient solution yields a complex eigenvalue to all orders in the interelectronic and the electron ac or dc field interactions. When the real part is subtracted from the unperturbed energy of the free state, we are left with the frequency-dependent total energy shift Δ(ω). This is then fitted to a polynomial expansion whose coefficients are the required polarizabilities representing the induced polarization averaged over a cycle. Results are given for the α, α(ω), and ϒ, ϒ(ω) of H and of Li−. For Li−, only α had been computed earlier by many-electron approaches. The dynamic α(ω) was computed before in a quasi-classical approximation with a simple wave function. Comparison shows a qualitative agreement but not a quantitative one.
Coherent states and a newly developed form of the density operator are used to relate the third-order susceptibility to the first-order susceptibility. The theoretical result is shown to be in fair agreement with the ...
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The standard method of matching boundary conditions at the interfaces of a multilayer plane dielectric stack is shown to be numerically unstable for the evanescent orders when a large number of layers is present. For ...
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The standard method of matching boundary conditions at the interfaces of a multilayer plane dielectric stack is shown to be numerically unstable for the evanescent orders when a large number of layers is present. For an isolated dielectric stack with an incident propagating beam there is no need to calculate the evanescent orders; however, when a diffraction grating is buried under the stack there is mixing of orders, and it may be important to calculate the evanescent as well as the propagating orders. It is shown that the impedance formalism removes the numerical instability completely. This method may be coupled to either boundary integral or differential equation methods for the grating to provide the complete solution for the grating-stack system.
We compare the vector finite element, scalar finite element, and effective refractive index methods for the calculation of the modal properties of active rectangular waveguide couplers. We find that the scalar finite ...
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We compare the vector finite element, scalar finite element, and effective refractive index methods for the calculation of the modal properties of active rectangular waveguide couplers. We find that the scalar finite element method is highly reliable when the refractive index difference between the core and the cladding is <15% and/or for large aspect ratios. We also find that the effective refractive index method is particularly difficult to use in treating active waveguides.
We consider quantized motion of neutral atoms cooled below the recoil limit in a quadrupole magnetostatic trap. Because of Majorana transitions to untrapped levels near the point of zero field at the trap center, all ...
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We consider quantized motion of neutral atoms cooled below the recoil limit in a quadrupole magnetostatic trap. Because of Majorana transitions to untrapped levels near the point of zero field at the trap center, all quantum levels have a nonzero decay rate. The Schrödinger equation associated with the potential gμ B · S ( S is the total atomic spin) takes the form of coupled equations in r when the spinor components are expanded in spherical harmonics. We integrate the multichannel problem numerically to obtain asymptotic phase shifts, resonance energies, and widths. For S = 1/2, the lowest levels have widths somewhat less than their spacing. Thus the trap quantum-level structure might possibly be observable if the atoms are sufficiently cold, namely, in the 0.1- μ K regime for most atoms and attainable trap field gradients. The width decreases rapidly with increasing M J , the angular momentum about the symmetry axis. Spectroscopic linewidths of a few hertz are possible if there is enough population in the lowest levels with a few M J quanta. The decay rate of the lowest levels, however, is probably too rapid for studying Bose–Einstein condensation in such a trap.
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