Edward B. Rockower

Statistics of the Stokes parameters for gaussian distributed fields

Abstract We present a statistical characterization of the Stokes parameters S j (through their first-order cumulants and probability density functions) for a set of partially polarized, quasi-monochromatic plane waves which is gaussian distributed. The coherency matrix formalism along with the geometric interpretation of the Stokes parameters provide guidance for these analytical calculations. Among many results, it is found that, except for totally unpolarized light, the probability density functions of S j ( j =1, 2, 3) are not generally symmetric around their means.

Integral identities for random variables

Abstract Using a general method for deriving identities for random variables, we find a number of new results involving characteristic functions and generating functions. The method is simply to promote a parameter in an integral relation to the status of a random variable and then take expected values of both sides of the equation. Results include formulas for calculating the characteristic functions for x 2, √x, 1/x, x 2 + x, R 2 = x 2 + y 2, and so forth in terms of integral transforms of the characteristic functions for x and (x, y), and so forth. Generalizations to higher dimensions can be obtained using the same method. Expressions for inverse/fractional moments, E{n!}, and so forth are also presented, demonstrating the method.

Lasers in materials processing

We analyze the general requirements for an economically viable laser materials-processing application. Laser light is not only expensive relative to other forms of energy but at ∼

Quantum derivation of K-distributed noise for finite (N)

10/kg of product for laser processing costs (corresponding to one 2 eV photon per product molecule) it is expensive relative to most bulk chemicals. We identify four criteria for a successful application that allows efficient utilization of this costly source of energy. In reviewing the status of uranium laser isotope separation (LIS) at the Lawrence Livermore National Laboratories (LLNL), we show how this program satisfies our criteria.

Laser beam-quality/aperture-shape scaling relation

Semiclassical derivations of the fluctuations of light beams have relied on limiting procedures in which the average number, 〈N〉, of scattering elements, photons, or superposed wave packets approaches infinity. We show that the fluctuations of thermal light having a Bose–Einstein photon distribution and of light with an amplitude distribution based on the modified Bessel functions, Kα−1, which has been found useful in describing light scattered from or through turbulent media, may be derived with a quantum-mechanical analysis as the superposition of a random number, N, of single-photon eigenstates with finite 〈N〉. The analysis also provides the P representation for K-distributed noise. Generalizations of K noise are proposed. The factor-of-2 increase in the photon-number second factorial moment related to photon clumping in the Hanbury Brown–Twiss effect for thermal (Gaussian) fields is shown to arise generally in these random superposition models, even for non-Gaussian fields.

Intensity Fluctuations of Amplified Spontaneous Emission in Bidirectional Laser Amplifiers

Many high-energy lasers (HELs) have noncircular output apertures. Some are rectangular in shape with or without a central or noncentral (up to 30%) obscuration. However, most high-energy laser propagation codes (especially those developed for systems analysis) model the aperture as either an unobscured circle or as a circle with fixed (e.g., 10%) obscuration. We present a beam-quality/aperture-shape scaling relation which can be useful when applying these codes to realistic designs for HELs. Our analysis also yields a generalized formula for angular size of the Airy disk and definitions of a characteristic aperture length and aperture quality.

Self‐similarity and long‐tailed distributions in the generation of thermal light

Intensity fluctuations of amplified spontaneous emission (ASE) in a bidirectional laser amplifier are analysed using a noise amplifier rate equation model. In contrast to the unidirectional case, in which saturation leads to laser-like intensity statistics, we have found that the saturation, as the mechanism for coupling between the counter-propagating beams, in general leads to a non-zero asymptotic value for the intensity fluctuations. For a symmetric amplifier the normalized variance of the output intensity fluctuations declines with increasing amplifier length from the initial value of unity to a limiting value of approximately 0·277. In contrast, when the noise sources of the two counter-propagating beams have unequal mean intensities, the normalized variance of the stronger beam declines more rapidly with length to less than 0·277 while for the weaker beam it reaches a limiting value greater than 0·277. We also find that there are features of the mode competition which are closely related to those o...

Intensity Fluctuations in a Two-mode Ring Laser

Two counterintuitive phenomena are studied. (1) It is well known that a thermal electromagnetic field has a Bose–Einstein (geometric) distribution of photons within a coherence volume. This arises because of the photon clumping characteristic of a thermal Boson field. On the other hand, the distribution of the number of atoms emitting photons through spontaneous emission must be Poisson if emissions are truly independent. (2) The average time between atomic decays is finite, being just the inverse of the total decay rate of the atoms. However, it is shown that in a coherence volume or in a single mode of the resulting Gaussian electromagnetic field, the average photon interarrival time is infinite. Hence, on average, an infinite length of time must pass before 〈N〉 photons arrive in the field. These apparent paradoxes are discussed, showing how both arise from random interference of Boson fields. The infinite waiting time is seen to be one manifestation of a long‐tailed distribution. Such distributions are...

A relativistic mass tensor with geometric interpretation

Intensity fluctuations in a two-mode ring laser with zero detuning are derived using a noise amplification rate-equation model. Both approximate and exact forms of the gain saturation are treated. Steady-state distributions of the intensity are derived analytically permitting calculation of the mean and normalized variance. Numerical solutions yield the time-dependent evolution of these quantities from initial input noise. Recently derived mode competition effects, such as a steady state value of } for the normalized variance (rather than zero as in a conventional laser) and negative correlations between the intensity fluctuations of the two modes, appear more simply here and their statistical origin is explained.

Evolution of the quantum statistics of light

We derive a relativistic mass tensor (dyadic or matrix) whose origin and properties have a direct geometric interpretation in terms of projection operators related to the particle’s world line and local inertial frame in Minkowski space, yet whose eigenvalues are simply the longitudinal (ml) and the transverse (mt) mass. Writing the noncovariant equations of motion (EOM) for a point particle in terms of this mass tensor bridges the gap between the compact but sterile form of the Lorentz covariant EOM and the usual (‘‘unwieldy’’) noncovariant EOM in which ml and mt appear. General expressions for 3‐ and 4‐space mass (inverse mass) tensors are presented in terms of the system Lagrangian (Hamiltonian).