Transformation of pulsed nonideal beams in a four-dimension domain

Spatio-temporal coupling of random electromagnetic pulses interacting with reflecting gratings

Matrix optics is applied to a class of random, in time and space, electromagnetic pulsed beam-like (REMPB) radiation interacting with linear optical elements. A 6×6 order matrix describing transformation of a six-dimensional state vector including four spatial and two temporal positions within the field is used to derive conditions for spatio-temporal coupling. An example is included which deals with a spatio-temporal coupling in a typical REMPB on reflection from a reflecting grating. Electromagnetic nature of such interaction is explored via considering dependence of the degree of polarization of the reflected REMPB on its source and on the structure of the grating.

Chirped-pulse amplification with narrowband pulses

We demonstrate a compact hyperdispersion stretcher and compressor pair that permit chirped-pulse amplification in Nd:YAG. We generate 750 mJ, 0.2 nm FWHM, 10 Hz pulses recompressed to an 8 ps near-transform-limited duration. The dispersion-matched pulse compressor and stretcher impart a chirp of 7300 ps/nm, in a 3 m x 1 m footprint.

Propagation of partially coherent pulsed beams in the spatiotemporal domain

A generalized model to describe the spatiotemporal partially coherent pulsed beams is presented. The corresponding propagation formula is derived by using the partially coherent light theory. Based on this formula, we obtain a nonstationary generalized ABCD law (which illustrates the transformation of optical beams or pulses passing through media) to describe the spatiotemporal behavior of partially coherent Gaussian pulsed beams. The physical meaning of such generalized pulsed beams is discussed. An example to illustrate the application of this law is given.

Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams

A 4 x 4 complex curvature tensor M>(-1) is introduced to describe partially coherent anisotropic Gaussian-Schell model (GSM) beams. An analytical propagation formula for the cross-spectral density of partially coherent anisotropic GSM beams is derived. The propagation law of M(-1) that is also derived may be called partially coherent tensor ABCD law. The analytical formulas presented here are useful in treating the propagation and transformation of partially coherent anisotropic GSM beams, which include previous results for completely coherent Gaussian beams as special cases.

Propagation of polychromatic Gaussian beams through thin lenses

The transformation by a lens of a polychromatic laser beam composed of on-axis superposed monochromatic TEM00 Gaussian modes in the paraxial approximation is studied. The chromatic aberrations are described by allowing the waist position on the z axis and the Rayleigh range to depend on wavelength. The beam radius, the far-field divergence, the Rayleigh range, the beam product, the beam propagation factor, and the kurtosis parameter are calculated. The relationship between the fourth-order and the second-order moments of Hermite-Gaussian and Laguerre-Gaussian modes is obtained and is used for calculating kurtosis parameter. The results are generalized to polychromatic modes of higher orders. It is shown that the on-axis superposition of monochromatic TEM00 modes with no chromatic aberration is leptokurtic.

Universal invariants of quantum-mechanical and optical systems

We give a brief review of the theory of quantum and optical universal invariants, i.e., certain combinations of the second- and higher-order moments (variances) of quantum-mechanical operators or the transverse phase-space coordinates of optical paraxial beams that are preserved in time (or along the axis of the beam) independently of the concrete form of the coefficients of the Hamiltonian or the parameters of the optical system, provided that the effective Hamiltonian is either a generic quadratic form of the generalized coordinate-momenta operators or a linear combination of generators of certain finite-dimensional algebras. Using the phase-space representation of quantum mechanics (paraxial optics) in terms of the Wigner function, we elucidate the relation between the quantum invariants and the classical universal integral invariants of Poincaré and Cartan. The specific features of the Gaussian beams are discussed as examples.

Diffraction integral formulas of the pulsed wave field in the temporal domain

To resolve the diffraction problems of the pulsed wave field directly in the temporal domain, we extend the Rayleigh diffraction integrals to the temporal domain and then discuss the approximation condition of this diffraction formula.