Momentum transfer from a laser-supported detonation wave to a solid target has been studied by means of a time-dependent, two-dimensional, two-temperature Lagrangian hydrodynamics code. Its dependence on laser pulse length has been calculated and pulse length conditions obtained for optimizing impulse transfer to a target of finite area embedded in a larger plane surface, taking into account the laser coupling efficiency. Computer solutions are compared with existing analytical models for laser-induced surface pressures and impulse, and a summary is given of the pulse time regime of applicability of blast-wave models proposed by previous investigators. Scaling laws are given for optimized pulses that predict the laser parameters required to deliver a given impulse to a target of given area in an atmosphere of given density.

Conditions which seed the self focussing of high-power broadband laser beams are determined by examining growth rates for plane-wave perturbations on a strong pump field as a function of frequency and angle. Measurements verifying predictions of growth based on the linearized stability analysis of Bespalov and Talanov extended to broadband fields are reported.

We demonstrate accurate modeling of ultrawide-angle beam propagation in homogeneous media by Lanczos orthogonalization for acceptable longitudinal step sizes. Accuracy is determined by comparison with solutions to the Helmholtz equation obtained by a band-limited Fourier series method.

A propagation scheme for solving the scalar Helmholtz wave equation, based on matrix diagonalization in a low-dimensional Lanczos space has been previously proposed.1 We review the scheme briefly here.

The numerical scheme for solving the Helmholtz equation, based on the Lanczos orthogonalization scheme, is generalized so that it can be applied to media with space-dependent absorption or gain profiles.

The solution of the Helmholtz equation requires the application of an exponentiated square root operator to an initial field. This operation is greatly facilitated by the introduction of a representation in which the above-mentioned operator is diagonal. The Lanczos method permits this diagonalization to be performed in a low-dimensional space and the propagation to be carried out to arbitrary order. An iteration scheme to be carried out in conjunction with the Lanczos method is also described. This scheme permits, in principle, the bound mode of a monomode waveguide to be calculated to machine accuracy. Results for some well-known test examples of rib waveguides are presented.

The Lanczos recursion algorithm is used to determine forward-propagating solutions for both the paraxial and Helmholtz wave equations for longitudinally invariant refractive indices. By eigenvalue analysis it is demonstrated that the method gives extremely accurate solutions to both equations.

The solution of the paraxial wave equation by means of the split-operator fast-Fourier transform method, also known as the beam-propagation method (BPM), is now a firmly established approach for solving a variety of integrated-optics problems. One shortcoming of the paraxial equation is, however, that it is restricted to slowly varying index profiles. This means that application of the method to rib waveguide devices, which are characterized by large refractive-index discontinuities, will in general not be accurate. We need instead to apply the full Helmholtz equation, which after extraction of a carrier wave can be expressed as To generate the solution to this equation by marching requires application of a square root operator at each propagation step. 1

The solution of the Helmholtz wave equation requires the application of an exponentiated square root operator to an initial field. This operation is greatly facilitated by the introduction of a representation in which the aforementioned operator is diagonal. The Lanczos method allows this diagonalization to be performed in a low dimensional space, e.g., of the order of 4-6, if one is interested in advancing the field over a limited propagation step of length Az. Although some boundary conditions may be ill-posed for the unapproximated Helmholtz equation, in the sense that certain plane wave components cannot propagate in the forward direction, the Lanczos method damps all of these components exponentially, thus guaranteeing the correctness of the solution.

Employing a time-dependent model with counterpropagating beams and saturable gain, we calculate the degree of coherence for a range of x-ray lasers. From these results we infer a scaling law that can be used to estimate the degree of coherence of a general class of x-ray lasers.

The property of coherence is important for many suggested applications of x-ray lasers. For x-ray holography, the longitudinal coherence length is required to be larger than the pathlength difference between the object beam and the reference beam, estimated to be about 5 µm in a Fourier transform holography system. The longitudinal coherence length is related to the line width by Lℓ = λ2/Δλ, where λ is the laser wavelength. Using the thermal Doppler width for an estimate we get Lℓ = 37 µm for a 45Å laser. This estimate is supported by a measurement at 206Å. We therefore expect that longitudinal coherence will not be a problem. The transverse coherence length must be larger than the extent of the sample, typically ≈ 10 µm, and a certain amount of energy must irradiate the sample in order provide a high signal to noise hologram. The coherence length is obtainable straightforwardly by placing a pinhole in front of the laser, or by placing the object far from the laser. The combined requirement of energy and coherence is, however, much more difficult, requiring efficient production of coherent radiation.

We describe a time-dependent wave-optics propagation model applicable to laboratory x-ray lasers and amplified spontaneous emission devices described in the literature. The model embodies a stochastic treatment of spontaneous emission, counterpropagating beams, diffraction, gain saturation, transverse variation of gain, and refractive effects due to electron density gradients. The model has been used to describe the output beam characteristics and spatial coherence properties of some plausible lasers.

Many of the projected applications of x-ray lasers require high quality output radiation with properties such as short wavelength, high power, good focusability, short pulse, and a high degree of coherence. We discuss the requirements of an x-ray laser for the application of holography of biological samples. We present ideas for achieving these properties. Given that population inversions can be established to provide laser gain, we discuss how the propagation and amplification of x-rays within the lasing medium affect the quality of the output radiation. Particular attention is given towards the development of transverse coherence. Results are presented from several methods for calculating the coherence, including a modal analysis and a numerical-wave propagation code. Calculations of the expected degree of coherence of standard x-ray lasers are given, as well as designs for more coherent lasers.

The propagating beam method (PBM) is known to be an accurate tool for modeling propagation in waveguides with graded-index profiles. Intuition suggests, on the other hand, that the PBM is inappropriate for waveguides such as rib waveguides that exhibit refractive-index discontinuities. We demonstrate here that the PBM is indeed applicable to rib waveguides, although extremely small longitudinal integration steps may be required. Comparison with other numerical methods for calculating mode indices for single waveguides shows good agreement. The assessment of accuracy for modeling rib-waveguide directional couplers, on the other hand, is less certain because of a general lack of consistency among the various methods used in the comparison.

We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage.

The paraxial wave equation, as is well known, predicts the catastrophic collapse of self-focusing beams. It is pointed out that this collapse is due to the loss of validity of the paraxial wave equation in the neighborhood of a self-focus. If nonparaxiality of the beam propagation is taken into account, on the other hand, a lower limit of the order of one optical wavelength is imposed on the diameter of a self-focus. A nonparaxial algorithm for the Helmholtz equation is applied to the self-focusing of Gaussian and ring-shaped beams. The self-focusing is noncatastrophic, and the results give insight into filament formation and beam breakup resulting from the self-focusing of optical beams.

The propagating beam method is used to carry out a fully three-dimensional analysis of a nonlinear optical waveguide and a directional coupler formed from a pair of nonlinear waveguides. It is shown that, for interesting levels of the index nonlinearity, a beam in a monomode waveguide can undergo mild self-focusing and self-phase modulation. The behavior or the nonlinear coupler, on the other hand...

The propagating beam method is used to carry out a fully 3-D analysis of a nonlinear optical waveguide and a directional coupler formed from a pair of nonlinear waveguides. It is shown that for interesting levels of the index nonlinearity a beam in a monomode waveguide can undergo self-focusing and self-phase modulation. The latter effect results in an apparent shifting of the propagation constant. Both effects make it difficult to describe the field accurately in terms of modes. In the light of this behavior it is not surprising that the propagating beam method and coupled-mode theory predict different characteristics for the nonlinear coupler. The self-focusing induced in the waveguides is interesting of itself because it occurs at powers several orders of magnitude below the threshold for self-focusing in an unguided medium.