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A specialized coupler formed by two identical multimode graded-index slab fibers is described. This special coupler can be used to examine the tilt or the roughness of a surface through the reflected beam. It may also find applications as a mode filter, an alignment sensor, or a feed component of an optical monopulse tracking radar. Coupled-mode theory is generalized for this application. The coupling length for maximum power transfer of the higher-order modes from the excited to the coupled fiber, leaving as much power of the lowest mode as possible to continue in the excited fiber, is computed. The fields are computed at the output of the system for incident optical beams with different axial displacements and beams launched on axis with tilted wavefronts. This desired coupling length is shown to be substantially independent of characteristics of the incident light beam. To compute the fields propagated through the tapered section introduced to separate the slab fibers, the stairwise approximation is used, and mode matching is used to connect the fields at the junctions between the successive segments. An optimum taper to separate the coupled fibers, with minimal perturbation of the fields, is present at the right-hand end of the coupling section.

A technique, firmly based on a development from ray optics, is presented for calculating the loss due to the finite sizes of curved mirrors when these form an unstable optical resonator. If paraxial rays launched within such a resonator are confined near the resonator axis, the resonator is termed stable; otherwise it is termed unstable, and is known to have high losses. Siegman has recently presented a geometrical method, brilliantly constructed ad hoc, for calculating these losses in unstable resonators, and indicated where these might be advantageous in laser application. The ray optical theory presented here, which employs the concept of ray modes in an equivalent beam waveguide, is shown to yield results equivalent to those of Siegman for all cases considered by him. However, being derived from conventional ray optics, the validity of the formulas is independently established, and these formulas are immediately applicable to re-entrant resonators and resonators containing inhomogeneous media. The fractional loss per resonator pass is equal to 1-|lambda(2)|, where |lambda(2)| < this 1 is an eigenvalue of the transfer matrix T, representing the corresponding ray transformation.

In stable resonators any given initially paraxial rays remain close to the axis of the structure and are, in fact, confined within well-defined contours-the envelope of the ray system. Previously, envelopes of rays in empty resonators had been found and their form identified with the variation of the spot size. This geometric optical approach is extended to general resonators, comprising arbitrary arrangements of lenses and convergent or divergent inhomogeneous focusing media. An invariant quadratic form involving parameters descriptive of any of the ray segments that result from a given initial ray segment leads to a differential equation satisfied by the ray segments and their envelope in portions of the resonator. A maximum-minimum problem for the envelope is formulated and solved. In convergent media the envelope function is found to be periodically modulated. The period of the modulation depends only on the properties of the convergent medium; the location of relative maxima and minima, as well as their ratio, depends on both the medium and associated optics. In special cases, results are compared with available solutions of the corresponding electromagnetic problem. A particularly simple resonator is analyzed, and envelope characteristics correlated with the stability limits.

Fluid flow measurement capabilities of a traveling wave laser oscillator (or ring laser) are assessed theoretically and experimentally. The feasibility of this alternative optical technique for measuring gas flow profiles without insertion of a mechanical probe is examined. Measurements are reported for a range of Reynolds numbers including both laminar and turbulent flows and for a variety of tube diameters. The experimental results are compared with the theory of conditions preceding the establishment of the equilibrium laminar flow profile in round tubes.

A simple theory is developed for optical resonators, in which the mirrors are each composed of two planes forming a nearly straight dihedral angle and an equivalent beam-waveguide comprising a sequence of narrow angle prisms. Geometric optical considerations yield the variation of the intensity within the resonator in a manner analogous to (although not entirely as satisfying as in) the case of the spherical mirror resonator. Modes of the continuous medium, identified as the limit of particular sequences of closely spaced weak prisms, characterized by a parameter Omega, are found in terms of Airy functions. An appropriate spot size parameter is given by [Omega/2k0(2)]1/3, where k(0) is the wavenumber.