H. Kogelnik

Laser Beams and Resonators

This paper is a review of the theory-of laser beams and resonators. It is meant to be tutorial in nature and useful in scope. No attempt is made to be exhaustive in the treatment. Rather, emphasis is placed on formulations and derivations which lead to basic understanding and on results which bear practical significance.

Laser beams and resonators

This paper is a review of the theory of laser beams and resonators. It is meant to be tutorial in nature and useful in scope. No attempt is made to be exhaustive in the treatment. Rather, emphasis is placed on formulations and derivations which lead to basic understanding and on results which bear practical significance.

STIMULATED EMISSION IN A PERIODIC STRUCTURE

We have investigated laser oscillation in periodic structures in which feedback is provided by backward Bragg scattering. These new laser devices are very compact and stable as the feedback mechanism is distributed throughout and integrated with the gain medium. Intrinsic to these structures is also a gratinglike spectral filtering action. We discuss periodic variations of the refractive index and of the gain and give the expression for threshold and bandwidth. Experimentally we have induced index periodicities in gelatin films into which rhodamine 6G was dissolved. The observed characteristics of laser action in these devices near 0.63 μm are reported.

Off-Axis Paths in Spherical Mirror Interferometers

When a spherical mirror interferometer is illuminated by an off-axis ray of light, the repeated reflections cause the ray to trace a path which lies on the surface of a hyperboloid, with the points of reflection on the mirrors on ellipses. Under special conditions, these ellipses may become circles, with the points of reflection displaced by an angle 2θ after every round trip. When 2νθ = 2μπ, ν and μ being integers, the rays retrace their paths. These ray paths give rise to additional resonances which were observed. Pictures of the points of reflection are reproduced. The theory is in good agreement with the experimental observations. In laser amplifiers these ray paths enable one to obtain long effective path lengths in the active medium which may be contained in a thin annular cylindrical or hyperboloidal shell.

On the Propagation of Gaussian Beams of Light Through Lenslike Media Including those with a Loss or Gain Variation

A theoretical analysis is made of Gaussian beam propagation in media where the refractive index and/or the gain constant varies quadratically with the distance from the optic axis. Use of a complex beam parameter simplifies the analysis. A differential equation for the complex beam parameter is deduced from the wave equation for the complex beam parameter is deduced from the wave equation, and various of its solutions are discussed. This includes a discussion of light propagation in media with a gain profile, which are found capable of supporting stationary beams of constant diameter.

Switched directional couplers with alternating ΔΒ

Coupled waveguide structures with sections of alternating phase mismatch are proposed as switched directional coupler configurations in which complete conversion of light from one guide to the other can be achieved by an electrical adjustment. These structures can be used to make electrooptic switches and amplitude modulators in integrated optics form with improved conversion and on-off ratios. Couplers with 2, 3, 4, and N sections of alternating phase mismatch are analyzed, and diagrams describing their switching characteristics are given.

Astigmatically compensated cavities for CW dye lasers

An analysis is given of folded 3-mirror laser resonators with an internal cell set at Brewsters angle. A method is described to compensate the astigmatic distortions introduced by both the internal mirror and the cell. This compensation is achieved for a specific relation between cell thickness and folding angle. It allows the formation of a tight intracavity focus as required in applications such as CW dye lasers. A discussion is given of the mode characteristics of compensated cavities and of the limitation on beam concentration set by the thickness of the Brewster cell.

Polarization-Mode Dispersion

Publisher Summary Polarization mode dispersion (PMD) is a linear effect that can be compensated in principle. In an ideal circularly symmetric fiber, the two orthogonally polarized modes have the same group delay. However, in reality, fibers exhibit a certain amount of birefringence because of imperfections in the manufacturing process or mechanical stress on the fiber after manufacture. It is noted that fluctuations in the polarization mode and fiber birefringence produced by the environment lead to dispersion that varies statistically with time and frequency. PMD causes different delays for different polarizations and when the difference in the delays approaches a significant fraction of the bit period, it leads to pulse distortion and system penalties. Environmental changes— including temperature and stress—cause the fiber PMD to vary stochastically in time. PMD, illustrating the basic concepts, the measurement techniques, the PMD measurement, the PMD statistics for first- and higher orders, the PMD simulation and emulation, the system impairments, and the mitigation methods has been summarized in the chapter. Both the optical and the electrical PMD compensations are considered.

TUNABLE DISTRIBUTED‐FEEDBACK DYE LASER

Efficient broadly tunable dye‐laser action with a narrow line output has been demonstrated with a mirrorless laser system using distributed feedback. The feedback was obtained from a spatial modulation of both gain and index of refraction, induced by pumping a liquid organic dye solution with fringes formed by the interference of two coherent light beams. The device was tunable over 640 A either by varying the angle between interfering pump beams or the refractive index of the dye solvent. Linewidths less than 0.01 A were measured and a peak power of 36 kW was observed.

Scaling Rules for Thin-Film Optical Waveguides

An asymmetry measure is introduced to characterize thin-film optical waveguides that are asymmetric in refractive index. Together with the usual normalized frequency this allows the plotting of universal charts from which the guide cutoff, the effective guide index, and the effective guide thickness can be determined by the use of simple scaling rules. The minimum value of the effective guide thickness is found to be a simple function of wavelength and the film and substrate indices.