Gradient index (GRIN) lenses are used both in imaging and beam shaping optical systems. Usually, to design a GRIN lens system, we would find the equivalent lens effective focal length and the principal planes position. Then if we design an imaging system the Newton formula gives the image position or, if we design a beam shaping system the Kogelnik's ABCD law gives the Gaussian beam waist size and position. The Hamilton's phase plane approach gives the same result as these sets of formulas, but is more spectacular and clearer. Hamilton's phase plane approach gives a vivid and clear illustration of GRIN lens imaging and beam shaping properties and does not require substitution by an equivalent lens. Hamilton's phase plane approach allows easy derivation of transparent and simple direct formulas for a GRIN lens created image and beam transformation, including Gaussian beams and multimode fiber beams. These formulas and graphical illustrations facilitate solving, and give a clearer understanding of practical problems.
The common approach to designing multimode fiber coupling lenses is based on fiber end-face imaging. A model, proposed here, deals with beam profiles. Paraxial ray tracing shows that the output of a graded-index multimode fiber has a hyperbolic profile, similar to a singlemode beam. Focusing this beam by a lens is similar to a Gaussian beam focusing. Light focused from a step-index multimode fiber has two waists. Matching their size and NA to fiber parameters is not enough for good coupling: the beam profile should in fact be corrected. The propagation properties of graded-index multimode fiber beams are similar to singlemode beams and differ from step-index multimode fiber beams. The beam profile approach defines these properties, while the imaging approach often fails. A ray model, describing the beam profile, is convenient in computer simulation of lens systems for fiber optics. It visualizes beams in ray-tracing codes such as ZEMAX and allows aberration optimization regarding minimal beam distortion. Gaussian beam diffraction is not an issue, if there is no beam clipping - the ray model is consistent with the traditional wave model. These results are important for correct design of fiber coupling lenses.
Silver halide polycrystalline MIR-fibers are coming to practical exploitation in CO-laser medicine through the development of core/clad fibers technology and design of suitable flexible delivery systems, convenient and reliable for operations. Recent results of such development and useful exploitation features are presented.
New medical applications of IR lasers are possible with flexible cables and catheters for laser power delivery. Optical parameters of fibers for Er; CO- and CO2-lasers along with design of special optical connectors, efficient coupling units, and optics at distal end are reviewed. Applications of cables and catheters for laser therapy and medical diagnostics are analyzed.