Hollow Glass Waveguides
Hollow waveguides present an attractive alternative to other solid-core IR fibers. Key features of hollow guides are: their ability to transmit wavelengths well beyond 20 µm; their inherent advantage of having an air core for high-power laser delivery; and their relatively simple structure and potential low cost. Initially these waveguides were developed for medical and industrial applications involving the delivery of CO2 laser radiation, but more recently they have been used to transmit incoherent light for broadband spectroscopic and radiometric applications. In general, hollow waveguides enjoy the advantages of high laser power thresholds, low insertion loss, no end reflection, ruggedness, and small beam divergence. Potential disadvantages, however, include an additional loss on bending and a small NA. Nevertheless, they are today one of the best alternatives for both chemical and temperature sensing as well as for power delivery in IR laser surgery or in industrial laser delivery systems with losses as low as 0.1 dB/m and transmitted cw laser powers as high as 2.7 kW.
Hollow-core waveguides may be grouped into two categories: 1.) those whose inner core materials have refractive indices greater than one (leaky guides) and 2.) those whose inner wall material has a refractive index less than one (attenuated total reflectance, i.e. ATR, guides). Leaky or n>1 guides have metallic and dielectric films deposited on the inside of metallic, plastic, or glass tubing. ATR guides are composed of dielectric materials with refractive indices less than one in the wavelength region of interest. Therefore, n<1 guides are fiberlike in that the core index (n<1) is greater than the clad index. Hollow sapphire fibers operating at 10.6 µm (n=0.67) are an example of this class of hollow guide. In general, hollow structures with n>1 have been made from metal, plastic, and glass tubes while the n<1 or ATR guides are made of sapphire or some special n<1 oxide glass.
The theory of hollow waveguide transmission has been described from the viewpoint of both wave and ray optics. Marcatili and Schmeltzer (MS) have used a wave optic approach which predicts for either metallic or dielectric waveguides that αnbsp;~nbsp;1/a3, where α is the attenuation coefficient and a is the bore radius. Bending the hollow waveguides increases the total loss. Recently, Miyagi, et al. have shown that the additional bending loss varies as 1/R, where R is the bending radius. Therefore, we have, in contrast to the solid-core fibers, a loss that depends strongly on the diameter and bending radius of the fiber. For the thin film waveguide structures, Miyagi and Kawakami have shown that for dielectric coatings deposited over a metallic layer, the attenuation coefficient, is given by:
where aµ is the loss for a straight guide; Uo is a mode-dependent parameter which for the lowest order HE11 mode equals 2.405; n and k in (...)metal refer to the optical constants of metal film, and Ffilm is a term which accounts for the loss due to the dielectric film(s).