A square-core optical fiber makes a better match with laser diode output beams, allowing greater coupling efficiency. Square-core fibers also offer advantages over circular fibers in applications such as spectroscopy and laser machining, where rectilinear illumination patterns are needed. Although the circular cross section of a traditional optical fiber offers many useful attributes, there are many applications where a different geometry would serve better. The near-field output beam of a laser diode, for example, typically has a 10:1 oblong shape with a greater divergence along the short axis than on the long axis. This beam does not match well with a traditional optical fiber unless the core diameter is much larger than the beam’s long axis. The circular output beam of a fiber also creates challenges when generating sharp corners and rectangular shapes during laser surface treatments of materials. Figure 1. Optical fibers with a square core (second from top) are commercially available with traditional round cladding as well as with square cladding. Courtesy of CeramOptec. It is easier to manufacture optical fibers having a circular cross section, but there is no fundamental reason that fiber cores cannot have other shapes, including octagonal, rectangular and square, and CeramOptec now offers all of these alternative core shapes. Fibers with a square core can have a circular cladding (Figure 1) so that they are compatible with standard ferrules and mountings, or they can have a uniform cladding to maintain the square shape. Numerical apertures between 0.2 and 0.37 are typical. Uniform output intensity As might be expected, square fibers are highly multimode and perform a great deal of ray mixing during optical propagation. The result of this mixing, however, is homogeneous output beam intensity across the core area. This nearly ideal top-hat intensity profile (Figure 2) is particularly useful in laser machining and surface treatment applications. Imaging the square core onto the target surface readily produces rectangular treatment areas with sharp corners and edges1, with minimal cost. Creating a square treatment beam from a circular fiber output beam requires masking – which reduces the usable beam energy – as well as a complex and costly optical design. Figure 2. The output beam of a square fiber exhibits homogeneous power density across the emitting surface. Courtesy of CeramOptec. Besides having a square near-field output beam, the square fiber has a noncircular acceptance region. The result is a greater coupling efficiency between the fiber and a laser diode. The typical laser diode produces an output beam with initial dimensions of approximately 1 x 100 μm. Further, along its wide-dimension beam, the divergence is 5° to 10°, while across the long dimension, the divergence is 25° or more. A round fiber can capture this rapidly diverging beam effectively near the fiber’s center, but the capture percentage declines quickly with distance for the off-center beam. A square fiber can capture the beam with equal efficiency along the length of the diode’s beam. The square-core fiber with square cladding offers several advantages when used as part of a fiber bundle in applications such as spectroscopy. In these cases, the fiber bundle is packed together at one end to maximize the capture of the light, then arranged so the fibers form a line at the bundle’s other end to maximize the illumination of the spectroscope’s entry slit (Figure 3). At the capture end, the square fiber array can provide up to 25 percent greater energy capture by eliminating gaps found in circular fiber arrays. At the output end, the square fibers provide a more uniform slit illumination than is possible with circular fibers. Figure 3. Square optical fibers have greater capture area in bundles than round fibers and can provide a more uniform linear illumination pattern for spectroscopic applications. Courtesy of CeramOptec. Astronomical spectroscopy Square fibers are particularly useful in astronomical spectroscopy applications, which have several unusual requirements. In an astronomical spectroscope, the telescope images the star field onto a fiber bundle, with the result that each fiber typically captures the light from a different star. The rearranged bundle at the spectrograph end aligns with the input slit, but because there is sufficient space left between fibers, the instrument produces a column of individual spectrum from each fiber. Because the mapping from the image end to the spectrograph end is known, the spectrograph can analyze all the individual objects in the image field simultaneously. Optical fibers used in astronomical applications must meet many requirements.2 One is high transmission for the optical spectrum of interest. This is a function of the core and cladding material choices, not shape, and is not significantly different between square and circular fibers. A second requirement is low focal ratio degradation. The ideal fiber in an astronomical spectroscope would preserve the f number of the imaging optics when delivering light to the spectroscope. In practice, however, the fiber output has a higher f number than that of the imaging optics, and the amount of focal ratio degradation increases with f number. An optical fiber receiving an f/8 image from the telescope, for instance, might deliver only an f/16 image to the spectrograph. This focal ratio degradation complicates the spectroscope’s optical design as well as decreases the amount of light available for forming the spectrum. A third requirement for astronomical optical fibers is a high degree of image scrambling. Scrambling prevents the optical fiber from carrying any information on the star image’s radial position at the fiber input. If position information were preserved, it would affect the optical geometry inside the spectrograph, and a shift in the star’s radial position on the fiber (such as from atmospheric refraction) would result in a shift of the spectrum’s position on the CCD sensor (Figure 4). Because the spectrograph uses a CCD array to sense the spectral pattern, with each pixel in a row collecting energy for a specific wavelength, a change in the spectrum’s position on the CCD would place optical energy into the wrong bins. Figure 4. Insufficient image scrambling in round optical fibers can cause shifting in the spectrum’s position within a spectrograph as the star image moves across the fiber surface, decreasing the instrument’s effective wavelength resolution. Courtesy of Gerardo Avila, European Southern Observatory. As with focal ratio degradation, the amount of image scrambling a fiber exhibits increases with increasing f number. This forces instrument developers into a trade-off. The faster (more light gathering) the optical design, the less the focal ratio degradation but the worse the spectral variations resulting from insufficient mixing. Square fibers eliminate trade-offs Early results from some CeramOptec customers indicate that square fibers exhibit less focal ratio degradation than corresponding circular fibers. In addition, the square fibers show much greater scrambling than circular fiber, so that, at low f numbers, the spectrograph is less affected by seeing conditions and guidance errors that alter a star’s radial position on the fiber. These improved attributes eliminate the need for a trade-off between focal ratio degradation and scrambling in astronomical spectroscope design. Coupled with the greater capture area of a square fiber bundle, the focal ratio degradation and scrambling improvements make square fibers a much better match to astronomical applications than traditional fibers. Figure 5. Although optical fibers with circular cross sections are easy to manufacture, there is no fundamental reason why fiber cores cannot have other shapes, including octagonal. Courtesy of CeramOptec. The shape of the square fiber core thus provides better solutions than the traditional circular fiber to a variety of application challenges. Increased capture area in bundles, efficient match to noncircular beams and uniform output power distribution have significant benefits in spectroscopy, laser surface treatments and diode laser coupling. The rectangular near-field beam shape also can be of benefit in any application that requires uniform rectilinear illumination. Meet the authors Franz Schuberts is sales manager of industrial and scientific fiber optics at CeramOptec GmbH in Bonn, Germany; Axel Hoben is a sales engineer for industrial and scientific fiber optics at CeramOptec GmbH; Kevin Bakhshpour is vice president of sales and marketing at CeramOptec Industries Inc. in East Longmeadow, Mass.; and Cheryl Provost is a scientific/industrial sales engineer at CeramOptec Industries Inc.; e-mail: salesengineering@ceramoptec.com. References 1. J.R. Hayes et al (Oct. 30, 2006). Square core jacketed air-clad fiber. J Opt Soc Amer, Vol. 14, No. 22, pp. 10345-10350. 2. Samuel C. Barden (1998). Review of fiber-optic properties for astronomical spectroscopy. Astronomical Society of the Pacific Conference Series, Vol. 152, pp. 14-19.