We recently analyzed a new class of laser amplifier based on transverse Bragg ref lection. We show that the unique properties of Bragg confinement make it possible through modal loss discrimination to achieve single-transverse-mode operation with transverse modal size that is an order of magnitude larger than in lasers that depend on total internal ref lection A unique feature of the TBR structures is the large modal cross section, which makes them particularly attractive for applications such as high-power delivery and high-power lasers, for which the maximal power is limited by the transverse modal size and the power density at catastrophic optical mirror damage of the end facets. 4,5 In conventional waveguides based on total internal ref lection, to achieve good beam quality (single-lateral-mode operation) the core width is typically limited to several micrometers, such as in the well-known ridge waveguide laser.
5In this Letter we investigate the condition of single-transverse-mode guiding in a TBR waveguide with a much larger core width and demonstrate that the TBR waveguide can possess a much larger core width and thus can have a significant advantage over the traditional total internal ref lection waveguides for high-power laser applications. Futhermore, the basic idea proposed here can be used to increase the core widths of other types of photonic crystal waveguides.As shown in Fig. 1(a), the TBR waveguide consists of a slab (with dielectric constant´c o and width W co ) f lanked by two Bragg ref lectors, which alternate between a high-index layer with dielectric constant 1 and layer thickness L 1 and a low-index layer with dielectric constant´2 and layer thickness L 2 . In this Letter we consider only small index contrast, with co ´2 Х´1. We further require that L 1 L 2 b͞2, which provides optimal conf inement according to the results in Refs. 2 and 3. The z dependence of the guided mode can be described by a complex propagation constant b b R 1 ib I by the factor exp͑2ibz͒.Using the boundary condition of no incoming wave at the cladding edge, we f ind that a guided mode in a passive TBR waveguide satisf ies the following phase condition 2,3 :where m is an integer, S ͓jkj, Dk k 0 2 p͞b, and k v 2 ͑´1 2´2͒͑͞2k 0 c 2 p͒. k is the coupling constant