Just like large electrical current needs large diameter copper wires to carry, high power laser needs large mode to avoid optical damage and, even more, unwanted optical nonlinearities. Many approaches have been taken and one of them is index-antiguided (IAG) fibers, first proposed by\u00a0Siegman (Siegman,\u00a0JOSAA<\/em>\u00a0<\/em>20, pp. 1617-1628, 2003).\u00a0In IAG waveguides, the core has a negative index step with respect to the cladding such that all propagation modes are leaky with larger loss for higher-order modes.\u00a0The\u00a0idea of using IAG waveguides bears close analogy to conventional unstable resonator\u00a0(Siegman,\u00a0Proc. IEEE\u00a0<\/em>53, pp. 277-287, 1965).\u00a0Despite their diverging ray trajectories (e.g.<\/em>,\u00a0<\/em>rays 2 and 3 in\u00a0Figure\u00a01(a)), unstable resonators are known to support very stable transverse modes with large modal volume and good discrimination against high-order modes. The output modes of unstable resonators, however, have a dip at the center and suffer aperture-generated Fresnel fringes that rise from diffraction caused by the mirrors. In 1975, Dr. Lee Casperson, our co-PI on this project, has shown that unstable resonators with Gaussian-graded-reflectivity mirrors offer better mode quality than their hard-aperture counterparts (Figure\u00a01(b)) by removing Fresnel fringes (Casperson and Lunnam,\u00a0Applied Optics\u00a0<\/em>14, pp. 1193-1199, 1975). He further showed that an unfolded discrete Gaussian-graded unstable resonator (Figure\u00a01(c)), under the limit of weak lenses and closer separation between lenses, is equivalent to a waveguide with a positive quadratic gain profile and a negative quadratic index profile (Figure\u00a01(d)). He experimentally demonstrated such a gain-guided index-antiguided (GG-IAG) waveguide laser in a high-gain\u00a0Xe\u00a0laser (Casperson and Aariv,\u00a0Applied Physics Letters<\/em>12, pp. 355-357, 1968), and confirmed that the mode size is larger than that of a non-antiguided resonator (Casperson and Aariv,\u00a0\u00a0Appl. Opt.\u00a0<\/em>11, pp. 462-466, 1972). The output power of the GG-IAG Xe laser,\u00a0however,\u00a0was very low ~ 10 uW due to verty small saturation intensity except its very high gain. It is eveident that, however, such\u00a0IAG waveguide lasers can combine STM and LMA of discrete unstable resonators and superior Gaussian mode quality and ease of integration of optical waveguides.<\/p>\n
![\"\"](\"http:\/\/pages.charlotte.edu\/tsing-hua-her\/wp-content\/uploads\/sites\/144\/2012\/11\/resonators.jpeg\" "\\"resonators\\"")
<\/a><\/p>\nFigure\u00a01: Analogy among a conventional unstable resonator (a<\/em>), an unstable resonator with Gaussian graded reflectivity mirror\u00a0(b)<\/em>, an unfolded unstable resonator (c<\/em>), and a gain-guided index-antiguided waveguide (d<\/em>). 1, 2, and 3 are light rays with different propagation angles.<\/address>\n\u00a0<\/address>\n