Transverse mode control in high gain, millimeter bore, waveguide lasers (1977)

A technique is presented for assuring TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> transverse mode operation in visible wavelength lasers with bore diameters of 0.1- 1.0 mm. This then is a solution to the problem of obtaining TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode output from pulse pumped dye lasers which have high and non-uniform gain. The desired mode control is achieved by confining the lasing medium in a waveguide and placing each resonator mirror so that its focal plane, rather than its center of curvature, lies at the nearest waveguide opening. Thus, the far-field pattern of the field distribution emerging from the waveguide opening is focused by the mirror back into the waveguide. For the proper choice of mirror curvature, the width of the central lobe of the far-field pattern is such that over 99 percent of the energy couples into the two lowest order modes of the waveguide. The waveguide transmits this bell-shaped field distribution to the opposite end where the process of propagating to the mirror and being reimaged is repeated. The end result is that a pulsed, laser pumped, waveguide dye laser has been made to produce a mode of the same quality as a TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode, CW, HeNe laser. This technique has also improved the output mode distribution of flashlamp pumped dye lasers. Analysis of the resonator shows that a TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode having a curved wavefront at the waveguide opening couples primarily to both the EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> and EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf> waveguide modes. The amplitudes of the EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> and EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf> modes, however, have a complex phase difference which results in a refocusing of the field distribution when both propagate in a hollow waveguide. The refocusing is shown to be a periodic function of the length of the waveguide. In addition, it is shown that as a result of gain or propagation loss differences for the two waveguide modes, the phase radius of curvature of the TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode of a waveguide resonator does not in general match the mirror curvatures. This model of TEM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">00</inf> mode coupling to the EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> plus EH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf> modes results in a clearer physical insight into the interaction between the waveguide and free space portions of the resonator.