2ND-MOMENT APPROACH TO THE TIME-AVERAGED SPATIAL CHARACTERIZATION OF MULTIPLE-TRANSVERSE-MODE LASER-BEAMS

Analytical expressions are derived for the time-averaged propagation characteristics of multimode light beams made up of a superposition of paraxial transverse modes. The transverse-mode distributions are not restricted to the usual Hermite-Gaussian or Laguerre-Gaussian functions and may thus have arbitrary characteristics. It is shown that the propagation characteristics of multimode beams can be expressed in simple form in terms of those of the constituent transverse modes, which can be obtained directly from the modal complex-amplitude profiles in any given transverse plane. These expressions may simplify considerably the calculation of the second-moment characteristics of multimode beams because the numerical propagation of each modal field in free space is no longer required. The expressions are used to investigate numerically the degradation of the spatial quality of the output beam radiated by a broad-area semiconductor laser as its fundamental-lateral-mode operation ceases.