May 15 2014
Propagation of light in a free space, or a homogenous optical medium, changes the intensity profile of light. In certain electric field amplitude distributions, the shape of the amplitude profile remains constant. In addition to the re-scaling of the profiles, an overall change in optical phase, and total optical power, also takes place.
Hermite-Gaussian modes, including Gauss–Hermite modes and TEMnm modes, are available for each combination of a focus position, a beam axis, the beam radius of a Gaussian beam in the focus, and an optical frequency.
These are the solutions of the wave equation, which is valid for weak focusing. The electric field distributions are obtained as a function of a Hermite polynomial and a Gaussian function, which is given by the equation:
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where Hn (x) is the Hermite polynomial with a non-negative integer n. The n and m indices indicates the shape of the profile in x and y directions, respectively.
The electric field distributions of the Hermite–Gaussian modes include a system of mutually orthogonal functions. These modes can be used to represent the modes of an optical resonator, if the paraxial approximation is satisfied and the phase and intensity profiles change in the optical elements of the resonator.
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