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Consider the higher-order Gaussian beams, whose fields may be expressed either as Hermite-Gaussian modes of order (1,m), as in equation (4.88) of the notes, or as Laguerre-Gaussian modes of order

(p,m), as in equation (4.91) of the notes. Restricting your consideration to p =0, 1 and m = 0, 1, 2, address the following: (a) Plot the intensity patterns of the Laguerre-Gaussian modes. (b) Find the sum of (p,m) and (p.-m) modes and plot its intensity pattern. (c) Express the first four Laguerre-Gaussian modes in terms of a linear combination ofHermite-Gaussian modes. You must show your work. The answer alone is insufficient.

Fig: 1

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