Introduction to Terahertz Electronics by Jae-Sung Rieh

Author:Jae-Sung Rieh
Language: eng
Format: epub
ISBN: 9783030518424
Publisher: Springer International Publishing

(4.40)

Fig. 4.11Optical system considered to describe the Gaussian beam transformation by a thin lens

If the matrix elements of Eq. (4.40) is substituted into Eq. (4.39), we obtain:

(4.41)

where the relation qin = jzc is used, which is valid because R is infinite at the input beam waist location (recall Eq. (4.10)). It would be worthwhile to note that Eq. (4.41) is in fact valid for any point located right to the lens in Fig. 4.11 by substituting the distance from the lens for dout in the expression, although we will confine our discussion to dout where the output beam waist is located.

By examining the real and imaginary parts of 1/qout, the inverse of Eq. (4.41), we can retrieve two constraints that can be used to obtain dout and ω0out. First, at the output beam waist, the radius of curvature R is again infinity, leaving the real part of 1/qout zero. Based on Eq. (4.41), one can derive:

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