Page 38 - Tunable Lasers Handbook

2 Narrow-Linewidth Laser Oscillators 19

have used geometrical optics arguments in its derivation [39-42]. In addition,
recent work [1,38] indicates that the origin of Eq. (3) can be related to intra-
cavity interference as described using Dirac’s notation [43].

6. BEAM DIVERGENCE

An expression for beam divergence including all the intracavity components
except the active region is given by [ 1,441

where w is the beam waist, L, = m2/1 is the Rayleigh length, and A and B are
the corresponding propagation matrix elements. For propagation in free space A
= 1 and B = d so that A0 = hninw for d = L,., A0 = h fi/nw(L,.id) for d <dr,
and A0 = h inw for d >>Lr.
Appropriate ABCD matrices are given in Table 2. Matrices listed include those
for gratings, mirrors, etalons, and multiple-prism beam expanders. The matrices for
the multiple-prism beam expanders are general and enable a round-trip analysis.
Alternative 4 x 4 ray transfer matrices that include dispersion and other
optical parameters are discussed in [1,47,48]. The relation between the disper-
sion of multiple-prism arrays and 4 x 4 ray transfer matrices is discussed in the
Appendix.

7. INTRACAVITY DISPERSION

The return-pass intracavity dispersion for a multiple-prism grating assembly
(see Fig. 2) is given by

where the grating dispersion is given by [ 141

2(sin 0 + sin 0’)
[%)G= hcos0 (9)

for a grating deployed in a grazing-incidence configuration and