Page 364 - Tunable Lasers Handbook

324 Norman P. Barnes

TABLE 2 Effective Nonlinear Coefficient for Uniaxial Crystals0

Point group Interactions 001,010,100 Interactions 110,101,011

3 (d,, cos30 - d2: sin3Q) cos0 + d15 sin0 (dl , sin39 + d,, cos30) cos20
32 d,, cos0 cos30 d,, cos20 sin30
3m d,, sin0 - dll cos’0 sin34 dz2 cos10 cos30
4. Imm d,, sin0 0
4 (dlL sin20 + d, cos?@) sin0 (dI4 cos29 - d,, sin20) sin20)
32m d,, sin0 sin20 d36 sin20 cos29
6,6mm d,: sin0 0
6 (dl, COS30 - d,2 sin30) cos0 (d, , sin39 + dz2 ~0~30) cos%
6m2 d2: cos0 sin39 d2: cos10 cos0
<In this notation, 0 represents an ordinary wave and 1 represents an extraordinaq wave.

TABLE 3 Effective Nonlinear Coefficient in Biaxial Crystals

Point group Plane Interaction 001,010,100 Interaction 110,101,011
d,, cos4 d3, sin29
d,2 cos0 d,, sin20
0 dl, cos33 + dZ3 sin33 + dj6 sin20
0 d,, sin24
0 d,, sin20
0 dj, sin20
d,, sin4 d,, sin20 + d,? cos20
d3, sin0 d,, sin% + dIz cos20
d,, cos& dY2 sin0 0
0 d,, sin>@ + d32 cos24
d,, sin0 0
d,> sin0 0
aIn this notation, 0 represents an ordinaq wave and 1 represents an extraordinary wave.

can be obtained by evaluating the expressions given in tables, such as Tables 2
and 3 [28,29]. For these tables, Kleinman’s symmetry condition has been
assumed. Values for the nonlinear coefficients of several common nonlinear
crystals are found in Table 4 130-321.
Kleinman’s symmetry condition reduces the number of independent contri-
butions to the nonlinear matrix and thus simplifies the expressions. Kleinman’s
symmetry condition assumes that the components of the nonlinear matrix which