We present a systematic study of the birefringence (including Sellmeier equations valid in the 0.6-11.5 μm range) and
nonlinearity of the orthorhombic AgGaGenSe2(n+1) crystals for n=2...5, solid solutions in the system AgGaSe2-nGeSe2.
The birefringence, e.g. na-nc at 1064.2 nm, increases from 0.114 for n=2 (AgGaGe2Se6) to 0.149 for n=5 (AgGaGe5Se12)
which substantially exceeds the birefringence of the uniaxial AgGaSe2 (~0.022), the parent compound in the limit n=0.
All four quaternary compounds are optically negative biaxial crystals. The calculated SHG limit (minimum fundamental
wavelength) is ≈1470 nm for AgGaGe2Se6 and ≈1240 nm for AgGaGe5Se12, for type-I interaction and propagation along
the Y principal optical axis. These limits are much lower than the ≈3120 nm limit for type-I interaction in AgGaSe2.
Thus, the AgGaGenSe2(n+1) crystals can be used for SHG down to their band-edge. The results for the nonlinear
coefficients of AgGaGenSe2(n+1) (n=3, 4 and 5), obtained from phase-matched SHG, indicate weak dependence on the
composition. On the average, the larger nonlinear coefficient d31 is very close to d36 of AgGaSe2 (~30 pm/V) while d32 is roughly two times smaller.