SHG from planar surfaces Second-harmonic generation

early experiments in field demonstrated second harmonic generation metal surfaces. eventually, shg used probe air-water interface, allowing detailed information molecular orientation , ordering @ 1 of ubiquitous of surfaces. can shown specific elements of




χ

(
2
)




{\displaystyle \chi ^{(2)}}

:

a depiction of second harmonic generation set measuring orientation of phenol @ air-water interface.

χ

z
z
z


(
2
)


=

n

s


⟨
c
o

s

3


θ
⟩

α

z
z
z


(
2
)




{\displaystyle \chi _{zzz}^{(2)}=n_{s}\langle cos^{3}\theta \rangle \alpha _{zzz}^{(2)}}

χ

x
z
x


(
2
)


=


1
2



n

s


⟨
c
o
s
θ
s
i

n

2


θ
⟩

α

z
z
z


(
2
)




{\displaystyle \chi _{xzx}^{(2)}={\frac {1}{2}}n_{s}\langle cos\theta sin^{2}\theta \rangle \alpha _{zzz}^{(2)}}

where ns adsorbate density, θ angle molecular axis z makes surface normal z, ,




α

z
z
z


(
2
)




{\displaystyle \alpha _{zzz}^{(2)}}

dominating element of nonlinear polarizability of molecule @ interface, allow 1 determine θ, given laboratory coordinates (x, y, z). using interference shg method determine these elements of χ(2), first molecular orientation measurement showed hydroxyl group of phenol pointed downwards water @ air-water interface (as expected due potential of hydroxyl groups form hydrogen bonds). additionally shg @ planar surfaces has revealed differences in pk , rotational motions of molecules @ interfaces.