Subject: NLO; SOS

From: Andreas Goeller <[email-masked]>
Date: Fri, 16 Jan 1998 15:31:52 +0100

I've got some questions regarding 	Nonlinear optics
					Sum over States

The 3rd order polarisability (2nd order hyperpolarisability) gamma
for one molecule is regarding to Butcher, Cotter, The Elements of
Nonlinear Optics, Academic Press, defined as

gamma(ijkl)(-oms,om1,om2,om3) = e**4/(3! * h/2pi)**-3 * Perm-Op *
sum ( (rgm(i)*rmn(j)*rno(k)*rog(l))/(mg-oms)(ng-om2-om3)(og-om3) +     
      (rgm(j)*rmn(i)*rno(k)*rog(l))/(mg+om1)(ng-om2-om3)(og-om3) +
      (rgm(j)*rmn(k)*rno(i)*rog(l))/(mg+om1)(ng+om1+om2)(og-om3) +
(      rgm(j)*rmn(k)*rno(l)*rog(i))/(mg+om1)(ng+om1+om2)(og+oms) )
 
with oms=om1+om2+om3 
g, m, n, o are ground and exc. steates 
mg, ng, og are E(exc.)-E(ground)
r are transition dipole moments
i, j, k, l are cartesian coordinates
and the pairs (om1, j), (om2, k), (om3, l) are permuted by Perm-Op

1) there are some similar formulae in literature which I can't directly
deduce to this formula. Is this the right definition?
2) gm is the transition 1-2, 1-3 and so on. Analogously og is 2-1, 3-1
 ... Has one to take rgm(i) = -rog(i) for m = o? There should be a
difference between the transition dipole moment "upstairs" and
"downstairs".
3) Is it allowed to reach the ground state with the transition rmn(i)
 or rno(i)? Is it allowed to stay in one state, e.g. rmn(i) with m=n
would be the dipole moment of that state (corrected by the dipole moment
of the ground state)?

4) According to finite field NLO: There the field is always defined in
atomic units. What is 1au of the electric field in V/m (SI)?

I will post a summary of (hopefully many) answers to the list.
Thanks in advance. 

-- 
                                Andreas Goeller

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   Dr. Andreas Goeller       Institut fuer Physikalische Chemie
                               Friedrich-Schiller-Universitaet
                                       Lessingstr. 10
phone: +49(0)-3641-948352               D-07743 Jena
  fax: +49(0)-3641-948302 (secretary)     Germany
email: [email-masked]
http://www.uni-jena.de/chemie/photo/goeller/goeller.html
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   Dr. Andreas Goeller   ehemals Computer Chemie Centrum

email: [email-masked]
http://www.organik.uni-erlangen.de/clark/goeller/goeller.html
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