3.2.2 Coupled WEs of 4 photon SFG

Question 1

Assumptions about medium (metal vapour)

Answer 1

Isotropic (permitivity scalar)
lossy - abs due to w1 and w2 acc Beers law
disprsive
Slowly varying apmplitude can be applied d2A3/d2z negligable
Assmue desity across medium length L is constant

Question 2

what is the wavevector mismatch for this 4 phton SFG

Answer 2

dk = k2+2k1 -k3
the phase matchign condition

Question 3

small signal limit

Answer 3

Assume generated SFG w3 = 2w1+w2 is small compared to w1 and w2 input beams
A3&laquo_space;A1 and A3«A2

Question 4

what is Gamma_i and Gamma_3

Answer 4

Optical depths
since the medium absorbs w2 and w2 and is lossy we formula the absorption cross section sin terms of these gammas where
G3 is the optical depth of the mdium at the Sum freq
Gi =2G1+G2 is the total otpical depth of mediuma t incident freq

Question 5

Intensity of SFG

Answer 5

i = 0.5 nce0 AA*
where A is the amplitude of SFG wave
gives I3(L) which dep on
-phase matching factor F(dk,Gi,G3)
-L material length
I2(z=0), I1(z=0)
X3(w3,w1,w1,w2)

Question 6

How can you increase the SFG intensity

Answer 6

1) Phase matching (increase form factor value F)
2) Increase medium length L (just watch out for imperfect phase matching oscillations need to be pick with length)
3) Increase incident beam intensities (increase optimal spatial and temporal overlap of incident laser pulses, optimal focussing of beams)
4) increase X3(w3,w1,w1,w2) (resonance enhancement)

Question 7

What factors are fixed in I3(sfg) in experiment

Answer 7

Length of gaous medium
Gi,G3 optical depths (determined by absorption coeff of w1 w2 transitions in metal vapour)

Question 8

what does it mean for a medium to be optically ‘thin’?

Answer 8

The optical depths Gi and Gamma 3 tend to zero
aka they dont absorb so absorbtion coeff small

typically we can choose a medium for which this is ist eh case for Gamma i, but for Gamma 3 in VUV almsot everything absorbs so cannot ignore Gamma 3

Question 9

What can we change in exp to optimise sfg in terms of phase matching at diffrerent optical densities

Answer 9

Since Gamma 3 cannot be ignored (say why)
ohase mathcing factor F doesnt oscillate maximally

for large Gamma 3, (optically thick, long optical depth for VUV freq w3) F is a Lorens profile
No oscillatory structure
allows us to use experimentally measured phase mtching curve to calc Gamma3

Question 10

When can you use plane wave approx

Answer 10

When b» length of medium (of your gauss beam leng b)

typically PW approx cannot be used sicne geauss beams are tightly focused to get suff X3 generation have to get I(SFG) and its proper phase matching factor for b not set to inty (reduces to nromal PW case if b-> infty)

Question 11

3 NB beam focus cases to consider in sum freq gen

Answer 11

Plane wave approx (b»L)
Gaussian (b~L)
Tight focus b«L

Question 12

What happens for I (sfg) under tight focus conditions

Answer 12

Tight foucs => b &laquo_space;L
at the focus wave undergoes phase change
delta k = 0 results in 0 I3!!!
require non zero phase mismatch in order to compensate for phase change of diff incisdent beam waves which are different to be matched up to get phase matching
delta b approx = 2

Question 13

what is optimal focus for moderate intensities

Answer 13

Gaussian b~L (length of gas medium)
so not in the tight or PW approx schemes