4.2.3 Phase matching in a gaseous medium

Question 1

what are your two main options for phase matching in gas medium

Answer 1

-non colinear beam alignment
- anomlous dipersion and changing gas ratios to get phase matching (collinear beam alignment)

Question 2

what are the phase matching requirements for weak adn tight focused beams respectively

Answer 2

Weakly focused beams delta k approx = 0

TIghtly focused beams delta k * b approx = 2
(to compensate for phase flip at focus)

Question 3

Phasematching for SHG and for SFG

Answer 3

SHG
k3 = 3k1

SFG
k3 = 2k1+k2

but k = wn so
w3n3 = w1n1 and w3n3 = 2w1n1 +w2n2

Question 4

Normal dispersion

Answer 4

lower freq means higher refractive index

Question 5

What is anomalous dispersion

Answer 5

Lower freq -> lower refractive index

Question 6

What is the setup of eqns for using a mixture of gases and anomalous dipersion to phase match

Answer 6

Require two gases A and B one is normal positive dip one is anomalous disp
The pahse matching condiction is a SCALAR (all collinear beams) so there is no way to force them to add to same length (no angle freedom) so you msut chnage the n’s

change the two gases’ ratios/relative partial pressures
force n’2 to match the w’2 to get rquired phase matching conditions

Question 7

How do you setup if you dont want to use a mixture of gases but rathe rwant to use non collinear beams to get pahse matchhing in gas media

Answer 7

phasematching becoems a vector sum
vec{k3} = vec{k2} +2vec{k1}
and you can draw an angle between them and align so that the 3 incident vectors add to the k3 vector

Question 8

Disadvantage of using non collinear beams to get phase matching

Answer 8

There is only a small volume where the 2 beams cross where the non lienar process can take place

Question 9

What are the additional requirements for phase matching using non collinear beams

Answer 9

Still requires a neagtive dipersive medium so that the k3 vector is SHORTER than the sum of the 3 incident k vectors
(so that you can bend them with angles and get things to fit)

if th emedium was positive dispersive then k3 would be longer than incident k vects and could not acieve phase matching with non collinear beams