2.6 Sum frequency generation

Question 1

What situation do we disuciss in this section 2.6

Answer 1

w3 = w1+w2
where w2 is a STRONG visible photon
w1 is a weak IR photon
and q3 is generated as a visible photon easier to detect than IR

cannot assume undepeled w1 pump
can assume w2 strong beam is undepleted
start with no w3

Called Upconversion
(w1 beam is coverted to a HIGHER Freq)

Question 2

phase matching cond for sum freq gen

Answer 2

p = hbar k
k3 = k1+k2
n2w3 = n1w1 + n2w2

Question 3

In the derivation typically a Ki prefactor is introduced what is in it

Answer 3

deff (susceptibility constant)
wi, c, ki etc

Most NB is that A2 is in there since that is the strong undepleted pump it is treated as a constant

Question 4

boundary conditionas assumed in solving DEs for A1,2,3

Answer 4

dA2/dz = 0 (unchanged or undepeleted)
A1 and A3 depend on each other (feed off each other, great a1 implies larger dA2/dz which depletes A1 faster and vice versa)
assume start with A3(0)=0

Question 5

Explain the solns of this section (perfect phase matching situation)

Answer 5

A2 is constant (assumption) thorughout the medium

A1 and A2 compete for population because each time the A3 is created A1 is annihilated thius depleting the A1 population

A1 = A1(0) cos(kappa z) (STARTS AT MAX)
a2 = -A1(0) C sin (kappa z) (STARTS AT MIN)
and these two oscillate complimentary as a fucntions of z

choose material length z such that youg et max A3 out

Question 6

why do the A1 and A3 solutions have to sum to a fixed numbre

Answer 6

Manley Rowe eqns, conservations of energy and #photons
for each A3 created an A1 must be destroyed and for every A3 not crated an A1 from the incicdnet weak IR beam can be present and increase A1 population (temporarily at least)

Question 7

What is the result for non perfect phase matching
REMEMBER the plots are Intensities so the sin and cos are only positive valued

Answer 7

delta k != 0
still get oscillatory A1 and A3 behaviour with a3 proportioanl to A1 and starting at zero (sin gz) function

Now the osicallations are smaller in amplitude -> full conversion of all A1 photons cannot take place due to phase mismatch. at its lowest A1 is never zero and a3 never = a1 as before

the oscillation period is shorter (more rapid)