A remarkable difference between linear and nonlinear processes lies in the fact that the efficiency of the latter depends on the coherence properties of the electromagnetic

field (pump) from which the process is driven

Crosignani, B.

DiPorto, P.

Ganiel, U.

Solimeno, S.

Yariv, A.

English

Caltech Authors - Main

in the scattered signal intensity wb.en the 
idler frequency approaches the l~ttice ab-
sorption bands in these matenals. Two 
explanations for this effect have been pro-
posed.l,t,a They have been. interpreted as 
contradictory 2·a·6 and t.lus has led to 
some contro~ersy aod confusion in the 
publi!!hed literature. 
In the first in terpreta lion 1 the decrease 
in signal intensity has bee~ attribu~ to 
(2 phonon) lattice absorption at. the. 1dler 
frequency, which limil.s the effectwe mter-
action length in the crystal. Over the ~re­
quency ranges studied, this in~erpretation 
was in excellent agreement w1th tbc ex-
perimental results. 
Subsequent measurements by Klyshko 
et at.: showed t,hat the signal intensit! 
again increases as the idler f~quenc~ JS 
tuned farther into the absorption reg10n. 
These authors pointed out that idler ab-
sorption alone cannot explain this in-
crease. In order to explain their obserya-
tions they assumed that idler absorption 
is c~mplet.ely negligible and ha~e at-
tempted to describe t~e ob.served. d1p a~d 
subsequent increase m Slgnal mtens1ty 
solely in terms of dispersion in the non-
line~tr suscept.ibility which arises :frot;n r~­
onant contributions from the lai t1ce rn 
the absorbing region. We feel ~at a 
proper description of the parametnc scat-
tering should include. the ~ffe~ts of both 
idler nbsorption and d1spers10n 1n the non-
linenr susceptibility. 
Our experiments enable us to determine 
quant.itatively the role of e~ch of th~se 
phenomena in the parametnc scattenng 
process. Using an argon ion laser operat-
ing at 4880 A, a tandem double mon<?-
chroma.wr, and synchronous photoelectric 
detection and using aogular frequency 
tuning ~ achieve phase matching, we 
measure the frequency dependence of the 
spontaneous scattering intensity at a fixed 
tempcrn~ure. A complete set of such me~ 
surements in both lhe absorbing and non-
absorbing regions is made at several tem-
peratures between 2.5 :rnd 250•C. From 
these me!IBUrements, the known lattice ab-
sorption spectn1m,o and the l.'!lown tem-
perature dependence of this a.bsorption,1 
we quantitatively determine the effect of 
idler absorption on the ecattered signal 
intensity. Having thus included the effects 
of absorption, we cao determine the dis-
persion in the nonlinear susceptibility due 
to lattice contributions. 
Our measurement techniques compen-
sate for any small effec~ of temperature 
on tho electronic contribution to the sus-
ceptibility. Any temperature dependence 
of the lattice contribution is included in 
our analysis by using the measured tem-
perature dependence oi the LO and TO 
phonon Raman scat.tering. 
Our results show that a consistent de-
scription of the experimental data is pos-
sible when both idler absorption aod dis-
penion in the nonlinca.r susceptibility are 
included. This work should resolve the 
controversy. now present in the literature. 
• A. S. Darker and R. Loudon, Plty1. Rw., vol. 
ISS, p. 433, 1967. 
WB.DNES1>AY :MORNING 
L.9 CdSe Infrared Parametric Oscilla-
tor, R. L. Herbst and R. L. Bye~, 
Microt00ve LaboratoT'!I, Stanford Un._ 
versity, Stanford, Calif. 
We have obwned single resonant par~ 
metric oscillation in the infrared at 2.2 ,.. 
aod 9.6 p using CdSe as the nonlinear 
crystal. A Q-switched Nd:YAG laser 
operating at 1.833-p. pumps the oscillator 
which has a tJ1reshold of 660 W. 
Phase matching for positive birefringent 
CdSe is Type H with the pump and idler 
an ordinary wave and the 2.2-p. signal an 
extraordinary wave. The oscillator may be 
angle tuned over the 2-2.2-p. and 9.6-14-p. 
region.1 The present oscillator operates at 
the oo•-phase-matched orientation. To 
prevent feedback at the idler and also 
provide output coupling at 9.6 ,.., a fu...o:ed 
silica Brewster angle plate is inserted in 
the oscillator cavity. With a pump power 
of 2.4 kW in the crystal, 40 percent pump 
depletion was seen. Using the Manley-
Rowe relations, the available power at the 
9.6-JL nonresonant idler is 180 W. 
Experiments are in progress :rnd results 
for tuning, bandwidth, and crystal quality 
will be discussed. Surface damage is a 
problem in some crystals, aod work is 
continuing toward an understanding of 
the damage problem. 
The simplicity of construction together 
with room temperature operation and the 
availability of high quality CdSe crystals 
make this oscillator an attractive tunable 
source in the middle infrared. 
1 R. L. Herbst and R. L. Bler "Efficient J>a· 
rametric mixing in C4Se," At>{> . Pltys. L,l., vol. 
19, p. S27, 1971. 
L .lO Coherence and Efficiency in Non-
linear Optical Processes, B. Crosignani, 
P. DiPorto,1 U. Ganiel,2 8. Solimenol 
e.nd A. Yariv.• 
A remarkable difference between linear 
and nonlinear processes lies in the fact 
that the efficiency of the latter depends 
on the coherence properties of the electro-
magnetic field (pump) from which the 
process is driven. In this frame, the trend 
toward a decrease in the energy exchange 
rate with increasing of pump incoherence 
bas been suggested.5 A fairly complete 
detailed analysis is presented here for the 
specific case of optical parametric amJ?li-
fico.tion (P A) and frequency convers10n 
(FC}. The dynamic models have the for-
mal features which are common to a large 
class of problems. Their aoalytic behavior 
cannot, in general, be deduced by extrap-
olation of the existing theory for ideally 
coherent pump, but has to be investigated 
1 B. Crosignani and P . DiPorto are with Fonda· 
zione Uco Bordoai, Istituto Superiorc P.T., 
Ro,mu: ~1:id ia wit.h the Wcizmann Institute of 
Science, Rebovot, Israel. . 
• S. Solimeno 1S with the Istituto E lecttrotecn•co, 
Universit.a di Napoli, Naples Italy. 
• A. Yariv is with the California Institute of 
Technology, Pasadena, Calif. 91109. . d 
• B. Crosignani. U. Ganiel, S. Soluneno, an 
A. Yariv, Pltys. Rw. Leu., vol 2?, p. 237, 1971. 
575 
resorting to more sophisticated methods 
of statistical physics. . 
We consider some of the effects of t hJS 
limited coherence on the efficiency and 
the statistical properties of both the para-
meLric amplification and frequency. con-
version processes. 'Ne assume tho mter-
actiou process to be driven by e.n external, 
stochastic, centered field of constant am-
plitude, aa the one associated with 1\ real 
laser operating well above threshold. ~e 
two limiting situations arc treated 10 
which tho coherence time of the pump is 
large or small compared with the char-
acteristic time of the P A and FC pro-
cesses, when driven by a perfectly co-
herent field. 
The lack of coherence of the pump in 
parametric amplification is shown to in-
duce significant changes with respect to 
the ideal situation. Specifically, tho growth 
rate of the processes is always reduced, 
the degradation becoming extreme in the 
case oi strongly incoherent pump. 
In the case of t.he frequency converter, 
even the qualitative nature of the inter-
action is changed from that o{ the ideal 
case. The most striking departure concerns 
the gmdual deterioration and eventual 
disappearance of the periodic energy ex-
change between the lo"' a.nd high fre-
quency fields in the frequency converter. 
This is shown quali tatively. In the fast--
fluctuating pump case (dashed line), the 
periodic nature of the exchaoge process 
is completely damped out: In the other 
case (dotted~a.sbed line), the modifica-
tion depends on the detailed na.ture of 
the correlation function oi the frequency 
fluctuations, and it is less relevant. The 
continuous line represents the ideal co-
herent pump case. The lack of coherence 
leads to an eventual (average) equal 
number of photons in the signal and 
idler channels. 
SESSION M 
Wednesday, May 10, 1972 
8:30 A.M.-12:00 
Spectroscopy II 
M .1 High-Resolution Infrared Spectro-
scopy of Gases,! V. J . Corcoran, J . M. 
Marlin, and W. T. Smith, Marti~M<Jri.­
etta Corporation, Orlando, Fla. S~06. 
The spectrometer has been developed 
which uses the signal generated by mixing 
a co~ laser and a. miUimetcr wave kly-
stron in o. gallium arsenide loaded wave-
guide as a source.2 This spectrometer has 
the tuning range of the klystron and the 
resolution of the CO. laser. Since the 
frequencies of tho CO. laser and the 
klystron can be measured, the tunable 
'This work waa supported by tbe Air Force 
Office of Scientific Research, under Contract No. 
F44620·70·C-010l. . .. 
• V. J. Cocoran and W. T. South, "Liller·mollo· 
meter wave techniques," _pr~t~ at the 197.1 
IEEE/OSA Coof. Laser Enl!lDtttiDa and Appli· 
catJona, Pa~r 6.7, June 1971. 


Coherence and Efficiency in Nonlinear Optical Processes

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Coherence and Efficiency in Nonlinear Optical Processes

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