Nonlinear transmission, degenerate four-wave mixing,photodarkening, and the effects of carrier-density-dependent
nonlinearities in semiconductor-doped glasses
K. W. DeLong, A. Gabel, C. T. Seaton, and G. I. Stegeman
Optical Sciences Center, University of Arizona, Tucson, Arizona 85721
Received February 3, 1989; accepted March 17, 1989
A model for nonlinear transmission and degenerate four-wave mixing in semiconductor-doped glasses was devel-oped and compared with experiment. The results of a plasma screening theory were used to model the nonlinearresponse of the semiconductor microcrystallites. The effects of carrier-density-dependent relaxation times, two-photon absorption, free-carrier absorption, and background absorption were included in the analysis. Goodagreement between theoretical predictions and both nonlinear transmission and degenerate four-wave mixingexperiments at A = 532 nm was obtained for 15-nsec laser pulses. For 30-psec pulses, with which higher intensitieswere available, features suggestive of two-photon absorption and background absorption were observed. Weconclude that free-carrier absorption is not significant in these systems. Finally, it was shown that photodarkeningis associated with the semiconductor crystallites in the glass matrix and that the host glass itself and unstrucksamples exhibit little or no photodarkening.
INTRODUCTION
Composite materials containing semiconductor microcrys-tallites offer interesting possibilities for applications to all-optical signal-processing devices. In particular, glassesdoped with microcrystallites (100-A diameter) of CdSxSel1 xhave been the subject of investigation because of their strongnonlinearity, the absence of significant carrier diffusion, andtheir relatively fast response time.1-6 In addition, it hasproved easy to fabricate waveguides in the host glass, and anumber of nonlinear guided-wave interactions have alreadybeen demonstrated.7 -1 3
These semiconductor-doped glasses (SDG's) have shownsome rather interesting nonlinear-optical properties. Al-though the basic nonlinear mechanism has been identifiedas band filling,34 13"14 the response of SDG's in an experi-ment such as degenerate four-wave mixing has been found tosaturate more slowly with increasing intensity than expectedfrom simple models of the nonlinear response. There havealso been observations of Auger-type recombination pro-cesses15"6 and two-photon absorption'7 occurring in theSDG's.
There has been some disagreement about the value of theresponse time in these glasses.12' 4"8 Much of this contro-versy has been resolved with the observation of the photo-darkening effect in SDG.4"8 When a sample of SDG isexposed to many high-intensity laser pulses, the glass oftenvisibly darkens, and its fluorescence yield decreases. Rous-signol et al. were the first to correlate the photodarkeningeffect with fundamental alterations of the optical responseof the glass: the nonlinear-optical response is weakened, thenonlinearity response time shortens, and the linear trans-mission of the sample decreases.4 Unfortunately, much ofthe previously reported work has not contained information
on the degree of photodarkening of the glass, making itimpossible to compare results from different experiments.In general, the larger the degree of photodarkening, thefaster the nonlinearity recovery time. Values ranging fromnanoseconds down to some saturation value of a few tens ofpicoseconds have been reported.1 2 4"14"18 These changes arenot yet understood on a microscopic level, although defectsites and trap states are thought to play a role.18
There has also been evidence for a response time that isdependent on the number of carriers in the conduction band:a relaxation time with a strong intensity dependence hasbeen seen151 6"1819 and ascribed to Auger recombination.15,16
We present here the results of a series of experiments onone of these semiconductor-doped glasses, Corning 3-68 col-or filter glass. The glass was studied by using nonlineartransmission measurements and degenerate four-wave mix-ing. A theoretical model was developed to shed light on theexperimental results and to clarify the effects of variousprocesses that can occur in a semiconductor system, such ascarrier-density-dependent relaxation rates, two-photon ab-sorption, absorption caused by intraband transitions of car-riers in the conduction band (hereafter called free-carrierabsorption), and a possible density-independent unsatura-ble component to the absorption. We also investigated thephotodarkening properties of the glass in an attempt toascertain the role of the microcrystallites in the photodar-kening process.
We begin by describing the model. We comment in par-ticular on the roles of carrier-density-dependent recombina-tion rates, two-photon absorption, free-carrier absorption,and residual nonsaturable absorption. We then comparethe model's predictions with the experimental data to deter-mine the importance of the various effects. We add someobservations on the role of the microcrystallites in the pho-
todarkening process observed to occur in these glasses athigh incident light intensities. We then summarize our re-sults.
The nonlinear transmission model follows a pulse of lightthrough the material, tracking the local carrier density byEq. (1) and the intensity by
THEORY
A theoretical model was developed to describe the responseof the SDG's and was adapted to address both nonlineartransmission and degenerate four-wave mixing experiments.The resulting equations were evaluated numerically.
The plasma theory of Banyai and Koch was used to de-scribe the reponse of the semiconductor to incident light.20
Previous experiments verified the predictive power of thismodel. 2 ' The plasma theory is a two-band model, which
includes nonlinearities due to band filling, band-gap renor-malization, and exciton screening. The theory predicts theone-photon interband absorption coefficient u(N) and thechange in refractive index An(N) of the semiconductor as afunction of the carrier density N in the conduction band.The predicted absorption shows a functional dependence ofthe form A exp(-N/No) - B. Here the values of A, B, and Noare dependent on specific system parameters, such as theratio of sulfur to selenium in the microcrystallites, the de-tuning of the laser wavelength from the band gap, and thetemperature. Note that if enough carriers are excited to theconduction band, the system can reach population inversionand exhibit gain. The crossover from absorption to gain (forour particular set of system parameters) occurs in this the-ory at carrier densities of 1.4 X 1018 cm-3 (inside the crystal-
lites of the SDG). The predicted change in refractive indexrelative to that of the unexcited semiconductor is approxi-mately linear in carrier density and reaches a value of 4.5 Xi0-5 at the absorption/gain crossover point. These two re-sponse curves a(N) and An(N) form the basis of the model-ing of the response of the SDG.
The model tracks the optical intensity and carrier densityin the material as a function of space and time. An initialvalue of 10'5 cm-3 is assigned to the equilibrium carrierdensity (chosen to be well within linear ranges). The photo-generated carrier density is driven by the local optical inten-sity I according to
dN = + (N1 (1 + AN + BN)) +dt To hwp 2hop
where the free-carrier relaxation time has been written as To!
(1 + AN + BN2). Herero is the linear relaxation time, A is aradiative relaxation term, B describes Auger recombination,a and 13 are the macroscopic one- and two-photon absorptioncoefficients, respectively, hw is the photon energy, and p is
the volume fill fraction of the semiconductor in the hostglass matrix (approximately 10-3). We can write such a rate
equation because the intraband relaxation time (thermaliza-tion of hot carriers) and the dephasing time of interbandcoherences by intraband scattering are much faster than thepulse widths of interest (femtosecond as opposed to picosec-ond). Here a and 1 are the macroscopically measured ab-sorption coefficients of the entire composite structure. Wemust include the fill fraction p in the source terms in Eq. (1)to account for the locally higher values of a and 1 in themicrocrystallites themselves. The host glass is assumed tobe transparent.
(2)d = _a(N)I - I -NPI- nsJ,
where a is the microscopic free-carrier absorption cross sec-
tion and n, is a possible nonsaturable component of theabsorption. The intensity of the pulse leaving the materialis then integrated and divided by the input energy to give thetotal energy transmittance, which was the experimentallymeasured quantity.
The degenerate four-wave mixing (FWM) model is more
complicated. The experimental arrangement used was theconventional phase-conjugate geometry2 2 for degenerateFWM (see Fig. 1), with two orthogonally polarized strongpump beams counterpropagating and the weak probe inci-dent at a small angle (3°-5°) to one of the pumps (called theforward pump). The weak probe beam is polarized parallelto the forward pump. This combination of polarizationsensures that only one grating contributes to the FWM sig-nal.23 The two strong pumps can saturate the absorption ofthe material owing to the photoexcitation of carriers by Eq.(1). In solving this part of the problem, we assume that theperturbation of the pump beams by the FWM process isnegligible, that is, there is no significant depletion of thepump beams by conversion into the signal beam. [In ourexperiments, the maximum degenerate four-wave mixing(DFWM) reflectivity was _1%.] Furthermore, we assumethat any saturation of the material by the probe beam issmall compared with the saturation due to the pump beams.Experimentally, the probe was 20-40 times weaker in inten-sity than either pump; therefore we believe that this as-sumption is reasonable.
The role of the interference between the probe and theforward pump in the generation of the signal beam is nowconsidered (the backward pump does not interfere with ei-ther of these beams since it is polarized in an orthogonaldirection). The interference between these two beams pro-duces local intensity minima and maxima in the material,
I(r) = If + I + 2Ip- cos[(kf -kp)r], (3)
resulting in minima and maxima in the carrier density.
Here Ifp() and kf(kp) are the intensity and the wave vector,respectively, of the forward pump (probe) beams. This spa-tial modulation of carrier density translates into a spatialmodulation of the absorption and the refractive index, thusproducing a volume grating structure perfectly Braggmatched to scatter the backward pump into the signal (con-jugate) direction. To model this scattering, the volume dif-fraction grating theory developed by Kogelnik was em-ployed.2 4 In this framework, the coupling constant is
7riŽno iao (4)
where ao and Ano are the amplitudes of the (intensity) ab-sorption and phase gratings, respectively. For cross-polar-ized pump beams the coupled mode equations, followingKogelnik, are written as
ds a= - - -iKEb, (5a)dz 2 b'(a
dEb -2 -iKE, (5b)dz 2 b~(b
where E (Eb) is the signal (backward pump) complex fieldamplitude. The coupled mode equations for the signal andbackward pump are solved, and again the output intensity ofthe signal is integrated and divided by the input energy ofthe probe to yield a FWM energy reflectivity.
As the intensities of the two pumps become sufficientlyhigh, the one-photon interband absorption coefficient a iseverywhere bleached to zero. The amplitude of the carriergrating thus also approaches zero, implying that the absorp-tion and index gratings also disappear. This is the reasonfor the saturation of the FWM reflectivity with increasingintensity.
This model contains the adjustable parameter To, the lin-ear relaxation time. This parameter essentially scales theintensity axis: decreasing To by an order of magnitude in-creases the intensity required to obtain a given materialresponse by approximately an order of magnitude. Report-ed values of To have ranged from >1 nsec (for fresh glass) to_ 10 psec for glass that has been altered by extended expo-sure to high-intensity light (photodarkened glass)."2 4"4"8
The value of o used in these calculations is 0.1 nsec, whichgave the best fit to the experimentally measured intensities.
There are several other material parameters that are notknown to sufficient precision to permit an attempt at anabsolute prediction of the SDG response. Among these arethe exact ratio of sulfur to selenium in the microcrystallitesand the volume fill fraction of the semiconductor material.Furthermore, the models developed here are based on plane-wave calculations, while the experiments were done with alaser that operated in higher-order transverse modes. Thusthe qualitative predictions of the model are more importantthan the quantitative aspects when compared with experi-ment.
In addition, we have included other effects in the model,namely, carrier-density-dependent relaxation rates, two-photon absorption, free-carrier absorption, and residualnonsaturable absorption. These effects are considered be-low.
Nonlinear RelaxationMany workers have seen a relaxation time in the SDG's thatis dependent on the state of system excitation.15 16"19 It wasfound by us, and by others,'5 that in fitting FWM data it wasnecessary to include a carrier-density-dependent relaxationtime in the equation of motion for the carrier density. Thenonlinear-optical response was found to saturate too slowlywith increasing intensity for simple, single relaxation timemodels to be valid. The density-dependent relaxationterms are A and B in Eq. (1). These terms cause an effec-tively density-dependent relaxation time:
Tr (N) = TO1 + AN+ BN2 (6)
The effect of a nonlinear relaxation time is to stretch theintensity axis as the intensity increases. That is, increasingthe intensity leads to the generation of more carriers andthus to a faster relaxation time [see Eq. (1)]. Hence theincremental intensity that is required to increase the carrierdensity incrementally increases faster than linearly.
Evidence of Auger recombination [term B in Eq. (1)] hasbeen reported in SDG's.15"16 These workers obtained rea-sonable fits to their data by using this form for the nonlinear
1.0
7 0.8
U0
.ECn 0.6C
0.4>
a)0.2
0.0 L
>1. 1 0 -._(J
0 1
LL
in O -:
> :
Q)
aC 1 0
2 1,
peak intensity 0(MW/sq.cm)
peak intensity (MW1 /sq.cm) 100Fig. 2. Effect of density-dependent relaxation on (a) nonlineartransmission and (b) FWM for different values of the parameters Aand B in Eq. (1). A = 5 indicates A = 5 X 10-18 cm
3, B = 5 indicates
B = 5 X 10-36 cm6 .
DeLong et al.
Vol. 6, No. 7/July 1989/J. Opt. Soc. Am. B 1309
relaxation time. However, Auger processes in large-band-
gap semiconductors such as these are usually quite small,25
although they may be enhanced in small crystallite volumes.An alternative to the Auger-type recombination is the (non-geminate) radiative recombination term [A in Eq. (1)].Roussignol et al. argue that this term will be small in thesesystems.'6 Therefore they ascribed the density dependenceof the relaxation to Auger processes. The value of the Auger
coefficient B given in Ref. 16 is 5 X 10-36 cm 6 (after scaling
for our value of To, which is 10-10 sec). This is the value
assigned to B for the calculations in Fig. 2.Figures 2(a) and 2(b) present a comparison of the effects
of the two types of density-dependent relaxation. Exami-nation of these figures reveals that for nonlinear transmis-sion and FWM there is a large difference between totally
linear relaxation (A and B equal to zero) and the case of
carrier-density-dependent relaxation (A and/or B nonzero).However, it is clearly difficult to distinguish between the two
different forms of nonlinear relaxation on the basis of thesetypes of experiment. Note that the value of the Augercoefficient is rather large.2 5 Using a value of B an order of
magnitude smaller almost eliminates its effects on the calcu-lations.
One must be careful in drawing conclusions from these
types of parameterized fit. The fact that the experimentaldata match the model's predictions is not conclusive evi-dence that one has determined the processes involved.
Roussignol et al. presented further evidence, beyond FWMand nonlinear transmission, to support their hypothesis ofAuger recombination.' 6 Such data should also be consid-
ered when one is drawing conclusions about the nonlinear
response of these glasses. However, all the data support theconclusion that density-dependent relaxation is importantin this material system.' 5 "16"19
Two-Photon AbsorptionWe now consider the effects of two-photon absorption
(TPA) on nonlinear transmission and DFWM. TPA occurswhen a carrier simultaneously absorbs two photons from thefield to make the transition from the valence to the conduc-
tion band. The intermediate state in this process is virtu-al.26 When the virtual state's energy is near the energy of a
real state, the TPA transition probability is enhanced.TPA is likely to occur in SDG for many reasons. When
the semiconductor is excited near the band edge, as in ourexperiments, TPA should be enhanced because the conduc-tion-band and near-conduction-band states can contributesignificantly to the virtual intermediate state's probabilityin the TPA process. Furthermore, in glasses there should bemore defect and surface states available to contribute tointermediate TPA levels than in a perfect crystal. There-fore an enhanced TPA coefficient is expected in these glass-
es.TPA can play a significant role in the photogeneration of
free carriers. If carriers are generated only by single-photon
absorption, the carrier density can never become greaterthan the amount needed to change the sign of the interbandabsorption coefficient a, that is, to change absorption to
gain. This is evident through careful examination of Eq.
(1). However, if free carriers are generated also through
TPA, the carrier density can increase above the absorption/
gain transition point. TPA can take place into high-energystates that are away from the center of the Brillouin zoneand so are unaffected (to first order) by the filling of thelower conduction-band states. TPA-generated carriers en-ter the conduction band "hot," that is, at high energies, butquickly thermalize to the bottom of the conduction band,leaving the higher-energy states available to receive moreTPA-generated carriers, thereby avoiding the band fillingthat reduces the one-photon absorption process. It shouldbe noted that two-photon absorption enters the model onlyphenomenologically: it has no dependence on the numberof carriers or the state of the system. One must therefore beextremely cautious when attempting to apply this model tohigh levels of excitation, as these assumptions are likely toprove unfounded.
We investigated the effect of TPA on FWM and nonlineartransmission. TPA has several effects on the model. First,there is the generation of free carriers by TPA, through theterm /32/2hwp in Eq. (1), as discussed above. The second
effect of TPA is the nonlinear attenuation of the beamthrough the flI2 term in Eq. (2). This should reduce both thetransmission and the FWM signals.
A final effect of TPA is to provide an alternative source for
an absorption grating in the material that contributes to theFWM signal. To illustrate this effect, we write an effectiveabsorption aeff a + #. Since the forward pump and probecreate an intensity grating, an absorption grating that canscatter the backward pump is created through the TPAinteraction. Note that for the backward pump to be affect-ed by this absorption grating the material must absorb twophotons that are orthogonally polarized (one from Ib and onefrom the intensity grating formed by If and Ip). In general,this process is weaker than the absorption of two photons of
like polarizations (for degenerate frequencies) and can evenvanish. Note also that this TPA absorption grating has thesign opposite that associated with the band-filling grating.Wherever the local intensity is high, the one-photon inter-band absorption is low and the TPA absorption is high (aeff
a). Thus the presence of this grating will reduce theFWM signal.
Van Stryland and co-workers have measured the TPAcoefficient in doped glasses of this type and have extracted avalue of 0.2 cm/GW for the TPA coefficients This appearsto be a small enhancement over the bulk value27 (multipliedby the volume fill fraction p). This value of A3 does not have
an observable effect on the predictions of the theory at theintensities used in our calculations. We have therefore used
a larger value of /3 in our calculations to make the effects of
TPA clear.The detailed effects of TPA on the calculations are shown
in Fig. 3. In transmission [Fig. 3(a)] we see that the trans-
mitted energy begins to decrease with sufficiently high in-tensity, as expected from the nonlinear-absorption term. InFWM [Fig. 3(b)] TPA has little effect until fairly high inten-sities, whereit causes first a decrease, then a strong increasein the FWM reflectivity. At these high intensities the gen-eration of carriers becomes dominated by TPA and the carri-er grating once again begins to grow. We have defined y =
/3perp/flpar, the ratio of TPA for two orthogonally polarizedphotons to that for two copolarized photons. We have plot-ted the limiting cases of-y = O and -y = 1 in Fig. 3(b). We see
DeLong et al.
1310 J. Opt. Soc. Am. B/Vol. 6, No. 7/July 1989 DeLong et al.
1.0
(C)
U0 .6
0. 0.4
C 0.2 ~ No TPA___---- 10 cm/GW
0.00.1 1 1 100
Intensity (MWsq.cm.)
4>1/
<[)+1 0 ~~3 / *Y = 9perp/lpar \
Lx / ~~No TPA> / ~----- = 1 0 cm/GW, =
B / -- : = 1 0 cm/GW, = l 0 -4I . I II I
0. 2 1Q
Peak Intensity (MW/sq.cm3Fig. 3. Effects of TPA on (a) nonlinear transmission and (b) FWM.Here A = 2 x -18CM3 and Ba, andaetnsare all zero. In (b), zyis theratio of the TPA coefficient for absorption of cross-polarized pho-tons to that for copolarized photons.
that higher values of cause the reflectivity to rise morequickly with increasing intensity.
Free-Carrier Absorption and Nonsaturable AbsorptionAt high laser intensities large numbers of conduction-bandcarriers are generated. These carriers can absorb additionallight and make transitions to higher-energy states in theconduction band, then rapidly thermalize back to the bot-tom of the conduction band. Thus light is absorbed withoutchanging the number of carriers present in the conductionband. This process is called free-carrier absorption (FCA)and is characterized by the FCA cross section af [see Eq. (2)].
At the high excitations needed to bleach the interbandabsorption coefficient ca, we can expect an additional absorp-tion due to FCA. We therefore do not expect the absorptionto bleach to zero at high intensities. Such a nonzero satura-tion value for the absorption has frequently been seen ex-perimentally.28 It can also be explained by introducing aresidual nonsaturable component of the total absorption,represented by atn, in Eq. (2).
To discriminate between residual background absorptionand FCA, it is necessary to generate a large number of carri-ers. Absorption due to FCA will continue to increase linear-ly with carrier density, while the nonsaturable absorption
will, by definition, stay constant. Thus in principle itshould be possible to measure the FCA coefficient a and todetermine whether FCA has any effect at the experimentallyavailable carrier densities. Unfortunately, it is not possiblethrough photogeneration of carriers by one-photon absorp-tion to create a carrier density higher than the value requiredto bleach out the absorption completely. This is evidentfrom an examination of Eq. (1). This a = 0 point shouldoccur in our system at a carrier density of -10'8 cm-3.
The value of a for bulk CdS and bulk CdSe has been foundto be (1-2) X 1018 cm2 in the near infrared and is expected todecrease at shorter wavelengths.2 9 We expect the value forCdSSel-. to be of a similar magnitude. Assuming thatapproximately 1018 -cm-3 carriers are generated, and assum-ing a a of 10-18 cm2, the local FCA in the microcrystalliteswill be aff-icro = N = 1 cm-'. In the SDG it is necessary toweight the FCA-induced absorption by the volume fill frac-tion p of the semiconductor in the glass, approximately 10-3.Therefore the macroscopic aeffmacro is 10-3 cm-', a negligibleamount. We thus conclude that, barring a large enhance-ment of a in the microcrystallites, FCA will probably nothave a large effect at the carrier densities available throughphotogeneration.
The effects of FCA and nonsaturable absorption on non-linear transmission and FWM are shown in Fig. 4. Note
1.0
C_.0 0.8U)U)
0.6
I0.4>1
002Q) 0.2C_
LL
0.0
>101 0
. _
0a)
100•100'
Wi0
3U-
No FCA------ ~~ (T - 0-15 cm'
= 2.16 cm1
0.1 1 10 100Intensity (MW/sq.cm)
0.1 1 10 100Peak Intensity (MW/sq.cm)
Fig. 4. (a) Nonlinear transmission and (b) FWM for the cases offree-carrier absorption and nonsaturable absorption. Here A = 2 X10-l3 cm3 and B, = 0.
Vol. 6, No. 7/July 1989/J. Opt. Soc. Am. B 1311
that we have plotted a value of a that is 3 orders of magni-
tude higher than expected to make the effects of FCA clear.The theoretical predictions for a = 10-18 cm2 are indistin-
guishable from those for a = 0.In transmission, the effect of a sufficiently large FCA is to
prevent the absorption from saturating to zero, as expected.We see that in transmission, the background absorptionbehaves nominally as FCA, except for differences in the
magnitude of the effect. It therefore would appear difficultto distinguish between FCA and a residual absorption on thebasis of transmission experiments alone.
The effect of FCA or FWM, an overall lowering of the
reflectivity [Fig. 4(b)], is due to the fact that FCA increases
the absorption of the medium. FCA also produces an ab-sorption grating through the spatial modulation of the carri-er density (aeff = aNp). Just as in the TPA case, the sign ofthis nonlinear absorption is opposite that of the band-fillingnonlinearity: an increase in the carrier density implies less
interband absorption (band filling) but more intraband ab-sorption (FCA). If residual absorption is substituted forFCA, the effect on the predictions of the model is virtuallythe same, except for the magnitude of the reduction in FWMefficiency. Once more it would appear difficult to distin-
guish between the two processes.
EXPERIMENTAL DATA
The Corning 3-68 glasses were studied primarily with a
pulsed Nd:YAG laser, frequency doubled to yield 15-nsec
pulses with a 532-nm wavelength at a 10-Hz repetition rate.The nonlinear response of the glasses was studied with non-linear transmission measurements and DFWM. Some ex-periments were also performed with a frequency-doubledNd:YAG, which produced 30-psec pulses.
All the experiments were conducted with glass that hadundergone previous exposure to laser radiation, which in-
duced the photodarkening effect in the glass. This was done
in order to avoid modifying the properties of the glass during
the experiment.In the transmission experiments the glass was illuminated
with a single laser beam, and the ratio of transmitted toincident pulse energies was measured for a range of incident
intensities.The usual phase-conjugate geometry was used for the
FWM experiments (see Fig. 1). In these experiments thebackward-traveling pump was cross polarized to the for-
ward-traveling pump and probe beams. This isolates thecoarse grating formed by the interference of the forwardpump and probe beams. The backward pump scatters fromthis grating to produce the signal pulse.2 2' 23 The ratio ofsignal pulse energy to probe pulse energy was measured and
plotted against the pump intensity of a single pump beam.The intensities of all three beams were varied by a half-wave
plate and polarizer combination. The two pumps had equalintensities, while the probe had an intensity of one-twenti-eth to one-fourtieth of a single pump beam; no change in the
FWM reflectivity versus intensity data was observed as theratio I/If was varied.
The predictions of the model were compared with theexperimental results as shown in Figs. 5-8. Unless stated
otherwise, all the theoretical curves were generated with A =
2 X 10-i' cm 3 , B = 0, a = 10-'8 cm 2 , / = 0.2 cm/GW, and a
peak intensity (MW/sqlcm)Fig. 5. Experimental results for nonlinear transmission for 15-nsecpulses and the theoretical fit for different values of ans- Otherparameters are given in the text.
-I
C)CDN+-
L10
a)
CCD 1 0 -4:
-5
0.01 0.1 . 1 iC0.0 peak intensity (MW/sq.cm)
Fig. 6. Experimental results for FWM for 15-nsec pulses. Here wesee that large two-photon absorption does not make a difference atthese intensities. Other parameters are as given in the text.
1.0
9 0. 8a)
E 0.60
E 0.2Cn
c-
0 .0 1 1 . ' I 1
.1 ~ 1 1 0 100 10'000 o peak intensity (MW/sq.cm)
Fig. 7. Experimental results for nonlinear transmission for 30-psecpulses and comparison with theory for different values of ans. Ex-perimentally we see a sharper feature than predicted theoretically.
3o o ExperimentFit
----- fl = 200 cm/GW, y =3
_9 1/D~~~~~~~~~~1-, .... , I I 1 ,- , I I
Doooo ExperimentUans =
= 2.16 cm'
0 --
0--0
, . . . ..... ...... . . . .
DeLong et al.
1312 J. Opt. Soc. Am. B/Vol. 6, No. 7/July 1989 DeLong et al.
C 0]
v z z a a DExperiment
aD B 0.2 cm/GW :>----: = 20 cm/GW
1 0 4
, 0.1 1 10 100intensity
Fig. 8. Experimental results for FWM for 30-psec pulses and com-parison with theory for different values of TPA.
residual absorption of a,, = 2.16 cm-l. This value of a,,, waschosen to account for the amount of residual absorption seenat high intensities in the 30-psec transmission experiments(Fig. 7).
The results for the 15-nsec pulse experiments are shown inFigs. 5 and 6. There is relatively good agreement with thecalculations for both the nonlinear transmission and FWMmeasurements. In Fig. 5 we see the difference made byadding the nonsaturable component ns. If the value of anis chosen to agree with the amount of residual absorptionseen in the experiments using 30-psec pulses (Fig. 7), we getfine agreement with experiment. In FWM (Fig. 6) we seethat even a large value of TPA ( = 200 cm/GW) does nothave an appreciable effect at these intensities.
Experiments were also conducted using a second lasersystem with 30-psec pulses and higher peak intensities. InFig. 7 the residual absorption in the transmission data isevident for the first time. However, the overall fit to thedata is not so good as it was for the 15-nsec pulse case; in Fig.7 the absorption saturates more sharply with intensity thanpredicted theoretically.
For the FWM data shown in Fig. 8, relatively good agree-ment with calculations was found, except for a rise in thereflectivity at higher intensities. (Similar features wereseen in Fig. 6 of Ref. 4.) This is reminiscent of the effects ofTPA, but TPA at these intensities should be negligible.Theoretically, TPA leads to a slightly sharper feature thanthe relatively broad and slow rise observed experimentally.(By using a large value for the Auger coefficient, B 5, wecan bring the curves into closer agreement with experiment;however, we cannot justify this on the basis of the other fits.)Also note that to get a reasonable fit we used a that is 2orders of magnitude higher than that reported in Ref. 17.This high value of TPA should have caused large effects inthe nonlinear transmission experiments [see Fig. 3(a)],which were not seen experimentally. This discrepency re-mains unresolved.
PHOTODARKENING
We also investigated the photodarkening process that occursin these glasses. To interpret the results properly it is nec-
essary to understand the fabrication process for SDG's.30
First a melt is prepared in which small amounts of cadmium,sulfur, and selenium are added to the host glass, in this case asoda-lime glass. In this form, the glass is nearly clear, sincethe semiconductor dopant atoms have not yet combined toform semiconductor crystallites. In a process known asstriking, the glass is heated to -650'C. This allows micro-crystallites of the semiconductors to form with their charac-teristic band structure that produces the sharp absorptionedge that makes the SDG's useful. Not all the semiconduc-tor material present is allowed to crystallize; this affordscontrol over the absorption properties of the resulting colorglass filter. Thus there is uncrystallized dopant materialleft in the glass matrix.
We investigated the importance of the state of the semi-conductor dopants on the photodarkening properties of theglass. There are three possible constituents of the compos-ite that could trigger the photodarkening mechanism: thehost glass itself, the uncrystallized dopant atoms in the glassmatrix, and the actual microcrystallites. We obtained sam-ples of the undoped host glass, the doped but unstruck glass,and the fully struck SDG. The different glasses were illumi-nated with a frequency-doubled Nd:YAG laser beam thathad pulse energies of 1600 mJ/cm 2 in a 15-nsec pulse. Eachsample was left in the beam for 5 min (3000 pulses) and theninspected for photodarkening.
The fully prepared and struck glass exhibited the usualbehavior after exposure to the laser beam: a visible andmarked photodarkening where the laser was incident. Thistype of photodarkening has been observed by many investi-gators and is known to be a spectrally broad and featurelessdecrease in transmission. 4 A loss of fluorescence was alsoobserved after the sample was photodarkened. When thesample was translated spatially so that the laser was incidentonto another spot on the surface, the fluorescence increasedsignificantly. This loss of fluorescence was permanent.(No attempt at annealing or other methods to restore thefluorescence was made.)
The doped but unstruck sample exhibited a small de-crease in transmission, a small (measureable) decrease influorescence, and a very slight (barely visible) photodarken-ing. The undoped host glass showed none of these effectsunder the same illumination conditions.
The conclusion is that the photodarkening mechanismis associated with or greatly enhanced by the crystallitesthemselves and not the free semiconductor dopant atoms inthe glass or the host glass by itself. This could be mediatedby a thermal mechanism, since the undoped and unstruckglasses are relatively transparent at 532 nm, while the filterglass absorbs heavily. Another possibility is that the semi-conductor crystallites produce a band structure that cancouple to existing energy levels in the host glass. The exactnature of the photodarkening mechanism is still a subject ofinvestigation by many groups.
CONCLUSIONS
We have developed a model for the nonlinear response ofSDG for DFWM and for nonlinear transmission experi-ments. The effects of carrier-density-dependent relaxationtimes, FCA, and TPA were explored by using this model.The predictions of the model were compared with experi-
DeLong et al.
ment. The effect of density-dependent relaxation timeswas found to be important. However, on the basis of these
experiments we were unable to distinguish between a radia-tive-type recombination and an Auger-type recombination.TPA was found to have little effect at the intensities occur-ring in the experiment when the values of the TPA coeffi-
cient reported in the literature were used. We note, howev-er, that some features reminiscent of TPA were observed
experimentally, implying a large value of the TPA coeffi-cient. FCA is probably not significant in these systemsunless there is a several-orders-of-magnitude enhancementin the FCA cross section of the microcrystallites relative tothe bulk semiconductor. Instead, the partial saturation ofthe absorption observed in these glasses is probably due to a
residual nonsaturable background absorption, which in turncould be the result of defect centers or trapping sites intrin-sic to the composite material.
The solarization or photodarkening effect reported inSDG is triggered or enhanced by the actual microcrystallitesand is not nearly so strong or even totally absent in theundoped, or doped but unstruck, glass at laser intensitiesthat easily darken the fully prepared SDG.
ACKNOWLEDGMENTS
This research was supported by the National Science Foun-dation (EET-860-4374) and the U.S. Army Research Office(DAAG-29-85-K-0173). The samples used in the photodar-
kening study were provided by D. Hall of Corning Glass
Works. The authors are grateful to S. W. Koch and E. M.
Wright for making the results of the plasma theory availableto us. The authors thank E. M. Wright for many stimulat-ing and useful discussions. K. W. DeLong acknowledges
support given through the Newport Research Award.
REFERENCES
1. R. K. Jain and R. C. Lind, "Degenerate four-wave mixing in
semiconductor-doped glasses," J. Opt. Soc. Am. 73, 647-653(1983).
2. S. S. Yao, C. Karaguleff, A. Gabel, R. Fortenberry, C. T. Seaton,and G. I. Stegman, "Ultrafast carrier and grating lifetimes insemiconductor-doped glasses," Appl. Phys. Lett. 46, 801-802(1985).
3. G. R. Olbright and N. Peyghambarian, "Interferometric mea-surement of the nonlinear index of refraction, n2, of CdSSel-,-doped glasses," Appl. Phys. Lett. 48, 1184-1186 (1986).
4. P. Roussignol, D. Ricard, J. Lukasik, and C. Flytzanis, "Newresults on optical phase conjugation in semiconductor-dopedglasses," J. Opt. Soc. Am. B 4, 5-13 (1987).
5. P. Horan and W. Blau, "Dispersion of the third-order opticalnonlinearity in semiconductor-doped glasses," Semicond. Sci.Technol. 2, 382-384 (1987).
6. D. W. Hall and N. F. Borelli, "Absorption saturation in commer-cial and quantum-confined CdSSel-,-doped glasses," J. Opt.Soc. Am. B 5, 1650-1654 (1988).
7. T. J. Cullen, C. N. Ironside, C. T. Seaton, and G. I. Stegeman,"Semiconductor-doped glass ion-exchanged waveguide," Appl.Phys. Lett. 49, 1403-1405 (1986).
8. A. Gabel, K. W. DeLong, C. T. Seaton, and G. I. Stegeman,"Efficient degenerate four-wave mixing in an ion-exchangedsemiconductor-doped glass waveguide," Appl. Phys. Lett. 51,1682-1684 (1987).
9. S. Patela, H. Jerominiek, D. Delisle, and R. Tremblay, "Nonlin-ear prism coupling in waveguiding structure deposited ontosemiconductor-doped glass," Electron. Lett. 22,411-412 (1986).
10. S. Patela, H. Jerominiek, C. Delisle, and R. Tremblay, "Nonlin-ear optical properties of thin film waveguides deposited onto
Vol. 6, No. 7/July 1989/J. Opt. Soc. Am. B 1313
semiconductor-doped glass," J. Appl. Phys. 60, 1591-1594(1986).
11. G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Iron-side, and T. J. Cullen, "All-optical switching in prism couplingto semiconductor-doped glass waveguides," Electron. Lett. 23,484-485 (1987).
12. N. Finlayson, W. C. Banyai, E. M. Wright, C. T. Seaton, G. I.Stegeman, T. J. Cullen, and C. N. Ironside, "Picosecond switch-ing induced by saturable absorption in a nonlinear directionalcoupler," Appl. Phys. Lett. 53, 1144-1146 (1988).
13. W. C. Banyai, N. Finlayson, C. T. Seaton, G. I. Stegeman, M.O'Niell, T. J. Cullen, and C. N. Ironside, "Saturation of thenonlinear refractive index change in a semiconductor-dopedglass channel waveguide," Appl. Phys. Lett. (to be published).
14. J. T. Remillard and D. G. Steel, "Narrow nonlinear-opticalresonances in CdSSe-doped glass," Opt. Lett. 13, 30-32 (1988).
15. F. de Rougemont, R. Frey, P. Roussignol, D. Ricard, and C.Flytzanis, "Evidence of strong Auger recombination in semicon-ductor-doped glasses," Appl. Phys. Lett. 50, 1619-1621 (1987).
16. P. Roussignol, M. Kull, D. Ricard, F. de Rougemont, R. Frey,and C. Flytzanis, "Time-resolved direct observation of Augerrecombination in semiconductor-doped glasses," Appl. Phys.Lett. 51, 1882-1884 (1987).
17. E. Canto, E. Miesak, D. J. Hagan, M. J. Soileau, and E. W. VanStryland, "Two-photon absorption and free-carrier absorptionin semiconductor-doped glass," in Digest of Conference on La-sers and Electro-Optics (Optical Society of America, Washing-ton, D.C., 1988), paper WM41.
18. M. Mitsunaga, H. Shinojima, and K. Kuboderaj "Laser anneal-ing effect on carrier recombination time in CdS.Sel-,-dopedglasses," J. Opt. Soc. Am. B 5, 1448-1452 (1988).
19. D. Cotter, "High-contrast ultrafast phase conjugation in semi-conductor-doped glass," J. Opt. Soc. Am. B 3, P246-P249,(1986).
20. L. Banyai and S. W. Koch, "A simple theory for the effects ofplasma screening on the optical spectra of highly excited semi-conductors," Z. Phys. B 63, 283-291 (1986).
21. Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H.Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A.C. Gossard, and W. Wiegmann, "Room-temperature opticalnonlinearities in GaAs," Phys. Rev. Lett. 57, 2446-2449 (1986).
22. D. M. Pepper and A. Yariv, in Optical Phase Conjugation, R. A.Fisher, ed. (Academic, New York, 1983), Chap. 2.
23. H. A. Mac Kenzie, D. J. Hagan, and H. A. Al-Attar, "Four-wavemixing in indium antimonide," IEEE J. Quantum Electron.QE-22, 1328-1340 (1986).
24. H. Kogelnik, "Coupled wave theory for thick hologram gra-tings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
25. D. H. Auston, C. V. Shank, and P. LeFur, "Picosecond opticalmeasurements of band-to-band Auger recombination of high-density plasmas in germanium," Phys. Rev. Lett. 35, 1022-1025(1975), and references therein; P. E. Peterson, in Semiconduc-tors and Semimetals, R. K. Willardson and A. C. Beer, eds.(Academic, New York, 1981), Vol. 18, pp. 121-155.
26. V. Nathan and A. H. Guenther, "Review of multiphoton absorp-tion in crystalline solids," J. Opt. Soc. Am. B 2, 294-316 (1985).
27. E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J.Soileau, A. L. Smirl, S. Guha, and T. F. Bogess, "Two-photonabsorption, nonlinear refraction, and optical limiting in semi-conductors," Opt. Eng. 24,613-623 (1985); A. F. Stewart and M.Bass, "Intensity-dependent absorption in semiconductors,"Appl. Phys. Lett. 37, 1040-1043 (1980); V. V. Arsen'ev, V. S.Dneprovskii, D. N. Klyshko, and A. N. Penin, "Nonlinear ab-sorption and limitation of light in semiconductors," Sov. Phys.JETP 29, 413-415 (1969).
28. N. Finlayson, W. C. Banyai, C. T. Seaton, G. I. Stegeman, M.O'Neill, T. J. Cullen, and C. N. Ironside, "Optical nonlinearitieson CdSxSel-.-doped waveguides," J. Opt. Soc. Am. B 6,675-684(1989).
29. W. W. Piper and D. T. F. Marple, "2-5 and 2-6 compounds," J.Appl, Phys. Suppl. 32, 2237-2241 (1961); A. F. Stewart and M.Bass, "Intensity-dependent absorption in semiconductors,"Appl. Phys. Lett. 37, 1040-1043 (1980).
30. N. F. Borelli, D. W. Hall, H. J. Holland, and D. W. Smith,"Quantum confinement effects of semiconducting microcrystal-lites in glass," J. Appl. Phys. 61, 5399-5409 (1987).
![[3.4]_Fiber Nonlinearities](https://static.documents.pub/doc/80x56/55cf8e81550346703b92da6f/34fiber-nonlinearities.jpg)
