Optical nonlinearities in CdSSejr-doped glass...

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Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B 67& Optical nonlinearities in CdSSejr-doped glass waveguides N. Finlayson, W. C. Banyai, C. T. Seaton, and G. I. Stegeman Optical Sciences Center, University of Arizona, Tucson, Arizona 85721 M. O'Neill, T. J. Cullen, and C. N. Ironside Department of Electronics and Electrical Engineering, University of Glasgow,Glasgow,G12 8QQ,Scotland, UK Received October 27, 1988; accepted December 16, 1988 A pump-probe Mach-Zehnder interferometer wasused to investigate the nonlinear-optical properties of CdSxSel- doped glass channel waveguides. The technique is used in situ and may be used to determine the suitability of the material under investigation for all-optical switching. The saturation and dynamical properties of the material are readily determined by using the technique, as are thermal effects. Semiconductor-plasma theory was used to predict the nonlinear optical properties, and reasonable agreement with experiment was obtained. 1. INTRODUCTION Mainly because of the potentially huge bandwidth that op- tics affords, there is widespread interest in all-optical com- munications, processing, and signal control. Integration of optical devices onto planar substrates is particularly attrac- tive owing to the state of maturity of planar technology and the ability to sustain optical fields over long propagation distances in waveguides.1 The latter feature, together with the large power densities that can be attained in waveguides, makes integrated optics well suited for nonlinear optics, a field that shows promise for the implementation of all-opti- cal signal processing. 2 Semiconductor materials operated close to the band-gap resonance are good candidate materi- als for the implementation of nonlinear-optical devices since they can exhibit large optical nonlinearities with relatively fast response times, are fabricated fairly easily and have well-understood physical properties. 3 One particular mate- rial that exhibits interesting nonlinear-optical properties is semiconductor-doped glass (SDG), a material in which rela- tively large and fast nonlinearities have been observed 4 and in which low-loss integrated-optical waveguides can be readily fabricated. 5 SDG's are available in the form of colored-glass filters. The glasses contain small semiconductor crystallites, typi- cally the mixed semiconductor CdS.Selx, that strongly in- fluence the optical properties of the filters. The doped glasses have been of interest in nonlinear optics since Bret and Gires discovered that they exhibited saturable absorp- tion and could thus be used as Q-switching elements in lasers. 6 Eichler et al. created real-time holograms in such glasses, using the saturable absorption effect. 7 More re- cently, Jain and Lind conducted degenerate four-wave mix- ing experiments in SDG that showed that the magnitude of the third-order susceptibility x(3)near the band-gap reso- nance was of the order of 10-8 esu.8 Ekimov and Onush- chenko demonstrated quantum size effects in the glasses. 9 Yao et al. conducted time-resolved photoluminescence and degenerate four-wave mixing experiments that indicated that the relaxation time of the excited carrier population in SDG was of the order of tens of picoseconds.1 0 Numerous experiments were subsequently conducted on these materi- als, some of which concentrated on determining the underly- ing mechanism and the response time for -the nonlinear- ity, 4 1'-1 3 while others investigated quantum size effects fur- ther. 1415 The combination of large x(3) and fast response time made SDG attractive for optical signal-processing applications. It was recognized that the material could prove useful in guided-wave configurations. Fast nonlinear-optical effects were measured in integrated-optical waveguides1 6 -1 9 and in SDG fibers. 20 We previously reported time-resolved obser- vations of fluence-dependent absorption in channel wave- guides, 18 but accurate measurements of several other param- eters remained to be carried out. Of these, the saturated change in refractive index was the most important. 2 The nonlinearities in the materials were measured close to the semiconductor band gap, and therefore saturation was to be expected. Interferometric techniques are attractive for measur- ing the third-order nonlinear-optical properties of materi- als. 21 - 26 They are especially suited to a guided-wave format, in which optically induced phase changes can be accumulat- ed over lengths that are not limited by diffraction and large power densities can be generated. In this paper we summa- rize the results of an extensive series of experiments using a time-resolved Mach-Zehnder interferometer designed to test the suitability of CdSSe-glass waveguidesfor all-optical switching. In Section 2 the linear-optical properties of the experimental glasses are presented, and the waveguide fab- rication process is briefly reviewed. In Section 3 the perti- nent characteristics of optical nonlinearities in a guided- wave format are discussed and the Banyai-Koch semicon- ductor plasma model 27 invoked to predict the size of the optical nonlinearities expected in the glasses. An in situ experimental technique for obtaining most of the important parameters relevant to device design is discussed in Section 4 and experimental results presented in Section 5. Finally, in Section 6 we summarize our results and present our con- clusions. 0740-3224/89/040675-10$02.00 ©0 1989 Optical Society of America Finlayson et al.

Transcript of Optical nonlinearities in CdSSejr-doped glass...

Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B 67&

Optical nonlinearities in CdSSejr-doped glass waveguides

N. Finlayson, W. C. Banyai, C. T. Seaton, and G. I. Stegeman

Optical Sciences Center, University of Arizona, Tucson, Arizona 85721

M. O'Neill, T. J. Cullen, and C. N. Ironside

Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow, G12 8QQ, Scotland, UK

Received October 27, 1988; accepted December 16, 1988

A pump-probe Mach-Zehnder interferometer was used to investigate the nonlinear-optical properties of CdSxSel-doped glass channel waveguides. The technique is used in situ and may be used to determine the suitability of thematerial under investigation for all-optical switching. The saturation and dynamical properties of the material arereadily determined by using the technique, as are thermal effects. Semiconductor-plasma theory was used topredict the nonlinear optical properties, and reasonable agreement with experiment was obtained.

1. INTRODUCTION

Mainly because of the potentially huge bandwidth that op-tics affords, there is widespread interest in all-optical com-munications, processing, and signal control. Integration ofoptical devices onto planar substrates is particularly attrac-tive owing to the state of maturity of planar technology andthe ability to sustain optical fields over long propagationdistances in waveguides.1 The latter feature, together withthe large power densities that can be attained in waveguides,makes integrated optics well suited for nonlinear optics, afield that shows promise for the implementation of all-opti-cal signal processing.2 Semiconductor materials operatedclose to the band-gap resonance are good candidate materi-als for the implementation of nonlinear-optical devices sincethey can exhibit large optical nonlinearities with relativelyfast response times, are fabricated fairly easily and havewell-understood physical properties.3 One particular mate-rial that exhibits interesting nonlinear-optical properties issemiconductor-doped glass (SDG), a material in which rela-tively large and fast nonlinearities have been observed4 andin which low-loss integrated-optical waveguides can bereadily fabricated.5

SDG's are available in the form of colored-glass filters.The glasses contain small semiconductor crystallites, typi-cally the mixed semiconductor CdS.Selx, that strongly in-fluence the optical properties of the filters. The dopedglasses have been of interest in nonlinear optics since Bretand Gires discovered that they exhibited saturable absorp-tion and could thus be used as Q-switching elements inlasers.6 Eichler et al. created real-time holograms in suchglasses, using the saturable absorption effect. 7 More re-cently, Jain and Lind conducted degenerate four-wave mix-ing experiments in SDG that showed that the magnitude ofthe third-order susceptibility x(3) near the band-gap reso-nance was of the order of 10-8 esu.8 Ekimov and Onush-chenko demonstrated quantum size effects in the glasses.9

Yao et al. conducted time-resolved photoluminescence anddegenerate four-wave mixing experiments that indicatedthat the relaxation time of the excited carrier population in

SDG was of the order of tens of picoseconds.1 0 Numerousexperiments were subsequently conducted on these materi-als, some of which concentrated on determining the underly-ing mechanism and the response time for -the nonlinear-ity, 4 1'-13 while others investigated quantum size effects fur-ther. 1 4 1 5

The combination of large x(3) and fast response time madeSDG attractive for optical signal-processing applications.It was recognized that the material could prove useful inguided-wave configurations. Fast nonlinear-optical effectswere measured in integrated-optical waveguides16-19 and inSDG fibers.2 0 We previously reported time-resolved obser-vations of fluence-dependent absorption in channel wave-guides,1 8 but accurate measurements of several other param-eters remained to be carried out. Of these, the saturatedchange in refractive index was the most important.2 Thenonlinearities in the materials were measured close to thesemiconductor band gap, and therefore saturation was to beexpected.

Interferometric techniques are attractive for measur-ing the third-order nonlinear-optical properties of materi-als.21-26 They are especially suited to a guided-wave format,in which optically induced phase changes can be accumulat-ed over lengths that are not limited by diffraction and largepower densities can be generated. In this paper we summa-rize the results of an extensive series of experiments using atime-resolved Mach-Zehnder interferometer designed totest the suitability of CdSSe-glass waveguides for all-opticalswitching. In Section 2 the linear-optical properties of theexperimental glasses are presented, and the waveguide fab-rication process is briefly reviewed. In Section 3 the perti-nent characteristics of optical nonlinearities in a guided-wave format are discussed and the Banyai-Koch semicon-ductor plasma model2 7 invoked to predict the size of theoptical nonlinearities expected in the glasses. An in situexperimental technique for obtaining most of the importantparameters relevant to device design is discussed in Section4 and experimental results presented in Section 5. Finally,in Section 6 we summarize our results and present our con-clusions.

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2. LINEAR-OPTICAL PROPERTIES ANDWAVEGUIDE FABRICATION

A K+/Na+ ion exchange is a useful technique for creatinglow-loss waveguides in glass substrates. 5 Commerciallyavailable SDG filters have a low sodium concentration sincethe base glass host is generally borosilicate. It was foundnecessary to use in this work a special melt host glass (Schott#7183), which was rich in sodium. The absorption spec-trum of a 2-mm-thick sample of the CdSSe-doped experi-mental glass was measured with a Cary spectrophotometer.The spectrum is shown as a semilog plot in Fig. 1. Theabsorption was calculated from transmission measurementsusing the well-known formula

aL = log(1 - R)2 + [R2 + ( -R)4]}, (1)

where a is the absorption, L is the sample length, R is thereflectivity of the sample face, and T is the uncorrectedtransmission. The spectrum is similar to that obtained forcommercial samples and gives rise to a sharp-cut transmis-sion characteristic in a 2-mm-thick sample. The linear por-tion of the curve has a slope of 1/kT, where T corresponds toroom temperature (300 K). This linear portion correspondsto the phonon-broadened exponential density of states com-monly referred to as the Urbach tail. At low photon ener-gies the absorption is higher than predicted by the Urbachexpression, probably owing to defects or impurities. Itshould be observed that the absorption coefficient in thesesamples is 3 orders of magnitude or so lower than in the bulksemiconductor owing to the small volume fill fraction of thecrystallites.

Also shown in Fig. 1 is the band-edge fluorescence spec-trum generated when the sample is excited by a green He-Ne laser line at 543 nm. A least-squares cubic fit to the dataexhibits a peak at 2.19 eV, corresponding to a wavelength of566 nm. The measured fluorescence, unlike the absorption,was extremely inhomogeneous and varied in intensity fromone area of the sample to another as well as from sample tosample. The energy of the peak remained fairly constant,

6.00

4.00

2.00 F-

0.00

-2.00 I-

-4.00

-6.00 I-

-8.00 _1.90

I I

1.95 2.00 2.05

PHOTON

1.00Cl)

-I

0

LIi0.50 C)

Ld

OL)(I)

0D

-IILI

I I I _0o.oo2.10 2.15 2.20 2.25 2.30

ENERGY (eV)Fig. 1. Absorption and fluorescence spectra of the experimentalglass in the vicinity of the band edge.

however, and may be taken as an estimate of the band-gapenergy.2 8 There is a strong luminescence at longer wave-lengths (700-800 nm) in samples freshly received from themanufacturer. When the low-energy luminescence is excit-ed by a pulsed Nd:YAG laser at 532 nm, it is found that theintensity decays with a time constant of the order of tens ofseconds. This phenomenon is associated with photodarken-ing and has some bearing on the optical nonlinearity, asdiscussed by Roussignol et al.4 All experiments describedbelow were conducted with already-darkened samples.

A detailed description of the fabrication of the planar andchannel waveguides used in this work has been given byCullen et al.5 Single-mode channel waveguides can be fab-ricated in less than 1 h by immersing photolithographicallymasked samples in molten KNO3 . The waveguides have across-sectional area of approximately 10 ,um2 and a length of6 mm. We have measured the loss due to scattering in thesewaveguides to be less than 0.5 dB/cm. All the experimentalresults reported in this paper were obtained using a singlewaveguide.

3. THEORY OF OPTICAL NONLINEARITIES

In order to have at least a qualitative understanding of theresponse of SDG to optical excitation, we use the Banyai-Koch plasma theory.27 In this theory, the absorption coeffi-cient a at frequency w in the presence of a density N ofelectron-hole (e-h) pairs is given by

a(w,N) = P tanh(hw - AT)

X E0 Im(r = 0)126r(hw - Em - Eg). (2)m

Here P is proportional to the modulus squared of the inter-band matrix element, ji is the net chemical potential of thee-h system, km(r) is an eigenfunction of the Wannier equa-tion describing the relative motion of the e-h pair in whichthe bare Coulomb potential is replaced by the screened one,Em is the corresponding energy eigenvalue, and T is thetemperature. The band gap Eg is renormalized according toEg = Eg° + bEg, where Eg0 is the bare band gap (at low N) andc3Eg is the band-gap shift due to the excited carrier density.br is a broadened delta function having the form

brfx) = (ER )cosh( xER) (3)

which is a phenomenological broadening factor intended tosimulate the Urbach smearing of the band edge. Here ER isthe exciton Rydberg energy, and r = 1.5ER. The carrier-induced changes in the refractive index can be calculatedfrom the carrier-induced changes in absorption through theKramers-Kronig transformation

n( = - d.V. 7 d (c)' (4)

where P.V. denotes the principal value.The plasma theory has been used to predict the excited-

carrier-induced changes in the absorption spectrum for bulkSDG, and qualitative agreement was obtained with experi-ment." A shift of the absorption edge to higher energies as

SLOPE = 1 /kT

0-v,

l

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a function of excited-carrier density was observed. A mea-sured shift in the absorption spectrum to higher energies(blue shift) is consistent with a band-filling mechanism.Band filling for a direct band-gap semiconductor may beunderstood as follows: The semiconductor is pumped withphoton energies above the band-gap energy such that elec-trons are elevated from the valence band to the conductionband; the excited electrons relax through phonon interac-tions to the lowest available states; consequently, as theconduction band fills, the density of states available forvalence-band-to-conduction-band transitions decreases,causing a decrease in absorption or, equivalently, a shift ofthe absorption edge to higher photon energies. The blueshift is accompanied by corresponding changes in the refrac-tive index, which are negative at energies below the gap andpositive above it. We shall see below that this mechanism isalso adequate for describing optical excitation in the Urbachtail of the density of states function.

The band-gap wavelengths for CdS and CdSe at T = 300 Kare 490.1 and 713.9 nm, respectively. 2 9 The band gap for themixed compound CdSxSel-x can be estimated at a givenfraction x by a linear interpolation between the two band-gap energies. At x = 0.6, for example, the band-gap wave-length so calculated is at 562 nm, close to the band-gapwavelength estimated above. A theoretical linear absorp-tion spectrum for bulk CdSO.6 SeO.4, assuming a band-gapwavelength of 562 nm, was calculated by using the plasmatheory. In order to calculate the absorption for the semicon-ductor-glass composite we divided the calculated absorp-tion by the volume fill fraction (p = 0.001) commonly quotedfor commercial SDG."1,14 While the errors in the fill fractionmay be expected to be quite large, we find reasonable agree-ment between experiment and theory when such a proce-dure is used, as shown in Fig. 2. The SDG absorption spec-tra predicted by the plasma theory for different densities ofgenerated e-h pairs are shown in Fig. 3. The absorptionedge shifts to higher photon energies with increasing densityof excited carriers. A Kramers-Kronig transformation ofthe differential absorption spectra yields curves of change in

25

EXPERIMENTAL

20 THEORETICAL

Z

a 10 \

<t5

'-'15 ~ ~ \

540 560 580 600 620WAVELENGTH (nm)

sorption spectrum used in semiconductor plasma theory (dashedcurve).

20

E-5 U ~~~~~~~ISCM-3

0

5405 - 6 8 0 2

0

L()m< 0

540 560 580 600 620WAVELENGTH (nm)

Fig. 3. Theoretical blue shift of absorption spectrum with increas-ing excited-carrier concentration.

3 x 10-'.

540 560 580WAVELENGTH

600 620(nm)

Fig. 4. Theoretical refractive-index changes with increasing excit-ed-carrier concentration calculated using Kramers-Kronig trans-formation of the data of Fig. 3.

refractive index versus excited-carrier density that are plot-ted in Fig. 4. These curves illustrate the sign reversal under-gone by the index change in the vicinity of the band gap.

4. EXPERIMENT

The experiment that we describe in this section is capable ofmeasuring most of the relevant parameters characterizingthe nonlinear-optical response of our material and has theadded advantage of operating in situ. In consequence, thecommonly quoted benefits of guided-wave configurationsfor nonlinear optics-diffractionless propagation, high pow-er densities, etc.-are taken advantage of. A time-resolved,pump-probe Mach-Zehnder interferometer is employed toprobe changes in the waveguide effective refractive index, aquantity that is, in general, complex.

The experiment is a modified version of a technique dem-

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PBSPBS . - M . . . I

P P PBS L L P

P BS

M

Fig. 5. The experimental apparatus: M's, mirrors; BS's, beam splitters; PBS's, polarizing beam splitters; P's, polarizers; HWP, half-waveplate; DL's, delay lines; L's, lenses.

onstrated by Halbout and Tang2 6 and recently adapted foruse in optical fibers by Cotter et al.3 0 The experimentalapparatus is shown in Fig. 5. A Nd:YAG-pumped R6G-dyelaser, which is mode locked and cavity dumped, is used togenerate 2-psec pulses at a repetition rate of 3.8 MHz. Ahalf-wave plate and a polarizing beam splitter divide thepulse into pump and probe components. The pump compo-nent is routed through a delay line and an electro-opticattenuator and is then coupled to the quasi-TEO mode of theSDG channel waveguide. The probe component is dividedbetween two arms of a Mach-Zehnder interferometer. Thewaveguide is situated in one arm, designated the signal arm,and the other arm is designated the reference arm. Theprobe polarization is rotated through 900 with respect to thepump so that the signal pulse train is coupled to the quasi-TM mode of the SDG waveguide. Since the pump andprobe pulses cannot be propagated in different directions ina guided-wave configuration, orthogonal polarizations arerequired in order to achieve discrimination between pumpand probe. The pump and probe fluences used in the ex-periment are 0.1-25 mJ/cm 2 and 50 ,uJ/cm2, respectively,

thus minimizing probe-induced effects. The pump beam isblocked by polarizing elements after it has traveled throughthe sample. The signal and reference beams generate an

interference pattern at the faceplate of a vidicon camerahead, and the fringe patterns are digitized and sent to apersonal computer for analysis using fast-Fourier-transformtechniques. The fast Fourier transform yields both thephase 0 and the amplitude A of the fringe pattern, thusallowing the real and imaginary parts of the complex refrac-tive index to be monitored independently. The influence ofadditive noise is minimized by using the fast-Fourier-trans-form procedure.

Several experiments can be conducted with this setup:(A) The probe beam can be blocked, and the changes intransmission of the waveguide induced by the pump beamcan be measured as a function of pump fluence. (B) Theprobe and the pump can be temporally overlapped, and thechanges in transmission of both pump and probe beams canbe measured as a function of pump fluence. In this case,optically induced anisotropy in the waveguide can be esti-mated. (C) The pump and probe beams can first be tempo-rally overlapped and then separated in time and fringe phaseshifts measured as a function of pump fluence in each case.The different response times and signs of thermal and elec-tronic nonlinearities in SDG then allow the thermal andelectronic contributions to be resolved. (D) Finally, thepump fluence can be set so that the waveguide is fully satu-

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Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B 679

rated and the fringe phase shifts and visibility changes mea-sured as a function of the time delay between pump andprobe. The changes in the real and imaginary parts ofrefractive index can then be deduced, together with thesaturated values of these quantities. The wavelength of thelaser can be varied in all these experiments, and thereforethe spectral response can be obtained. A comprehensivecharacterization of the nonlinear-optical response of the ma-terial in waveguide form is attained when the experimentsdescribed above are conducted.

5. RESULTS

(A). Saturable AbsorptionThe transmission of the waveguide measured as a function ofoptical fluence at several wavelengths below the gap is de-picted in Fig. 6(a). Fluence, rather than intensity, is therelevant independent quantity in all our experiments, since

60r .. I I .

50

40z0C.! 30

U)Z 20

10

A

U- - - L- - M- .'

0- _ _Z- _ _0 , _0 _

V- -& -- -A - A-

QL0.01

590 nm

587.5 nm

E.,IsU

- 585 nm

90 ' 580 nm,A- A

, _ -A

FLUENCE (J/cm2)10

U, . .. ... ....... _, . ..

(b) 0.01 0.1 1 10FLUENCE (mJ/cm2)Fig. 6. (a) Measured increase of transmission with input fluence.Note that unity transmission is not achieved even when the wave-guide is fully saturated. (b) Calculated increase of transmissionwith input fluence. Unity transmission is predicted under satura-tion conditions.

our laser pulses (2 psec) are shorter than the interbandrelaxation time (20 psec). The evolution of a pulse througha medium that exhibits carrier-dependent absorption can becharacterized by the following two equations 31:(a n a(+ o )I(zt) = -a(A, N)I(z, t),

N N- N. +( N)at hco

(5)

(6)

where no is the linear index of refraction, c is the speed oflight in vacuo, I is the instantaneous intensity at position zand at time t in the waveguide, a is the absorption coeffi-cient, A is the normalized detuning from resonance, N is theexcited-carrier density, Ni is the intrinsic carrier density, isthe phenomenological relaxation time, and X is the angularoptical frequency. The functional dependence of the ab-sorption coefficient on carrier density and frequency in SDGcan be calculated with the plasma theory, as described inSection 3. A numerical solution of Eqs. (5) and (6) using aplane-wave approximation with a 10-,um2 waveguide cross-sectional area, a relaxation time of 20 psec, an intrinsiccarrier density of 1015 cm-3 , and a length of 6 mm yieldscurves of transmission versus fluence as shown in Fig. 6(b).The low-power transmission of the theoretical curves is low-er than those of the experimental curves owing to the mis-match between the tail absorption and the plasma modeldepicted in Fig. 2. The theoretical curves differ from theexperimental curves in one crucial respect: The theoreticaltransmission tends to unity in the Urbach tail, whereas theexperimental transmission tends to a well-defined value lessthan unity, which is different for each wavelength. Thelatter type of functional dependence of the transmission onfluence resembles that of four-level systems, 32 in which free-carrier absorption plays an important role in preventingunity transmission from being attained. Values of the ex-perimental saturation fluence Tsat versus wavelength aretabulated in Table 1, where t'fsat is defined as the fluence atwhich the waveguide transmission is the average of the lin-ear and fully saturated values. The saturation fluence de-creases as the detuning from the band-gap wavelength in-creases, owing to the rapid decrease in the density of states.

(B). Optically Induced AnisotropyIt is well known that the induced nonlinear refractive-indexchange experienced by a probe beam polarized parallel tothe pump beam is, in general, different from that experi-enced by a probe beam polarized perpendicular to thepump.25 Optically induced anisotropy arising from momen-tum state filling has been observed in semiconductors bySmirl et al.33 The anisotropy can be observed only on timescales shorter than the momentum relaxation time, which isusually much shorter than the interband recombinationtime. To test the influence of optically induced anisotropyin these experiments, in which the pump and probe beamsare perpendicularly polarized of necessity (owing to theguided-wave format), we measured self-induced transmis-sion changes of the pump beam and transmission changes ofthe perpendicularly polarized probe beam at zero delay.These changes are shown in Fig. 7. No appreciable differ-ences are observed. This may be due to the limited timeresolution of our pulses. Also, the (presumably) random

(a)

zI-,W0LO

LO

F-

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Table 1. Waveguide Saturation Fluence

Wavelength (nm) Saturation Fluence (mJ/cm2)

590 1.6587.5 2.6585 3.0580 3.7576 4.5

1 .00

C)C 0.80

-0E 0.60

-0 400.2U)

U):70.20

DI

ooo L0.00 1.00 2.00 3.00 4 00 5.00

INPUT FLUENCE (mJ/cm 2 )Fig. 7. Absorption saturation at wavelength of 585 nm. The solidcurve shows the transmission of the quasi-TE pump mode. Theopen circles show the transmission of the quasi-TM probe mode inthe presence of a quasi-TE pump.

orientation of the crystallites would tend to average tran-sient anisotropies over all possible probe polarizations. Itcan be concluded, therefore, that optically induced anisotro-py was not a significant factor in our experiments.

(C). Thermal and Electronic Components of theNonlinearityThe change in refractive index measured in the waveguide atan optical delay TD of -50 psec (equivalent to a delay of 260nsec between the probe and the previous pump pulse) isplotted in Fig. 8 as a function of incident fluence. A wave-length of 580 nm was used in this experiment. The changein index is clearly linear, has a positive sign, and is thermal inorigin. If we assume that the thermal relaxation time isconsiderably longer than 260 nsec, then the slope of thecurve yields the thermal n2 for the SDG waveguide underpulsed excitation conditions. The dependence of refractiveindex on temperature in CdS, CdSe, and CdS.Selx singlecrystals has been studied by Lisitsa et al. 3 4 A positive rateof change of index with respect to temperature (dn/dT) of10-4 deg-' is typical. The glass host used in our experi-ments (Schott #7183) has a composition dominated by sili-con, sodium, and zinc oxides and is therefore similar to zinccrown glasses, which typically have positive dn/dT of magni-tude 10-6 to 10-5 deg-. 35 Since the volume fraction ofsemiconductor in the glass-semiconductor composite usedin our experiments is approximately 3 orders of magnitudelower than the volume fraction of glass, we suspect that the

thermal nonlinearity shown in Fig. 8 is dominated by theresponse of the glass. The slope of the curve yields a ther-mal n2,T of approximately 4 X 10-14 m 2/W in a sample havingan absorption coefficient of 5 cm-'. Bertolotti et al.3 6 haveobserved a thermal n2,T of order 10-12 m 2/W in a Corningcolored-glass filter having an absorption of approximately100 cm-'. If we make the reasonable assumption that n2,Tscales linearly with the absorption coefficient,36 then ourmeasurement of n2,T and that of Bertolotti et al. are in goodagreement. Patela et al. have presented evidence of a ther-mal nonlinearity having negative sign in a 7059 glass wave-guide-SDG substrate.3 7 These measurements were con-ducted at a wavelength (488 nm) shorter than the band-gapwavelength for pure CdS, and a negative change in refractiveindex as a function of increasing temperature could indeedbe expected in such a case.

Also shown in Fig. 8 is the change in refractive indexmeasured at TD = 4 psec. This curve first exhibits a negativechange in refractive index, passes through a minimum, andthen rises with fluence. The curve crosses the axis andassumes a net positive, linear dependence at high fluence.We attribute the refractive-index dependence on fluence atTD = 4 psec to the influence of competing thermal and elec-tronic nonlinearities. The electronic nonlinearity saturatesas the tail states of the band are filled. After the tail stateshave been filled, the dominant mechanism underlying ob-served refractive-index changes is thermal. The slope of thehigh fluence dependence at TD = 4 psec is smaller than theslope of the line measured at TD = -50 psec. This is consis-tent with the saturable absorption results presented in Sub-section 5.A. At time delays less than the interband relax-ation time TR the absorption coefficient of the waveguide isless than at times greater than T

R, owing to the effect of bandfilling. The energy transferred to the lattice is proportional-ly smaller, and, therefore, the rate of change of refractiveindex with respect to the incident fluence is smaller in the

4 x 10-5

*0 5 10 15 20 25

FLUENCE (mJ/cm 2 )30

Fig. 8. Refractive-index changes in the waveguide measured as afunction of fluence. At a time delay of 260 nsec, the refractive-index change is induced by purely thermal effects. At a time delayof 4 psec, the refractive-index changes are induced by a combinationof electronic and thermal effects, with thermal effects dominating athigh fluences.

3 3n A-260nsec delay

2

- An - 4psec delay -

-1=dea

_7

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Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B 681

1 4

1 2

10

ELECTRONIC + THERMAL8

6 THERMAL

U)>4

2

00 5 10 15 20 25 30

INPUT FLUENCE (mJ/cm 2 )Fig. 9. Fringe visibility change as a function of fluence. For a timedelay rD = 260 nsec, which is greater than the interband relaxationtime TR = 20 psec, the visibility change is negative and is thermal inorigin (curve marked THERMAL). For a time delay 'D = 4 psec(i.e., shorter than the interband relaxation time), the visibilitychange is initially dominated by electronic effects, which saturate(curve marked ELECTRONIC + THERMAL). Thermal effectsthen begin to dominate and cause the visibility to decrease.

thermally dominated limit. In Fig. 8 we finally exhibit thecurve at TD = 4 psec, corrected to show only the electroniccomponent. Saturation of the electronic changes in refrac-tive index establishes limits on the minimum length re-quired for successful operation of an all-optical device.

Further evidence of the influence of thermal nonlineari-ties is provided on examination of the fringe visibility depen-dence on fluence in the two time regimes. Visibility is heredefined as the ratio of the peak-to-peak amplitude of thespatially varying fringe component to the average amplitudeof the fringe. The interferometer is initially adjusted suchthat, at low fluences, the signal beam has a lower intensitythan the reference beam. This ensures that the interferom-eter initially operates at less than optimal fringe visibility.We first consider the case when TD is much longer than TR.

In this case, the visibility of the fringes decreases linearlywith increasing fluence owing to a thermally induced in-crease of the absorption, as shown in Fig. 9. When TD is

shorter than TR the onset of absorption saturation due toband filling in the waveguide initially improves the visibilityof the fringes. When the band has been filled up to energiescorresponding to the pump photon energy, the visibilitychange saturates and subsequently decreases with increas-ing fluence. The high fluence visibility decrease corre-sponds to a red shift arising from thermal effects.

(D). Electronic Components of the NonlinearityWe now consider the case when the thermal contributionsare assumed to be constant in the experiment, i.e., the sam-ple is investigated under hot conditions with the pumpfluence maintained at a constant value. Convolutionsamong the pump-induced excitation of the waveguide, theprobe response, and the time-averaging response of the vid-eo camera are likely to be quite important in the interpreta-

tion of this experiment and are currently under theoreticalinvestigation. We neglect these effects here. The intensitydistribution of the probe fringes at the output of the inter-ferometer may be described approximately by the plane-wave interferometer equation

(7)

where I, and 12 are the reference and signal beam intensities,respectively. The signal intensity I2 is dependent on theabsorption a, and the phase difference between the signaland reference beams is dependent on the (effective) refrac-tive index n of the waveguide. The quantities a and n inturn depend on the probe delay TD and on the local density ofphotoexcited carriers N. Thus a and n are functions of thespatial coordinates in the waveguide. Changes in amplitudeand position of the fringes measure the transmission changesand phase shift in the waveguide, respectively. The ob-served phase shift AO. is related to the nonlinear refractive-index change An by

ILAO~~~~/ = (27T/X) foAn(z)dz, (8)

where X is the free-space wavelength. When the waveguideis fully saturated,

AI\¢sat = (27r/X)AnsatL. (9)

The normalized transmission change of the waveguide isgiven by

I _______-__I I I

-50 0 50 1 00

TIME (psec)Fig. 10. Raw fringe data obtained from the time-resolved Mach-Zehnder interferometer. The data are portrayed as a time-depen-dent interferogram by the following procedure: Each fringe wasnormalized to a peak value of unity and a threshold value of 0.7chosen. Below this value the fringe amplitude is depicted in black,while amplitudes above threshold are depicted in white. The move-ment of the fringes in space is easily depicted as a result. However,changes in fringe amplitude (visibility) cannot be depicted by usingthis procedure.

Finlayson et al.

I = I, I2(a) 2 CIlCI2Wcos[O(n)],

682 J. Opt. Soc. Am. B/Vol. 6, No. 4/April 1989

135

U,a)

0) 90

_0

I-Ir 45C)

C')100nA:M

-50 -25 0 25 50 75 100(a) PROBE DELAY (psec)

20-

15

0I- 10

-1

5

0

probe delay is shown in Fig. 11(a). A pump fluence of3.61 X 10 approximately 24 mJ/cm 2 was used for the measurements so

that the waveguide was fully saturated. The increase inphase angle near zero delay corresponds to the turn-on of the

2.41 waveguide as the pump pulse excites the material. Thepeak phase change at this wavelength was 1350 70, corre-sponding to a saturated index change Ansat of -3.6 + 0.2 X10-5. The sign of the refractive-index change was estab-

1.20 < lished by an independent adjustment of the reference pathlength. Exponential relaxation with a time constant of ap-proximately 19 psec was determined by plotting the phase

0.00 change on a logarithmic scale.The change in transmission, calculated from the change in

fringe amplitude using Eq. (10), is plotted in Figure 11(b).- -1.20 The saturated transmission at this wavelength is 20 times125 the linear transmission. The magnitude of the transmission

change was independently confirmed by a direct measure-ment of transmission saturation. When plotted as absorp-

1.0

(nI

C-

Icoz

(a)

() \ -50 -25 0 25 50 75 100 125(b) PROBE DELAY (psec)

Fig. 11. (a) Phase shift and corresponding saturated refractive-index change as a function of probe delay. (b) Transmission changeas a function of probe delay.

0.8

0.6

0.4

0.2

0.05.0 -2.5 0.0

TIME (psec)

1.0

ATITO T- ToT -

= [2(a) - 12(aO)]/12(aO) (10)

for constant signal intensity incident on the waveguide. T isthe transmission of the sample, To is the linear transmission,and ao is the corresponding linear absorption. Since thefringe amplitude A is related to I2(a) through A2 = 4&112(a),the normalized transmission change can be written as

T/T = (A2 -A2)/AO2, (11)

where A is the fringe amplitude when the probe is wellseparated from the pump in time.

The behavior of the fringes as a function of time delay isdepicted in Fig. 10 for a wavelength of 578 nm. A sharpmovement of the pattern is evident in the vicinity of TD = 0-A corresponding increase occurs in the fringe amplitude. Asthe probe delay is increased, the fringes return to their equi-librium positions as the excited-carrier population in thesemiconductor decays owing to recombination. The de-tailed functional dependence of the nonlinear phase shift on

- 0.8

C

_ 0.6

- 0.4

zF 0.2z

0. 0 I--5.0

(b)0.0

TIME (psec)Fig. 12. (a) Measured autocorrelation trace of pump pulses in a1.2-cm waveguide at a wavelength of 588.5 nm. (b) Theoreticalsharpening of leading edge of pulse in a 0.6-cm waveguide at awavelength of 580 nm owing to saturable absorption.

I-

I I I I

I I

II

INPUT PULSE AIm

I~~~~~~~

/1 TUT PULSE

_ /1/ \\f~~~~~~~~~~~~/ ~~~~~~~~~~~~~~~I I|

2.5 5.0

I5 I .

Finlayson et al.

I I I

Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B 683

5 x 10- I

4

3

570 580 590 600 610 620WAVELENGTH (nm)

Fig. 13. Spectral dependence of Ansat. The experimental pointsare shown as filled circles with error bars. The theoretical predic-tion is shown as the smooth solid curve.

tion, on a logarithmic scale, exponential decay was observedwith a time constant of approximately 22 psec, close to thatmeasured for the phase changes.

The turn-on times of the absorption and phase curvesdiffer by a factor of 2, and, in the phase measurement case,changes are apparent some 8-10 psec before the pump andthe probe are temporally overlapped at zero delay. Zerodelay was determined in the experiment by interferingequal-intensity pump and probe beams having parallel po-larizations without the waveguide in the apparatus. Thefringes obtained in this fashion were visible over time delaysclose to the pulse widths measured using autocorrelationtechniques. The earlier and slower rise in the phase-shiftcurve may be due to the high fluence used in the experiment.An autocorrelation trace of the dye-laser pulse used in theexperiment is shown in Fig. 12(a). It is apparent that thebase of the pulse is several times wider than the FWHM.Since the fluence used in the experiment (24 mJ/cm 2 ) ismuch greater than the saturation fluences quoted in Table 1,it is evident that the waveguide can be saturated by leadingportions of the pulse such that the effective rise time issmeared over time scales longer than 2 psec.

We attribute the sharper turn-on time of absorption tonarrowing of the pump pulse as it passes through the SDG,which acts as a saturable absorber. The dashed curve in Fig.12(a) shows a typical autocorrelation trace of a pulse after ithas passed through a 1.2-cm waveguide at a wavelength of588.5 nm. Comparison of a number of traces shows that theoutput pulse is approximately 16% narrower, on average,than the dye-laser pulse. Figure 12(b) shows the theoreticalnarrowing of a sech2 pulse passing through a 0.6-cm SDGwaveguide at a wavelength of 580 nm, calculated using Eqs.(5) and (6). Allowing for the different conditions for whichthe experimental and theoretical curves were obtained, it isevident that substantial pulse narrowing occurs in thesewaveguides in the vicinity of the band gap. Thus, while thephase-shift curves obtained in our experiment represent theintegrated change in phase of the pulse as it passes throughthe waveguide, the transmission (absorption) curves repre-

sent the ratio of the instantaneous pulse intensities at theoutput to the instantaneous pulse intensities at the input.Consequently, the turn-on times of the two curves are differ-ent.

Finally, we present the experimentally measured disper-sion in the saturated refractive-index change with wave-length. The results are shown in Fig. 13, together with theresults predicted by the plasma theory. Good agreement isfound at longer wavelengths, and the peaks of the dispersionoccur at the same wavelength. The experimental peak re-fractive-index change is a factor of 2 higher than that pre-dicted by theory.

6. DISCUSSION AND CONCLUSIONS

We have presented details of a pump-probe interferometricexperiment that is capable of determining saturated valuesof optically induced changes in the complex refractive indexof a material in waveguide form. Using the experiment, weinvestigated CdSSel-x-doped glass channel waveguides andfound reasonable agreement with the Banyai-Koch semi-conductor plasma theory, which finds band filling to be theprimary mechanism underlying the observed nonlinearity.A residual absorption, possibly due to free-carrier effects, isobserved in the experiment that is not predicted by thetheory in its current form. The interferometric experimentyields information on the dynamical response of the materi-al, including relaxation and pulse-narrowing effects. Therelaxation time in SDG channel waveguides is fast and isconsistent with results obtained by other authors on photo-darkened samples.4 The fast relaxation time is probablydue to e-h recombination enhanced by a high concentrationof surface defects. An important feature of the interfero-metric technique is that thermal and electronic nonlineari-ties are rendered separable.

The most important question to be answered by this studyis the following: Do the SDG waveguides studied here ex-hibit nonlinear-optical phase changes that make them agood choice for phase-dependent integrated-optical switch-ing? The answer to this question is, definitively, no. Stege-man et al. have established a parameter W for nonlinear-optical directional coupler operation that is a useful figure ofmerit for a given material. 38 The parameter W combinestwo criteria that must be met for successful device operation:a switching criterion that says that the integrated phase shift(0 = k0IAnsatlL) in a half-beat-length directional coupler oflength L must be at least 4ir for complete switching to occurand a throughput criterion that says that L must be less thanone absorption length (Lo = 1/ao) if a substantial amount ofpower is to be available at the device output. When the twocriteria are taken together, the figure-of-merit parameter Wthen becomes

(12)Ansata 0 X

A plot of W versus wavelength is shown in Fig. 14. Alsoshown is the device length Lo that would be required to meetthe W figure of merit. A reasonable fit to the W data isobtained with a straight line, indicating that the saturatedrefractive-index change is directly proportional to the ab-sorption and varies with the second power of the wavelength.A linear relationship between the small signal XM3) and ao was

Finlayson et al.

684 J. Opt. Soc. Am. B/Vol. 6, No. 4/April 1989

0.5 100.0

0.4 80.0

0.3/ 60.0

r A/~~~~~~~~~

EE

0.2 40-0 )

0.1 2~~~~~/ 0.00.0 - /.50. 580.0 590.0 600.0 610.0 620.0

WAVELENGTH (nm)Fig. 14. Spectral dependence of the figure of merit W. The solidline is a linear least-squares fit to the experimental data. Alsoshown in the device length Lo required in order to attain the corre-sponding value of W.

previously observed by Roussignol et al.4 and Horan et al.13

The maximum value of W is less than 0.4, and, therefore,CdSO.6SeO.4 semiconductor-doped glass has a figure of meritthat is too low for practical device application. This con-firms the prediction of Wright et al. based on theoreticalstudies.3 9 The trend of W versus wavelength is upward, andit can be expected that at longer wavelengths W > 2. Insuch a case the device length Lo would be of the order ofmeters, making device operation possible only in a fiberconfiguration.

The nonlinear absorptive changes that are available inSDG can possibly find application, however, since they areboth substantial and fast. We recently described switching/modulation behavior observed in directional couplers fabri-cated in SDG.16 In that paper we presented experimentaland theoretical evidence that the switching was dominatedby absorptive rather than dispersive effects. The interfero-metric results presented here confirm these conclusions.

ACKNOWLEDGMENTS

We gratefully acknowledge the assistance of Stephan Kochin providing us with the plasma code on which the theoreti-cal calculations presented in this paper are based. We alsothank Ewan Wright for his many helpful suggestions regard-ing this work and Alain Villeneuve, Mike Sundheimer, andBarrett Potter for their assistance in the laboratory. Thisresearch was supported by the National Science Foundation(EET-860-4374), the U.S. Army Research Office (DAAG-29-85-K-0173), and the Optical Circuitry Cooperative in theUnited States and by the Science and Engineering ResearchCouncil in the UK. Collaboration between the groups wassupported by a NATO travel grant.

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1. Special issue on integrated optics, IEEE J. Lightwave Technol.LT-6 (1988).

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