292 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988
Frequency doubling in Ti:MgO:LiNbO 3 channel waveguides
Fredrik Laurell and Gunnar Arvidsson
Institute of Optical Research, S-100 44 Stockholm, Sweden
Received July 31, 1987; accepted September 25, 1987
Second-harmonic generation (SHG) in channel waveguides fabricated by titanium diffusion into MgO-dopedlithium niobate is studied. A conversion efficiency for SHG of 2.4%/W has been obtained for a 16-mm-longwaveguide by using a Nd:YAG laser as pump source. The conversion efficiency is lower than the theoreticalprediction. This difference is attributed to inhomogeneities along the waveguide. The channel waveguides usedcarried several modes at the second-harmonic wavelength; those modes, phase matched above room temperature(-80C), showed substantially lower sensitivity for photorefractive damage than others phase matched at roomtemperature.
1. INTRODUCTION
Waveguides are showing promise for exploiting nonlinearphenomena, as they make long interaction lengths with highpower densities possible.' Small compact wavelength con-verters with high conversion efficiencies, primarily based onsecond-order nonlinear phenomena, can be built.2 Suchcomponents would find applications easily. The high quali-ty of Ti:LiNbO:3 waveguides, the ease of fabrication, and thefairly high nonlinear coefficients have made them the mostsuccessful type of waveguide for nonlinear integrated opticsto date. 3
Certain disadvantages exist with Ti:LiNbO3 waveguides,however. The wavelength region over which phase match-ing is possible is limited. Furthermore, the photorefractiveeffect, often referred to as optical damage, limits the power-handling capability, especially at short wavelengths. Mg-doped LiNbO : has some advantages compared with conven-tional materials, especially for nonlinear applications.LiNbO;, doped with more than 4.5% MgO has shown a con-siderable reduction of the photorefractive effect in bulksamples. 4' 5 Becker6 studied interferometers fabricated byTi diffusion in this material and found a reduction of thephotorefractive effect, although not so drastic as measure-ments on bulk samples have shown.4'5
The Mg doping changes the birefringence slightly.Therefore the bulk phase-matching temperature (90° phasematching) for second-harmonic generation (SHG) at X =1.064 ,um changes from approximately +50 C in undopedcongruent LiNbO:3 to approximately +105 0 C in congruentMgO:LiNbO. 5 7 8 In general, phase matching in LiNbO3waveguides is achieved at temperatures below the bulkphase-matching temperature. The higher temperaturemakes the experiments more convenient, and waveguidescould be designed for SHG at room temperature. Also, witha higher operating temperature, the conductivity is higher,and thus the photorefractive effect is reduced.
These features make Ti:MgO:LiNbO:l waveguides an in-teresting alternative for wavelength conversion. Promisingresults, in terms of high average powers generated at 532 nm,for planar waveguides have been reported by Fejer et al.9
We recently reported results of fabrication and character-
ization of waveguides in MgO-doped LiNbO3 .-' We nowreport experiments on SHG in channel waveguides in thismaterial. We have achieved a high conversion efficiency forSHG in 10-,vm-wide channel waveguides at fairly low inputpower. We have also seen an important reduction of thephotorefractive effect above room temperature.
2. THEORY FOR SECOND-HARMONICGENERATION IN OPTICAL WAVEGUIDES
Both the theoretical description of second-order nonlinearinteraction and the coupling of energy in waveguides havebeen treated by several authors.1- 13 We will use the follow-ing notation in this paper. The TE field components for thepropagating modes will be described by
E(x, y, z) = Af(x, y)e-ioz + c.c., (1)
where , = 27rNeff/X, Neff is the effective refractive index andA corresponds to the amplitude. If the transverse distribu-tion C (x, y) is normalized so that
(2)f: J:6(X, y)12 dxdy = 1,
and if we define an overlap integral according to
IOVL = J J ~fw6w@2w* dxdy
and a corresponding effective overlap area as
Aov, = (IOVL) ,
we obtain for the conversion efficiency ij,
P2w deN22 A s2(AL= = L9 sincll
(3)
(4)
(5)
where PI is the fundamental power, p2, is the second-har-
monic power, N., and N((,, are the effective refractive indicesat w and 2 , respectively, L is the length of the waveguide,and
Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 293
C = 2 7 C 3E0 CE0X2
We have assumed that depletion of the pump can beneglected. The effective refractive indices introduced arethose that are appropriate in the case of 900 phase matchingin LiNbO3 when the birefringence is used to obtain phasematching. For this case an ordinary mode at the fundamen-tal frequency can be phase matched to a second harmonic(SH) extraordinary mode.
Equation (5) is identical to the corresponding expressionfor the case of plane waves with the fundamental intensity I0= P0/AovL. Thus for guided waves we have the same con-version efficiency as we would have in a plane-wave case withthe same power uniformly distributed over a cross sectionAOVL = (IOVL)
To optimize the conversion efficiency we need to maxi-mize the overlap integral by choosing appropriate waveguideparameters. Under optimal conditions the effective overlaparea AOVL could be of the same order of magnitude as thecross-section area of the guide. The optimization is rathercomplicated, as the field distributions vary with both wave-length and polarization as well as with the waveguide profile;the waveguide profile also depends on a number of fabrica-tion parameters.' 4
The phase-matching condition is also of great importance.If it is not fulfilled along the whole waveguide the conversionefficiency will be reduced drastically.
A long waveguide is desirable because the conversion effi-ciency increases with the square of the length [ L2; Eq.(5)], but the phase-matching condition is simultaneouslydependent on L. The longer the channel, the more sensitiveit will be for variations in A#. For long channels there is acertain risk for variations in channel width caused by non-ideal image reproduction in the photolithographic process.
3. WAVEGUIDE FABRICATION
The substrate material was commercially available LiNbO3doped with 5% MgO and was supplied by Crystal Technol-ogy Inc. We fabricated different samples on x-cut materialoriented for y propagation by using two Ti thicknesses-470and 680 A-and two diffusion times-16 and 25 h. The Tiwas deposited by electron-beam evaporation, and the wave-guide pattern was formed by lift-off. Diffusion was carriedout at 10500C in an atmosphere of oxygen bubbled throughwater (1.5 liters/min, 250C). The waveguide length was 16mm.
tions and overlap integrals for different channel widths inthe samples to determine the channel width that gave thehighest conversion efficiency. The most efficient appearedto be a 10-sAm-wide waveguide fabricated from 680-A Tidiffused for 25 h. This guide was single mode for TM polar-ization at 1.064 Am and multimode for TE at 532 nm. Tocheck our calculations, we measured the intensity distribu-tion for the different modes at 532 nm with a charge-coupleddevice (CCD) array by exploiting SHG. The waveguide was
CHANNEL WAVEGUIDE INTENSITY DISTRIBUTION
i 0.5 0
NORMALIZED INTENSITY
CALCULATED -
MEASURED -----------
532 NM
TE 10
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-8 -6 -4 -2 0 2 4 6LATERAL DISPLACEMENT (m)
-8 - -2 6-3 -6 -4 -2 0 2 4 6 E
(am)Fig. 1. Comparison between calculated and measured near-fieldintensity distribution for the TE10 mode in a 10-,um channel wave-guide (680-A Ti, 25 h) at 532 nm.
CHANNEL WAVEGUIDE INTENSITY DISTRIBUTION
NORMALIZED INTENSITY LATERAL DISPLACEMENT (m)
4. WAVEGUIDE CHARACTERIZATION ANDEVALUATION
The conventional prism-coupling method was used to deter-mine the effective indices of planar and channel waveguidesfor both TE and TM polarization. This determination wasdone for nine different wavelengths between 0.458 and 1.15gm. Index profiles were deduced for planar and channelwaveguides by using the WKB method and the effective-index method.' 5
As mentioned in Section 2, good overlap between the fun-damental and the SH waves is important. Therefore, usingthe effective index method, we calculated the field distribu-
-._' I ICALCULATED a:
MEASURED -----------
1064 NM -J
TM 0o 0ty \
-10 -8 -6 -4 -2 0 2 4 6 8 10MICRONS
(Am)Fig. 2. Comparison between calculated and measured near-fieldintensity distribution at 1.064 ,um for the TMOO mode in the samewaveguide as in Fig. 1.
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F. Laurell and G. Arvidsson
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294 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988
XY RECORDER
Fig. 3. The experimental setup used for the conversion-efficiencymeasurements.
excited with light from a Nd:YAG laser at X = 1.064 Am. Bytuning the phase matching with temperature we could selec-tively excite the modes at half the wavelength, one by one.The near-field distribution was determined from scans inboth vertical and transverse directions. Our results werefound to be in very good agreement with the calculateddistribution (Fig. 1).
The CCD array unfortunately could not be used at 1.064gm since it has a poor modulation-transfer function thatsmears the image. Instead we magnified the near-field pat-tern of the waveguide and scanned the image with a small Gedetector and thereby deduced the intensity distribution.We had a somewhat larger deviation from the calculation inthis case, as can be seen in Fig. 2.
5. MEASUREMENT TECHNIQUE
A Nd:YAG laser at A = 1.064 Am was used as a pump for theSHG experiments. To achieve high peak power but lowaverage power, which is attractive to minimize the influencefrom the photorefractive effect, the laser was run Q-switchedwith 250-nsec-long pulses at a repetition rate of 1200 Hz.
The experimental setup is illustrated in Fig. 3. The lightwas launched into the waveguide through the end face with a5X microscope objective, and the coupling efficiency wasapproximately 50%.
We used the conventional temperature-tuning method toachieve phase matching. The sample was mounted in ametal block, and the temperature of the metal block wascontrolled with high accuracy by using a Peltier element forboth cooling and heating.
To measure the SH light we generally used a photomulti-plier with a phase-locked amplifier. But for the conversion-efficiency measurements, which are described in Section 6,we used calibrated Si and Ge detectors in the visible andinfrared regions, respectively.
6. RESULTS AND DISCUSSION
The result from a typical measurement is seen in Fig. 4. TheSH intensity is plotted as a function of the temperature. Asthe temperature is increased the fundamental TMoo modewill be phase matched to different SH modes. The threehighest peaks correspond to phase matching to TEoo, TE10,and TE20 -
Figure 5(a) shows a calculated phase-matching diagramfor the 10-prm channel waveguide, for which the highestconversion efficiency was predicted. The fabrication pa-rameters are given in Section 4. The crossing points (opencircles) in the diagram correspond to the expected phase-matching temperatures for the most important mode combi-nations. These temperature values are in close agreementwith the experimentally obtained phase-matching tempera-tures, given in Fig. 5(b). The diagram of Fig. 5(a) is based onmeasured effective indices for this waveguide and Sellmeir'sequations for the refractive indices of the bulk material as afunction of temperature and wavelength. The parametersin the Sellmeir equations were deduced from phase-match-ing temperatures measured in bulk material at several wave-lengths.
We measured the SH power as a function of input power at1.064 pm for the different mode combinations and comparedthem with calculations. From the detector signal we calcu-lated the power levels inside the crystal, considering theFresnel loss. We also compensated for the depletion of thepump. Figure 6 shows the result of the measurements. Thesquare root of the SH power is plotted as a function of inputpower. Within the experimental errors, our curves are inagreement with the ideal case, which should be a straight
I-
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z
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z
w
I-zn
0 20 40
TEMPERATURE60
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80 100
Fig. 4. Measured SH power for a 10-ym channel waveguide (680-ATi, 16 h) as a function of temperature. The ripple at temperaturesbelow the main peaks is assumed to have its origin in inhomogenei-ties in the waveguide.
F. Laurell and G. Arvidsson
Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 295
(a)
-10 0 . 10pm -10-L4 L J -l I
TEQ0 1 90C
0 10pm
TE10 54 0C TE20 8l 0 C
(b)
Fig. 5. (a) Calculated diagram illustrating the phase-matching condition for a 10-jum channel waveguide (680-A Ti, 25 h). The waveguide issingle mode for TM polarization at 1.064 /im and multimode for TE at 532 nm. The TMOO mode is phase matched to the TE modes at differenttemperatures. The crossing points (open circles) correspond to the phase matching. For clarity, not all modes are shown. (b) Photographs ofthe observed near-field patterns at the SH frequency. The corresponding measured phase-matching temperatures are also given. They are ingood agreement with the calculated values.
line. As can be seen from the figure, the phase matchingfrom TMoo to TE10 is the most efficient. This mode combi-nation gave 43 mW of SH power for a fundamental power of1350 mW, which is equivalent to a conversion efficiency of3.2%. This conversion efficiency corresponds to a conver-sion efficiency of 2.4% for 1 W of input power. The powerrelationship between the peaks was in reasonably goodagreement with calculations of the overlap integrals, as canbe seen in Table 1. (The values in the table are normalizedto 1.0 for the strongest interaction.) Two sets of calculatedvalues are given. The first set is based on the waveguideprofiles deduced from measured effective indices. The sec-ond set is based on measured near-field patterns for theinfrared wavelength. The latter values are in better agree-ment with the experimental results. For the most efficientinteraction, TMoo - TEo0, both methods for calculationgave the same result: an effective overlap area AOVL = 215,um2. This value corresponds to a conversion efficiency of9.5%/W for the 16-mm waveguide length used.
The absolute conversion efficiencies are thus a factor of 4lower than the theoretical values. This occurrence is proba-bly due to some type of inhomogeneity in the waveguide.For example, a small variation in effective refractive indicesalong the waveguide gives a drastic reduction of the phase-matching peak and thereby a reduction of the conversionefficiency. Such a variation can be of different origin, for
example, varying toichiometry, Ti thickness, or stripewidth. Another cause could be temperature variationsalong the waveguide during the experiment. Because theexperimental phase-matching curve for waveguides hadpeaks of a characteristic shape with ripples (Fig. 4) insteadof the expected sinc2 function, some type of inhomogeneityin the waveguide is probably indicated. Bulk phase-match-ing experiments in these samples gave a 0.53 0C broad curve(FWHM) at 1050C for X = 1.064 Atm without this type ofripple. We therefore presume that the stoichiometry andtemperature are homogeneous, at least in the bulk crystal.Furthermore the appearance of ripple at room temperature,as can be seen for the TE0 2 mode in Fig. 4, tells againsttemperature fluctuations in the waveguide case. Also, gen-eration of second-harmonic light in higher-order modescould contribute to the ripple. Inspection of the near-fieldpatterns indicates, however, that such a contribution wasnegligible.
To investigate further the possible cause for this ripple wecarried out some simulations. We assumed a parabolic vari-ation of AS along the waveguide and calculated how it wouldaffect the phase matching as a function of the temperature.Examples of the result are seen in Fig. 7. In Fig. 7a, A isconstant along the whole waveguide. In Figs. 7b and 7c,where A/O varies along the waveguide, one sees a drasticreduction of the height of the main peak and a ripple of the
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F. Laurell and G. Arvidgson
296 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988
500 1000FUNDAMENTAL PEAK POWER (mW)
(a)
I~~~~~~~~~~500 1000
FUNDAMENTAL PERK POWER (W)
0
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F. Laurell and G. Arvidsson
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(c)
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(b)
Fig. 6. Square root of the SH power plotted versus input power for the TEoo (a), TE 1o (b), and TE20 (c) modes.
same type as in the experiments (Fig. 4). The experimentalcurve looks like a combination of Figs. 7b and 7c. From theamount of ripple observed, it seems plausible that inhomo-geneities along the waveguide can explain the deviation be-tween theory and experiment for the conversion efficiency.
A variation of AO along the waveguide could be compen-sated for by locally modifying the birefringence. This modi-fication could be implemented by using metal electrodes andthe electro-optic effect. Another possibility is to use a fur-nace with several adjustable temperature zones.
During the conversion-efficiency measurements we no-ticed a shift in the phase-matching temperature with in-creasing input power (Fig. 8). This shift was most obviousfor the TEO(O and TEl) modes. We assigned this shift to thephotorefractive effect.
The photorefractive effect has a strong wavelength depen-dence with a high sensitivity in the visible region and aproportionately low sensitivity in the near-infrared re-.rion.1'6, 7 We therefore assumed that the SH power leveldetermines the magnitude of the photorefractive effect.
In the illuminated region impurities are ionized by the SHlight. The photoexcited electrons are drifting along the +caxis out of the illuminated region where they are trapped.T[he charge separation gives rise to an electric field that
reduces the refractive indices locally through the electro-optic effect.'8 The extraordinary index in particular is af-fected because of the greater electro-optic coefficient. Tomaintain the phase matching, the decrease in the effectiverefractive indices has to be compensated for by temperaturetuning.
To explain the shift of the phase-matching temperature asfunction of the SH power we adopted a simple model. Weassumed that the SR light had a Gaussian intensity distribu-tion and, furthermore, that impurities within an area with anintensity exceeding some critical value were photoionized.Thus the area exposed for photoionization increases with the
Table 1. Normalized Conversion Efficiencies-Experimental versus Calculated Values for Various
Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 297
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Fig. 7. Simulation of the phase-matched power as a function of temperature deviation from the optimal phase-matching point in theunperturbed case. a, A homogeneous waveguide, that is, a waveguide with Afl constant along its length. b and c, A#f varies parabolically alongthe waveguide. Amax = 8 X 10-4 ,m- 1 and AMmax = 47 X 10-4 Am-1 are equivalent to temperature deviations of 1 and 60C, respectively; for atypical 10-Mm-wide channel waveguide the same values for Almax would correspond to a perturbation of the Ti stripe width of 0.3 and 1.7 um, re-spectively.
logarithm of the input power. Therefore, with a constantimpurity density in the crystal, the number of photoexcitedelectrons, the electric field, and the change in refractiveindices would increase logarithmically with the SH power.In Fig. 8 the phase-matching temperature is plotted for thedifferent mode combinations as a function of the logarithmof the SH power. The phase-matching temperature showssuch a predicted logarithmic dependence on SH powerabove a certain level, which is specific for each mode.
The locally induced charge distribution is neutralized bythe conductivity in the material at low power levels. At acertain power threshold the number of photoionized impuri-ties can no longer be balanced through the conductivity, anda change of the refractive indices will arise.
With higher operating temperature the conductivity isincreased, and thus the power limit for the photorefractive
effect is also increased, as can be seen in Fig. 8. The TEOOmode, phase matched at 191C, showed a detectable changein the refractive indices for a peak power as low as 0.45 mW,corresponding to an average power of 100 nW. The TE2 0mode, which was phase matched at 81'C, could carry 15times more power before the same change was observed.
For the TE10 mode, for which the highest conversion effi-ciency was obtained, the phase-matching temperature wasshifted from 54.3 to 59.10C, which corresponds to a change inthe effective refractive-index difference A(NeO - N,) = 3 X10-4. This value must represent a considerable modifica-tion of the refractive-index profiles and thereby the fielddistributions. At the highest power levels we also observeda slight distortion of the intensity distribution for the SHlight. Furthermore, when the field distribution is changedthe overlap integral should be affected, and thus the conver-
A~max - 410 pm 1
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F. Laurell and G. Arvidsson
io
A. .I
298 J. Opt. Soc. Am. B/Vol. 5, No. 2/February 1988 F. Laurell and G. Arvidsson
.01 7 0.1 . , ,,"1 ..,,.-,,,. ,
SECOND HARMONIC PEAK POWER
(a)
I0(MILLIWATTS)
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(c)
1 10POWER (MILLIWATTS)
1.001 0.-1 0.1 I 10 100SECOND HARMONIC PERK POWER (MILLIWATTS)
(b)
Fig. 8. The phase-matching temperature as function of SH power for the TE00 (a), TB10 (b), and TB20 (c) modes.
sion efficiency is also affected. In spite of these changes, wecould not observe any significant deviation from the expect-ed linear relation between square root of the SH power andthe pump power (Fig. 6).
7. CONCLUDING REMARKS
We have obtained a conversion efficiency of 2.4%/W in a 16-mm-long Ti:MgO:LiNbO 3 channel waveguide. This value ishigher than values previoulsy obtained for MgO-dopedLiNbO: by using planar waveguides.9 Our experimentalconversion efficiency is lower than the theoretical predic-tions for this specific waveguide by a factor of 4. We attri-bute this result to inhomogeneities in the waveguides. Fur-ther studies are needed to enable us to understand fully thecause of these inhomogeneities so that they can be mini-mized. Both experimental and theoretical values for theconversion efficiencies of the waveguides that we have inves-tigated are lower than our best results for Ti-diffused wave-guides in undoped LiNbO:1.' 9 The waveguide profiles ob-tained in MgO-doped material are different from those inundoped material. The most important difference is thatthe ordinary index increase varies almost linearly with theextraordinary index increase,' 5 which is in strong contrast tothe case of undoped LiNbO3. Therefore the optimal wave-guide parameters will be substantially different. Further
work is needed to optimize the waveguide parameters andthereby the conversion efficiency for the doped material.
We have observed changes in the phase-matching tem-peratures with increasing power, which we attribute to pho-torefractive index changes. When comparing mode combi-nations phase matched at different temperatures, we ob-served that these changes were substantially lower at highertemperatures. Thus an increased power-handling capabili-ty for visible cw light is possible at high operating tempera-tures, as demonstrated for SHG by Fejer et al.9
The phase-matching temperature in the bulk material wasfound to be 1050C, which is in close agreement with previ-ously published data.5 It is approximately 1000C higherthan for udoped LiNbO3. A consequence of this differenceis that new wavelength combinations could be phasematched at reasonable temperatures. This fact is anotherreason why MgO-doped material is an interesting alterna-tive to undoped LiNbO:3 for nonlinear applications.
ACKNOWLEDGMENTS
We are grateful to Anders Sjbberg for the fabrication andcharacterization of the waveguides as well as for many fruit-ful discussions. We also want to thank Leif Kjellberg forvaluable technical assistance and Kurt Bergvall, Rifa AB,for carrying out the Ti evaporation for some of the samples.
27 -
25-
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Vol. 5, No. 2/February 1988/J. Opt. Soc. Am. B 299
This work has been supported in part by the National Swed-ish Board for Technical Development.
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Fredrik LaurellFredrik Laurell was born in Lund, Swe-den, on October 6, 1957. He receivedthe M.Sc. degree in electrical engineer-ing from the Institute of Technology inLund in 1983. In the same year hejoined the Institute of Optical Research,Stockholm, where he is currently study-ing frequency conversion in LiNbO3waveguides.
