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spzs

1564 J. Opt. Soc. Am. B/Vol. 24, No. 7 /July 2007 Stivala et al.

Guided-wave frequency doubling in surfaceperiodically poled lithium niobate:

competing effects

S. Stivala,1,2 A. Pasquazi,1 L. Colace,1 G. Assanto,1,* A. C. Busacca,2 M. Cherchi,2 S. Riva-Sanseverino,2,3

A. C. Cino,3 and A. Parisi3

1Department of Electronic Engineering, and Nonlinear Optics and OptoElectronics Laboratory (NooEL),Consorzio Nazionale Italiano di Struttura della Materia (CNISM), Istituto Nazionale di Fisica Nucleare (INFN),

University “Roma Tre,” Via della Vasca Navale 84, 00146 Rome, Italy2Department of Electrical, Electronic and Telecommunication Engineering, University of Palermo,

Viale delle Scienze, 90128 Palermo, Italy3Centro per la Ricerca Elettronica in Sicilia (CRES), Via Regione Siciliana 49, 90046 Monreale (PA), Italy

*Corresponding author: assanto@ele.uniroma3.it

Received January 16, 2007; revised March 22, 2007; accepted March 22, 2007;posted March 28, 2007 (Doc. ID 78916); published June 15, 2007

We carried out second-harmonic generation in quasi-phase-matched �-phase lithium niobate channelwaveguides realized by proton exchange and surface periodic poling. Owing to a limited ferroelectric domaindepth, we could observe the interplay between second-harmonic generation and self-phase modulation due tocascading and cubic effects, resulting in a nonlinear resonance shift. Data reduction allowed us to evaluateboth the quadratic nonlinearity in the near infrared as well as the depth of the uninverted domains. © 2007Optical Society of America

OCIS codes: 190.2620, 190.4390.

(r[anw

2WAhf[LUtuoTgeemoaidpda

. INTRODUCTIONespite its extensive use and numerous applications since

he advent of electric field assisted periodic poling foruasi-phase-matched (QPM) parametric interactions,ithium niobate (LN) remains one of the most investigatedielectrics for harmonic generation (HG) [1–4]. Severalechniques have been developed for periodic poling basedn LN ferroelectric properties, including electric fieldoling and electron bombardment [5–7]. In addition,rocesses for waveguide fabrication in LN have beenastered. The most successful are those based on

itanium in-diffusion and proton exchange (PE) [8,9].ecently, aiming at the realization of shorter and shorteromain lengths for QPM-HG at lower wavelengths [10],s well as counterpropagating wave mixing [11–14],urface periodic poling (SPP) was introduced as a tech-ique to better control mark-to-space ratios in short-eriod QPM [10,15,16]. Surface periodic poling relies onverpoling a ferroelectric substrate and yields surface-ound periodic poled patterns with shallow domainepths as compared to the thickness of the treated sub-trate [15]. This approach, used in conjunction withaveguides of comparable depth, is expected to push for-ard some of the existing frontiers in backward HG by

hort-period QPM, presently limited to high-order inter-ctions [17–21].In this paper, we report the first results on picosecond

econd-harmonic generation (SHG) in surface periodicallyoled channel waveguides realized by proton exchange in-cut LN. The experimental results exhibit a linearhift of the SHG resonance with fundamental frequency

0740-3224/07/071564-7/$15.00 © 2

FF) excitation in the near infrared. The latter shift,eadily interpreted in terms of both quadratic cascading22–30] from the homogeneous portion of the waveguidend Kerr self-focusing, allowed us to infer the quadraticonlinearity and the domain depth in PE-SPP LNaveguides.

. SURFACE PERIODICALLY POLEDAVEGUIDES IN LITHIUM NIOBATE

lbeit initially demonstrated a few years ago, SPP of LNas only been recently combined with PE for waveguideabrication in order to enhance the nonlinear response31]. The 500 �m thick z-cut substrates of congruentN were spin-coated with photoresist (1.3 �m thick) andV exposed to define a �=16.8 �m periodic pattern on

he −z surface. The samples were then electric field poledsing 1.3 kV voltage pulses over a 10 kV bias in order tovercome the LN coercive field ��22 kV/mm�.o this extent, the −z surface was connected to theround and the +z to the high-voltage (HV) electrode,nsuring a uniform field distribution by means of anlectrolyte gel [15]. Applied voltage and current wereonitored via the HV generator–amplifier and an

scilloscope in order to achieve the sample “overpoling”fter domain merging, i.e., a complete ferroelectricnversion with the exception of relatively shallow unpoledomains at the −z LN surface under the photoresistattern (see Fig. 1) [15]. Chemical etching in diluted hy-rofluoric acid (HF) allowed to reveal the QPM gratingnd its 50:50 mark-to-space ratio. For waveguide fabrica-

007 Optical Society of America

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3SPEn

deasmfipei1tacvmVmsatt

dp

Ffi

FWfng

Fwp

Fcp

Stivala et al. Vol. 24, No. 7 /July 2007 /J. Opt. Soc. Am. B 1565

ion, the poled LN was initially coated with a SiO2 layer,here channel openings, from 1 to 7 �m in width, wereefined by standard photolithography and wet etching inF. Proton exchange was then carried out by dipping theN sample by the sealed-ampoule method [32] in a solu-ion of benzoic acid and lithium benzoate (3%) in order tobtain low-proton-concentration (� phase [33]) channelaveguides supporting TM-polarized modes. We verified

he compatibility between SPP and PE by chemicallytching the samples and using scanning electron micros-opy. Figure 2(b) is the optical micrograph of a typicalPM channel after HF etching. We also employed the pla-ar waveguides formed on the +z face of the samples foristributed (prism and/or grating) coupling at 632.8 nmnd evaluating the extraordinary index profile versus zsing the standard WKB technique [34]. This yieldede�z�=2.2027+0.0150 exp�−�z /2.601�1.8355�, i.e., a wave-uide depth of 2.6 �m, as shown in Fig. 2(a). Using Sell-eier equations [35] and measured TM effective indices

rom planar waveguides at �FF=1.55 �m (single mode,0=2.1395) and �SH=775 nm (two modes, N0=2.1845 and1=2.1801), respectively, we derived the profiles ne�z��ne�z�+ne�0� with ne�0�=2.1381 and �ne�z�0.01185 exp�−�z /2.601�1.8355� at �FF and ne�0�=2.1788nd �ne�z�=0.01395 exp�−�z /2.601�1.8355� at �SH, respec-ively, to be employed in the interpretation of the datarom SHG in the SPP-PE channels.

. SECOND-HARMONIC GENERATION INURFACE PERIODIC POLINGROTON-EXCHANGED LITHIUM NIOBATExperiments on SHG were carried out to characterize theonlinear response of the QPM channels. To minimize the

ig. 1. (Color online) Comparison of (a) bulk poling via electriceld and (b) surface poling owing to overpoling.

ig. 2. (a) Extraordinary index profile calculated by inverseKB from distributed coupling data. The dots are measured ef-

ective indices at 632.8 nm; the solid curve is a WKB fit. (b) Scan-ing electron microphotograph of a typical sample: the PE wave-uide is clearly visible on the inverted domain grating.

etrimental effects of photorefractive damage [36], wemployed a source operating at a repetition rate of 10 Hznd producing 25 ps pulses in the near infrared. Theource, sketched in Fig. 3, consisted of an optical para-etric generator fed by a tunable oscillator and an ampli-ed frequency-doubled Nd:YAG pump at 1.064 �m. A dis-ersive element (grating) was introduced in the cavity toffectively narrow the pulse linewidth to �2 cm−1 in thenterval of wavelength tunability between 1.1 and.6 �m. Following a spectrometer and a single-pulse au-ocorrelator, the beam was spatially filtered, collimated,nd end-fire coupled in the channels through a 20� mi-roscope objective. A TEM00 spot of waist w0�3.6 �m pro-ided the best in-coupling efficiency. The output funda-ental and second-harmonic profiles were imaged withidicon and Si-CCD cameras, respectively, using a 63�icroscope objective; energy and peak power were mea-

ured with Ge and Si photodiodes and a dual-input boxcarverager. All measurements were taken at room tempera-ure with the aid of a Peltier cell and a temperature con-roller.

Second-harmonic generation measurements were con-ucted either at a fixed wavelength by varying the FF in-ut power or by scanning the FF wavelength, ratioing the

ig. 3. (Color online) Setup for SHG measurements. HWP, half-ave-plate; BS, beam splitter; OB, microscope objective; PD,hotodetector.

ig. 4. Measured (open circles) and predicted (solid curve) SHGonversion efficiency versus FF wavelength for a launched peakower of 2 kW.

stwoLFttst�ccPr

o(cfsas

sS

4Ctstctlpc�svggfgqa1ntmc

poQwcertimpacontat

wa

Fett

Fv

Fa

1566 J. Opt. Soc. Am. B/Vol. 24, No. 7 /July 2007 Stivala et al.

econd-harmonic output to the fundamental input to ob-ain the conversion efficiency. At variance with [37], pulsealk-off and group-velocity dispersion were uninfluent,wing to the picosecond pulse duration and sample length=1 cm. Typical results versus wavelength are shown inig. 4 for an FF input peak power of 2 kW: even thoughhe data (symbols) are plotted versus wavelength ratherhan detuning, a sinclike shape is apparent and in sub-tantial agreement with the expected one for cw excita-ion (solid curve). The full width at half maximum is1 nm, yielding an effective QPM grating length of 1 cm,

oincident with the sample length. Despite the low effi-iency, the latter result confirmed a good uniformity of theE poled sample in both QPM grating and waveguide pa-ameters [38].

By repeating the SHG scan at higher peak powers webserved that the wavelength of maximum conversionthe FF resonance wavelength for SHG) shifted with ex-itation, as visible in Fig. 5. Otherwise stated, when per-orming a power scan at fixed FF wavelength, the conver-ion efficiency first increased with power (as expected)nd then decreased. By adjusting �FF, conversely, we ob-erved a linear dependence in maximum conversion to

ig. 5. SHG resonance shift in wavelength for increasing peakxcitations 7.4, 8.9, 11.2, and 12.7 kW from left to right, respec-ively. The experimental values (open circles) are numerically in-erpolated using Eq. (2) (solid curves).

ig. 6. (a) Peak SHG wavelength shift and (b) maximum con-ersion efficiency versus FF peak power.

econd harmonic (SH) [see Fig. 6(b)], as well as in peakHG wavelength [see Fig. 6(a)].

. MODEL AND DATA REDUCTIONonsidering the measured conversion efficiencies, using

he standard model of an ideal (first-order, 50:50 mark-to-pace) QPM channel waveguide and taking into accounthe measured modal overlap integral (input and output),oupling, and Fresnel losses—as well as material absorp-ion at FF and SH—we could estimate an effective non-inear coefficient �2 orders of magnitude smaller thanreviously reported d33 values in LN [35]. Since no appre-iable reduction in nonlinearity can be attributed to PE in-phase waveguides [33], a low (effective) nonlinear re-ponse can be ascribed to the limited depth of the nonin-erted domains as compared to the depth of the wave-uide; hence, to the limited overlap between (FF and SH)uided modes and the transverse size of the periodicerroelectric (nonlinear) grating. In fact, for the wave-uide depth evaluated in the previous section and the ac-uired transverse distributions of TM eigenmodes at FFnd SH (see Fig. 7), domains extending into z for less than–2 �m from the surface would greatly limit the perti-ent effective area. The latter would imply light propaga-ion and QPM in a partially inverted medium, with detri-ental effects on SHG and a nonlinear phase shift due to

ascading under phase mismatch [22,23].Therefore, in order to quantitatively interpret the ex-

erimental data, we took into account not only the peri-dically poled transverse region providing first-orderPM, but also the homogeneously inverted portion of theaveguides extending in z below the actual domains. This

ontribution is not expected to alter the peak conversionfficiency as the SH generated in the completely invertedegion is not phase matched, but it should play an impor-ant role in the phase coherently accumulated by the FFn propagation, therefore, on the wavelength for maxi-

um conversion [22,24,29]. A cascaded ��2� :��2� process inhase mismatch can mimic a ��3� response, giving rise ton equivalent Kerr response (i.e., an index change) thatan combine with or even dominate the cubic nonlinearityf the bulk material itself [23] and shift the SHG reso-ance [37]. Since the QPM grating extended well beyondhe channel width (Fig. 2), no particular care needs bedopted along the other transverse coordinate �y�, wherehe domains can be assumed infinitely wide.

For monochromatic TM-polarized first-order guided-ave modes at FF and SH, we write the electric field E ofn x-propagating eigenmode as

ig. 7. (a) FF and (b) SH output intensity modal distributionss imaged with a Vidicon tube and a CCD camera, respectively.

E

wtsrggtbmpt

w(t(tKso

If−b�tc

w

dt

w(Qdhgmp

seosd

hp

Stivala et al. Vol. 24, No. 7 /July 2007 /J. Opt. Soc. Am. B 1567

�x,y,z;t� =1

2Eu�x,y,z;t�exp�iut − iux� + c.c.,

Eu =� 2�0

Nu�−�

� �−�

�

�eu�y,z��2dydz

u�x�eu�y,z�, �1�

ith eu�y ,z� the dimensionless transverse profile, u�x , t�he slowly varying amplitude (in space and time) mea-ured in �W, �0 the vacuum impedance, Nu the effectiveefractive index, and u=uNu /c the guided-wave propa-ation constant. In the presence of a rectangular QPMrating with limited-depth inverted domains and an in-rinsic third-order response, assuming a negligible contri-ution from higher-order modes at SH (non-quasi-phase-atched to the FF fundamental mode) and a first-order

erturbation, the coupled-mode equations for SHG takehe form

wx +wt

cw= − w*v��1 exp�− i�1x� + i�2 exp�− i�2x��

− in2

2

�FF�fww�w�2 + 2fwv�v�2�w −

�w

2,

vx +vt

cv= w2��1 exp�i�1x� − i�2 exp�i�2x��

− in2

4

�FF�2fvw�w�2 + fvv�v�2�v −

�v

2, �2�

ith w�x , t� and v�x , t� being the amplitudes [u�x , t� in Eq.1)] of fundamental and second-harmonic fields, respec-ively; cw and cv (�w and �v) being the group velocitieslinear absorption coefficients) at FF and SH, respec-ively; and n2 being the nonresonant intensity-dependenterr coefficient [39]. The third-order nonlinear effects,

elf- and cross-phase modulation, are weighed by theverlap integrals fjk:

fjk

�−�

+��−�

+�

�ej�y,z��2�ek�y,z��2dydz

�−�

+��−�

+�

�ej�y,z��2dydz�−�

+��−�

+�

�ek�y,z��2dydz

�j,k = v,w�. �3�

n Eq. (2), we also distinguished the SHG contributionsrom unpoled (�2, �2=v−2w) and poled (�1, �1=�2kG) regions of the waveguide [40], respectively, governedy mismatches �i �i=1,2� and nonlinear coefficients �ii=1,2�, with kG=2 /� the wave-vector contribution ofhe QPM grating with period �. The constants �1 and �2an be expressed as

�i = deffi�i�8 2�0fSHG

�FF2 Nw

2 Nv, �4�

ith f the SHG overlap integral

SHG

fSHG �

−�

+��−�

+�

ev*�y,z�ew

2 �y,z�dydz�2

�−�

+��−�

+�

�ew�y,z��2dydz�2�−�

+��−�

+�

�ev�y,z��2dydz

,

�5�

eff1=2d33/ , deff2

=d33, and �i parameters accounting forhe waveguide section

�1 =

�−�

+��Z0

+�

ev*�y,z�ew

2 �y,z�dydz

�−�

+��−�

+�

ev*�y,z�ew

2 �y,z�dydz

,

�2 =

�−�

+��−�

Z0

ev*�y,z�ew

2 �y,z�dydz

�−�

+��−�

+�

ev*�y,z�ew

2 �y,z�dydz

= 1 − �1, �6�

ith Z0 delimiting the domain depth d. Note that in Eq.2) we did not include the cubic nonlinearity due to thePM grating [41]. In fact, the low conversion efficiency in-icates that d0 is quite smaller than the waveguide depth,ence �2 :�1 and the induced Kerr term �1 :�1 can be ne-lected when compared with the cascaded effect stem-ing from the phase-mismatched SHG in the uniformly

oled channel.While Eqs. (2) model SHG in a partially poled QPM

ample, as we deal with picosecond SHG in our low-fficiency samples and focus on the power-dependent shiftf the peak conversion wavelength, we can leave out ab-orption and temporal walk-off as well as the cubic termsepending on the SH field [42,43], reducing the system to

w�x,��x = − w*v��1 exp�− i�1x� + i�2 exp�− i�2x��

− i2

�FFn2fww�w�2w,

v�x,��x = w2��1 exp�i�1x� − i�2 exp�i�2x��

− i8

�FFn2fvw�w�2v, �7�

aving introduced �= t−x /cw and �w�2=w02 for the x=0 in-

ut power.Defining

w = W exp�− i2

�FFn2fwwwo

2x ,

v = V exp�− i8

�FFn2fvwwo

2x , �8�

t

Fc

Ipr

f�c

w

Fw�

Efbcmtshww

ppltcscs=pcS

soltt�cS−p

���=dd[a�r

5Wfcrweentpmpidtmt

ATtt

R

1568 J. Opt. Soc. Am. B/Vol. 24, No. 7 /July 2007 Stivala et al.

�ki = �i +8

�FFn2fvwwo

2 −4

�FFn2fwwwo

2 �i = 1,2�, �9�

he coupled equations for W�x ,�� and V�x ,�� take the form

Wx = − W*V��1 exp�− i�k1x� + i�2 exp�− i�k2x��,

Vx = W2��1 exp�i�k1x� − i�2 exp�i�k2x��. �10�

inally, since �k2��k1 and �2��1, neglecting rapidly os-illating terms such as sin���2−�1�x�,

Wxx + i�k2Wx � − �22��W�2 − �V�2�W. �11�

n the small conversion limit and after defining the FFhase � as in W=wog���exp�−i�� with g��� the FF tempo-al profile, Eq. (11) admits the solution [23]

� = −�k2x

2��1 +

4�22wo

2g���2

��k2�2 − 1� � −�2

2wo2g���2

�2x,

or low powers wo2��k2 /�2

2; in the same limit �2�8 /�FF�n2fwvwo

2, �4 /�FF�n2fwwwo2 and the cascading

ontribution is self-defocusing [22–29].For the SH output,

�v�2 = �12wo

4g4���L2 sinc2��1 + �Cwo2g2����

L

2� , �12�

ith L as the sample length and

�C =8

�FFn2fvw −

4

�FFn2fww +

2�22

�2.

rom Eq. (12), the peak efficiency �0 (the SHG resonantavelength in the limit of zero FF power) corresponds to1+�Cwo

2g2���=0; therefore, at first order,

� = �C�o

kGwo

2g2��� + �o. �13�

xpression (13) is consistent with the linear trend weound experimentally (Fig. 6) for a positive �C, therebyoth cross-phase modulation (with a positive n2) and cas-ading (with �2�0) dominate the � shift. Since no per-anent or semipermanent material effects such as hys-

eresis, memory, or damage could be detected in theamples, other effects (photorefractive, photovoltaic,igher order) potentially contributing to a resonance-avelength shift were entirely negligible in ouraveguides.We numerically solved Eq. (2) assuming a Gaussian

rofile for the FF pulses, a propagation length L=1 cm,ropagation losses of �w=�v=0.2 cm−1 at both wave-engths (accounting for both the �-phase waveguides andhe domain inversion [44,45]), and an input coupling effi-iency of 73% consistent with the experimentally mea-ured throughput of 60%. The overlap integrals were cal-ulated from the acquired intensity distributions andhown in Fig. 7, resulting in effective areas 1/ fww52.99 �m2 and 1/ fvv=23.11 �m2 for FF and SH self-hase modulation, respectively; 1/ fwv=44.08 �m2 forross-phase modulation and 1/ fSHG=76.68 �m2 for SHG.ince both cubic and quadratic terms contribute to the

hift [expression (13)], we adopted Kerr coefficients previ-usly measured by independent methods and reported initerature in order to estimate the pertinent QPM quanti-ies, i.e., nonlinearity d33 and the constant �1 related tohe depth d of the domains. The latter was extracted from1 using a modal solver. The index profile along z was re-onstructed from the experimental data as described inection 1; along y we used a generalized Gaussian exp��y /WG��� with � and WG parameters to best fit the modalrofiles (Fig. 7).The largest value of n2�10�10−20 m2/W [46] provided

1=0.0104, corresponding to d33=16.5 pm/V and d440 nm. Conversely, the smallest reported n2�510−20 m2/W [47] gave �1=0.0095, corresponding to d3318 pm/V and d�430 nm. Therefore, while the domainepth is marginally affected by the size of n2, the qua-ratic response appears lower than previously reported38]. Noticeably, neglecting the third-order nonlinearityltogether but keeping the propagation losses, we found1=0.0088, with d33=19.5 pm/V and d�420 nm. Theseesults are perfectly consistent with expression (13).

. CONCLUSIONSe carried out the first experimental demonstration of

requency doubling in proton-exchanged lithium niobatehannel waveguides quasi-phase-matched via surface pe-iodic poling. Despite a good mark-to-space ratio of 50:50,e found that a limited depth of the noninverted ferro-lectric domains not only limited the overall conversionfficiency to the second harmonic, but also induced a non-egligible quadratic cascading. The latter combined withhe inherent cubic response of the crystal to yield an ap-reciable SHG resonance shift in wavelength. The experi-ental results confirm the compatibility of �-phase

roton-exchanged waveguides with surface periodic pol-ng even for periods exceeding 16 �m but pinpoint therawback of rather shallow domains as compared withhe waveguide index profile. Work is in progress to opti-ize the PE-SPP technology and achieve deeper ferroelec-

ric domains.

CKNOWLEDGMENTShis work was funded by the Italian Ministry for Scien-

ific Research through PRIN 2005098337 and, in part,hrough project APQ RS-19 (CIPE 17/2002, BCNanolab).

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