Laser Photonics Rev. 7, No. 3, L17–L20 (2013) / DOI 10.1002/lpor.201200116

LASER & PHOTONICSREVIEWS

LETTERA

RTIC

LE

Abstract All optical inscription of quasi phase matching struc-tures in an x-cut LiNbO3 crystal is demonstrated. Quasi phasematching is obtained by periodically lowering the nonlinear re-fractive index of the crystal using focussed ultrashort pulses.The structures were used to frequency double 1.55 μm light.The converted signal could be enhanced by a factor of 70 withrespect to the unmodified material. From these measurementit could be deduced that the nonlinearity has been periodicallydamped up to 20%.

Quasi phase matching in femtosecond pulse volumestructured x-cut lithium niobate

Jens Thomas1,∗, Vinzenz Hilbert1, Reinhard Geiss1, Thomas Pertsch1,Andreas Tunnermann1,2, and Stefan Nolte1,2

Within the past years the aim to provide light in any wave-length regime has driven the field of nonlinear optics. Appli-cations range from single frequency sources to broad bandparametric frequency conversion. In most cases, secondorder nonlinearities are exploited for sum and differencefrequency generation - with second harmonic generation(SHG) being the most prominent example.

In many applications, the artificial, anisotropic crystallithium niobate (LiNbO3 ) is used, which has high nonlin-ear coefficients. In order to achieve efficient photon con-version, the phases of the photons of the incident and of thedoubled frequency ω and 2ω have to be matched. Oth-erwise, back conversion of the second harmonic powerP2ω to the pump Pω occurs due to the phase mismatch�k = 2ω (n2ω − nω) /c depending on the difference of re-fractive indices nω, n2ω at the fundamental and second har-monic frequency.

Figure 1(a) displays P2ω as a function of propagationlength in the nonlinear medium. All curves have been com-puted by numerically integrating the coupled-amplitudeequation for a lossless medium [1]. For the case of per-fect phase matching (�k = 0), the dependence is quadratic(Fig. 1(a), black curve I), for a given mismatch (�k �= 0),back conversion starts to occur at the point where the phasemismatch amounts to π (Fig. 1(a), blue curve IV), thus ata coherence length of

Lc = π/�k. (1)

1 Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universitat Jena, Max-Wien-Platz 1, 07743 Jena, Germany2 Fraunhofer Institute for Applied Optics and Precision Engineering, Albert-Einstein-Str. 7, 07745 Jena, Germany∗Corresponding authors: e-mail: thomas@iap.uni-jena.de

In a birefringent crystal, phase matching can be achievedfor conversion of ordinary polarized light to extraordinarypolarized light, by finding an axis of propagation for whichtheir respective refractive indices are equal. Alternatively,back conversion can be diminished [2] (Fig. 1, curve III)or avoided (Fig. 1, curve II) with quasi phase matching(QPM). Here, the nonlinearity is altered with a period of2Lc. Ideally, the sign of the second order nonlinearity d isreversed (Fig. 1(b), green solid line).

Usually QPM structures are fabricated by means ofelectric field poling, where a high voltage is applied tothe crystal through a patterned masking layer. This tech-nique is restricted to the d33 component of the nonlinearity,consequently just z-cut crystals can be poled such that theindividual domains range through the entire crystal. How-ever, there are certain applications that require the use ofx-cut crystals, e. g. electro-optic modulators. At the sametime they would benefit from efficient frequency conversionmediated by QPM. While poling of x-cut crystals has beendemonstrated with surface electrodes, the reversed domainsextended only a few micrometers below the surface [3, 4].

Our aim is to realize a QPM structure that extends farinto the volume of an x-cut LiNbO3 wafer. Instead of elec-tric field poling, we use ultrashort laser pulses to structurethe crystal. This approach has many benefits. Most im-portantly, it is more flexible since it does not require anymicro structuring technology to lithographically define therespective poling patterns. Additionally, it can easily be

C© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

LASER & PHOTONICSREVIEWS

L18 J. Thomas et al.: Quasi phase matching in femtosecond pulse volume structured x-cut lithium niobate

Figure 1 Second harmonic power over propagation length (inunits of Lc) and a sketch of the longitudinal profile of the sec-ond order nonlinearity d, the solid line displays domain reversaland the dashed line the investigated periodical lowering of thenonlinearity.

combined with ultra-short pulse laser based direct writingof optical waveguides; thus enabling all-optical processingof integrated optical devices. Several functional elementscould already be demonstrated with the direct write tech-nique: modulators as well as frequency converters [5] andmost recently Bragg reflectors [6]. QPM waveguides how-ever were only demonstrated in crystals that were poledalready [7–9]. Mailis et al. demonstrated that the field of afemtosecond UV-laser can induce a domain inversion [10].Albeit, these modifications were limited to the surface ofthe z-cut sample.

In this paper, we aim not to switch the sign but to peri-odically lower the nonlinearity by v = d/dmax as sketchedin Figure 1(b), red dashed line. This approach has beensucessfully demonstrated on other platforms where domainpoling is not possible, e.g. by reducing the nonlinearity ofGaAs by ion-implantation [2, 11, 12], by Frozen-in field-induced second order nonlinearity in optical fibers [13] ormore recently in the design of a meta-metarial with a QPMperiodicity [14]. A Fourier transform of the second ordernonlinearity profile yields

deff = dmax

π(1 − v) (2)

for the effective second order nonlinearity deff . The effi-ciency of a QPM structure with lowered nonlinearity iswell below that of a poled one, because back-conversion al-though reduced is allowed (Fig. 1(a), red dashed curve, III).Its conversion efficiency directly depends on how stronglythe nonlinearity of the crystal is affected by the modifi-cation. Ultrashort pulses can locally alter the crystalinestructure of LiNbO3 in two ways. They either raise the

Figure 2 Schematic of the sample and inscription setup (a), thecoordinate system is that of the crystal. The inset (b) outlines theinscription routine of each segment. Inset (c) shows a microscopeimage of the endfacet of the QPM structure (inscription pulseenergy of 650 nJ).

extraordinary refractive index (Type I) or destroy the crys-taline structure, inducing stress fields (Type II) [15]. Twoprevious studies addressed how the nonlinearity is affectedwithin fs written modifications. In both a Type I waveguidehad been inscribed in a periodically poled LiNbO3 and thedecrease of the second order nonlinearity was estimatedby measuring the SHG generated within the waveguide andcomparing it with the numerically calculated conversion ef-ficiency [7,8]. Lee et al. measured a substantially decreasednormalized conversion efficiency of 0.0003 %W−1cm−2

[7], while Osellame et al. achieved 6.5 %W−1cm−2 and de-duced that the second order nonlinearity can be conservedfor a certain parameter regime within a Type I modification[8].

The sample used for the experiments here is a congru-ent LiNbO3 wafer, (MgO, 5mol% doped), 0.5 mm thick,polished as x-cut, with the z-axis of the crystal parallel tothe surface (Fig. 2). The maximum second order nonlinear-ity dmax = d33 can be observed for light polarized along thez-axis. For pump light of λ = 2π/ω = 1545 nm, the coher-ence length Lc was determined to be 9.5 μm [16]. In thefollowing we assume that the dispersion for the modifiedregions is approximately equal and Lc likewise (see Eq.(1)). In the pristine crystal, the losses for the fundamentaland second harmonic light were measured to be αω = 0.02dB/cm α2ω = 0.05 dB/cm for polarizations parallel to thez-axis of the crystal.

The structures were inscribed with a cross-bearingtranslation stage (Aerotech ALS130, bidirectional repeata-bility of σ = 100 nm) and a regenerative amplifier (Coher-ent Reg A, operated at 800 nm, 170 fs pulses, repetitionrate 100 kHz). Its pulse energy could be continously ad-justed up to 750 nJ with a half wave plate and polarizer

C© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.lpr-journal.org

LETTERARTICLE

Laser Photonics Rev. 7, No. 3 (2013) L19

Figure 3 Beam profiles of fundamental (a) and second harmoniclight (b), double arrows indicating the direction of polarization. Thecoordinate system is that of the crystal.

combination. The light was focussed with a 40 times mi-croscope objective (NA = 0.65) into the sample. We aimedfor a period of � = 2Lc with a filling factor of 0.5. N = 220periods were realized. For each modified volume, the sam-ple was translated with a velocity of 1 mm/s as sketched inthe inset of Figure 2. The red part of the arrows indicatewhere the shutter of the laser was open. Each of these mod-ification lines has an elliptical cross-section with a width of3–4 μm and 14–16 μm in height. In order to obtain a largercross-section of overlapping modifications, each modifiedregion consists of seven vertically overlapping ‘layers’ of�L = 1 μm spaced lines, which are �h = 13 μm apart.The final structure had a cross-section of w = 500 μm timesh ≈ 90 μm (Fig. 2(c)). In propagation direction the crystalwas L = 4.6 mm long. The sample was hence character-ized in a free beam setup. The pump laser was a tunablelaser (Agilent 8164B) combined with an erbium doped fiberamplifier (EDFA). The system was operated in the pulsedregime with 40 ns pulses at a 166 kHz rate, delivering a peakpower of 12 W. The light was coupled into the sample witha lens of 50 mm focal length. Outcoupling was achieved bya microscope objective (40x, NA=0.65).

In the following we describe the results for the QPMstructure that has been inscribed with 650 nJ pulses.Although this structures had high propagation losses(αω = 16.4 dB/cm and α2ω = 24.5 dB/cm), a significantconversion could be obtained. Figure 3 shows the beamprofiles of fundamental and second harmonic light afterpassage through the QPM structure. Note that both funda-mental and second harmonic light are polarized parallel tothe z-axis of the crystal, which clearly distiguishes quasiphase matching from polarization phase matching. Whilethe beam width is conserved, the beam height of the secondharmonic light is approximately a third of that of the fun-damental. This indicates that the nonlinearity has not beenmodified homogenously over the cross-section. A possi-ble explanation is that the modification of the non-linearityfollows the same graded profile in the x-direction as thedarkening (Fig. 2c). Thus, the beam size reduction by SHGis asymmetrically enhanced, because the conversion effi-ciency is higher in the central region of the structure.

Figure 4 displays the tuning curve at room tempera-ture. QPM and best conversion is obtained at 1545 nm. Forcomparison, the SHG signal of the pristine crystal is alsoincluded (red curve). The conversion efficiency could be

Figure 4 Tuning curves for the inscribed QPM structure and thepristine crystal for comparison.

Figure 5 SHG power vs. input power at the phase matchingwavelength.

enhanced by a factor of up to 70 with respect to the bulksignal.

Figure 5 shows the power dependence at the phasematched wavelength. In the structure investigated, we didnot observe saturation due to pump depletion. Thus, theeffective second order nonlinearity can be determined fromthe quadratic power law

P2ω = ηA · d2eff P2

ω, (3)

where η denotes the overal efficiency of the QPM structureand

A = πnωn2ωε0c4

2ω3L ′hF(4)

www.lpr-journal.org C© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

LASER & PHOTONICSREVIEWS

L20 J. Thomas et al.: Quasi phase matching in femtosecond pulse volume structured x-cut lithium niobate

is a proportionality constant, which depends on thelength of the QPM structure L ′ = N�, a loss term F =exp (−(αω + 1/2α2ω)) and the Boyd-Kleinmann focussingparameter h = 1.022 (for the focussing conditions withinthe experiment) [17, 18]. By inserting the calculated deffand the measured bulk d33 = 22.49 pm/V in Eq. (2),we estimated the contrast of the QPM structure to bev = d/dmax = 0.82. However, this is an upper limit, sinceour estimate assumes η = 1 , thus we do not take system-atic and statistical errors of fill factor and periodicity intoaccount [19, 20].

QPM structures were also realized with lower andhigher pulse energies, but yielded lower or no conver-sion. This has two reasons: For low pulse energies, theinduced modification is primarily a positive index change,which seems to leave the nonlinearity almost untouched[8]. Higher pulse energies result in a partial darkening(Fig. 2(c)), which is not only accompanied by a signif-icant decrease of the second order nonlinearity of up to20 percent but also by significantly higher losses. Both fac-tors have to be balanced to obtain a QPM structure withgood efficiency. While the overall conversion efficiency islow compared to z-cut PPLN or surface poled x-cut PPLNwaveguides [3,4], our approach enables deeply embeddingboth modulator and frequency converter on a monolithicchip. In combination with current research on femtosecondinduced second order nonlinearities in glass [21], QPMwith damping domains might pave the way to truly three-dimensional nonlinear devices.

Acknowledgements. We like to acknowledge financial supportby the German Research Foundation (DFG) under priority pro-gram 1157 and the Leibniz program. Jens Thomas is supportedby the Carl-Zeiss-Foundation.

Received: 5 December 2012, Revised: 30 January 2013,Accepted: 15 February 2013

Published online: 11 March 2013

Key words: Integrated optics, laser writing, lithium niobate,nonlinear optics, quasi phase matching.

References

[1] R. W. Boyd, Nonlinear Optics, March 2008.[2] D. Artigas, E. U. Rafailov, P. Loza-Alvarez, and W. Sibbett,

Quantum Electron. 40(8), 1122–1130.

[3] T. Sugita, K. Mizuuchi, Y. Kitaoka, and K. Yamamoto, Opt.Lett. 24(November), 1590 (1999).

[4] F. Genereux, G. Baldenberger, B. Bourliaguet, and R. Vallee,Appl. Phys. Lett. 91(23), 231112 (2007).

[5] J. Thomas, M. Heinrich, P. Zeil, V. Hilbert, K. Rademaker,R. Riedel, S. Ringleb, C. Dubs, J. P. Ruske, S. Nolte,and A. Tunnermann, Phys. Stat. Sol. A 208(2), 276–283(2011).

[6] W. Horn, S. Kroesen, J. Herrmann, J. Imbrock,and C. Denz, Optics Express 20(24), 26922–26928(2012).

[7] Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C.Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K.Kim, and H. Y. Lee, Appl. Phys. Lett. 89(October), 1103(2006).

[8] R. Osellame, M. Lobino, N. Chiodo, M. Marangoni, G.Cerullo, R. Ramponi, H. T. Bookey, R. R. Thomson, N.D. Psaila, and A. K. Kar, Appl. Phys. Lett. 90(June), 1107(2007).

[9] J. Thomas, M. Heinrich, J. Burghoff, and S. Nolte, Appl.Phys. Lett. p. 151108 (2007).

[10] Y. J. Ying, C. E. Valdivia, C. L. Sones, R. W. Eason,and S. Mailis, Optics Express 17(October), 18681–18692(2009).

[11] J. P. Bouchard, M. Tetu, S. Janz, D. X. Xu, Z. R. Wasilewski,P. Piva, U. G. Akano, and I. V. Mitchell, Appl. Phys. Lett.77(26), 4247 (2000).

[12] K. Zeaiter, D. C. Hutchings, R. M. Gwilliam, K. Moutzouris,S. Venugopal Rao, and M. Ebrahimzadeh, Opt. Lett. 28(1),911–913 (2003).

[13] P. G. Kazansky, V. Pruneri, and P. S. J. Russell, Opt. Lett.20(8), 843–845 (1995).

[14] A. Rose and D. Smith, Phys Rev A 84(1), 013823 (2011).[15] J. Burghoff, S. Nolte, and A. Tunnermann, Appl. Phys. A

89, 127 (2007).[16] I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, J

Opt Soc Am B 14(September), 2268 (1997).[17] G. D. Boyd and D. A. Kleinman, J. Appl. Phys. 39(July),

3597 (1968).[18] Y. F. Chen and Y. C. Chen, Appl. Phys. B pp. 645–647

(2003).[19] D. S. Hum and M. M. Fejer, Comptes Rendus Physique

8(March), 180 (2007).[20] L. Yunchu, Q. Wang, X. Zhang, D. Yuan, and Z. Liu, Opt.

Comm. 247, 205–212 (2005).[21] J. Choi, M. Bellec, A. Royon, K. Bourhis, G. Papon, T.

Cardinal, L. Canioni, and M. Richardson, Opt. Lett. 37(6),1029–1031 (2012).

C© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.lpr-journal.org