3496 OPTICS LETTERS / Vol. 34, No. 22 / November 15, 2009

Generation of multi-octave-spanninglaser harmonics by cascaded quasi-phase matching

in a monolithic ferroelectric crystal

Wei-Chun Hsu,1,2 Ying-Yao Lai,3 Chien-Jen Lai,1,4 Lung-Han Peng,3 Ci-Ling Pan,2,5,6 and A. H. Kung1,2,6,*1Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan2Department of Photonics, National Chiao Tung University, Hsinchu 30010, Taiwan

3Institute of Photonics and Optoelectronics, National Taiwan University, Taipei 10617, Taiwan4EECS Department, MIT, Cambridge, Massachusetts 02139, USA

5Physics Department, National Tsing Hua University, Hsinchu 30013, Taiwan6Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan

*Corresponding author: akung@pub.iams.sinica.edu.tw

Received August 28, 2009; revised October 8, 2009; accepted October 9, 2009;posted October 16, 2009 (Doc. ID 116379); published November 9, 2009

We report the generation of the second to the sixth harmonics of a fundamental frequency covering two anda half octaves in a multiply-periodically poled lithium tantalate crystal by cascaded quasi-phase-matchedfrequency mixing. A frequency comb that is composed of these harmonics will permit the synthesis of a trainof periodic subcycle subfemtosecond pulses in a compact setting. © 2009 Optical Society of America

OCIS codes: 190.4160, 230.7405, 160.4330.

Fourier synthesis of periodic subfemtosecond lightpulses consists of the generation and the superposi-tion of a properly phased comb of equally spaced op-tical frequencies [1]. There are two main approachesthat have been used to generate frequency combs. Inone approach, phase-coherent frequency combs aregenerated by driving a Raman coherence adiabati-cally [2] or impulsively [3]. Another approach em-ploys phase-locking two or more cw [4] or mode-locked Ti:sapphire lasers [5], by mixing pulses from amode-locked laser with pulses from a synchronouslypumped optical parametric oscillator (OPO) [6] or bydifference-frequency mixing to produce a widebandfrequency spectrum [7]. These approaches employhigh-power lasers and/or complex optical arrange-ments to generate the comb frequencies. It is desir-able to explore alternatives that can be compact andefficient for the same purpose.

The frequency �q and phase �q of the qth compo-nent of a frequency comb useful for periodic wave-form synthesis can be expressed as [8]

�q = q�m, �q = �0 + q�m, �1�

where �m is the comb frequency spacing, �0 is astatic offset phase, and �m is the phase difference be-tween adjacent comb components; q is an integerwith value from a few for the Raman approach totens of thousands for the mode-locked lasers ap-proaches. Equation (1) shows that all the componentsof the comb are simply harmonics of �m, a conditionwhere the comb frequencies are called being com-mensurate. Since harmonics can be generated bynonlinear optical mixing [9], the case of generating acommensurate comb can amount to generating asmany harmonics of an initial frequency �m by nonlin-ear mixing as is practical. Once generated it followsfrom Fourier transform theory that such a comb

would synthesize to periodic pulses. The temporal

0146-9592/09/223496-3/$15.00 ©

pulse spacing will be 2�c /�m, where c is the speed oflight, and the pulse width will be of the order of2�c / �n�m� where n is the number of harmonics in thecomb.

A common approach to generating laser harmonicsis phase-matched harmonic generation and mixingusing birefringent crystals. Owing to the nature ofphase matching the harmonics are phase coherentrelative to each other. However, birefringent phasematching has beam walk-offs, and polarization cor-rection is required to generate many harmonics sothat the process is quite complicated. There would bephase fluctuations when the harmonics are split andthen recombined during generation. Thus using bire-fringent phase matching will require elaborate phaselocking and stabilization to maintain phase coher-ence among the harmonics [1]. Quasi-phase-matched(QPM) nonlinear mixing is another efficient approachto generating laser harmonics. Two-stage cascadedparametric generation and generation to the thirdharmonic in a single QPM crystal have been demon-strated [10,11]. By judicious engineering of the poleddomains of a ferroelectric crystal it should be possibleto extend the QPM approach to produce multiple har-monics all in one crystal. Thus multiharmonic gen-eration becomes a simpler task and phase fluctuationwill be minimized. In this Letter, we report success-ful generation of the second to the sixth phase-coherent harmonics in a single periodically poledferroelectric crystal. The second to the fifth harmon-ics are produced via four consecutive stages of QPMfrequency mixing from the fundamental frequency.The sixth harmonic is produced via random QPMthat will be explained later. The harmonics covermore than two octaves in frequency. When monochro-matic light is used with such a crystal to produce theharmonics it will permit the synthesis of a train of

femtosecond to subfemtosecond pulses. Cascaded

2009 Optical Society of America

November 15, 2009 / Vol. 34, No. 22 / OPTICS LETTERS 3497

QPM generation in a single crystal is stable, com-pact, and efficient. It can therefore be an effectivemeans of producing repeatable and lasting ultrafastwaveforms.

Figure 1 depicts our scheme to obtain the first fiveharmonics. The input of 2406 nm is chosen simply be-cause it is in use in another experiment. At this inputwavelength, the synthesized pulses will be 8 fs apart.Note that we use only nonlinear mixing stages thatinvolve the fundamental frequency, because this isthe most effective utilization of the input pulse en-ergy, and these mixing processes have the largestQPM periods for generation at every harmonic sothat this increases the probability of success whenfabricating the crystal. We use congruent grownlithium tantalate (CLT) and a multimode OPO todemonstrate the concept of monolithic multihar-monic generation. The approach certainly works forany QPM crystal material. Eventually, to synthesizeperiodic pulse trains, a monochromatic input will berequired.

The domain periods for first-order QPM mixing of2406 nm in CLT to the second to the fifth harmonic at100°C, calculated using published Sellmeier equa-tion [12], are 34.09 �m, 22.37 �m, 13.14 �m, and7.99 �m, respectively. The demand to achieve quasi-phase matching at one crystal temperature for allstages puts a very stringent requirement on the fab-rication of the crystal. The biggest challenge comes inpoling the segment for generating the fifth harmonic,since it has the smallest domain period. Domainmerging has limited the poling process to periods oflarger than several micrometers. To circumvent this,we use second order QPM with a 25% duty cycle forthe fifth harmonic stage. The period for this stage isthen 15.95 �m, with an estimated tolerance in do-main width of 20 nm. To compensate for the smallersecond-order QPM nonlinearity, we proportionatelyincrease the length of interaction for this stage. Wealso aimed to produce equal amplitudes at all of theharmonics. The design length of each segment wasthen calculated to be 7.2, 4.0, 3.3, and 5.5 mm, re-spectively. The calculation was based on an incidentintensity of 100 MW/cm2 using plane-wave approxi-mation. Recognizing that there can be uncertainty in

Fig. 1. (Color online) Schematic of cascaded multiple har-monics generation in a single ferroelectric crystal. 2406 nmis used as a sample input wavelength. The four left to rightsegments have different QPM periods.

Fig. 2. (Color online) Micrographs of poled domains in +z

transition boundaries from one period to another. The correspo

the accuracy of the refractive indices of CLT we de-signed masks to have a range of QPM periods thatspan across the calculated values for each of the fourstages so that at least one combination of QPM peri-ods would be right for our purpose. This results inseveral crystals that are fabricated for the experi-ment. Finally, we employ the technique of restricteddomain growth to pole the crystal to minimize do-main merging and to meet the tolerance on the pe-riod width [13]. Shown in Fig. 2 is a set of micro-graphs of areas of a successfully poled crystal wherethe domain period values are varied.

For the harmonic generation experiment, we useda 2 kHz nanosecond OPO tuned to around 2406 nm[14]. The linewidth of the OPO is �0.5 cm−1, and thepulse duration is 20 ns. The average power of theOPO was about 44 mW that was focused to12.5 MW/cm2 at the center of the uncoated PPLTcrystal. The generated collinearly propagating har-monics were dispersed with a Pellin-Broca prism forpower measurements. The first experiment was toidentify a crystal that can generate all five harmonicswithin a given wavelength and temperature param-eter space. We did this by varying the crystal tem-perature and the OPO wavelength to find a crystalthat gives the highest power at the fifth harmonic.The resulting measurements of the crystal that givesthe best fifth harmonic power are shown in Fig. 3.This crystal has periods of 34.09 �m, 22.44 �m,13.18 �m, and 15.90 �m, respectively, for the foursegments. From these results it is determined thatthe optimal wavelength and QPM temperature are2410 nm and 123°C. The crystal parameters thatworked: optimal wavelength, domain periods, andQPM temperature are different from the design pa-rameters. Such differences have been reported inother QPM devices [15,16] and they likely originatefrom insufficient accuracy of the Sellmeier equationfor the material, in particular for the blue andshorter wavelengths.

Nearly equal conversion to every harmonic was ob-served from this crystal. The measured temperaturedependence of the harmonics for a 2410 nm input isshown in Fig. 4. The overall power conversion to theharmonics after correction for refractive losses isnearly 20%. Indeed the intermediate harmonics aredepleted in the temperature range where the fifthharmonic is phase matched. Taking into account thisdepletion we find that the QPM temperature is aboutthe same for every stage, at 123°C. The power of theharmonics is nearly equal at 123°C and 126°C asshown in the inset in Fig. 4. Hence, this devicereadily provides the harmonics for subsequent syn-thesis of transform-limited periodic pulses.

hed PPLT crystal, showing domains in the vicinity of the

etc nding periods are as shown.

3498 OPTICS LETTERS / Vol. 34, No. 22 / November 15, 2009

The sixth harmonic was also observed in the ex-periment. This harmonic is not a part of the QPM de-sign. The measured power of this harmonic is smallbut is still several orders larger than what is calcu-lated from non-phase-matched generation. We be-lieve that this sixth harmonic results from randomphase-matched generation as a consequence of slightunevenness in the fabricated domain periods [17].

Now we compare the merits of this monolithicQPM approach with the adiabatic Raman approachfor harmonic frequency comb generation. With theRaman technique a large number ��8–10� of har-monics can be produced. It is thus suitable for gener-ating pulses with the shortest durations and synthe-sizing waveforms to have better precision than whenusing fewer harmonics. The cascaded QPM technique

Fig. 3. Measured average output power of the fifth har-monic as a function of the input wavelength and the corre-sponding QPM temperature.

Fig. 4. (Color online) Average power of the generated har-monics measured as a function of the crystal temperature.Asymmetry of the curves for the second to fourth harmonicis evidence of depletion at the respective stage of genera-tion. The inset shows nearly equal power distribution of thegenerated harmonics and the residual power of the funda-mental after passage through the crystal at 123°C and126°C.

reported here offers complementary advantages.First, the pulse period is not locked to a Raman fre-quency. A crystal can be designed to work for any ini-tial frequency or wavelength, limited only by theQPM crystal’s transmission. This means �10 �mwhen using diffusion bonded GaAs, or �5 �m for pe-riodically poled CLT and CLN. Second, we haveshown that the QPM process is highly efficient sothat it may be possible to use quasi-cw mode-lockedlasers, and even cw lasers when combined with QPMwaveguide technology to generate a comb of multipleharmonics [18]. Finally, simultaneous amplitude andphase control in a monolithic QPM crystal may alsobe possible [19].

We thank Yu-Pei Tseng, Wei-Ting Chen, and Zhi-Ming Hsieh for helpful discussions. This work wassupported by the National Nanoscience and Technol-ogy Program (grant NSC 97–2120-M-001–002) andthe Academia Sinica.References

1. T. W. Hänsch, Opt. Commun. 80, 71 (1990).2. S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019

(1997).3. A. Nazarkin and G. Korn, Phys. Rev. A 58, R61 (1998).4. T. Mukai, R. Wynands, and T. W. Hänsch, Opt.

Commun. 95, 71 (1993).5. R. K. Shelton, L. S. Ma, H. C. Kapteyn, M. M.

Murnane, J. L. Hall, and J. Ye, Science 293, 1286(2001).

6. J. Sun and D. Reid, Opt. Lett. 34, 854 (2009).7. H. Han, Y. Zhao, Q. Zhang, H. Teng, and Z. Wei, in

Conference on Lasers and Electro-Optics (OpticalSociety of America, 2009), paper CMY3.

8. Z. M. Hsieh, C. J. Lai, H. S. Chan, S. Y. Wu, C. K. Lee,W. J. Chen, C. L. Pan, F. G. Yee, and A. H. Kung, Phys.Rev. Lett. 102, 213902 (2009).

9. Y. R. Shen, The Principles of Nonlinear Optics (WileyInterScience, 1984).

10. Z. D. Gao, S. N. Zhu, S. Y. Tu, and A. H. Kung, Appl.Phys. Lett. 89, 181101 (2006).

11. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, Science 278, 843(1997).

12. A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, andS. Ruschin, Opt. Lett. 28, 194 (2003).

13. L.-H. Peng, Y.-P. Tseng, K.-L. Lin, Z.-X. Huang, C.-T.Huang, and A. H. Kung, Appl. Phys. Lett. 92, 092903(2008).

14. C. S. Yu and A. H. Kung, J. Opt. Soc. Am. B 16, 2233(1999).

15. U. Strössner, A. Peters, J. Mlynek, S. Schiller, J.-P.Meyn, and R. Wallenstein, Opt. Lett. 24, 1602 (1999).

16. Shih-Yu Tu, A. H. Kung, Z. D. Gao, and S. N. Zhu, Opt.Lett. 30, 2451 (2005).

17. C.-J. Lai, W. T. Chen, and A. H. Kung, Conference onLasers and Electro-Optics (Optical Society of America,2009), paper CThD2.

18. K. P. Parameswaran, J. R. Kurz, R. V. Roussev, and M.M. Fejer, Opt. Lett. 27, 43 (2002).

19. W.-H. Lin and A. H. Kung, Opt. Express 17, 16342(2009).