Kaertner, Franz X.

Morgner, Uwe

Muecke, Oliver D.

Tritschler, T.

Wegener, Martin

English

KITopen

December 1, 2002 / Vol. 27, No. 23 / OPTICS LETTERS 2127First published in:Determining the carrier-envelope offset frequency of 5-fspulses with extreme nonlinear optics in ZnOO. D. Mücke, T. Tritschler, and M. WegenerInstitut für Angewandte Physik, Universität Karlsruhe (TH), Wolfgang-Gaede-Strasse 1, 76131 Karlsruhe, GermanyU. MorgnerInstitut für Hochfrequenztechnik und Quantenelektronik, Universität Karlsruhe (TH), Engesserstrasse 5, 76131 Karlsruhe, GermanyF. X. KärtnerDepartment of Electrical Engineering and Computer Science and Research Laboratory of Electronics,Massachusetts Institute of Technology, Cambridge, Massachusetts 02139Received June 13, 2002We excite ZnO samples with two-cycle optical pulses directly from a mode-locked oscillator with average powersof several tens of milliwatts. The emitted light reveals peaks at the carrier-envelope offset frequency ff andat 2ff in the radio-frequency spectra. These peaks can still be detected in layers as thin as 350 nm—a steptoward determining the carrier-envelope offset phase itself. © 2002 Optical Society of AmericaOCIS codes: 190.7110, 300.6470.The carrier-envelope offset (CEO) phase, f, is thephase between the rapidly oscillating carrier wave ofa laser pulse and its electric f ield envelope. The timederivative of f is the CEO frequency, ff. Recently,several approaches to measuring the CEO frequencyfor pulses directly out of a mode-locked oscillator werereported.1 – 4 Related work for amplified pulses5 – 7addressed the role of the CEO phase. The under-lying basic idea1 – 4 is to consider the interferencecontribution that results from the superposition of thefundamental pulse spectrum, which by definition hasa phase 1f, and its second (third) harmonic, whichhas a phase 2f 3f. The resulting beating withdifference phase 1f 2f can be used to determine theCEO frequency ff 2ff; Ref. 8). To actually measurethis interference for pulses directly derived from amode-locked oscillator, researchers have used differentapproaches. For extremely short pulses, which coverone octave in the frequency spectrum, this term imme-diately occurs when the second harmonic is generatedin a suitable crystal. In Ref. 4, a 1-mm-thick crystaland the complete laser output power were used toobserve the ff peak. For somewhat longer pulses,the fundamental needs to be spectrally broadenedto generate sufficient spectral overlap.1,2 In such asetup the laser pulses are sent into a (photonic crystal)fiber for spectral broadening via self-phase modulation(SPM) before they are again focused onto a separatesecond-harmonic-generation (SHG) crystal, where thetwo contributions interfere.Apart from being quite complex, such setups1,2 havethe inherent drawback that the CEO phase changeswithin the setup because of different group and phasevelocities in the fiber, in the thick SHG crystal, and inthe air in between. Ideally, one would like to gener-ate the spectral components that are due to SPM andSHG in one medium, which is so thin that f does not0146-9592/02/232127-03$15.00/0EVA-STAR (Elektronisches Volltextahttp://digbib.ubka.uni-karlsruhe.de/vchange within the medium, and still get a large beatingsignal. Ultimately, this would allow one not only tomeasure the CEO frequency but also to determine theCEO phase. A simplif ied measurement of the CEOfrequency along these lines and the potential to deter-mine the CEO phase itself is the subject of this work.Our home-built laser system delivers 5-fs opticalpulses at fr  81 MHz repetition frequency andaverage powers up to 230 mW. The spectrum coversthe range from 650-nm wavelength to 1050 nm,the center photon energy is h̄v0  1.5 eV. All pulseproperties are very nearly similar to Ref. 9. Theselinearly polarized pulses are sent into a balancedMichelson interferometer that is actively stabilized bymeans of Pancharatnam’s screw.10 Using a ref lectivemicroscope objective with a numerical aperture (NA)of 0.5, we can tightly focus these pulses to an intensityprofile that is roughly Gaussian with a measured1-mm radius (the Rayleigh length is 2.9 mm). At theoutput of the interferometer, an average power of8 mW in one arm corresponds to a peak intensity ofI0  0.6 3 1012 Wcm2 (same definition as in Ref. 11).The maximum accessible intensity of I  2.04 3 I0corresponds to an intensity of 5.0 3 1012 Wcm2 forconstructive interference of the two arms, equiva-lent to a peak of the electric field envelope ofẼ0  6 3 109 Vm  6 Vnm. Note that ZnO has nocenter of inversion and that it is birefringent. Forthe approximately 100-mm-thick single crystal, thecrystallographic c axis lies in the plane of the platelet.For the 350-nm-thin epitaxial f ilm grown on a sap-phire substrate, c is perpendicular to the film. Thelight emitted into the forward direction is collected bya second ref lective microscope objective (NA, 0.5) andspectrally f iltered (3-mm Schott BG 39) for removalof the prominent fundamental laser spectrum and issent into a 0.25-m focal-length grating spectrometer© 2002 Optical Society of Americarchiv – Scientific Articles Repository) olltexte/17612002 2128 OPTICS LETTERS / Vol. 27, No. 23 / December 1, 2002connected to a CCD camera. Alternatively, we sendthe light through a combination of f ilters (3-mmSchott BG 39, 3-mm Schott GG 455, and Coherent35-5263-000 480-nm cutoff interference filter for the100-mm ZnO single crystal and Coherent 35-5289-000500-nm cutoff interference filter for the 350-nmepitaxial film, respectively) onto a 50 V-terminatedphotomultiplier tube (Hamamatsu R 4332 bialkaliphotocathode), connected to a radio-frequency (rf )spectrum analyzer (Agilent PSA E4440A).Figure 1 shows measured optical spectra in thespectral region energetically above the laser spectrum(which has its short-wavelength cutoff above 650 nm)and below the bandgap of ZnO of Eg  3.3 eV for[Fig. 1(a)] low and [Figs. 1(b) and 1(c)] high excitation.All spectral components shown in Fig. 1 disappear ifthe ZnO crystal is moved out of focus. Polarization-dependent experiments under these conditions showthat all these spectral components have the samelinear polarization as the laser pulses. In Fig. 1(a),the light near the 390–470-nm wavelength is dueto SHG, and the components above 500 nm are dueto SPM. Interestingly, the independently measuredinterferometric autocorrelation of the laser pulses[with a thin b-barium borate SHG crystal; curvelabeled IAC in Fig. 1(b)] is closely reproduced bythe cut at the 395-nm wavelength [black curve inFig. 1(c)]. This result indicates that the pulses arenot severely broadened in the ZnO crystal as a resultof, e.g., group-velocity dispersion. Furthermore, thespectral width of the SHG contribution indicates thatphase-matching effects do not play a major role, whichis not surprising considering the short Rayleigh rangeof the microscope objective. For higher intensities,the spectral overlap of SPM and SHG becomes im-mediately obvious from the spectra in Figs. 1(b) and1(c), and a rich fine structure appears in this spectralregion as a function of t. Such measurements arecrucial for comparison with theory (see discussionbelow). Feeding the spectral components in the inter-ference region of Fig. 1 into the rf spectrum analyzer(Fig. 2), we find a large peak $30 dB above noiselevel) at the carrier-envelope offset frequency ff as aresult of the interference of the SPM and SHG and anadditional smaller peak at 2ff resulting from the in-terference of the SPM with the third harmonic.12 Toour knowledge a 2ff peak has not been observed inany approach. The ff peak remains prominent fort corresponding to two optical cycles (not shown),equivalent to a four-cycle pulse 10-fs duration) atthe output of the interferometer, showing that ourapproach would also work for longer pulses. Also,note that the average power at t  0 corresponds to64 mW, only a third of the total laser power. Thisaverage power potentially allows us to lock ff of thelaser oscillator to some fixed frequency and use themain part of the laser power for further experiments.In the 350-nm-thin ZnO film, both the ff peak andthe 2ff peak are still visible. Interestingly, the 2ffpeak is even larger than the ff peak [Fig. 2(b)].In conclusion, in our experiments we focused intensetwo-cycle optical pulses from a mode-locked laser oscil-lator onto ZnO and analyzed the emitted light with a rfspectrum analyzer. These experiments revealed twoaspects.(1) Using 100-mm-thick ZnO single crystals, wefound a large peak $30 dB above noise level at 10-kHzbandwidth and 64-mW average power) at the CEOfrequency, ff. The simplicity and robustness of theapproach makes it attractive, e.g., for applications infrequency metrology1,2 or for stabilization of the CEOfrequency.(2) A peak at the CEO frequency is still observedwith a 350-nm-thin ZnO film. This might pave theroad for the next step: Assuming that the CEOfrequency is stabilized to zero by whatever means,using the 350-nm ZnO film, one could in principlemeasure the CEO phase of the incident pulses itself,which would be the ultimate complete characteriza-tion of the laser pulses. To get there, two necessaryconditions have to be fulfilled: (i) Neither the electricfield envelope nor the CEO phase must change sig-nificantly within the measurement apparatus. TheFig. 1. Spectra of light emitted by the 100-mm-thick ZnOsingle crystal into the forward direction versus time delayt of the Michelson interferometer, Ekc. (a) I  0.15 3 I0,(b) I  2.04 3 I0, and (c) same as (b) but with differentsaturation of the gray scale. The light intensities decaynear the ZnO bandgap of Eg  3.3 eV. The white curvein (b) labeled IAC is the interferometric autocorrelationmeasured independently with a b-barium borate crystal,and the black curve in (c) is a cut through the ZnO dataat the 395-nm wavelength (indicated by the arrow). Theoptical spectra of the 350-nm-thin ZnO epitaxial layer aresimilar.December 1, 2002 / Vol. 27, No. 23 / OPTICS LETTERS 2129Fig. 2. rf spectra with 10-kHz resolution and videobandwidth, t  0 fs. (a) 100-mm-thick ZnO single crys-tal corresponding to Fig. 1; 455–480-nm optical filter.(b) 350-nm-thin ZnO epitaxial layer; 455–500-nm opticalfilter. The peaks at repetition frequency fr, carrier-envelope offset frequency ff, its second harmonic 2ffand mixing products fr 2 ff and fr 2 2ff are labeled.The black and gray data correspond to slightly differentswivel mirror positions. When intracavity prism materialCaF2 is removed, the ff and 2ff fr 2 ff and fr 2 2ffpeaks shift to the left (right).latter condition is more stringent. The linear opticalchange of the CEO phase, dflin, results from thedifferent phase and group velocities4 and can easilybe calculated from the known Sellmeier coeff icients ofZnO.13 At l0  2pc0v0  826 nm and l  350 nm,dflin is merely 4.6% of 2p —a level of precision thatmight be suff icient for many applications. (ii) Oneneeds a calibration or a detailed theory of how themeasured beat signal is related to f. Solving theMaxwell equations together with the known off-resonant values of x 2  6 3 10212 mV (bulk) andx 3  7 3 10221 m2V2 (bulk) for the actual ZnOsample geometry without further approximations, wecan reproduce the behavior shown in Fig. 1 very well.Translating x 3 into a nonlinear refractive index ofn2  5 3 10215 cm2W, the nonlinear shift of the CEOphase results as dfNL  n2I2pl0l  1% of 2p forI  5.0 3 1012 Wcm2 and l  350 nm, even smallerthan the linear optical shift. Unlike in the experi-ment, this off-resonant, perturbative treatment doesnot, however, deliver any significant peak at 2ff inthe rf spectra. This aspect is currently not resolved.Recently, a 2ff peak was predicted theoretically8for resonant excitation of a semiconductor underthe condition that the Rabi energy approaches thecenter photon energy, h̄v0, of the laser pulses, corre-sponding to the nonperturbative regime. In our ZnOexperiments, the peak of the electric field envelope,Ẽ0  6 3 109 Vm, translates into a Rabi energy ofh̄VR  1.1 eV  h̄v0  1.5 eV. However, these reso-nant excitation conditions8 cannot be directly appliedto our ZnO experiments, in which intraband processesare expected to be important as well. Indeed, forthe same electric field of Ẽ0  6 3 109 Vm, theponderomotive electron energy of Ekin  1.27 eV andthe Bloch energy of h̄VBloch  3 eV are comparableto h̄v0 and h̄VR. Apart from being important foraspect (ii), this represents an exciting, unexplored, andchallenging new regime of extreme nonlinear optics insolids in general.This work is supported by Deutsche Forschungs-gemeinschaft (DFG) projects DFG-We 1497/11-1 andDFG-Mo 850/2-1, and by the DFG graduate schoolGRK 284. The work of F. X. Kärtner is supported bythe U.S. Off ice of Naval Research and National ScienceFoundation grant ECS-0217358; that of M. Wegener bythe DFG Leibniz Award 2000. O. D. Mücke’s e-mailaddress is oliver.muecke@physik.uni-karlsruhe.de.References1. A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann,Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz,Phys. Rev. Lett. 85, 740 (2000).2. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz,R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science288, 635 (2000).3. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger,D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327(1999).4. U. Morgner, R. Ell, G. Metzler, T. R. Schibli, F. X.Kärtner, J. G. Fujimoto, H. A. Haus, and E. P. Ippen,Phys. Rev. Lett. 86, 5462 (2001).5. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin,and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).6. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi,M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri,Nature 414, 182 (2001).7. A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett.88, 133901 (2002).8. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner,and F. X. Kärtner, Phys. Rev. Lett. 89, 127401 (2002).9. U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen,H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Scheuer,G. Angelow, and T. Tschudi, Opt. Lett. 24, 411 (1999).10. M. U. Wehner, M. H. Ulm, and M. Wegener, Opt. Lett.22, 1455 (1997).11. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner,and F. X. Kärtner, Phys. Rev. Lett. 87, 057401 (2001).12. With additional experiments we have carefully checkedthat the 2ff peak is not due to nonlinearities of thephotomultiplier.13. X. W. Sun and H. S. Hwok, J. Appl. Phys. 86, 408(1999).

Determining the carrier-envelope offset frequency of 5-fs pulses with extreme nonlinear optics in ZnO

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Determining the carrier-envelope offset frequency of 5-fs pulses with extreme nonlinear optics in ZnO

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