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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 15 — Jul. 23, 2007
  • pp: 9748–9754
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Ultrashort pulse characterization by ultra-thin ZnO, GaN, and AlN crystals

Yohei Kobayashi, Dai Yoshitomi, Kakuya Iwata, Hideyuki Takada, and Kenji Torizuka  »View Author Affiliations


Optics Express, Vol. 15, Issue 15, pp. 9748-9754 (2007)
http://dx.doi.org/10.1364/OE.15.009748


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Abstract

Ultra-thin semiconductor crystals were investigated as nonlinear materials for second-harmonic generation. Nonlinear susceptibilities of sub-micrometer-thick ZnO, GaN, and AlN crystals were measured, and these crystals were used for sub-10-fs pulse measurement by a fringe-resolved autocorrelation method. We found that a one-cycle pulse could be characterized by using these ultra-thin-film crystals.

© 2007 Optical Society of America

1. Introduction

In this report, we characterize the nonlinear properties and pulse propagation of molecular-beam epitaxially grown semiconductor films, and demonstrate ultrashort pulse measurement by using them. Second-order nonlinear coefficients of ZnO, GaN, and AlN were compared with that of BBO crystal, and were found to have large enough nonlinear coefficients and wide enough conversion bandwidth for SHG to measure sub-10-fs Ti:sapphire laser pulses by conventional auto-correlation techniques.

2. Pulse propagation in semiconductor ultra-thin films

A femtosecond pulse is broadened by propagation in a material. The pulse broadening can be estimated by the material dispersions. We adopted Sellmeier’s equations of bulk semiconductors for the propagation calculations since the refractive indexes of ZnO, GaN, and AlN thin-film crystals are not clearly established. The adopted Sellmeier’s equations of ZnO, GaN, AlN are nZnO=1.9148 + 0.0569/λ 2-0.0136/λ 4+0.002168/λ6, nGaN=(1+4.295×λ 2/(λ 2-0.18992))0.5, nAIN=(1+3.335×λ 2/(λ 2-0.13922))0.5, where λ denotes the wavelength in micrometers [13

13. W. L. Bond, “Measurement of the refractive indices of several crystals,” J. of Appl. Phys. 36, 1674–1677 (1965). [CrossRef]

15

15. U. Ozgur, G. Webb-Wood, H. O. Everitt, F. Yun, and H. Morkoc, “Systematic measurement of AlxGa1-xN refractive indices,” Appl. Phys. Lett. 79, 4103–4105 (2001). [CrossRef]

]. We used the refractive index of the extra-ordinary polarized light for the propagation calculation since the polarization of the incident beam is perpendicular to both a- and b- axes, although the incident angle is not exactly parallel to the c axis.

We assumed a one-optical-cycle transform-limited pulse at a center wavelength of 800 nm as the incident light. The incident electric field in the time domain is Fourier transformed to the frequency domain and multiplied by an additional phase term by the material. The inverse-Fourier transformation gives the propagated electric field. We calculated only the propagation of the fundamental pulse. The pulse is expressed by using envelope and carrier terms, and this calculation uses no approximation because this calculation deals only the linear dispersion. One should care about the slowly-varying envelope approximation in this time region when the nonlinear processes such as wavelength conversion or nonlinear refractive index are included. Figure 1 plots the result of the pulse propagation calculation. Figure 1(a) depicts the incident and output electric field of 5µm-thick BBO crystal. The output time shifts in accordance with the group velocity delay produced by a crystal, and the output electric field shape changes due to the material dispersion. Although the pulse duration change by the 5µm-thick BBO crystal is not so large, it is too thick to estimate the absolute optical-electric field from this calculation because the optical-electric field shape changes significantly in the material. Thus BBO crystal can not be used for the field characterization of Fourier-synthesized attosecond pulse train by ultra-broad femtosecond pulses [4

4. T. W. Hänsch, “A proposed sub-femtosecond pulse synthesizer using separate phase-locked Laser Oscillators,” Opt. Commun. 80, 71–75 (1990). [CrossRef]

6

6. Y. Kobayashi, D. Yoshitomi, M. Kakehata, H. Takada, and K. Torizuka, “Long-term optical phase locking between femtosecond Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 30, 2496–2498 (2005). [CrossRef] [PubMed]

].

Figure 1(b) illustrates the pulse propagation of ultra-thin-film semiconductor crystals. The crystal thickness is assumed to 0.3µm. The output electric-field shapes do not change so much compared to the BBO calculation. The 0.3µm-thick ZnO, AlN, and GaN crystals can then be used for pulse characterization of a one-cycle optical pulse in terms of the pulse broadening due to the propagation.

Fig. 1. One-optical-cycle electric field propagation through 5µm-thick BBO crystal (a). Incident (output) electric field is indicated by the black (red) curve. Pulse propagation results of 0.3µm-thick ZnO, GaN, and AlN crystal (b). The output electric fields of ZnO, GaN, and AlN crystals are represented by red, green, and blue curves.

3. Conversion bandwidth for second-harmonic generation of semiconductor crystals

Fig. 2. (a). Coherent lengths of ZnO (red curve), GaN (green curve), and ZnO (blue curve) crystals. (b) Relative intensity of the SH light versus the fundamental wavelength.

4. Nonlinear coefficient measurements of ultra-thin films

ZnO, GaN, and AlN thin-film crystals were grown by molecular-beam-epitaxial (MBE) methods on sapphire crystals. Their c-axes are perpendicular to the substrate surfaces. The uniformity of a- and b-axes of these samples is not clear, but they should be good since they were grown by MBE. The refractive indexes of polarized light parallel to the c-axes are much different from those of a- and b-axes polarized light. However, the difference is not large to achieve phase matching. Therefore, full-tensor of the second-order nonlinear optical susceptibility should be considered for SHG. ZnO, GaN, and AlN crystals we used are hexagonal materials with 6-mm symmetry, then d33, d31=d32, and d15=d24 should be considered. The effective nonlinear susceptibility can be derived considering the wave vector of the fundamental beam and the projection of the second-order polarization. For hexagonal materials with 6-mm symmetry, the effective second-order nonlinear susceptibility of the sand p-polarized SH lights are given by dseff=2d 15 sin θ sin ρ cos ρ, and dpeff=(d 33 sin3 θ+2d 15 sin θ cos2 θ+d 31 sin θ cos2 θ)cos2 ρ+d 31 sin θ sin2 ρ, respectively, where ρ is the fundamental polarization angle, and θ is the incidence angle in the crystal. In our experiment, both p- and s-polarized SH lights were observed. Then the total effective second-order nonlinear susceptibility can be written by deff=deffs2+deffp2. Since there is a relation of d31=d32=d15=d24 in a case of A1N, can be simlified as deff=d 33 sin3 θ+3d 31 sin θ cos2 θ when the fundamental light is p-polarized.

Sub-10-fs Ti:sapphire laser pulses were focused by an f=25.4mm parabolic mirror with an incident angle of 45 degrees. The SH powers of thin crystals were measured by a photomultiplier tube (Hamamatsu R7400 U-3). Figure 3(a) shows the measured dependence of the SH intensity on the fundamental polarization angle with AlN crystal. Measured SH power was well agreed with the theory. The SH powers of semiconductor crystals were compared with that obtained by a 10µm-thick BBO crystal. The ZnO crystal is 220nm thick; the AlN crystal, 340nm thick; and the GaN crystal, 340nm thick. 340-nm GaN is grown with a thin buffer layer on a sapphire crystal. This layer is negligible since the generated SH power from GaN layer is two-orders higher than that from this buffer layer. The SH power with thinner AlN crystal was below the detection limit, then the observed SHG was not the surface SHG. The obtained SH powers and relative nonlinear coefficients of thin-film crystals are depicted in Fig. 3(b). Blue rectangles represent measured SH powers, and red circles, the normalized nonlinear coefficients (deff) relative to that of BBO. The phase-match angle of BBO crystal is θ=29.2 degrees. The SH power of BBO crystal is highest due to the greater crystal thickness, although its deff was lowest. The deff of GaN is seven times larger than that of BBO crystal. This measurement indicates that ultra-thin-film semiconductor crystals have higher nonlinear coefficients than BBO crystals. These crystals can thus be used for ultra-short pulse characterization by the autocorrelation technique.

Fig. 3. (a). Measured dependence of the SH intensity on the fundamental polarization angle by AlN crystal. (b) Second-harmonic powers and nonlinear efficiencies of semiconductor thin-film crystals.

5. Auto-correlation measurement of sub-10fs Ti:sapphire laser pulse

A mode-locked Ti:sapphire laser oscillator produces an ultra-short femtosecond pulse train with a repetition frequency of 80MHz. The output power is about 200mW with a spectrum width exceeding 140nm. The Fourier-transformed-limited pulse width is about 7fs in this spectrum. The pulse train was split by a Cr-coated beam splitter with a broad spectrum bandwidth. The split beams were recombined collinearly after some time delay by a piezoelectric transducer. The superimposed pulse was focused into thin-film crystals by a parabolic mirror, and generated SH was detected by a photomultiplier tube. SH power versus changing time delay was recorded by an oscilloscope. Figure 4 plots the obtained laser spectrum and autocorrelation traces. Figure 4(a) is the mode-locked Ti:sapphire laser spectrum. The spectrum is in the region of 670nm to 950nm, thus the absorption edge of the crystal should be less than 335 nm.

Fig. 4. Ti:sapphire laser spectrum (a), and autocorrelation traces obtained by 10µm BBO (b), 220nm ZnO (c), 340nm GaN (d), and 340nm thick AlN (e) crystals.

Figure 4(b) graphs the autocorrelation trace of the Ti:sapphire laser pulse obtained by using a 10µm-thick BBO crystal, which is shown as a reference. Figures 4(c), 4(d), and 4(e) are the autocorrelation traces obtained by using 220nm-thick ZnO, 340nm-thick GaN, and 340nm-thick AlN crystals. A contrast ratio of 1:8 was obtained for all crystals, thus all ultra-thin crystals worked well for ultra-short pulse measurement. All crystals can be used for 7fs pulse characterization. However, 10µm-thick BBO crystals cannot be used for shorter pulse measurements due to their narrow conversion bandwidth. AlN crystals have the greatest bandwidth and least propagation effects. Thus, thin AlN crystals are promising candidates for one-cycle optical pulse characterization, although they have poor conversion efficiency.

6. Summary

The pulse propagation and the second-harmonic conversion of ultra-thin semiconductor crystals were investigated by numerical calculation. The results reveal that sub-micrometer-thick ZnO, GaN, and AlN crystals are appropriate for ultra-wide-spectrum pulse characterization. The nonlinear coefficients of these crystals for SHG were measured and were found to exceed that of BBO crystal. These crystals were thus found to be appropriate for ultrashort pulse measurement by autocorrelation techniques and were used to characterize 7-fs Ti:sapphire laser pulses.

Acknowledgments

This work was supported by Grant-in-Aid for Young Scientists (A) 17686009.

References and links

1.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414, 509–513 (2001). [CrossRef] [PubMed]

2.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605–608 (2004). [CrossRef] [PubMed]

3.

E. Matsubara, K. Yamane, T. Sekikawa, and M. Yamashita, “Generation of 2.6 fs optical pulses using induced-phase modulation in a gas-filled hollow fiber,” J. Opt. Soc. Am. B 24, 985–989 (2007). [CrossRef]

4.

T. W. Hänsch, “A proposed sub-femtosecond pulse synthesizer using separate phase-locked Laser Oscillators,” Opt. Commun. 80, 71–75 (1990). [CrossRef]

5.

K. Shimoda, “Theory and application of optical subharmonic oscillator,” Jpn. J. Appl. Phys. 34, 3566–3569 (1995). [CrossRef]

6.

Y. Kobayashi, D. Yoshitomi, M. Kakehata, H. Takada, and K. Torizuka, “Long-term optical phase locking between femtosecond Ti:sapphire and Cr:forsterite lasers,” Opt. Lett. 30, 2496–2498 (2005). [CrossRef] [PubMed]

7.

A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, “Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers,” Opt. Lett. 29, 403–405 (2004). [CrossRef] [PubMed]

8.

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28, 947–949 (2003). [CrossRef] [PubMed]

9.

U. Griebner, R. A. Kaindl, T. Elsaesser, and W. Seeber, “Frequency doubling and autocorrelation studies of 20 fs pulses using polycrystalline zinc oxide thin films,” App. Phys. B 67, 757–760 (1998). [CrossRef]

10.

H. Yang, S. J. Xu, Q. Li, and J. Zhang, “Resonantly enhanced femtosecond second-harmonic generation and nonlinear luminescence in GaN film grown on sapphire,” Appl. Phys. Lett. 88, 161113 (2006). [CrossRef]

11.

J. Miragliotta, D. K. Wickenden, T. J. Kistenmacher, and W. A. Bryden, “Linear- and nonlinear-optical properties of GaN thin films,” J. Opt. Soc. Am. B 10, 1447–1456 (1993). [CrossRef]

12.

G. T. Kiehne, G. K. L. Wong, and J. B. Ketterson, “Optical second-harmonic generation in sputter-deposited AlN films,” J. Appl. Phys. 84, 5922–5927 (1998). [CrossRef]

13.

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. of Appl. Phys. 36, 1674–1677 (1965). [CrossRef]

14.

M. J. Bergmann, U. Ozgur, H. C. Casey, H. O. Everitt, and J. F. Muth, “Ordinary and extraordinary refractive indices for AlxGa1-xN epitaxial layers,” App. Phys. Lett. 75, 67–69 (1999). [CrossRef]

15.

U. Ozgur, G. Webb-Wood, H. O. Everitt, F. Yun, and H. Morkoc, “Systematic measurement of AlxGa1-xN refractive indices,” Appl. Phys. Lett. 79, 4103–4105 (2001). [CrossRef]

OCIS Codes
(310.6860) Thin films : Thin films, optical properties
(320.7100) Ultrafast optics : Ultrafast measurements
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Ultrafast Optics

History
Original Manuscript: June 4, 2007
Revised Manuscript: July 16, 2007
Manuscript Accepted: July 18, 2007
Published: July 20, 2007

Citation
Yohei Kobayashi, Dai Yoshitomi, Kakuya Iwata, Hideyuki Takada, and Kenji Torizuka, "Ultrashort pulse characterization by ultra-thin ZnO, GaN, and AlN crystals," Opt. Express 15, 9748-9754 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9748


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References

  1. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001). [CrossRef] [PubMed]
  2. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, "Nonlinear optics in the extreme ultraviolet," Nature 432, 605-608 (2004). [CrossRef] [PubMed]
  3. E. Matsubara, K. Yamane, T. Sekikawa, M. Yamashita, "Generation of 2.6 fs optical pulses using induced-phase modulation in a gas-filled hollow fiber," J. Opt. Soc. Am. B 24, 985-989 (2007). [CrossRef]
  4. T. W. Hänsch, "A proposed sub-femtosecond pulse synthesizer using separate phase-locked Laser Oscillators," Opt. Commun. 80, 71-75 (1990). [CrossRef]
  5. K. Shimoda, "Theory and application of optical subharmonic oscillator," Jpn. J. Appl. Phys. 34, 3566-3569 (1995). [CrossRef]
  6. Y. Kobayashi, D. Yoshitomi, M. Kakehata, H. Takada, and K. Torizuka, "Long-term optical phase locking between femtosecond Ti:sapphire and Cr:forsterite lasers," Opt. Lett. 30, 2496-2498 (2005). [CrossRef] [PubMed]
  7. A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, "Broadband phase-coherent optical frequency synthesis with actively linked Ti:sapphire and Cr:forsterite femtosecond lasers," Opt. Lett. 29, 403-405 (2004). [CrossRef] [PubMed]
  8. T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, F. X. Kaertner, "Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation," Opt. Lett. 28, 947-949 (2003). [CrossRef] [PubMed]
  9. U. Griebner, R. A. Kaindl, T. Elsaesser, and W. Seeber, "Frequency doubling and autocorrelation studies of 20 fs pulses using polycrystalline zinc oxide thin films," App. Phys. B 67, 757-760 (1998). [CrossRef]
  10. H. Yang, S. J. Xu, Q. Li, and J. Zhang, "Resonantly enhanced femtosecond second-harmonic generation and nonlinear luminescence in GaN film grown on sapphire," Appl. Phys. Lett. 88, 161113 (2006). [CrossRef]
  11. J. Miragliotta, D. K. Wickenden, T. J. Kistenmacher, and W. A. Bryden, "Linear- and nonlinear-optical properties of GaN thin films," J. Opt. Soc. Am. B 10, 1447-1456 (1993). [CrossRef]
  12. G. T. Kiehne, G. K. L. Wong, J. B. Ketterson, "Optical second-harmonic generation in sputter-deposited AlN films," J. Appl. Phys. 84, 5922-5927 (1998). [CrossRef]
  13. W. L. Bond, "Measurement of the refractive indices of several crystals," J. of Appl. Phys. 36, 1674-1677 (1965). [CrossRef]
  14. M. J. Bergmann, U. Ozgur, H. C. Casey, Jr., H. O. Everitt, and J. F. Muth, "Ordinary and extraordinary refractive indices for AlxGa1-xN epitaxial layers," App. Phys. Lett. 75, 67-69 (1999). [CrossRef]
  15. U. Ozgur, G. Webb-Wood, H. O. Everitt, F. Yun, and H. Morkoc, "Systematic measurement of AlxGa1-xN refractive indices," Appl. Phys. Lett. 79, 4103-4105 (2001). [CrossRef]

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