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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 16 — Aug. 3, 2009
  • pp: 14023–14028
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Wide-time-range spectral-shearing interferometry

Hitoshi Tomita and Hajime Nishioka  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 14023-14028 (2009)
http://dx.doi.org/10.1364/OE.17.014023


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Abstract

A long-time-range spectral-shearing interferometry has been demonstrated by frequency mixing with two-color monochromatic fields. Strongly chirped pulses with quadratic and cubic phase distortion have been characterized. A linearly chirped pulse having 2.2 ps (full duration of 6 ps) has been measured with a coaxial two-color field generated by a narrow-gap passive etalon. Substantial extensions in the time range can be expected with a highly coherent two-color source, i.e., frequency stabilized lasers, or two longitudinal modes in the frequency comb.

© 2009 OSA

1. Introduction

Spectral-phase interferometry [1–10

1. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23(10), 792–794 (1998). [CrossRef]

] is widely used for characterizing few-cycle laser pulses. Spectral shearing interferometry generally has extremely high sensitivity, wide dynamic range [9

9. H. Nishioka and H. Tomita, “Wide-range spectral shearing interferometry,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CWB3. [PubMed]

], and wide spectrum range near one-octave spanning [7

7. A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31(12), 1914–1916 (2006). [CrossRef] [PubMed]

]. These characteristics are suitable for measuring few-cycle phenomena [11–13

11. M. Yamashita, K. Yamane, and R. Morita, “Quasi-automatic phase control technique for chirp compensation of pulses with over-one-octave-bandwidth generation of few- to mono-cycle optical pulses,” IEEE J. Sel. Top. Quantum Electron. 12(2), 213–222 (2006). [CrossRef]

], including coherent transient responses [14

14. T. Kobayashi, J. Du, W. Feng, and K. Yoshino, “Excited-state molecular vibration observed for a probe pulse preceding the pump pulse by real-time optical spectroscopy,” Phys. Rev. Lett. 101(3), 037402 (2008). [CrossRef] [PubMed]

], ultrafast highly nonlinear phenomena [15

15. H. Nishioka and K. Ueda, “Super-broadband continuum generation with transient self-focusing of a terawatt laser pulse in rare gases,” Appl. Phys. B 77(2–3), 171–175 (2003). [CrossRef]

], and diagnosis of a pre-pulse from a CPA system coupled with adaptive phase correction [16

16. K. Yamakawa, M. Aoyama, Y. Akahane, K. Ogawa, K. Tsuji, A. Sugiyama, T. Harimoto, J. Kawanaka, H. Nishioka, and M. Fujita, “Ultra-broadband optical parametric chirped-pulse amplification using an Yb: LiYF(4) chirped-pulse amplification pump laser,” Opt. Express 15(8), 5018–5023 (2007). [CrossRef] [PubMed]

].

In the SPIDER technique, a frequency-chirped pulse is assumed to be monochromatic in the short pulse duration. The assumption is valid for few-cycle analysis but limits the maximum possible pulse duration. The maximum pulse duration limited by the coherent time of the frequency chirped pulse is given by TTLM , where TTL is transform-limited (TL) pulse duration and M is stretching magnification. For example, a linearly chirped 1-ns pulse stretched from a 10-fs TL pulse has a coherent time of 3.16 ps. Thus a material stretcher, i.e., a glass block, is limited within sub-ps application. Even with a grating stretcher, it is difficult to measure regions created by pulses longer than 10 ps.

In this paper, a long-time range spectral shearing interferometry with few-cycle resolution has been proposed. Our configuration uses coaxial two-color fields that produce a temporally coherent field at different frequencies [8

8. H. Tomita and H. Nishioka, “Wide temporal coverage spectral shearing interferometer with a dual frequency mixer,” in Proceedings of IEEE conference on Lasers and Electro-Optics Society (IEEE, 2007), pp. 842–843.

,9

9. H. Nishioka and H. Tomita, “Wide-range spectral shearing interferometry,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CWB3. [PubMed]

]. (During the preparation of this paper, we found another work carried out recently [10

10. T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34(7), 881–883 (2009). [CrossRef] [PubMed]

] using quasi-monochromatic fields with noncoaxial three-beam configuration.) A signal pulse mixed with the two-color fields simultaneously results in the sum-frequency fields forming the spectral shearing interferogram. This configuration is suitable for measuring long pulse duration with the scaling parameters. The frequency shear giving spectral resolution is freely chosen by the differential frequency between two-color fields. The maximum measurable pulse duration can be extended with the coherent time of the local laser.

2. Experimental setup for wide-time-range spectral shearing interferometry

For the first demonstration, two longitudinal modes of a narrow gap etalon (CVI, model ETA-20-25-800-97, 25 µm air spaced) are used for the two-color fields, as shown in Fig. 1(a). An interferometric bandpass filter (ANDOVER, model 800FS10-25) is used to select two adjacent longitudinal modes. A signal pulse and the monochromatic fields are focused onto a 20-μm-thick BBO crystal with an off-axis parabolic mirror (of focal length 50 mm). Type-II phase matching is used to obtain a large acceptance angle and to suppress second harmonic generation. A polarization of the two-color fields is adjusted with a zero-order λ/2 wave plate. This setup takes care to minimize internal GDD by eliminating transmission optics for the signal pulse. The spectral fringes at the sum frequency are monitored with a spectrometer (HAMAMATSU, model PMA-50 with groove density 300/1200 lp/mm, resolution: 60 GHz) providing a back-illuminated cooled CCD with 16-bit A/D resolution (model C5809). The detection sensitivity also decreases with the line width of the etalon selected. Because of the nature of spectral filtering, the sensitivity is essentially same as the conventional SPIDER using a chirped pulse for the temporal-spectral filtering.

A shear frequency of 5.9 THz and a linewidth of 70 GHz were measured as shown in Fig. 1(b). A coherent time Tc given by the linewidth was 14 ps.

Fig. 1. Experimental setup for a spectral shearing interferometry with coaxial two-color fields. (b) Spectrum of the two-color fields.

3. The phase-retrieval/pulse reconstruction algorithm

The coaxial two-color fields and the zero-delay configuration have the advantage of a specific measured pulse-width error for a given delay-time error [4

4. J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31(13), 2063–2065 (2006). [CrossRef] [PubMed]

] between the original and the replica pulses. On the other hand, due to lack of the fixed delay, an additional delay scan is required to determine the sign of GDD.

The shearing interferogram I(ω,ϕ) is expressed with Fourier components of electric field E(ω) = a(ω)exp j[ωt + φ(ω)] as

I(ω,ϕ)=E(ω)2+E(ω+Ω)2+2E(ω)E(ω+Ω)×cos[φ(ω+Ω)φ(ω)+ϕ],
(1)

where a(ω) is Fourier amplitude, φ(ω) is Fourier phase, and Ω is shear frequency. Giving additional time delay τ between the signal and the two-color fields, phase shift ϕ is given to the interferogram as ϕ = Ωτ . In the following experiments, the 2-D interferogram I(ω,ϕ) is recorded with a few-cycle delay scan, then G(ω) = exp j[φ(ω + Ω)-φ(ω) + Ωτ] components are extracted from I(ω,ϕ) by FFT filtering for Ω . The Fourier phase is given by φ(ω+Ω)-φ(ω) = arg(G(ω)). For the pulse reconstruction, the Fourier amplitude is separately given by the fundamental spectral intensity S(ω) = ∣E(ω)∣2.

Generally, by Nyquist’s sampling theorem, the maximum possible time range is limited within t max <2π /Ω i.e. ∣φ(ω+Ω)-φ(ω)∣ <2π. However, a pulse longer than t max can be measured with the assumption

φ(ω+Ω)φ(ω)=Ω(ω).
(2)

This assumption is valid when φ(ω+Ω)-φ(ω) changes monotonically with ω. For example, with a linearly chirped pulse because the term φ(ω +Ω)- φ(ω) is in proportion to ω, the maximum pulse duration is free of the shear frequency Ω limit. A pulse duration up to the coherent time Tc can be measured. On the other hand, in the case of double pulses having the same pulse structure with separation Ts, the φ(ω + Ω)- φ(ω) term is cyclic for the pulse separation Ts . We cannot detect a double pulse sequence longer than t max . The shear frequency should decrease when we reconstruct the general waveform, as a result of the t max <2π/Ω limit. The minimum possible shear frequency Ωmin in this scheme corresponds to the line width of two-color fields. Thus, in general cases, the maximum time range can be extended up to the coherent time.

4. Results and discussion

First, we have monitored a near-transform-limited (TL) pulse from a mode-locked Ti:Sapphire laser operated at 800 nm. The spectral interferograms obtained for a bandwidth of 90 THz are shown in Fig. 2(a). Our setup takes the zero-delay configuration so a zero-fringe is observed for a TL pulse, as shown in Fig. 2(a). A few-cycle pulse has been reconstructed as shown in Fig. 2(c). When a glass block (SF10, a thickness of 50 mm) was placed, the interferogram had several fringes as shown in Fig. 2(b). Each fringe corresponds to a group delay of 2π/Ω . The reconstructed phase structure (GDD of 8.2 × 103 fs2 + 4 x 103 fs3) agrees well with a calculation based on Sellmeier’s equation (8.05 × 103 fs2 + 5 × 103 fs3). A pulse duration of 2.2 ps (the foot is extended to 6 ps) has been measured as shown in Fig. 2(d).

Fig. 2. Interferogram for (a) a 11-fs near-TL pulse and (b) a 2.- ps chirped pulse (the foot has 6 ps) by a 50-mm-thick SF10 glass block. (c), (d) are reconstructed pulse shapes, respectively. The dashed curve in (b) shows the GDD in the glass block calculated with Sellmeier’s equation.

We have characterized a pulse having cubic phase distortion. A test pulse is generated with a 100-mm thick SF10 glass block followed by a grating pair (groove density: 672 g/mm, grating separation: 17.3 mm). A sub-ps pulse with cubic phase modulation (π-step phase shift) was characterized as shown in Fig. 3(b). Figure 3(a) shows spectral fringes as a function of the phase-shift. The third-order group-delay dispersion (TOD) was measured to be TOD = 3.1 ×104 fs3 that agrees with a calculation of 3.05 × 104 fs3 over the bandwidth of 60 THz. The residual phase error between the measurement and calculation [a red line shown in Fig. 3 (a)] was within π/4 for the bandwidth. In the cubic phase measurement, the phase error φerr (ω) from the assumption Eq. (2) is expressed as

φerr(ω)=φ(ω+Ω)φ(ω)Ω(ω)=Ω2[3(ωω0)+Ω]×TOD,
(3)

where ω 0 is center frequency. φerr = 0.24π at 400 THz (ω 0/ 2π = 365 THz) agree with the measurement.

Fig. 3. A pulse has cubic phase distortion. (a) Interferogram as a function of phase shift and Fourier phase. The red line shows the phase difference between the measurement and the calculation. (b) A reconstructed pulse shape and instantaneous phase.

In order to reconfirm the maximum possible time range with this setup in the time domain, fringe contrast has been evaluated as a function of time as shown in Fig. 4. The contrast ratio has been kept constant up to the coherent time of 14 ps that is measured by the linewidth of etalon. The coherent time (dephasing time) agree with a decoherence time of 2πτd = 16 ps estimated with a decay time constant of τd = 2.54 ps.

Fig. 4. Fringe contrast ratio as a function of time. The coherent time Tc of 14 ps is set by the linewidth of the etalon.

5. Conclusion

We have demonstrated a spectral-shearing interferometry with the temporally coherent fields. It has been shown that a pulse duration far exceeding the shear-frequency limit can be measured for the quadratic and cubic phase cases. Substantial extension in the time range can be expected with a highly coherent two-color source, i.e., a frequency-stabilized two-color laser or two longitudinal modes in the frequency comb.

Part of this work is supported by the 21st Century Center of Excellence (COE) program from the Ministry of Education, Culture, Science, Sports and Technology, Japan.

References and links

1.

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23(10), 792–794 (1998). [CrossRef]

2.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24(18), 1314–1316 (1999). [CrossRef]

3.

P. Baum, S. Lochbrunner, and E. Riedle, “Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses,” Opt. Lett. 29(2), 210–212 (2004). [CrossRef] [PubMed]

4.

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31(13), 2063–2065 (2006). [CrossRef] [PubMed]

5.

M. Lelek, F. Louradour, A. Barthélémy, C. Froehly, T. Mansourian, L. Mouradian, J.-P. Chambaret, G. Chériaux, and B. Mercier, “Two-dimensional spectral shearing interferometry resolved in time for ultrashort optical pulse characterization,” J. Opt. Soc. Am. B 25(6), A17–A24 (2008). [CrossRef]

6.

V. Messager, F. Louradour, C. Froehly, and A. Barthelemy, “Coherent measurement of short laser pulses based on spectral interferometry resolved in time,” Opt. Lett. 28(9), 743–745 (2003). [CrossRef] [PubMed]

7.

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31(12), 1914–1916 (2006). [CrossRef] [PubMed]

8.

H. Tomita and H. Nishioka, “Wide temporal coverage spectral shearing interferometer with a dual frequency mixer,” in Proceedings of IEEE conference on Lasers and Electro-Optics Society (IEEE, 2007), pp. 842–843.

9.

H. Nishioka and H. Tomita, “Wide-range spectral shearing interferometry,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CWB3. [PubMed]

10.

T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34(7), 881–883 (2009). [CrossRef] [PubMed]

11.

M. Yamashita, K. Yamane, and R. Morita, “Quasi-automatic phase control technique for chirp compensation of pulses with over-one-octave-bandwidth generation of few- to mono-cycle optical pulses,” IEEE J. Sel. Top. Quantum Electron. 12(2), 213–222 (2006). [CrossRef]

12.

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28(20), 1987–1989 (2003). [CrossRef] [PubMed]

13.

K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28(22), 2258–2260 (2003). [CrossRef] [PubMed]

14.

T. Kobayashi, J. Du, W. Feng, and K. Yoshino, “Excited-state molecular vibration observed for a probe pulse preceding the pump pulse by real-time optical spectroscopy,” Phys. Rev. Lett. 101(3), 037402 (2008). [CrossRef] [PubMed]

15.

H. Nishioka and K. Ueda, “Super-broadband continuum generation with transient self-focusing of a terawatt laser pulse in rare gases,” Appl. Phys. B 77(2–3), 171–175 (2003). [CrossRef]

16.

K. Yamakawa, M. Aoyama, Y. Akahane, K. Ogawa, K. Tsuji, A. Sugiyama, T. Harimoto, J. Kawanaka, H. Nishioka, and M. Fujita, “Ultra-broadband optical parametric chirped-pulse amplification using an Yb: LiYF(4) chirped-pulse amplification pump laser,” Opt. Express 15(8), 5018–5023 (2007). [CrossRef] [PubMed]

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(320.5540) Ultrafast optics : Pulse shaping
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: April 28, 2009
Revised Manuscript: June 18, 2009
Manuscript Accepted: July 1, 2009
Published: July 29, 2009

Citation
Hitoshi Tomita and Hajime Nishioka, "Wide-time-range spectral-shearing interferometry," Opt. Express 17, 14023-14028 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-14023


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References

  1. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23(10), 792–794 (1998). [CrossRef]
  2. L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, “Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 24(18), 1314–1316 (1999). [CrossRef]
  3. P. Baum, S. Lochbrunner, and E. Riedle, “Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses,” Opt. Lett. 29(2), 210–212 (2004). [CrossRef] [PubMed]
  4. J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31(13), 2063–2065 (2006). [CrossRef] [PubMed]
  5. M. Lelek, F. Louradour, A. Barthélémy, C. Froehly, T. Mansourian, L. Mouradian, J.-P. Chambaret, G. Chériaux, and B. Mercier, “Two-dimensional spectral shearing interferometry resolved in time for ultrashort optical pulse characterization,” J. Opt. Soc. Am. B 25(6), A17–A24 (2008). [CrossRef]
  6. V. Messager, F. Louradour, C. Froehly, and A. Barthelemy, “Coherent measurement of short laser pulses based on spectral interferometry resolved in time,” Opt. Lett. 28(9), 743–745 (2003). [CrossRef] [PubMed]
  7. A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31(12), 1914–1916 (2006). [CrossRef] [PubMed]
  8. H. Tomita, and H. Nishioka, “Wide temporal coverage spectral shearing interferometer with a dual frequency mixer,” in Proceedings of IEEE conference on Lasers and Electro-Optics Society (IEEE, 2007), pp. 842–843.
  9. H. Nishioka, and H. Tomita, “Wide-range spectral shearing interferometry,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications SystemsTechnologies, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CWB3. [PubMed]
  10. T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34(7), 881–883 (2009). [CrossRef] [PubMed]
  11. M. Yamashita, K. Yamane, and R. Morita, “Quasi-automatic phase control technique for chirp compensation of pulses with over-one-octave-bandwidth generation of few- to mono-cycle optical pulses,” IEEE J. Sel. Top. Quantum Electron. 12(2), 213–222 (2006). [CrossRef]
  12. B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28(20), 1987–1989 (2003). [CrossRef] [PubMed]
  13. K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28(22), 2258–2260 (2003). [CrossRef] [PubMed]
  14. T. Kobayashi, J. Du, W. Feng, and K. Yoshino, “Excited-state molecular vibration observed for a probe pulse preceding the pump pulse by real-time optical spectroscopy,” Phys. Rev. Lett. 101(3), 037402 (2008). [CrossRef] [PubMed]
  15. H. Nishioka and K. Ueda, “Super-broadband continuum generation with transient self-focusing of a terawatt laser pulse in rare gases,” Appl. Phys. B 77(2-3), 171–175 (2003). [CrossRef]
  16. K. Yamakawa, M. Aoyama, Y. Akahane, K. Ogawa, K. Tsuji, A. Sugiyama, T. Harimoto, J. Kawanaka, H. Nishioka, and M. Fujita, “Ultra-broadband optical parametric chirped-pulse amplification using an Yb: LiYF(4) chirped-pulse amplification pump laser,” Opt. Express 15(8), 5018–5023 (2007). [CrossRef] [PubMed]

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