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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17173–17178
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Spectral shearing interferometer with frequency- and time-resolved sum-frequency mixing

Hitoshi Tomita and Hajime Nishioka  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 17173-17178 (2011)
http://dx.doi.org/10.1364/OE.19.017173


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Abstract

A two-dimensional spectral-shearing interferogram has been acquired instantaneously by frequency- and time-resolved sum-frequency conversion where the phase-matching angle and transverse-delay of crossed-pump beams in a nonlinear crystal serve as frequency-time decomposed imaging. The two spectrally sheared components travel the same path after upconversion. A picoseconds delay-scanned interferogram is accumulated on a 2D image sensor.

© 2011 OSA

1. Introduction

In this paper, we demonstrate SSI with frequency- and time-resolved sum-frequency mixing. This enables measurement at the repetition rate of a 2D sensor. The two spectrally sheared components in the output beam from a sum-frequency crystal are collinear, whereas they travel different paths after upconversion in other 2D methods.

2. Frequency- and time-resolved upconverter for spectral shearing interferometer

We use two vertical-focused horizontal-crossed pump beams for two-dimensional resolved-frequency mixing. Frequency decomposition is achieved utilizing phase-match angle dispersion in a nonlinear crystal [14

14. D. H. Auston, “Nonlinear spectroscopy of picoseconds pulses,” Opt. Commun. 3(4), 272–276 (1971). [CrossRef]

16

16. H. Tomita and H. Nishioka, “High-resolution spectral-shearing interferometry,” in Proceedings of IEEE conference on Lasers and Electro-Optics Society (IEEE, 2008), pp. 701–702.

]. The 2D interferogram I(ω,τ) is given by
I(ω,τ)=|E(ω+ΩS)|2+|E(ω)|2+2|E(ω+ΩS)E(ω)|cos[Φ(ω,τ)]
(1)
and
Φ(ω,τ)=φ(ω+ΩS)φ(ω)+ΩSτ,
(2)
where τ is delay between a measured pulse and two monochromatic fields, ΩS is shear frequency, and |E(ω)|2 and φ(ω) are spectrum and spectral phases of the measured pulse. The phase difference of the two frequency-shifted spectra Φ is detected with a one-dimensional Fourier transform on the delay axis. In the case of φ(ω+ΩS)φ(ω)>2π, phase jumps are unwrapped. φ(ω) is given by the finite sum of the group-delay dispersion (GDD), i.e., [φ(ω+ΩS)φ(ω)]/ΩS.

The experimental setup is shown in Fig. 1(a)
Fig. 1 (a) Experimental setup for SSI with a frequency time-resolved up converter. Spectral shear is given by frequency mixing between the signal pulse and two longitudinal modes of a narrow-gap etalon. BPF: band-pass filter; CM: cylindrical mirror (f = 50 mm); Sum-frequency generation (SFG): 1-mm-thick type-I BBO crystal for sum-frequency generation. (b) Spectrum of the two-monochromatic collinear fields. (c) A schematic for instantaneously acquired delay and frequency-resolved interferogram. Side view: frequency is resolved with phase-match angle dispersion of the SFG crystal. Top view: delay is scanned transversely by crossed pump beams. Crossing angle is 12°. (d) Time- and frequency-resolved image.
. Two monochromatic collinear fields are generated with an air-spaced narrow-gap etalon and a band-pass filter. The frequency difference of the two monochromatic fields, i.e., shear frequency, is 8.2 THz, as shown in Fig. 1(b). A measured pulse is up converted with the sum-frequency mixing of the two monochromatic fields. Figure 1(c) shows the frequency- and time-resolved up converter. An optically uniaxial crystal is used to prevent time-frequency coupling. Delay is given by a crossed-beam transverse position, as shown in the top view. A delay range is given by Dtanθcross, where D is the sensor size and θcross is the angle between the measured pulse beam and two monochromatic collinear beams. A 9 mm sensor with a 12° angle covers approximately 3 ps. Note that a delay scanning longer than the coherence time of the two collinear monochromatic fields is invalid. Figure 1(d) shows a two-dimensional shearing interferogram. The two-dimensional interferogram is acquired with a CMOS image sensor (744 × 480 pixels, 6 μm pixel pitch, 8 bit depth). The acquired image is processed for phase retrieval and waveform reconstruction. This setup does not use a prism or grating.

Figure 2(a)
Fig. 2 Phase-match angle as a function of sum frequency. (a) Calculated phase-match curves for frequency mixing between a broadband signal and cw (frequency: 375 THz). (b) Experimental result.
shows calculated phase-match angle dispersion of a BBO crystal. The phase-match angle is approximately proportional to the SFG frequency. Available bandwidth is given by the product of the angle width and the dispersive slope. We evaluated bandwidth and resolution of the SFG crystal in the instrument experimentally. Spectra of upconverted beams are measured with a spectrometer behind a horizontal slit. A contour plot of the angular dispersive upconverted spectra is shown in Fig. 2(b). Table 1

Table 1. Comparison of Phase-Match Type of a BBO Crystal: Ordinary (o)/Extraordinary (e) Wave Combinations of a Measured Broadband Pulse (signal), Two-Monochromatic Fields (CW) and a Broadband Sum-Frequency (SF)*

table-icon
View This Table
shows a BBO phase-match type comparison of an acceptance angle, a phase-match angle width ΔθPM, and linearity for a bandwidth of 60 THz. Linearity is defined as ΔθMD/ΔθPM, where ΔθMD is the maximum deviation of the curves as shown in Fig. 2(a) from the 1st order fitting. Type-I was selected because of minimum linearity. For example, ΔθMD is 0.04° (1.9%) at type-I, 60 THz bandwidth. In our setup the BBO thickness and ΔθPM are 1 mm and ~60 mrad, respectively. The generated sum frequency has a 60 THz bandwidth and a 5.2 THz sensitivity, corresponding to an effective thickness of 0.7 mm. After the SFG crystal, two spectrally sheared components in the upconverted beam are collinear. The far-field pattern for the frequency axis and the near-field pattern for the delay axis are required on the image sensor. The beam divergence of each frequency component is limited by the acceptance angle and thickness of the nonlinear crystal. The far-field range for the frequency axis is given by nλ/2πLΔθaccept at ~30 mm. On the other hand, half of the fringe period in the shearing interferogram is given by πc/Ωtanθcross at ~0.22 mm at ΩS/2π = 8.2 THz. The far-field range for the delay axis is ~76 mm. The distance between the SFG crystal and the image sensor is 33 mm, and we simplify an imaging lens.

Figure 3(a)
Fig. 3 (a) Instantaneously acquired delay sweeping of the spectral-shearing interferogram. One fringe corresponds to 122 fs. (b) Evaluation of filtering width and linearity of the delay sweeping. Power spectral density and phase of 1D FFT at a center frequency of 377 THz described as dots and triangles, respectively. The thin curve is the power density of the beat estimated from the two modes of the etalon. (c) Retrieved spectral phase with beat-frequency filtering. (d) Reconstructed waveform.
shows a typical 2D interferogram (exposure time: 1 s). The longitudinal axis is the time delay, and the lateral axis is the fundamental frequency (365 THz shift is given from the sum frequency). A mode-locked Ti:sapphire oscillator (pulse width: ~10 fs; pulse energy: ~6 nJ; repetition rate: 76 MHz) is used as the light source. Figure 3(b) shows the beat spectrum, i.e., the power spectral density (dot) and the phase (triangle) calculated with a 1D fast Fourier transform (FFT) at the center frequency. The estimated power density of the beat between two monochromatic fields is described as a thin curve. The estimated filtering width is 0.40 THz. In fact, the output from the etalon has an exponential-decay waveform, but its tail is soft apertured with the beam profile in the interferogram. The filtering width is broadening (~0.6 THz) and the pedestal is suppressed as compared to the estimation. The delay fringes observed during 2 ps are transform limited because of a flat phase. The delay is proportional to the sensor position. Figure 3(c) shows the spectrum and retrieved phases. The bandwidth of the sum frequency was suppressed with an angular distribution of focused beam. Figure 3(d) shows a reconstructed waveform.

The signal-to-noise ratio of the detector can be improved rapidly with data accumulation because there is no time jitter during upconversion. The delay drift between a measured pulse and two monochromatic collinear fields is evaluated. Figure 4
Fig. 4 Allan deviation of spectral-phase difference as a function of the accumulated number of interferograms. Squares and triangles are 33 ms and 1 s exposure time, respectively.
shows the Allan standard deviation (SD) of group delay at an optical frequency of 377 THz. It shows the delay drift or light source fluctuation during 100 s. The gamma of the Allan deviations is −0.5 because of white noise.

We measure the spectral phase added by synthesized quartz plates for relative accuracy verification. Figure 5(a)
Fig. 5 Relative accuracy verification using synthesized-quartz plates. (a) Spectral phase as a function of the glass thickness. Dotted line shows calculation from the Sellmeier equation. (b) Group delay. (c) Diamonds show second-order spectral phase as a function of the glass thickness. Thick line is calculation.
shows added spectral phase as a function of the propagation length in the glass. The experiments agree with the calculation from the Sellmeier equation (broken curves) given by
n(λ)1=B1λ2/(λ2C1)+B2λ2/(λ2C2)+B3λ2/(λ2C3),
where n is refractive index, and λ is the wavelength (μm). Coefficients B1, B2, B3, C1, C2, and C3are 0.669422575, 0.434583937, 0.871694723, 0.00448011239, 0.0132847049, and 95.3414824, respectively [17]. When the measured pulse has a smooth GDD, we can evaluate the group delay at above 2π/ΩS with unwrapping the retrieved phase of the interferogram. Figure 5(b) describes group-delay dispersion as a function of the glass thickness. Note that the spectral phase is averaged for a bandwidth of 8.2 THz. The added second-order spectral phase agrees well with the calculation (36.2 fs2/rad/mm), as shown in Fig. 5(c).

3. Conclusion

A real-time delay-scanned spectral-shearing interferometer with a frequency- and time-resolved up converter has been demonstrated. A 60 THz bandwidth and 2 ps delay range interferogram is accumulated on a 2D image sensor in the video rate. The scanned delay and upconverted bandwidth are 2 ps and 60 THz. The acquisition rate can be improved by use of 10 kHz vision chips [18

18. S. Kleinfelder, S. H. Lim, X. Liu, and A. El Gamal, “A 10 000 frames/s CMOS digital pixel sensor,” IEEE J. Solid-state Circuits 36(12), 2049–2059 (2001). [CrossRef]

,19

19. J. Dubois, D. Ginhac, M. Paindavoine, and B. Heyrman, “A 10 000 fps CMOS sensor with massively parallel image processing,” IEEE J. Solid-state Circuits 43(3), 706–717 (2008). [CrossRef]

]. This method has single-shot capability. The 2D measurement also allows measuring of the pulse-front tilt along one axis.

Acknowledgments

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.

References and links

1.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997). [CrossRef]

2.

J. Roslund, O. M. Shir, A. Dogariu, R. Miles, and H. Rabitz, “Control of nitromethane photoionization efficiency with shaped femtosecond pulses,” J. Chem. Phys. 134(15), 154301 (2011). [CrossRef] [PubMed]

3.

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] [PubMed]

4.

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] [PubMed]

5.

W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. De Silvestri, and U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28(4), 281–283 (2003). [CrossRef] [PubMed]

6.

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]

7.

E. M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, “Interferometric technique for measuring broadband ultrashort pulses at the sampling limit,” Opt. Lett. 30(3), 326–328 (2005). [CrossRef] [PubMed]

8.

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]

9.

T. Witting, F. Frank, C. A. Arrell, W. A. Okell, J. P. Marangos, and J. W. G. Tisch, “Characterization of high-intensity sub-4-fs laser pulses using spatially encoded spectral shearing interferometry,” Opt. Lett. 36(9), 1680–1682 (2011). [CrossRef] [PubMed]

10.

S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, “Spectral shearing interferometry with spatially chirped replicas for measuring ultrashort pulses,” Opt. Express 15(23), 15168–15174 (2007). [CrossRef] [PubMed]

11.

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]

12.

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.

13.

H. Tomita and H. Nishioka, “Wide-time-range spectral-shearing interferometry,” Opt. Express 17(16), 14023–14028 (2009). [CrossRef] [PubMed]

14.

D. H. Auston, “Nonlinear spectroscopy of picoseconds pulses,” Opt. Commun. 3(4), 272–276 (1971). [CrossRef]

15.

C. Radzewicz, P. Wasylczyk, and J. S. Krasinski, “A poor man’s FROG,” Opt. Commun. 186(4-6), 329–333 (2000). [CrossRef]

16.

H. Tomita and H. Nishioka, “High-resolution spectral-shearing interferometry,” in Proceedings of IEEE conference on Lasers and Electro-Optics Society (IEEE, 2008), pp. 701–702.

17.

Schott, http://www.schott.com/korea/korean/download/datasheet_fused_silica_.pdf.

18.

S. Kleinfelder, S. H. Lim, X. Liu, and A. El Gamal, “A 10 000 frames/s CMOS digital pixel sensor,” IEEE J. Solid-state Circuits 36(12), 2049–2059 (2001). [CrossRef]

19.

J. Dubois, D. Ginhac, M. Paindavoine, and B. Heyrman, “A 10 000 fps CMOS sensor with massively parallel image processing,” IEEE J. Solid-state Circuits 43(3), 706–717 (2008). [CrossRef]

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: July 1, 2011
Revised Manuscript: August 8, 2011
Manuscript Accepted: August 10, 2011
Published: August 17, 2011

Citation
Hitoshi Tomita and Hajime Nishioka, "Spectral shearing interferometer with frequency- and time-resolved sum-frequency mixing," Opt. Express 19, 17173-17178 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17173


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References

  1. T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997). [CrossRef]
  2. J. Roslund, O. M. Shir, A. Dogariu, R. Miles, and H. Rabitz, “Control of nitromethane photoionization efficiency with shaped femtosecond pulses,” J. Chem. Phys. 134(15), 154301 (2011). [CrossRef] [PubMed]
  3. 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] [PubMed]
  4. 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] [PubMed]
  5. W. Kornelis, J. Biegert, J. W. G. Tisch, M. Nisoli, G. Sansone, C. Vozzi, S. De Silvestri, and U. Keller, “Single-shot kilohertz characterization of ultrashort pulses by spectral phase interferometry for direct electric-field reconstruction,” Opt. Lett. 28(4), 281–283 (2003). [CrossRef] [PubMed]
  6. 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]
  7. E. M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, “Interferometric technique for measuring broadband ultrashort pulses at the sampling limit,” Opt. Lett. 30(3), 326–328 (2005). [CrossRef] [PubMed]
  8. 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]
  9. T. Witting, F. Frank, C. A. Arrell, W. A. Okell, J. P. Marangos, and J. W. G. Tisch, “Characterization of high-intensity sub-4-fs laser pulses using spatially encoded spectral shearing interferometry,” Opt. Lett. 36(9), 1680–1682 (2011). [CrossRef] [PubMed]
  10. S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, “Spectral shearing interferometry with spatially chirped replicas for measuring ultrashort pulses,” Opt. Express 15(23), 15168–15174 (2007). [CrossRef] [PubMed]
  11. 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]
  12. 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.
  13. H. Tomita and H. Nishioka, “Wide-time-range spectral-shearing interferometry,” Opt. Express 17(16), 14023–14028 (2009). [CrossRef] [PubMed]
  14. D. H. Auston, “Nonlinear spectroscopy of picoseconds pulses,” Opt. Commun. 3(4), 272–276 (1971). [CrossRef]
  15. C. Radzewicz, P. Wasylczyk, and J. S. Krasinski, “A poor man’s FROG,” Opt. Commun. 186(4-6), 329–333 (2000). [CrossRef]
  16. H. Tomita and H. Nishioka, “High-resolution spectral-shearing interferometry,” in Proceedings of IEEE conference on Lasers and Electro-Optics Society (IEEE, 2008), pp. 701–702.
  17. Schott, http://www.schott.com/korea/korean/download/datasheet_fused_silica_.pdf .
  18. S. Kleinfelder, S. H. Lim, X. Liu, and A. El Gamal, “A 10 000 frames/s CMOS digital pixel sensor,” IEEE J. Solid-state Circuits 36(12), 2049–2059 (2001). [CrossRef]
  19. J. Dubois, D. Ginhac, M. Paindavoine, and B. Heyrman, “A 10 000 fps CMOS sensor with massively parallel image processing,” IEEE J. Solid-state Circuits 43(3), 706–717 (2008). [CrossRef]

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