Abstract

Using 3.6- and 5.3-fs pulses, we demonstrated theoretically and experimentally that fringe-resolved autocorrelation (FRAC) traces are distorted by bandwidth limitations of the second-harmonic generation (SHG) in 10-µm-thick, type I β -BaB2O4 for pulses shorter than sub-5 fs. In addition, detailed numerical analysis of the SHG showed that the optimum crystal angle where the FRAC trace distortion becomes minimum is in disagreement not only with the phase-matching angle but also with the angle where the FRAC signal intensity becomes maximum. Furthermore, the apparent pulse duration measured at a nonoptimum angle was confirmed to become shorter than that of its transform-limited pulse, in excellent agreement with the calculated result.

© 2004 Optical Society of America

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References

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Appl. Opt. (2)

Appl. Phys. B (1)

M. Hirasawa, N. Nakagawa, K. Yamamoto, R. Morita, H. Shigekawa, M. Yamashita, �??Sensitivity improvement of spectral phase interferometry for direct electric-field reconstruction for the characterization of low-intensity femtosecond pulses,�?? Appl. Phys. B 74, S225-229 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

A. Shirakawa, I. Sakane, M. Takasaka, and T. Kobayashi, �??Sub-5-fs visible pulse generation by pulse-front-matched non-collinear optical parametric amplification,�?? Appl. Phys. Lett. 74, 2268 (1999).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. Baltuška, M. S. Pshenichnikov, and D. A.Wiersma, �??Second-harmonic generation frequency-resolved optical gating in the single-cycle regime,�?? IEEE J. Quantum Electron. 35, 459 (1999).
[CrossRef]

A. M. Weiner, �??Effect of group velocity mismatch on the measurement of ultrashort optical pulses via second harmonic generation,�?? IEEE J. Quantum Electron. 19, 1276 (1983).
[CrossRef]

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (1)

R.Morita,M. Hirasawa, N. Karasawa, S. Kusaka, N. Nakagawa, K. Yamane, L. Li, A. Suguro, and M. Yamashita, �??Sub-5 fs optical pulse characterization,�?? Meas. Sci. Technol. 13, 1710-1720 (2002).
[CrossRef]

Opt. Lett. (2)

Ultrafast Phenomena XI (1)

A. Cheng, G. Tempea, T. Brabec, K. Ferencz, and F. Krausz, �??Generation of intense diffraction-limited white light and 4-fs pulses,�?? in Ultrafast Phenomena XI (Springer-Verlag, Berlin, 1998), p. 8.
[CrossRef]

Other (1)

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).

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Figures (8)

Fig. 1.
Fig. 1.

Calculated FRAC traces for Gaussian TL pulses (tp,inTL=4.01 fs, Δν in, 110 THz; center wavelength, 600 nm; θ=25°; ε no_SFA,ideal/ε max=0.078; ε no_SFA,with SFA/ε max=0.0053; r no_SFA,ideal=0.88) (a) with taking account of the bandwidth-limited SH-generation effect without filter approximation [s no_SFA(τ)], (b) after filter approximation [s with SFA(τ)] and (c) without the bandwidth limitation effect [s ideal(τ)].

Fig. 2.
Fig. 2.

Contour plots of εα,β max (ε max=7.083×10-15) as functions of the input pulse duration tp,inTL and the crystal angle θ. ε no_SFA,ideal/ε max at (A) λc=600, (B) 700, and (C) 800 nm. (D) ε with SFA,ideal/ε max and (E) ε no_SFA,with SFA/ε max at λc=600 nm.

Fig. 3.
Fig. 3.

Contour plots of rα,β as functions of the input pulse duration tp,inTL and the crystal angle θ. r no_SFA,ideal at (A) λc=600, (B) 700, and (C) 800 nm. (D) r with_SFA,ideal and (E) r no_SFA,with SFA at λc=600 nm.

Fig. 4.
Fig. 4.

Plots of the SH frequency-dependent filter function R(Ω) of (A) normalized ones and (B) nonnormalized ones at various values of crystal angle θ.

Fig. 5.
Fig. 5.

Plots of r no_SFA,ideal at ε=εno_SFA,idealmin for the input pulse duration tp,inTLν in). Each plot for (a) λc, 600 nm; (b) λc, 700 nm; and (c) λc, 800 nm.

Fig. 6.
Fig. 6.

(A) Measured spectra at the pressure p=1.0 and 3.0 atm. (B) Dependency of ε no_SFA,ideal on the crystal angle θ for (a) TL pulse at p=1.0 atm, (b) retrieved one by M-SPIDER measurement at p=1.0 atm, (c) TL pulse at p=3.0 atm, and (d) retrieved one by M-SPIDER measurement at p=3.0 atm. (C) Dependency of r no_SFA,ideal on the crystal angle θ for (e) TL pulse at p=1.0 atm, (f) retrieved one by M-SPIDER measurement at p=1.0 atm, (g) TL pulse at p=3.0 atm, and (h) retrieved one by M-SPIDER measurement at p=3.0 atm.

Fig. 7.
Fig. 7.

Experimental results (Ar-gas pressure, 1.0 atm; fiber input, 150 µJ/pulse; fiber output, 16.5µJ/pulse). (A) (a) Intensity spectrum and spectral phases (b) before and (c) after feedback chirp compensation. (B) (d) Temporal intensity (pulse duration: 5.3 fs, center wavelength: 725.1 nm) and (e) temporal phase after chirp compensation. (f) Temporal intensity of the Fourier transform-limited pulse (pulse duration: 4.42 fs). (C) (i) Measured FRAC trace and retrieved FRAC traces (ii) with and (iii) without taking account of the filter effect by the nonlinear crystal.

Fig. 8.
Fig. 8.

Experimental results (Ar-gas pressure: 3.0 atm, fiber input: 140 µJ/pulse, fiber output: 18µJ/pulse). (A) (a) Intensity spectrum and spectral phases (b) before and (c) after feedback chirp compensation. (B) (d) Temporal intensity (3.6 fs, center wavelength: 617.5 nm) and (e) temporal phase after chirp compensation. (f) Temporal intensity of the Fourier transform-limited pulse (3.50 fs). (C) (i) Measured FRAC trace and retrieved FRAC traces (ii) with and (iii) without taking account of the filter effect by the nonlinear crystal.

Tables (2)

Tables Icon

Table 1. θ pm, θ R, θ opt, θ max for TL Gaussian pulses with λc=600, 700, and 800 nm (see the text for notation).

Tables Icon

Table 2. θ pm, θ R, θ opt, and θ max for Gaussian spectrum (G-i) and measured spectrum (Mi) (i=1, tp,inTL=4.42 fs λc=725.1 nm; i=2, tp,inTL=3.5 fs λc=617.5 nm (see text for notation a ).

Equations (18)

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S FRAC ( τ ) = 2 G ( 0 ) + 4 G ( τ ) + 4 Re [ F 1 ( τ ) ] + 2 Re [ F 2 ( τ ) ] ,
G ( τ ) = E ( t ) 2 E ( t τ ) 2 d t ,
F 1 ( τ ) = [ E ( t ) 2 + E ( t τ ) 2 ] E * ( t ) E * ( t τ ) d t ,
F 2 ( τ ) = E 2 ( t ) E * 2 ( t τ ) d t ,
E ( t ) = 0 ε ˜ ( ω ) exp [ i ω t ] d ω , ε ˜ ( ω ) = ε ( t ) exp [ i ω t ] d t .
I SH ( Ω , τ ) Ω n e ( Ω ) ω ( Ω ω ) exp [ i V ( Ω , ω ) L ] sinc [ V ( Ω , ω ) L ]
× [ n e 2 ( Ω ) 1 ] [ n o 2 ( Ω ω ) 1 ] ( n o 2 ( ω ) 1 )
× E ˜ ( ω ) E ˜ ( Ω ω ) ( 1 + exp [ i ω τ ] ) { 1 + exp [ i ( Ω ω ) τ ] } d ω 2
I SH , no _ SFA ( Ω , τ )
V ( ω , Ω ω ) = k o ( ω ) + k o ( Ω ω ) k e ( Ω ) 2 ,
I SH , no _ SFA ( Ω , τ ) R ( Ω ) I SH , ideal ( Ω , τ ) I SH , with _ SFA ( Ω , τ ) ,
R ( Ω ) = Ω 3 4 n e ( Ω ) [ ( n e 2 ( ω ) 1 ) ( n o 2 ( Ω 2 ) 1 ) 2 sinc [ V ( Ω 2 , Ω 2 ) L ] ] 2 ,
I SH , ideal ( Ω , τ ) = E ˜ ( ω ) E ˜ ( Ω ω ) ( 1 + exp [ i ω τ ] ) ( 1 + exp [ i ( Ω ω ) τ ] ) d ω 2 .
S SH , α ( τ ) = I SH , α ( Ω , τ ) d Ω ( α = no _ SFA , with _ SFA and ideal ) .
ε α , β ( s α ( τ ) s β ( τ ) ) 2 d τ ( α , β = no _ SFA , with _ SFA and ideal ) ,
r α , β Δ t α Δ t β ( α , β = no _ SFA , with _ SFA and ideal ) ,
s α ( τ ) 8 S SH , α ( τ ) S SH , α ( 0 ) ( α= no _ SFA , with _ SFA and ideal )
S env ( τ ) = 2 G ( 0 ) + 4 G ( τ ) + 4 F 1 ( τ ) + 2 F 2 ( τ ) .

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