A. Sullivan, W. E. White, K. C. Chu, J. P. Heritage, K. W. Delong, and R. Trebino, "Quantitative investigation of optical phase-measuring techniques for ultrashort pulse lasers," J. Opt. Soc. Am. B 13, 1965-1978 (1996)
We have performed a quantitative investigation into the capabilities and the limitations of two phase-measuring techniques: second-harmonic-generation frequency-resolved optical gating and direct optical spectral phase measurement. In particular, we have studied the reproducibility and the accuracy of these techniques in measuring the frequency-dependent phase of ultrashort pulses with varying amounts of cubic and quadratic phase. We find that both of these techniques are accurate to within 5% in measuring phase distortions in optical pulses.
Paul R. Bolton, Anthony B. Bullock, Chris D. Decker, Michael D. Feit, Anthony J. P. Megofna, Peter E. Young, and David N. Fittinghoff J. Opt. Soc. Am. B 13(2) 336-346 (1996)
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Bandwidth of Spectral Data in Fig. 4(a) as from a Gaussian Fit and Quadratic and Cubic Polynomial Fit Coefficients for the FROG Reproducibility Phase Data in Fig. 4(b)a
Scan
Bandwidth (nm)
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
9.24
0.0629
-0.00059
2
9.06
0.0769
-0.00147
3
8.98
0.0829
-0.00285
The pulses were adjusted for minimum residual phase as determined from cross-correlation measurements.
Table 2
Quadratic and Cubic Polynomial Fit Coefficients for the FROG Reproducibility Phase Data in Fig. 5a
Scan
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
0.201
0.0015
2
0.195
0.0007
3
0.192
0.0030
4
0.186
0.0015
5
0.200
0.000004
The compressor length was detuned 400 µm from optimum to introduce some quadratic phase.
Table 3
Quadratic and Cubic Polynomial Fit Coefficients for the FROG Reproducibility Phase Data in Fig. 7a
Scan
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
-0.587
-0.429
2
-0.596
-0.426
3
-0.658
-0.455
4
-0.622
-0.457
5
-0.640
-0.445
The second stretcher lens was displaced 1 mm from the optical axis of the stretcher to introduce cubic phase.
Table 4
Quadratic and Cubic Polynomial Fit Coefficients for the DOSPM Reproducibility Phase Data in Fig. 7a
Scan
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
0.0204
-0.0178
2
0.0401
-0.0115
3
0.0183
-0.0075
4
-0.0106
-0.00046
5
0.0485
-0.0114
The pulses were adjusted for minimum residual phase as determined by cross-correlation measurements.
Table 5
Quadratic and Cubic Polynomial Fit Coefficients for the DOSPM Reproducibility Phase Data in Fig. 8a
Scan
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
-0.9165
-0.0228
2
-0.9083
0.0035
3
-0.9093
-0.0037
4
-0.8771
-0.0246
5
-0.8990
-0.0363
The pulses were adjusted for minimum residual phase as determined by cross-correlation measurements.
Table 6
Quadratic and Cubic Polynomial Fit Coefficients for the FROG Accuracy Phase Data in Fig. 14a
Compressor Detuning (mm)
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
-2
-0.7515
0.1040
-1
-0.2871
-0.2222
0
0.1342
-0.2543
1
0.6601
-0.2040
2
1.1795
-0.2123
The stretcher lens was detuned 0.5 mm to introduce cubic phase, and the compressor length was varied about the optimum value.
Table 7
Quadratic and Cubic Polynomial Fit Coefficients for the DOSPM Accuracy Phase Data in Fig. 19a
Compressor Detuning (mm)
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
-2
1.0837
0.3883
-1
0.5566
0.4070
0
0.0759
0.3751
1
-0.4437
0.3774
2
-0.9095
0.4014
The stretcher lens was detuned 0.5 mm to introduce cubic phase, and the compressor length was varied about the optimum value.
Tables (7)
Table 1
Bandwidth of Spectral Data in Fig. 4(a) as from a Gaussian Fit and Quadratic and Cubic Polynomial Fit Coefficients for the FROG Reproducibility Phase Data in Fig. 4(b)a
Scan
Bandwidth (nm)
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
9.24
0.0629
-0.00059
2
9.06
0.0769
-0.00147
3
8.98
0.0829
-0.00285
The pulses were adjusted for minimum residual phase as determined from cross-correlation measurements.
Table 2
Quadratic and Cubic Polynomial Fit Coefficients for the FROG Reproducibility Phase Data in Fig. 5a
Scan
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
0.201
0.0015
2
0.195
0.0007
3
0.192
0.0030
4
0.186
0.0015
5
0.200
0.000004
The compressor length was detuned 400 µm from optimum to introduce some quadratic phase.
Table 3
Quadratic and Cubic Polynomial Fit Coefficients for the FROG Reproducibility Phase Data in Fig. 7a
Scan
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
-0.587
-0.429
2
-0.596
-0.426
3
-0.658
-0.455
4
-0.622
-0.457
5
-0.640
-0.445
The second stretcher lens was displaced 1 mm from the optical axis of the stretcher to introduce cubic phase.
Table 4
Quadratic and Cubic Polynomial Fit Coefficients for the DOSPM Reproducibility Phase Data in Fig. 7a
Scan
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
0.0204
-0.0178
2
0.0401
-0.0115
3
0.0183
-0.0075
4
-0.0106
-0.00046
5
0.0485
-0.0114
The pulses were adjusted for minimum residual phase as determined by cross-correlation measurements.
Table 5
Quadratic and Cubic Polynomial Fit Coefficients for the DOSPM Reproducibility Phase Data in Fig. 8a
Scan
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
1
-0.9165
-0.0228
2
-0.9083
0.0035
3
-0.9093
-0.0037
4
-0.8771
-0.0246
5
-0.8990
-0.0363
The pulses were adjusted for minimum residual phase as determined by cross-correlation measurements.
Table 6
Quadratic and Cubic Polynomial Fit Coefficients for the FROG Accuracy Phase Data in Fig. 14a
Compressor Detuning (mm)
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
-2
-0.7515
0.1040
-1
-0.2871
-0.2222
0
0.1342
-0.2543
1
0.6601
-0.2040
2
1.1795
-0.2123
The stretcher lens was detuned 0.5 mm to introduce cubic phase, and the compressor length was varied about the optimum value.
Table 7
Quadratic and Cubic Polynomial Fit Coefficients for the DOSPM Accuracy Phase Data in Fig. 19a
Compressor Detuning (mm)
Quadratic Phase (10-26 s2)
Cubic Phase (10-39 s3)
-2
1.0837
0.3883
-1
0.5566
0.4070
0
0.0759
0.3751
1
-0.4437
0.3774
2
-0.9095
0.4014
The stretcher lens was detuned 0.5 mm to introduce cubic phase, and the compressor length was varied about the optimum value.
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