Abstract

We propose an interferometric method that enables to measure a distance by the intensity measurement using the scanning of the interferometer reference arm and the recording of the interference fringes including the brightest fringe. With the consideration of the dispersion and absorption of the pulse laser in a dispersive and absorptive medium, we investigate the cross-correlation function between two femtosecond laser pulses in the time domain. We also introduce the measurement principle. We study the relationship between the position of the brightest fringe and the distance measured, which can contribute to the distance measurement. In the experiments, we measure distances using the method of the intensity detection while the reference arm of Michelson interferometer is scanned and the fringes including the brightest fringe is recorded. Firstly we measure a distance in a range of 10 µm. The experimental results show that the maximum deviation is 45 nm with the method of light intensity detection. Secondly, an interference system using three Michelson interferometers is developed, which combines the methods of light intensity detection and time-of-flight. This system can extend the non-ambiguity range of the method of light intensity detection. We can determine a distance uniquely with a larger non-ambiguity range. It is shown that this method and system can realize absolute distance measurement, and the measurement range is a few micrometers in the vicinity of Nlpp, where N is an integer, and lpp is the pulse-to-pulse length.

© 2014 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. P. Balling, P. Křen, P. Mašika, S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  9. J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (New York, 2005), pp. 12–23.
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  28. S. Kim, Y. Kim, “Advanced optical metrology using ultrashort pulse lasers,” Rev. Laser Eng. 36(suppl), 1254–1257 (2008).
    [CrossRef]

2013

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

2012

P. Balling, P. Mašika, P. Křen, M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[CrossRef]

S. A. van den Berg, S. T. Persijn, G. J. P. Kok, M. G. Zeitouny, N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[CrossRef] [PubMed]

H. Matsumoto, X. Wang, K. Takamasu, T. Aoto, “Absolute measurement of baselines up to 403 m using heterodyne temporal coherence interferometer with optical frequency comb,” Appl. Phys. Express 5(4), 046601 (2012).
[CrossRef]

M. Bitter, E. A. Shapiro, V. Milner, “Enhancing strong-field-induced molecular vibration with femtosecond pulse shaping,” Phys. Rev. A 86(4), 043421 (2012).
[CrossRef]

X. Wang, S. Takahashi, K. Takamasu, H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012).
[CrossRef] [PubMed]

2011

2010

J. Lee, Y. Kim, K. Lee, S. Lee, S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[CrossRef]

M. G. Zeitouny, M. Cui, N. Bhattacharya, H. P. Urbach, S. A. van den Berg, A. J. E. M. Janssen, “From a discrete to a continuous model for inter pulse interference with a frequency-comb laser,” Phys. Rev. A 82(2), 023808 (2010).
[CrossRef]

2009

2008

2006

2004

2000

1996

1990

Aoto, T.

H. Matsumoto, X. Wang, K. Takamasu, T. Aoto, “Absolute measurement of baselines up to 403 m using heterodyne temporal coherence interferometer with optical frequency comb,” Appl. Phys. Express 5(4), 046601 (2012).
[CrossRef]

Bae, E.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

Balling, P.

P. Balling, P. Mašika, P. Křen, M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[CrossRef]

P. Balling, P. Křen, P. Mašika, S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
[CrossRef] [PubMed]

Bhattacharya, N.

Bitter, M.

M. Bitter, E. A. Shapiro, V. Milner, “Enhancing strong-field-induced molecular vibration with femtosecond pulse shaping,” Phys. Rev. A 86(4), 043421 (2012).
[CrossRef]

Braat, J. J. M.

Ciddor, P. E.

Coddington, I.

I. Coddington, W. C. Swann, L. Nenadovic, N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

Cui, M.

Dändliker, R.

Doležal, M.

P. Balling, P. Mašika, P. Křen, M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[CrossRef]

Fulmer, E. C.

Han, S.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

Holzwarth, R.

Hyun, S.

S. Hyun, Y. Kim, Y. Kim, J. Jin, S. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

Janssen, A. J. E. M.

M. G. Zeitouny, M. Cui, A. J. E. M. Janssen, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, “Time-frequency distribution of interferograms from a frequency comb in dispersive media,” Opt. Express 19(4), 3406–3417 (2011).
[CrossRef] [PubMed]

M. G. Zeitouny, M. Cui, N. Bhattacharya, H. P. Urbach, S. A. van den Berg, A. J. E. M. Janssen, “From a discrete to a continuous model for inter pulse interference with a frequency-comb laser,” Phys. Rev. A 82(2), 023808 (2010).
[CrossRef]

Jin, J.

S. Hyun, Y. Kim, Y. Kim, J. Jin, S. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

Joo, K. N.

Kim, S.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

J. Lee, Y. Kim, K. Lee, S. Lee, S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[CrossRef]

S. Hyun, Y. Kim, Y. Kim, J. Jin, S. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

S. Kim, Y. Kim, “Advanced optical metrology using ultrashort pulse lasers,” Rev. Laser Eng. 36(suppl), 1254–1257 (2008).
[CrossRef]

Kim, S. W.

Kim, Y.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

J. Lee, Y. Kim, K. Lee, S. Lee, S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[CrossRef]

S. Hyun, Y. Kim, Y. Kim, J. Jin, S. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

S. Hyun, Y. Kim, Y. Kim, J. Jin, S. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

K. N. Joo, Y. Kim, S. W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express 16(24), 19799–19806 (2008).
[CrossRef] [PubMed]

K. N. Joo, Y. Kim, S. W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express 16(24), 19799–19806 (2008).
[CrossRef] [PubMed]

S. Kim, Y. Kim, “Advanced optical metrology using ultrashort pulse lasers,” Rev. Laser Eng. 36(suppl), 1254–1257 (2008).
[CrossRef]

Kok, G. J. P.

S. A. van den Berg, S. T. Persijn, G. J. P. Kok, M. G. Zeitouny, N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[CrossRef] [PubMed]

Kren, P.

P. Balling, P. Mašika, P. Křen, M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[CrossRef]

P. Balling, P. Křen, P. Mašika, S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
[CrossRef] [PubMed]

Le Floch, S.

Leaird, D. E.

Lee, J.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

J. Lee, Y. Kim, K. Lee, S. Lee, S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[CrossRef]

Lee, K.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

J. Lee, Y. Kim, K. Lee, S. Lee, S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[CrossRef]

Lee, S.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

J. Lee, Y. Kim, K. Lee, S. Lee, S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[CrossRef]

Lévêque, S.

Mašika, P.

P. Balling, P. Mašika, P. Křen, M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[CrossRef]

P. Balling, P. Křen, P. Mašika, S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
[CrossRef] [PubMed]

Matsumoto, H.

Milner, V.

M. Bitter, E. A. Shapiro, V. Milner, “Enhancing strong-field-induced molecular vibration with femtosecond pulse shaping,” Phys. Rev. A 86(4), 043421 (2012).
[CrossRef]

Minoshima, K.

Nenadovic, L.

I. Coddington, W. C. Swann, L. Nenadovic, N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

Newbury, N. R.

I. Coddington, W. C. Swann, L. Nenadovic, N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

Patel, J. S.

Persijn, S. T.

S. A. van den Berg, S. T. Persijn, G. J. P. Kok, M. G. Zeitouny, N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[CrossRef] [PubMed]

Salvadé, Y.

Schuhler, N.

Shapiro, E. A.

M. Bitter, E. A. Shapiro, V. Milner, “Enhancing strong-field-induced molecular vibration with femtosecond pulse shaping,” Phys. Rev. A 86(4), 043421 (2012).
[CrossRef]

Shim, S. H.

Strasfeld, D. B.

Swann, W. C.

I. Coddington, W. C. Swann, L. Nenadovic, N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

Takahashi, S.

Takamasu, K.

Urbach, H. P.

van den Berg, S. A.

Wang, X.

X. Wang, S. Takahashi, K. Takamasu, H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012).
[CrossRef] [PubMed]

H. Matsumoto, X. Wang, K. Takamasu, T. Aoto, “Absolute measurement of baselines up to 403 m using heterodyne temporal coherence interferometer with optical frequency comb,” Appl. Phys. Express 5(4), 046601 (2012).
[CrossRef]

Wei, D.

Weiner, A. M.

Wullert, J. R.

Ye, J.

Zanni, M. T.

Zeitouny, M. G.

Appl. Opt.

Appl. Phys. Express

H. Matsumoto, X. Wang, K. Takamasu, T. Aoto, “Absolute measurement of baselines up to 403 m using heterodyne temporal coherence interferometer with optical frequency comb,” Appl. Phys. Express 5(4), 046601 (2012).
[CrossRef]

Meas. Sci. Technol.

S. Hyun, Y. Kim, Y. Kim, J. Jin, S. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, Y. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[CrossRef]

P. Balling, P. Mašika, P. Křen, M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[CrossRef]

Nat. Photonics

I. Coddington, W. C. Swann, L. Nenadovic, N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

J. Lee, Y. Kim, K. Lee, S. Lee, S. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[CrossRef]

Opt. Express

K. N. Joo, Y. Kim, S. W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express 16(24), 19799–19806 (2008).
[CrossRef] [PubMed]

K. N. Joo, Y. Kim, S. W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express 16(24), 19799–19806 (2008).
[CrossRef] [PubMed]

D. Wei, S. Takahashi, K. Takamasu, H. Matsumoto, “Analysis of the temporal coherence function of a femtosecond optical frequency comb,” Opt. Express 17(9), 7011–7018 (2009).
[CrossRef] [PubMed]

P. Balling, P. Křen, P. Mašika, S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
[CrossRef] [PubMed]

M. G. Zeitouny, M. Cui, A. J. E. M. Janssen, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, “Time-frequency distribution of interferograms from a frequency comb in dispersive media,” Opt. Express 19(4), 3406–3417 (2011).
[CrossRef] [PubMed]

D. Wei, S. Takahashi, K. Takamasu, H. Matsumoto, “Time-of-flight method using multiple pulse train interference as a time recorder,” Opt. Express 19(6), 4881–4889 (2011).
[CrossRef] [PubMed]

M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, “Long distance measurement with femtosecond pulses using a dispersive interferometer,” Opt. Express 19(7), 6549–6562 (2011).
[CrossRef] [PubMed]

X. Wang, S. Takahashi, K. Takamasu, H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012).
[CrossRef] [PubMed]

K. N. Joo, S. W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954–5960 (2006).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

M. G. Zeitouny, M. Cui, N. Bhattacharya, H. P. Urbach, S. A. van den Berg, A. J. E. M. Janssen, “From a discrete to a continuous model for inter pulse interference with a frequency-comb laser,” Phys. Rev. A 82(2), 023808 (2010).
[CrossRef]

Phys. Rev. A

M. Bitter, E. A. Shapiro, V. Milner, “Enhancing strong-field-induced molecular vibration with femtosecond pulse shaping,” Phys. Rev. A 86(4), 043421 (2012).
[CrossRef]

Phys. Rev. Lett.

S. A. van den Berg, S. T. Persijn, G. J. P. Kok, M. G. Zeitouny, N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[CrossRef] [PubMed]

Rev. Laser Eng.

S. Kim, Y. Kim, “Advanced optical metrology using ultrashort pulse lasers,” Rev. Laser Eng. 36(suppl), 1254–1257 (2008).
[CrossRef]

Other

J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (New York, 2005), pp. 12–23.

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Figures (15)

Fig. 1
Fig. 1

Schematic of the experimental setup.

Fig. 2
Fig. 2

Relation between the intensity and N.

Fig. 3
Fig. 3

Comparison between shapes of different pulses.

Fig. 4
Fig. 4

Comparison between interference fringes based on different pulse models. (a) Gaussian. (b) Sech2. (c) Left Gaussian. (d) Right Gaussian. (e) Left sech2. (f) Right sech2.

Fig. 5
Fig. 5

Positions of the brightest fringe corresponding to different N. (a) N = 0. (b) N = 1. (c) N = 10. (d) N = 20. (e) N = 30. (f) N = 40. (g) N = 50. (h) N = 60. (i) N = 70. (j) N = 80. (k) N = 90. (l) N = 100.

Fig. 6
Fig. 6

Relation between the shifted displacement and N.

Fig. 7
Fig. 7

Interference fringe at equal arms (upper blue line) and the PZT driving signal (lower red line).

Fig. 8
Fig. 8

Intensity corresponding to 1 – 5 µm.

Fig. 9
Fig. 9

Intensity corresponding to 6 – 10 µm.

Fig. 10
Fig. 10

Positions of different intensities.

Fig. 11
Fig. 11

Deviations of different models.

Fig.
						12
Fig. 12

Schematic of the system.

Fig. 13
Fig. 13

Photograph of the system.

Fig.
						14
Fig. 14

Distances corresponding to the intensity of −0.34645.

Fig.
							15
Fig. 15

Relative positions between MT1 and MT2.

Tables (2)

Tables Icon

Table 1 Experimental results comparison between different pulse models.

Tables Icon

Table 2 Maximum deviation of different models at 9 µm.

Equations (19)

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E train (t,z)= m E z,m (t,z)exp[i( ω m t k m z)+i( φ 0 +Δ φ ce t)] h= + δ(zh l pp )
E(t,2L)= m E 2L,m (t,2L)exp[i( ω m t 2 n R ( ω m ) ω m L c )+i φ 0 ]
E(t,0)= m E 0,m (t,0)exp[i ω m t+i φ 0 +iNΔ φ ce ]
E total (t,2L)=E(t,2L)+E(t,0)
I= g | E total,g (t,2L) | 2 = g E total,g (t,2L) E * total,g (t,2L)
I= 1 T d T d | E total,g | 2 dt = 1 T d T d [E(t,2L)+E(t,0)] 2 dt = 1 T d T d [ E 2 (t,2L)+ E 2 (t,0)]dt + 2 T d T d Re[E(t,2L) E * (t,0)]dt = 2 T d {1+ [exp( 2 n I ( ω m ) ω m L c )] 2 } T d E 2 (t,0)dt + 2 T d exp( 2 n I ( ω m ) ω m L c )cos( 2 n R ( ω m ) ω m L c +N×Δ φ ce ) T d E 0,m 2 (t,0)dt
I= 2 T d {1+ [exp( 2 n I ( ω m ) ω m L c )] 2 } T d E 2 (t,0)dt + 2 T d exp( 2 n I ( ω m ) ω m L c )cos( n R ( ω m ) ω m d c +N×Δ φ ce ) T d E 0,m 2 (t,0)dt
L= N× l pp +d 2
I AC cos(N×Δ φ ce )
I DC 1+ [exp( n I ( ω c ) ω c n R ( ω c ) f rep ×N)] 2
E G (t)= A 1 e ( a 1 t) 2
E s (t)= A 2 e a 2 t + e a 2 t
E aG (t)={ A 3 e ( a 3 t) 2 t>0 A 3 e ( a 4 t) 2 t<0
E as (t)= A 4 e a 5 t + e a 6 t
n R ( ω m ) ω m d c +N×Δ φ ce =0
d= N×Δ φ ce ×c n R ω c
Δd= floor(2L, l pp )×Δ φ ce ×c 2 n R ω c = π×floor(2L, l pp )×c× f ceo n R ω c f rep
Δ d step = π×c× f ceo n R ω c f rep = f ceo λ c 2 n R f rep = 2×1550× 10 9 2×0.9982071×200 =0.00776μm
f= 2D T λ c = 2×55× 10 3 1548.2×7.82 =9.08Hz

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