Abstract

An approach for chromatic dispersion measurement is proposed and experimentally demonstrated based on an optoelectronic oscillator (OEO) incorporating a single bandpass microwave photonic filter (MPF), which is implemented by cascading a finite impulse response (FIR) MPF and an infinite impulse response (IIR) MPF jointly. The key concept of the proposed design is mapping the chromatic dispersion of a device under test (DUT) to the oscillating frequency of the OEO by embedding the DUT into the OEO loop. The oscillating frequency is mainly determined by the central frequency of the MPF, which depends on the length difference of the two arms of the Mach-Zehnder interferometer (MZI) and the chromatic dispersion value of the fiber cooperatively. The bandwidth of the MPF is further narrowed by an IIR filter based on a recirculating fiber loop for stabilizing OEO oscillation. The chromatic dispersion of fibers with lengths ranging from 20 km to 100 km are measured in the experiment.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

2017 (3)

2014 (1)

2013 (2)

F. Jiang, J. H. Wong, H. Q. Lam, J. Zhou, S. Aditya, P. H. Lim, K. E. K. Lee, P. P. Shum, and X. Zhang, “An optically tunable wideband optoelectronic oscillator based on a bandpass microwave photonic filter,” Opt. Express 21(14), 16381–16389 (2013).
[Crossref] [PubMed]

X. Han, M. Zhang, S. Li, N. Shi, Y. Gu, and M. Zhao, “A new method for fiber chromatic dispersion measurement with microwave interference effect,” Opt. Fiber Technol. 19(4), 319–324 (2013).
[Crossref]

2012 (1)

2011 (2)

2006 (2)

2005 (1)

K. S. Abedin, “Rapid, cost-effective measurement of chromatic dispersion of optical fibre over 1440-1625 nm using Sagnac interferometer,” Electron. Lett. 41(8), 469–471 (2005).
[Crossref]

2002 (1)

J. Keum-Soo, K. Hee-Ju, K. Dong-Sung, and P. Jae-Kyung, “Optical fiber chromatic dispersion measurement using bidirectional modulation of an optical intensity modulator,” IEEE Photonics Technol. Lett. 14(8), 1145–1147 (2002).
[Crossref]

2001 (1)

D. Guang-Hua and E. Gorgiev, “Non-white photodetection noise at the output of an optical amplifier: theory and experiment,” IEEE J. Quantum Electron. 37(8), 1008–1014 (2001).
[Crossref]

1996 (2)

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
[Crossref]

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

1992 (1)

B. Moslehi and J. W. Goodman, “Novel amplified fiber-optic recirculating delay line processor,” J. Lightwave Technol. 10(8), 1142–1147 (1992).
[Crossref]

1987 (1)

M. Fujise, M. Kuwazuru, M. Nunokawa, and Y. Iwamoto, “Highly accurate long-span chromatic dispersion measurement system by a new phase-shift technique,” J. Lightwave Technol. 5(6), 751–758 (1987).
[Crossref]

1985 (1)

L. Cohen, “Comparison of single-mode fiber dispersion measurement techniques,” J. Lightwave Technol. 3(5), 958–966 (1985).
[Crossref]

1977 (1)

Abedin, K. S.

K. S. Abedin, “Rapid, cost-effective measurement of chromatic dispersion of optical fibre over 1440-1625 nm using Sagnac interferometer,” Electron. Lett. 41(8), 469–471 (2005).
[Crossref]

Aditya, S.

Ali, J.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Amiri, I. S.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Andrés, M. V.

Aziz, M. S.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Capmany, J.

Chiangga, S.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Cohen, L.

L. Cohen, “Comparison of single-mode fiber dispersion measurement techniques,” J. Lightwave Technol. 3(5), 958–966 (1985).
[Crossref]

Cohen, L. G.

Cruz, J. L.

Díez, A.

Dong-Sung, K.

J. Keum-Soo, K. Hee-Ju, K. Dong-Sung, and P. Jae-Kyung, “Optical fiber chromatic dispersion measurement using bidirectional modulation of an optical intensity modulator,” IEEE Photonics Technol. Lett. 14(8), 1145–1147 (2002).
[Crossref]

Feng, S.

Fujise, M.

M. Fujise, M. Kuwazuru, M. Nunokawa, and Y. Iwamoto, “Highly accurate long-span chromatic dispersion measurement system by a new phase-shift technique,” J. Lightwave Technol. 5(6), 751–758 (1987).
[Crossref]

Gliese, U.

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

Goodman, J. W.

B. Moslehi and J. W. Goodman, “Novel amplified fiber-optic recirculating delay line processor,” J. Lightwave Technol. 10(8), 1142–1147 (1992).
[Crossref]

Gorgiev, E.

D. Guang-Hua and E. Gorgiev, “Non-white photodetection noise at the output of an optical amplifier: theory and experiment,” IEEE J. Quantum Electron. 37(8), 1008–1014 (2001).
[Crossref]

Grattan, K. T. V.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Gu, Y.

X. Han, M. Zhang, S. Li, N. Shi, Y. Gu, and M. Zhao, “A new method for fiber chromatic dispersion measurement with microwave interference effect,” Opt. Fiber Technol. 19(4), 319–324 (2013).
[Crossref]

M. Zhang, S. Li, N. Shi, Y. Gu, P. Wu, X. Han, and M. Zhao, “Novel method for fiber chromatic dispersion measurement based on microwave photonic technique,” Chin. Opt. Lett. 10, 070602 (2012).

Guang-Hua, D.

D. Guang-Hua and E. Gorgiev, “Non-white photodetection noise at the output of an optical amplifier: theory and experiment,” IEEE J. Quantum Electron. 37(8), 1008–1014 (2001).
[Crossref]

Han, X.

X. Han, M. Zhang, S. Li, N. Shi, Y. Gu, and M. Zhao, “A new method for fiber chromatic dispersion measurement with microwave interference effect,” Opt. Fiber Technol. 19(4), 319–324 (2013).
[Crossref]

M. Zhang, S. Li, N. Shi, Y. Gu, P. Wu, X. Han, and M. Zhao, “Novel method for fiber chromatic dispersion measurement based on microwave photonic technique,” Chin. Opt. Lett. 10, 070602 (2012).

Hee-Ju, K.

J. Keum-Soo, K. Hee-Ju, K. Dong-Sung, and P. Jae-Kyung, “Optical fiber chromatic dispersion measurement using bidirectional modulation of an optical intensity modulator,” IEEE Photonics Technol. Lett. 14(8), 1145–1147 (2002).
[Crossref]

Herschel, R.

Iwamoto, Y.

M. Fujise, M. Kuwazuru, M. Nunokawa, and Y. Iwamoto, “Highly accurate long-span chromatic dispersion measurement system by a new phase-shift technique,” J. Lightwave Technol. 5(6), 751–758 (1987).
[Crossref]

Jae-Kyung, P.

J. Keum-Soo, K. Hee-Ju, K. Dong-Sung, and P. Jae-Kyung, “Optical fiber chromatic dispersion measurement using bidirectional modulation of an optical intensity modulator,” IEEE Photonics Technol. Lett. 14(8), 1145–1147 (2002).
[Crossref]

Jalil, M. A.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Jiang, F.

Keum-Soo, J.

J. Keum-Soo, K. Hee-Ju, K. Dong-Sung, and P. Jae-Kyung, “Optical fiber chromatic dispersion measurement using bidirectional modulation of an optical intensity modulator,” IEEE Photonics Technol. Lett. 14(8), 1145–1147 (2002).
[Crossref]

Kim, D. Y.

Kuwazuru, M.

M. Fujise, M. Kuwazuru, M. Nunokawa, and Y. Iwamoto, “Highly accurate long-span chromatic dispersion measurement system by a new phase-shift technique,” J. Lightwave Technol. 5(6), 751–758 (1987).
[Crossref]

Lam, H. Q.

Lee, J. Y.

Lee, K. E. K.

Li, G.

Z. Yang, R. Mi, N. Zhao, L. Zhang, and G. Li, “Simultaneous measurement of chromatic and modal dispersion in FMFs using microwave photonic techniques,” IEEE Photonics J. 9(3), 1–9 (2017).
[Crossref]

Li, H.

Li, S.

X. Han, M. Zhang, S. Li, N. Shi, Y. Gu, and M. Zhao, “A new method for fiber chromatic dispersion measurement with microwave interference effect,” Opt. Fiber Technol. 19(4), 319–324 (2013).
[Crossref]

M. Zhang, S. Li, N. Shi, Y. Gu, P. Wu, X. Han, and M. Zhao, “Novel method for fiber chromatic dispersion measurement based on microwave photonic technique,” Chin. Opt. Lett. 10, 070602 (2012).

Lim, P. H.

Lin, C.

Liu, Y.

Maleki, L.

Mi, R.

Z. Yang, R. Mi, N. Zhao, L. Zhang, and G. Li, “Simultaneous measurement of chromatic and modal dispersion in FMFs using microwave photonic techniques,” IEEE Photonics J. 9(3), 1–9 (2017).
[Crossref]

Mora, J.

Moslehi, B.

B. Moslehi and J. W. Goodman, “Novel amplified fiber-optic recirculating delay line processor,” J. Lightwave Technol. 10(8), 1142–1147 (1992).
[Crossref]

Neumann, N.

Nielsen, T. N.

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

Norskov, S.

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

Nunokawa, M.

M. Fujise, M. Kuwazuru, M. Nunokawa, and Y. Iwamoto, “Highly accurate long-span chromatic dispersion measurement system by a new phase-shift technique,” J. Lightwave Technol. 5(6), 751–758 (1987).
[Crossref]

Ortega, B.

Pastor, D.

Plettemeier, D.

Pornsuwancharoen, N.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Punthawanunt, S.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Schäffer, C.

Schuster, T.

Shi, N.

X. Han, M. Zhang, S. Li, N. Shi, Y. Gu, and M. Zhao, “A new method for fiber chromatic dispersion measurement with microwave interference effect,” Opt. Fiber Technol. 19(4), 319–324 (2013).
[Crossref]

M. Zhang, S. Li, N. Shi, Y. Gu, P. Wu, X. Han, and M. Zhao, “Novel method for fiber chromatic dispersion measurement based on microwave photonic technique,” Chin. Opt. Lett. 10, 070602 (2012).

Shum, P. P.

Singh, G.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Tang, Y.

Wang, H.

Wang, M.

Wong, J. H.

Wu, P.

Wu, S.

Xue, X.

Yang, Z.

Z. Yang, R. Mi, N. Zhao, L. Zhang, and G. Li, “Simultaneous measurement of chromatic and modal dispersion in FMFs using microwave photonic techniques,” IEEE Photonics J. 9(3), 1–9 (2017).
[Crossref]

Yao, J.

Yao, X. S.

Yin, B.

Youplao, P.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Yupapin, P.

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Zhang, H.

Zhang, L.

Z. Yang, R. Mi, N. Zhao, L. Zhang, and G. Li, “Simultaneous measurement of chromatic and modal dispersion in FMFs using microwave photonic techniques,” IEEE Photonics J. 9(3), 1–9 (2017).
[Crossref]

Zhang, M.

X. Han, M. Zhang, S. Li, N. Shi, Y. Gu, and M. Zhao, “A new method for fiber chromatic dispersion measurement with microwave interference effect,” Opt. Fiber Technol. 19(4), 319–324 (2013).
[Crossref]

M. Zhang, S. Li, N. Shi, Y. Gu, P. Wu, X. Han, and M. Zhao, “Novel method for fiber chromatic dispersion measurement based on microwave photonic technique,” Chin. Opt. Lett. 10, 070602 (2012).

Zhang, S.

Zhang, X.

Zhang, Y.

Zhao, M.

X. Han, M. Zhang, S. Li, N. Shi, Y. Gu, and M. Zhao, “A new method for fiber chromatic dispersion measurement with microwave interference effect,” Opt. Fiber Technol. 19(4), 319–324 (2013).
[Crossref]

M. Zhang, S. Li, N. Shi, Y. Gu, P. Wu, X. Han, and M. Zhao, “Novel method for fiber chromatic dispersion measurement based on microwave photonic technique,” Chin. Opt. Lett. 10, 070602 (2012).

Zhao, N.

Z. Yang, R. Mi, N. Zhao, L. Zhang, and G. Li, “Simultaneous measurement of chromatic and modal dispersion in FMFs using microwave photonic techniques,” IEEE Photonics J. 9(3), 1–9 (2017).
[Crossref]

Zheng, X.

Zhou, B.

Zhou, J.

Zou, X.

Appl. Opt. (1)

Chin. Opt. Lett. (1)

Electron. Lett. (1)

K. S. Abedin, “Rapid, cost-effective measurement of chromatic dispersion of optical fibre over 1440-1625 nm using Sagnac interferometer,” Electron. Lett. 41(8), 469–471 (2005).
[Crossref]

IEEE J. Quantum Electron. (1)

D. Guang-Hua and E. Gorgiev, “Non-white photodetection noise at the output of an optical amplifier: theory and experiment,” IEEE J. Quantum Electron. 37(8), 1008–1014 (2001).
[Crossref]

IEEE Photonics J. (1)

Z. Yang, R. Mi, N. Zhao, L. Zhang, and G. Li, “Simultaneous measurement of chromatic and modal dispersion in FMFs using microwave photonic techniques,” IEEE Photonics J. 9(3), 1–9 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (1)

J. Keum-Soo, K. Hee-Ju, K. Dong-Sung, and P. Jae-Kyung, “Optical fiber chromatic dispersion measurement using bidirectional modulation of an optical intensity modulator,” IEEE Photonics Technol. Lett. 14(8), 1145–1147 (2002).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

J. Lightwave Technol. (5)

L. Cohen, “Comparison of single-mode fiber dispersion measurement techniques,” J. Lightwave Technol. 3(5), 958–966 (1985).
[Crossref]

M. Fujise, M. Kuwazuru, M. Nunokawa, and Y. Iwamoto, “Highly accurate long-span chromatic dispersion measurement system by a new phase-shift technique,” J. Lightwave Technol. 5(6), 751–758 (1987).
[Crossref]

J. Yao, “Optoelectronic oscillators for high speed and high resolution optical sensing,” J. Lightwave Technol. 35(16), 3489–3497 (2017).
[Crossref]

B. Moslehi and J. W. Goodman, “Novel amplified fiber-optic recirculating delay line processor,” J. Lightwave Technol. 10(8), 1142–1147 (1992).
[Crossref]

J. Mora, B. Ortega, A. Díez, J. L. Cruz, M. V. Andrés, J. Capmany, and D. Pastor, “Photonic microwave tunable single-bandpass filter based on a Mach-Zehnder interferometer,” J. Lightwave Technol. 24(7), 2500–2509 (2006).
[Crossref]

J. Opt. Commun. Netw. (1)

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

Opt. Express (4)

Opt. Fiber Technol. (1)

X. Han, M. Zhang, S. Li, N. Shi, Y. Gu, and M. Zhao, “A new method for fiber chromatic dispersion measurement with microwave interference effect,” Opt. Fiber Technol. 19(4), 319–324 (2013).
[Crossref]

Photon. Res. (1)

Res. Phys. (1)

J. Ali, P. Youplao, N. Pornsuwancharoen, M. A. Jalil, M. S. Aziz, S. Chiangga, I. S. Amiri, S. Punthawanunt, G. Singh, P. Yupapin, and K. T. V. Grattan, “Novel Kerr-Vernier effects within the on-chip Si-ChG microring circuits,” Res. Phys. 11, 144–147 (2018).
[Crossref]

Other (1)

https://www.pefiberoptics.com/measurement-solutions/chromatic-dispersion-cd .

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Figures (7)

Fig. 1
Fig. 1 Configuration of the OEO based on a single bandpass microwave photonic filter for dispersion measurement. EDFA: erbium-doped fiber amplifier, OF: optical filter, Pol: polarizer, OC: optical coupler, PC: polarization controller, Att: attenuator, VTDL: variable time delay line, PM: phase modulator, PD: photodetector, EC: electrical coupler, EA: electrical amplifier, ESA: electrical spectrum analyzer.
Fig. 2
Fig. 2 The optical spectrum at the output of the OC2 when the central wavelength of the OF is set to be 1540 nm.
Fig. 3
Fig. 3 Experimentally measured frequency spectra of the generated microwave signals when different fibers with different dispersion are inserted into the OEO loop (The central wavelength of the OF is 1540 nm).
Fig. 4
Fig. 4 Chromatic dispersion at the wavelength of 1540 nm measured by CD400 and our OEO, respectively.
Fig. 5
Fig. 5 The optical spectrum at the output of the OC2 with a central wavelength of 1550 nm.
Fig. 6
Fig. 6 Experimental measured frequency spectra of the generated microwave signals when different fibers with different dispersion are embedded to the OEO (The central wavelength of the OF is 1550 nm).
Fig. 7
Fig. 7 Chromatic dispersion at the wavelength of 1550 nm measured by CD400 and our OEO, respectively.

Tables (1)

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Table 1 Comparison of Dispersion Measurement Techniques

Equations (21)

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e(t)= 1 2π E(Ω) exp(jΩt)dΩ
E(Ω)= N(Ω) exp( jθ(Ω) )
<exp(jθ(Ω))>=0
<exp(j(θ(Ω)θ( Ω )))>=2πδ(Ω Ω )
E up (Ω)=E(Ω)exp(jΩΔτ)
Δτ= nΔl c
λ FSR λ 2 nΔl = λ 2 cΔτ
e down (t)=e(t)exp(j(γcos( ω m t))) =e(t) n= n= j n J n (γ)exp(jn ω m t) e(t)[ J 0 (γ)+j J 1 (γ)exp(j ω m t)+j J 1 (γ)exp(j ω m t)]
E down (Ω)= J 0 (γ)E(Ω)+j J 1 (γ)E(Ω ω m )+j J 1 (γ)E(Ω+ ω m )
E MZI (Ω)= E up (Ω)+ E down (Ω)
T(Ω)=| T(Ω) |exp[jΦ(Ω)]
Φ(Ω)Φ( Ω 0 )+ τ 0 (Ω Ω 0 )+ 1 2 β 2 (Ω Ω 0 ) 2
E DUT (Ω)= E MZI (Ω)T(Ω)
I(ω)=r< 1 2π E DUT (ω) E DUT (ω)> = r 2π < E MZI (Ω) E MZI (Ωω)> T(Ω) T (Ωω)dΩ
H(ω)=I(ω)/{πA[δ(ω ω m )+δ(ω+ ω m )]}= H 0 (ω)+ H 1 (ω)
H 0 (ω)= 2r J 0 (γ) J 1 (γ) πA exp(jω τ 0 )sin( β 2 ω 2 /2) H b (ω)
H 1 (ω)= r J 1 (γ) πA exp(jπ/2ω τ 0 β 2 ω 2 /2+Δτ Ω 0 ) H b (ω Δτ β 2 ) + r J 1 (γ) πA exp(jπ/2ω τ 0 + β 2 ω 2 /2Δτ Ω 0 ) H b (ω+ Δτ β 2 )
Δτ+ ω 0 β 2 =0
ω 0 = Δτ β 2 = 2π D λ FSR
H(ω)= η+(12η)exp(jω τ 2 ) 1ηexp(jω τ 2 )
f FSR2 = 1 τ 2 = c n L 2