Abstract

The power penalty characteristics of high-speed optical signals transmitted through a variety of filters based on multiple microring resonator devices are analyzed by numerical simulation. The technique used here has been verified with single-ring experimental measurements. Butterworth and Chebyshev filters are investigated, as are serial cascades of resonant devices. Although the power penalty is generally not prohibitive, it is a parameter which cannot be ignored for the design of complex high-bandwidth photonic interconnect systems that utilize microring resonators as filters and switches.

©2006 Optical Society of America

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References

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    [Crossref] [PubMed]
  2. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
    [Crossref]
  3. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
    [Crossref]
  4. M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23, 4222–4238 (2005).
    [Crossref]
  5. B. A. Small, B. G. Lee, K. Bergman, Q. Xu, J. Shakya, and M. Lipson, “High data rate signal integrity in micron-scale silicon ring resonators,” in Proc. CLEO, paper CTuCC4 (2006).
  6. B. G. Lee, B. A. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31 (2006).
    [Crossref] [PubMed]
  7. B. Zhang, D. Leuenberger, M.-C. M. Lee, S. Hu1, M. Haghi1, A. E. Willner, and M. C. Wu, “Error-free data transmission through a tunable-bandwidth filter based on MEMS-actuated microdisk resonator,” in Proc. CLEO, paper CFC3 (2006).
  8. M. Pfennigbauer, M. M. Strasser, M. Pauer, and P. J. Winzer, “Dependence of optically preamplified receiver sensitivity on optical and electrical filter bandwidths-measurement and simulation,” IEEE Photon. Technol. Lett. 14, 831–833 (2002).
    [Crossref]
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    [Crossref]
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    [Crossref]
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2006 (4)

2005 (2)

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23, 4222–4238 (2005).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

2004 (2)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

C. J. Kaalund and G.-D. Peng, “Pole-zero diagram approach to the design of ring resonator-based filters for photonic applications,” J. Lightwave Technol. 22, 1548–1559 (2004).
[Crossref]

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

2002 (2)

M. Pfennigbauer, M. M. Strasser, M. Pauer, and P. J. Winzer, “Dependence of optically preamplified receiver sensitivity on optical and electrical filter bandwidths-measurement and simulation,” IEEE Photon. Technol. Lett. 14, 831–833 (2002).
[Crossref]

Y. Yanagase, S. Suzuki, Y. Kokubun, and S. T. Chu, “Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter,” J. Lightwave Technol. 20, 1525–1529 (2002).
[Crossref]

2000 (1)

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12, 320–322 (2000).
[Crossref]

1999 (2)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguides: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[Crossref]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Absil, P. P.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12, 320–322 (2000).
[Crossref]

Agarwal, A.

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, New York, 2002).
[Crossref]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Banwell, T.

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Bergman, K.

B. G. Lee, B. A. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31 (2006).
[Crossref] [PubMed]

B. A. Small, B. G. Lee, K. Bergman, Q. Xu, J. Shakya, and M. Lipson, “High data rate signal integrity in micron-scale silicon ring resonators,” in Proc. CLEO, paper CTuCC4 (2006).

Blackman, R. B.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra, from the Point of View of Communications Engineering (Dover, New York, 1959).

Chen, W.

Chu, S. T.

Davidson, R.

Delfyett, P. J.

Donovan, K.

Etemad, S.

Fan, S.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Gill, D.

Haghi1, M.

B. Zhang, D. Leuenberger, M.-C. M. Lee, S. Hu1, M. Haghi1, A. E. Willner, and M. C. Wu, “Error-free data transmission through a tunable-bandwidth filter based on MEMS-actuated microdisk resonator,” in Proc. CLEO, paper CFC3 (2006).

Haus, H. A.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Heck, B. S.

E. W. Kamen and B. S. Heck, Fundamentals of Systems and Signals, 2nd ed. (Prentice-Hall, Englewood Cliffs, 2000).

Ho, P.-T.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12, 320–322 (2000).
[Crossref]

Hryniewicz, J.

Hryniewicz, J. V.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12, 320–322 (2000).
[Crossref]

Hu1, S.

B. Zhang, D. Leuenberger, M.-C. M. Lee, S. Hu1, M. Haghi1, A. E. Willner, and M. C. Wu, “Error-free data transmission through a tunable-bandwidth filter based on MEMS-actuated microdisk resonator,” in Proc. CLEO, paper CFC3 (2006).

Indukuri, T.

Jackel, J.

Jalali, B.

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Johnson, F.

Kaalund, C. J.

Kamen, E. W.

E. W. Kamen and B. S. Heck, Fundamentals of Systems and Signals, 2nd ed. (Prentice-Hall, Englewood Cliffs, 2000).

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

King, O.

Kokubun, Y.

Koonath, P.

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Lee, B. G.

B. G. Lee, B. A. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31 (2006).
[Crossref] [PubMed]

B. A. Small, B. G. Lee, K. Bergman, Q. Xu, J. Shakya, and M. Lipson, “High data rate signal integrity in micron-scale silicon ring resonators,” in Proc. CLEO, paper CTuCC4 (2006).

Lee, M.-C. M.

B. Zhang, D. Leuenberger, M.-C. M. Lee, S. Hu1, M. Haghi1, A. E. Willner, and M. C. Wu, “Error-free data transmission through a tunable-bandwidth filter based on MEMS-actuated microdisk resonator,” in Proc. CLEO, paper CFC3 (2006).

Lee, R. K.

Leuenberger, D.

B. Zhang, D. Leuenberger, M.-C. M. Lee, S. Hu1, M. Haghi1, A. E. Willner, and M. C. Wu, “Error-free data transmission through a tunable-bandwidth filter based on MEMS-actuated microdisk resonator,” in Proc. CLEO, paper CFC3 (2006).

Lipson, M.

B. G. Lee, B. A. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31 (2006).
[Crossref] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23, 4222–4238 (2005).
[Crossref]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

B. A. Small, B. G. Lee, K. Bergman, Q. Xu, J. Shakya, and M. Lipson, “High data rate signal integrity in micron-scale silicon ring resonators,” in Proc. CLEO, paper CTuCC4 (2006).

Little, B. E.

A. Agarwal, P. Toliver, R. Menendez, S. Etemad, J. Jackel, J. Young, T. Banwell, B. E. Little, S. T. Chu, W. Chen, W. Chen, J. Hryniewicz, F. Johnson, D. Gill, O. King, R. Davidson, K. Donovan, and P. J. Delfyett, “Fully programmable ring-resonator-based integrated photonic circuit for phase coherent applications,” J. Lightwave Technol. 24, 77–87 (2006).
[Crossref]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12, 320–322 (2000).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Manolatou, C.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Menendez, R.

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Pauer, M.

M. Pfennigbauer, M. M. Strasser, M. Pauer, and P. J. Winzer, “Dependence of optically preamplified receiver sensitivity on optical and electrical filter bandwidths-measurement and simulation,” IEEE Photon. Technol. Lett. 14, 831–833 (2002).
[Crossref]

Peng, G.-D.

Pfennigbauer, M.

M. Pfennigbauer, M. M. Strasser, M. Pauer, and P. J. Winzer, “Dependence of optically preamplified receiver sensitivity on optical and electrical filter bandwidths-measurement and simulation,” IEEE Photon. Technol. Lett. 14, 831–833 (2002).
[Crossref]

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

Scherer, A.

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

Sekaric, L.

Shakya, J.

B. A. Small, B. G. Lee, K. Bergman, Q. Xu, J. Shakya, and M. Lipson, “High data rate signal integrity in micron-scale silicon ring resonators,” in Proc. CLEO, paper CTuCC4 (2006).

Small, B. A.

B. G. Lee, B. A. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31 (2006).
[Crossref] [PubMed]

B. A. Small, B. G. Lee, K. Bergman, Q. Xu, J. Shakya, and M. Lipson, “High data rate signal integrity in micron-scale silicon ring resonators,” in Proc. CLEO, paper CTuCC4 (2006).

Strasser, M. M.

M. Pfennigbauer, M. M. Strasser, M. Pauer, and P. J. Winzer, “Dependence of optically preamplified receiver sensitivity on optical and electrical filter bandwidths-measurement and simulation,” IEEE Photon. Technol. Lett. 14, 831–833 (2002).
[Crossref]

Suzuki, S.

Toliver, P.

Tukey, J. W.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra, from the Point of View of Communications Engineering (Dover, New York, 1959).

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

Vlasov, Y. A.

Willner, A. E.

B. Zhang, D. Leuenberger, M.-C. M. Lee, S. Hu1, M. Haghi1, A. E. Willner, and M. C. Wu, “Error-free data transmission through a tunable-bandwidth filter based on MEMS-actuated microdisk resonator,” in Proc. CLEO, paper CFC3 (2006).

Wilson, R. A.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12, 320–322 (2000).
[Crossref]

Winzer, P. J.

M. Pfennigbauer, M. M. Strasser, M. Pauer, and P. J. Winzer, “Dependence of optically preamplified receiver sensitivity on optical and electrical filter bandwidths-measurement and simulation,” IEEE Photon. Technol. Lett. 14, 831–833 (2002).
[Crossref]

Wu, M. C.

B. Zhang, D. Leuenberger, M.-C. M. Lee, S. Hu1, M. Haghi1, A. E. Willner, and M. C. Wu, “Error-free data transmission through a tunable-bandwidth filter based on MEMS-actuated microdisk resonator,” in Proc. CLEO, paper CFC3 (2006).

Xia, F.

Xu, Q.

B. G. Lee, B. A. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31 (2006).
[Crossref] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

B. A. Small, B. G. Lee, K. Bergman, Q. Xu, J. Shakya, and M. Lipson, “High data rate signal integrity in micron-scale silicon ring resonators,” in Proc. CLEO, paper CTuCC4 (2006).

Xu, Y.

Yanagase, Y.

Yariv, A.

Young, J.

Zhang, B.

B. Zhang, D. Leuenberger, M.-C. M. Lee, S. Hu1, M. Haghi1, A. E. Willner, and M. C. Wu, “Error-free data transmission through a tunable-bandwidth filter based on MEMS-actuated microdisk resonator,” in Proc. CLEO, paper CFC3 (2006).

IEEE J. Quantum Electron. (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[Crossref]

IEEE Photon. Technol. Lett. (2)

M. Pfennigbauer, M. M. Strasser, M. Pauer, and P. J. Winzer, “Dependence of optically preamplified receiver sensitivity on optical and electrical filter bandwidths-measurement and simulation,” IEEE Photon. Technol. Lett. 14, 831–833 (2002).
[Crossref]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12, 320–322 (2000).
[Crossref]

J. Lightwave Technol. (6)

Nature (3)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

B. G. Lee, B. A. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31 (2006).
[Crossref] [PubMed]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled resonator optical waveguides: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[Crossref]

Other (5)

B. Zhang, D. Leuenberger, M.-C. M. Lee, S. Hu1, M. Haghi1, A. E. Willner, and M. C. Wu, “Error-free data transmission through a tunable-bandwidth filter based on MEMS-actuated microdisk resonator,” in Proc. CLEO, paper CFC3 (2006).

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, New York, 2002).
[Crossref]

B. A. Small, B. G. Lee, K. Bergman, Q. Xu, J. Shakya, and M. Lipson, “High data rate signal integrity in micron-scale silicon ring resonators,” in Proc. CLEO, paper CTuCC4 (2006).

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra, from the Point of View of Communications Engineering (Dover, New York, 1959).

E. W. Kamen and B. S. Heck, Fundamentals of Systems and Signals, 2nd ed. (Prentice-Hall, Englewood Cliffs, 2000).

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Figures (8)

Fig. 1.
Fig. 1. Power penalty (solid curve) and attenuation (dashed curve) for Lorentzian filters with Γ/F between 1/2 (green) and 2 (blue), logarithmically; black curves for Γ = F.
Fig. 2.
Fig. 2. Comparison between detuning values at observed power penalty minima (points) and predicted maximum signal integrity from Eq. (3) (curve); the inset is a sketch of the simplistic estimation upon which Eq. (3) is based.
Fig. 3.
Fig. 3. Comparison of filter shapes with Γ/F = 1.25, Lorentzian or first-order (black), second-and third-order Butterworth (blue), and second- and third-order Chebyshev (green).
Fig. 4.
Fig. 4. Power penalty (solid lines) and attenuation (dashed lines) for Butterworth filters with Γ/F = 1.25, from second-order (blue) to fifth-order (green); black curves for Lorentzian; inset of region near origin.
Fig. 5.
Fig. 5. Power penalty (solid lines) and attenuation (dashed lines) for Chebyshev filters with Γ/F = 1.25, from second-order (blue) to fourth-order (green); black curves for Lorentzian.
Fig. 6.
Fig. 6. Power penalty at zero detuning (Δf = 0) with different values of FWHM for Butterworth filters, from second-order (blue) to fifth-order (green); black curve for Lorentzian.
Fig. 7.
Fig. 7. Comparison of filter shapes with Γ/F = 1.25, single first-order filter (black), cascades of two and three successive devices (blue); Lorentzian lineshapes with FWHM scaled by √2/2 and √3/3 are given for reference (gray dashed curves).
Fig. 8.
Fig. 8. Power penalty (solid lines) and attenuation (dashed lines) for serial cascades of first-order filters with Γ/F = 1.25, from two (blue) to five (green); black curves for a single device.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

δ = ε + 1 ε 1 .
T ( f ) = 1 ( 2 f / Γ ) 2 + 1 .
Δ f 1 Δ f ( f Δ f + 1 ) ( 2 f / Γ ) 2 + 1 df = 1 Δ f 2 arctan [ 2 Γ Γ 2 + 4 Δ f 2 4 Δ f ] Γ + 1 8 log [ Γ 2 + 4 Δ f 2 Γ 2 + 4 ( 1 Δ f ) 2 ] Γ 2 .
R = α ( Δ f = F ) α ( Δ f = 0 ) .
T ( f ) = 1 [ P ( 2 f / Γ ) ] 2 + 1 .

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