Abstract

The frequency resolution of an active waveguide ring resonator spectrometer is fundamentally limited by spontaneous emission noise produced by the gain medium. A closed-form expression for this resolution is derived, and the result is used to determine the minimum, rms, angular rotation rate, random walk error achievable by an active ring resonator gyroscope. An active waveguide ring resonator is demonstrated in a neodymium-doped glass, and a finesse of 250 at a signal wavelength of 1060 nm is achieved for the 1.6 cm diameter ring under laser diode pumping. This finesse corresponds to an effective propagation loss on the order of 0.013 dB/cm, which is the lowest value reported to date for rings of this size.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
    [CrossRef]
  2. S. T. Chu, B. E. Little, W. Pan, T. Kaneko and Y. Kokubun, "A second-order filter response from parallel coupled glass microring resonators," IEEE Photon. Technol. Lett. 11, 1426-1428 (1999).
    [CrossRef]
  3. G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier and R. Baets, "Optical bistability and pulsating behavior in silicon-on-insulator ring resonator structures," Opt. Express 13, 9623-9628 (2005).
    [CrossRef] [PubMed]
  4. Q. Xu and M. Lipson, "All-optical logic based on silicon micro-ring resonators," Opt. Express 15, 924-929 (2007).
    [CrossRef] [PubMed]
  5. A. Ksendzov and Y. Lin, "Integrated optics ring-resonator sensors for protein detection," Opt. Lett. 30, 3344-3346 (2005).
    [CrossRef]
  6. P. Mottier and P. Pouteau, "Solid state optical gyrometer integrated on silicon," Electron. Lett. 33, 1975-1977 (1997).
    [CrossRef]
  7. J. Haavisto and G. A. Pajer, "Resonance effects in low-loss ring waveguides," Opt. Lett. 5, 510-512 (1980).
    [CrossRef] [PubMed]
  8. R. G. Walker and C. D. W. Wilkinson, "Integrated optical ring resonators made by silver ion-exchange in glass," Appl. Opt. 22, 1029-1035 (1983).
    [CrossRef] [PubMed]
  9. G. Li, K. A. Winick, H. C. Griffin and J. Hayden, "Systematic modeling study of channel waveguide fabrication by thermal silver ion exchange," Appl. Opt. 45, 1743-1755 (2006).
    [CrossRef] [PubMed]
  10. R. Adar, M. R. Serbin and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
    [CrossRef]
  11. T. Kitagawa, K. Hattori, Y. Hibino and Y. Ohmori, "Laser Oscillation in Erbium-Doped Silica-Based Planar Ring Resonators," in Proceedings of 18th European Conf. on Optical Commun. (ECOC), (1992), Th PD-II.5, pp. 907-910.
  12. W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche and R. Ricken, "Erbium-doped lithium niobate waveguide lasers," IEICE Trans. Electron.E 88-C, 990- 997 (2005).
    [CrossRef]
  13. T. A. Dorschner, H. A. Haus, M. Holz I. W. Smith, H. Statz, "Laser gyro at quantum limit," IEEE J. Quantum Electron. QE-16, 1376-1379 (1980).
    [CrossRef]
  14. L. F. Stokes, M. Chodorow and H. J. Shaw,"All-single-mode fiber resonator," Opt. Lett. 7, 288-290 (1982).
    [CrossRef] [PubMed]
  15. S. Ezekiel, S. P. Smith and F. Zarinetchi, "Basic principles of fiber-optic gyroscopes," in Optical fiber Rotation Sensing, W. K. Burns, ed., (Academic Press, NY, 1994), Chap. 1.
  16. S. Ezekiel and S. R. Balsamo, "Passive ring resonator laser gyroscope," Appl. Phys. Lett. 30, 478-480 (1977).
    [CrossRef]
  17. R. E. Meyer, S. Ezekiel, D. W. Stowe and V. J. Tekippe, "Passive fiber-optic ring resonator for rotation sensing," Opt. Lett. 8, 644-646 (1983).
    [CrossRef] [PubMed]
  18. K. Suzuki, K. Takiguchi and K. Hotate, "Monolithically integrated resonator microoptic gyro on silica planar lightwave circuit," J. Lightwave Technol. 18, 66-72 (2000).
    [CrossRef]
  19. H. Ma, X. Zhang, Z. Jin and C. Ding, "Waveguide-type optical passive resonator gyro using phase modulation spectroscopy technique," Opt. Eng. Lett. 45, 080506-1 - 080506-3 (2006).
  20. H. Okamura and K Iwatsuki, "A finesse-enhanced Er-doped-fiber ring resonator," J. Lightwave Technol. 9, 1554-1560 (1991).
    [CrossRef]
  21. J. T. Kringlebotn, "Amplified fiber ring resonator gyro," IEEE Photon. Technol. Lett. 4, 1180-1183 (1992).
    [CrossRef]
  22. J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne and R. I. Laming, "Amplified fibre delay line with 27 000 recirculations," Electron. Lett. 28, 201-202 (1992).
  23. W. T. Silfvast, "Radiation and thermal equilibrium," in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 6.
  24. W. T. Silfvast, "Conditions for producing a laser," in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 7.

2007 (1)

2006 (1)

2005 (3)

2000 (1)

1999 (2)

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

S. T. Chu, B. E. Little, W. Pan, T. Kaneko and Y. Kokubun, "A second-order filter response from parallel coupled glass microring resonators," IEEE Photon. Technol. Lett. 11, 1426-1428 (1999).
[CrossRef]

1997 (1)

P. Mottier and P. Pouteau, "Solid state optical gyrometer integrated on silicon," Electron. Lett. 33, 1975-1977 (1997).
[CrossRef]

1994 (1)

R. Adar, M. R. Serbin and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

1992 (2)

J. T. Kringlebotn, "Amplified fiber ring resonator gyro," IEEE Photon. Technol. Lett. 4, 1180-1183 (1992).
[CrossRef]

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne and R. I. Laming, "Amplified fibre delay line with 27 000 recirculations," Electron. Lett. 28, 201-202 (1992).

1991 (1)

H. Okamura and K Iwatsuki, "A finesse-enhanced Er-doped-fiber ring resonator," J. Lightwave Technol. 9, 1554-1560 (1991).
[CrossRef]

1983 (2)

1982 (1)

1980 (2)

J. Haavisto and G. A. Pajer, "Resonance effects in low-loss ring waveguides," Opt. Lett. 5, 510-512 (1980).
[CrossRef] [PubMed]

T. A. Dorschner, H. A. Haus, M. Holz I. W. Smith, H. Statz, "Laser gyro at quantum limit," IEEE J. Quantum Electron. QE-16, 1376-1379 (1980).
[CrossRef]

1977 (1)

S. Ezekiel and S. R. Balsamo, "Passive ring resonator laser gyroscope," Appl. Phys. Lett. 30, 478-480 (1977).
[CrossRef]

Adar, R.

R. Adar, M. R. Serbin and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

Baets, R.

Balsamo, S. R.

S. Ezekiel and S. R. Balsamo, "Passive ring resonator laser gyroscope," Appl. Phys. Lett. 30, 478-480 (1977).
[CrossRef]

Bogaerts, W.

Bruce, A. J.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Cappuzzo, M. A.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Chodorow, M.

Chu, S. T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko and Y. Kokubun, "A second-order filter response from parallel coupled glass microring resonators," IEEE Photon. Technol. Lett. 11, 1426-1428 (1999).
[CrossRef]

Das, B. K.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche and R. Ricken, "Erbium-doped lithium niobate waveguide lasers," IEICE Trans. Electron.E 88-C, 990- 997 (2005).
[CrossRef]

Dey, D.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche and R. Ricken, "Erbium-doped lithium niobate waveguide lasers," IEICE Trans. Electron.E 88-C, 990- 997 (2005).
[CrossRef]

Dorschner, T. A.

T. A. Dorschner, H. A. Haus, M. Holz I. W. Smith, H. Statz, "Laser gyro at quantum limit," IEEE J. Quantum Electron. QE-16, 1376-1379 (1980).
[CrossRef]

Dumon, P.

Ezekiel, S.

Gomez, L. T.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Griffin, H. C.

Haavisto, J.

Haus, H. A.

T. A. Dorschner, H. A. Haus, M. Holz I. W. Smith, H. Statz, "Laser gyro at quantum limit," IEEE J. Quantum Electron. QE-16, 1376-1379 (1980).
[CrossRef]

Hayden, J.

Hotate, K.

Iwatsuki, K

H. Okamura and K Iwatsuki, "A finesse-enhanced Er-doped-fiber ring resonator," J. Lightwave Technol. 9, 1554-1560 (1991).
[CrossRef]

Kaneko, T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko and Y. Kokubun, "A second-order filter response from parallel coupled glass microring resonators," IEEE Photon. Technol. Lett. 11, 1426-1428 (1999).
[CrossRef]

Kokubun, Y.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko and Y. Kokubun, "A second-order filter response from parallel coupled glass microring resonators," IEEE Photon. Technol. Lett. 11, 1426-1428 (1999).
[CrossRef]

Kringlebotn, J. T.

J. T. Kringlebotn, "Amplified fiber ring resonator gyro," IEEE Photon. Technol. Lett. 4, 1180-1183 (1992).
[CrossRef]

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne and R. I. Laming, "Amplified fibre delay line with 27 000 recirculations," Electron. Lett. 28, 201-202 (1992).

Ksendzov, A.

Laming, R. I.

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne and R. I. Laming, "Amplified fibre delay line with 27 000 recirculations," Electron. Lett. 28, 201-202 (1992).

Lenz, G.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Li, G.

Lin, Y.

Lipson, M.

Little, B. E.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko and Y. Kokubun, "A second-order filter response from parallel coupled glass microring resonators," IEEE Photon. Technol. Lett. 11, 1426-1428 (1999).
[CrossRef]

Madsen, C. K.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Meyer, R. E.

Mizrahi, V.

R. Adar, M. R. Serbin and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

Morkel, P. R.

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne and R. I. Laming, "Amplified fibre delay line with 27 000 recirculations," Electron. Lett. 28, 201-202 (1992).

Morthier, G.

Mottier, P.

P. Mottier and P. Pouteau, "Solid state optical gyrometer integrated on silicon," Electron. Lett. 33, 1975-1977 (1997).
[CrossRef]

Okamura, H.

H. Okamura and K Iwatsuki, "A finesse-enhanced Er-doped-fiber ring resonator," J. Lightwave Technol. 9, 1554-1560 (1991).
[CrossRef]

Pajer, G. A.

Pan, W.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko and Y. Kokubun, "A second-order filter response from parallel coupled glass microring resonators," IEEE Photon. Technol. Lett. 11, 1426-1428 (1999).
[CrossRef]

Pannell, C. N.

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne and R. I. Laming, "Amplified fibre delay line with 27 000 recirculations," Electron. Lett. 28, 201-202 (1992).

Payne, D. N.

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne and R. I. Laming, "Amplified fibre delay line with 27 000 recirculations," Electron. Lett. 28, 201-202 (1992).

Pouteau, P.

P. Mottier and P. Pouteau, "Solid state optical gyrometer integrated on silicon," Electron. Lett. 33, 1975-1977 (1997).
[CrossRef]

Priem, G.

Reza, S.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche and R. Ricken, "Erbium-doped lithium niobate waveguide lasers," IEICE Trans. Electron.E 88-C, 990- 997 (2005).
[CrossRef]

Ricken, R.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche and R. Ricken, "Erbium-doped lithium niobate waveguide lasers," IEICE Trans. Electron.E 88-C, 990- 997 (2005).
[CrossRef]

Scotti, R. E.

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Serbin, M. R.

R. Adar, M. R. Serbin and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

Shaw, H. J.

Sohler, W.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche and R. Ricken, "Erbium-doped lithium niobate waveguide lasers," IEICE Trans. Electron.E 88-C, 990- 997 (2005).
[CrossRef]

Stokes, L. F.

Stowe, D. W.

Suche, H.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche and R. Ricken, "Erbium-doped lithium niobate waveguide lasers," IEICE Trans. Electron.E 88-C, 990- 997 (2005).
[CrossRef]

Suzuki, K.

Takiguchi, K.

Tekippe, V. J.

Van Thourhout, D.

Walker, R. G.

Wilkinson, C. D. W.

Winick, K. A.

Xu, Q.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

S. Ezekiel and S. R. Balsamo, "Passive ring resonator laser gyroscope," Appl. Phys. Lett. 30, 478-480 (1977).
[CrossRef]

E (1)

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche and R. Ricken, "Erbium-doped lithium niobate waveguide lasers," IEICE Trans. Electron.E 88-C, 990- 997 (2005).
[CrossRef]

Electron. Lett. (2)

P. Mottier and P. Pouteau, "Solid state optical gyrometer integrated on silicon," Electron. Lett. 33, 1975-1977 (1997).
[CrossRef]

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne and R. I. Laming, "Amplified fibre delay line with 27 000 recirculations," Electron. Lett. 28, 201-202 (1992).

J. Lightwave Technol. (3)

H. Okamura and K Iwatsuki, "A finesse-enhanced Er-doped-fiber ring resonator," J. Lightwave Technol. 9, 1554-1560 (1991).
[CrossRef]

K. Suzuki, K. Takiguchi and K. Hotate, "Monolithically integrated resonator microoptic gyro on silica planar lightwave circuit," J. Lightwave Technol. 18, 66-72 (2000).
[CrossRef]

R. Adar, M. R. Serbin and V. Mizrahi, "Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator," J. Lightwave Technol. 12, 1369-1372 (1994).
[CrossRef]

J. Quantum Electron. (1)

T. A. Dorschner, H. A. Haus, M. Holz I. W. Smith, H. Statz, "Laser gyro at quantum limit," IEEE J. Quantum Electron. QE-16, 1376-1379 (1980).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Photon. Technol. Lett. (3)

J. T. Kringlebotn, "Amplified fiber ring resonator gyro," IEEE Photon. Technol. Lett. 4, 1180-1183 (1992).
[CrossRef]

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

S. T. Chu, B. E. Little, W. Pan, T. Kaneko and Y. Kokubun, "A second-order filter response from parallel coupled glass microring resonators," IEEE Photon. Technol. Lett. 11, 1426-1428 (1999).
[CrossRef]

Other (5)

T. Kitagawa, K. Hattori, Y. Hibino and Y. Ohmori, "Laser Oscillation in Erbium-Doped Silica-Based Planar Ring Resonators," in Proceedings of 18th European Conf. on Optical Commun. (ECOC), (1992), Th PD-II.5, pp. 907-910.

S. Ezekiel, S. P. Smith and F. Zarinetchi, "Basic principles of fiber-optic gyroscopes," in Optical fiber Rotation Sensing, W. K. Burns, ed., (Academic Press, NY, 1994), Chap. 1.

H. Ma, X. Zhang, Z. Jin and C. Ding, "Waveguide-type optical passive resonator gyro using phase modulation spectroscopy technique," Opt. Eng. Lett. 45, 080506-1 - 080506-3 (2006).

W. T. Silfvast, "Radiation and thermal equilibrium," in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 6.

W. T. Silfvast, "Conditions for producing a laser," in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 7.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Double arm ring resonator.

Fig. 2.
Fig. 2.

Effect of spontaneous emission on frequency.

Fig. 3.
Fig. 3.

Mask layout for single-arm racetrack active ring resonator with pump coupler. W=1.3 µm, Ds=8.4 µm, Lp=2.915 mm, Dp=7.55 µm

Fig. 4.
Fig. 4.

Spectral response of active ring resonator.

Fig. 5.
Fig. 5.

Spectral response of active ring resonator as a function of pump power at fixed signal power.

Fig. 6.
Fig. 6.

Spectral response of active ring resonator as a function of signal power at fixed pump power.

Fig. 7.
Fig. 7.

Lasing characteristic.

Equations (50)

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

A = [ A o 1 K cw j B o K cw ]
B = [ j A o K cw + B o 1 K cw ]
B o = B 1 K ccw exp ( ρ 2 L j β L )
T ( ϕ ) A A o 2 = 1 ( 1 x 2 ) ( 1 y 2 ) ( 1 xy ) 2 + 4 xy sin 2 ( ϕ 2 )
x 1 K ccw exp ( ρ 2 L )
y 1 K cw
ϕ β L = 2 π λ N eff L = ω N eff L c
D T max T min T max = 4 xy ( 1 x 2 ) ( 1 y 2 ) ( 1 xy ) 2 ( x + y ) 2
δ ϕ FWHM = 2 cos 1 [ 2 xy 1 + x 2 y 2 ]
T ( m π ± δ ϕ FWHM 2 ) T min T max T min = 1 2
F 2 π δ ϕ FWHM = 2 π c N eff L δ ω FWHM
F π 1 xy
B A o 2 = 1 y 2 [ 1 xy ] 2
B A o 2 F π
f m = m c N eff L
f m , ccw f m , cw = 4 A λ m L Ω
δ Ω rms ( λ m L 4 A ) [ 2 δ ω FWHM ( 2 π ) [ η D ( P in h f m ) τ int ] 1 2 ]
= ( λ m c 4 A N eff ) [ 2 F c [ η D ( P in h f m ) τ int ] 1 2 ] rad s
δ Ω rms ( λ m c 4 A N eff ) [ 1 F c F a [ ( P in h f m ) τ int ] 1 2 ] rad s
δ θ 1 · cos β < n >
< ( δ θ ) 2 > 1 2 < n >
< [ δ ϕ ( τ int ) ] 2 > M ( τ int ) 2 < n >
M ( τ int ) = τ int τ fl N 2 s
ρ b ( f ) = 8 π λ a 2 n r 3 c
S ( f ) = 1 1 + [ 2 ( f f a ) δ f a ] 2
s = 8 π λ a 2 n r 3 c V δ ω a 4 = 2 π λ a 2 n r 3 V c Δ ω a
τ p = n r L c 1 y 2 x 2
1 τ p δ ω FWHM = 2 π c n r L F c
G = e σ e N 2 L V 1 + σ e N 2 L V
y 2 x 2 G 1
N 2 V σ e L ( 1 x 2 y 2 ) = n r V σ e c 1 τ p
σ e = 1 2 π 1 τ fl λ a 2 n r 2 Δ ω a
< n > = n r P c L 2 h f a c
< [ δ ϕ ( τ int ) ] 2 > = 2 π τ int h f a c 2 F c P c n r 2 L 2
P c 1 π F a P in
< [ δ f cw ] 2 > = < [ δ f ccw ] 2 >
= < [ δ ϕ ( τ int ) ] 2 > ( 2 π τ int ) 2
( δ f cw ) rms = ( δ f ccw ) rms c 2 n r L [ 1 F a F c [ ( P in h f a ) τ int ] 1 2 ]
δ Ω rms = < [ δ Ω ] 2 > 1 2 = λ a L 4 2 π A τ int < [ δ ϕ ( τ int ) ] 2 > 1 2
δ Ω rms ( λ a c 4 A n r ) [ 1 F a F c [ ( P in h f a ) τ int ] 1 2 ]
( λ a c 4 A n r ) [ 1 F c F a F c [ ( P in h f a ) τ int ] 1 2 ] rad s
F c π 1 ( 1 K cw ) e ρ c L 2 2 π ρ c L
F a π K cw
reduction factor = F a F c ρ c L 2 K cw
P c = P in K cw
σ e N 2 ( sat ) ρ c
N 2 ( sat ) N 2 ( unsat ) 1 + 2 P c P sat
P sat h f a σ e τ fl A wg
P p = hc λ p τ fl N 2 ( usat ) A wg L
P p 4 λ a λ p F a F c P in

Metrics