Abstract

The use of a high-finesse Fabry–Perot ring cavity with an odd number of reflections as a high-extinction-ratio resonant polarizer is shown. Experimental results from quantum-noise measurements using resonant cavities as spatial and spectral filters and precision polarizers are presented.

© 2007 Optical Society of America

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References

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  1. B. C. Barish and R. Weiss, "LIGO and the detection of gravitational waves," Phys. Today 52(10), 44-50 (1999).
    [CrossRef]
  2. T. J. Kane and R. L. Byer, "Monolithic, unidirectional single-mode Nd:YAG ring laser," Opt. Lett. 10, 65-67 (1985).
    [CrossRef] [PubMed]
  3. N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, "Modeling of efficient mode-matching and thermal lensing effect on a laser-beam coupling into a mode-cleaner cavity," in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukhand and S. Basu, eds., Proc. SPIE 2989, 57-69 (1997).
    [CrossRef]
  4. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).
  5. R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
    [CrossRef]
  6. G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
    [CrossRef]
  7. B. Willke, N. Uehara, E. K. Gustafson, R. L. Byer, P. King, S. Seel, and R. L. Savage, Jr., "Spatial and temporal filtering of a 10 W Nd:YAG laser with a Fabry-Perot ring-cavity premode cleaner," Opt. Lett. 23, 1704-1706 (1998).
    [CrossRef]
  8. N. Uehara and K. Ueda, "Accurate measurement of the radius of curvature of a concave mirror and the power dependence in a high-finesse Fabry-Perot interferometer," Appl. Opt. 34, 5611-5619 (1995).
    [CrossRef] [PubMed]
  9. L. S. Meng, J. K. Brasseur, and D. K. Neumann, "Damage threshold and surface distortion measurement for high-reflectance, low-loss mirrors to 100+ MW/cm2 cw laser intensity," Opt. Express 13, 10085-10091 (2005).
    [CrossRef] [PubMed]
  10. G. D. Goodno, S. Palese, J. Harkenrider, and H. Injeyan, "High average-power Yb:YAG end-pumped zig-zag slab laser," in Advanced Solid-State Lasers, C. Marshall, ed., Vol. 50 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2-4.
  11. J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser. Part 1. Theory," IEEE J. Quantum Electron. 20, 289-301 (1984).
    [CrossRef]
  12. W. M. Tulloch, T. S. Rutherford, E. H. Huntington, R. Ewart, C. C. Harb, B. Willke, E. K. Gustafson, M. M. Fejer, R. L. Byer, S. Rowan, and J. Hough, "Quantum noise in a continuous-wave laser-diode-pumped Nd:YAG linear optical amplifier," Opt. Lett. 23, 1852-1854 (1998).
    [CrossRef]
  13. S. Saraf, K. Urbanek, R. L. Byer, and P. King, "Quantum noise measurements in a continuous-wave laser-diode-pumped Nd:YAG saturated amplifier," Opt. Lett. 30, 1195-1197 (2005).
    [CrossRef] [PubMed]
  14. H. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, "Astigmatically compensated cavities for CW dye lasers," IEEE J. Quantum Electron. 8, 373-379 (1972).
    [CrossRef]

2005 (2)

2004 (1)

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

1999 (1)

B. C. Barish and R. Weiss, "LIGO and the detection of gravitational waves," Phys. Today 52(10), 44-50 (1999).
[CrossRef]

1998 (2)

1997 (1)

N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, "Modeling of efficient mode-matching and thermal lensing effect on a laser-beam coupling into a mode-cleaner cavity," in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukhand and S. Basu, eds., Proc. SPIE 2989, 57-69 (1997).
[CrossRef]

1995 (1)

1985 (1)

1984 (1)

J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser. Part 1. Theory," IEEE J. Quantum Electron. 20, 289-301 (1984).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

1972 (1)

H. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, "Astigmatically compensated cavities for CW dye lasers," IEEE J. Quantum Electron. 8, 373-379 (1972).
[CrossRef]

Armandula, H.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

Barish, B. C.

B. C. Barish and R. Weiss, "LIGO and the detection of gravitational waves," Phys. Today 52(10), 44-50 (1999).
[CrossRef]

Black, E.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

Brasseur, J. K.

Byer, R. L.

Cagnoli, G.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

Crooks, D. R. M.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

Dienes, A.

H. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, "Astigmatically compensated cavities for CW dye lasers," IEEE J. Quantum Electron. 8, 373-379 (1972).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Eggleston, J. M.

J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser. Part 1. Theory," IEEE J. Quantum Electron. 20, 289-301 (1984).
[CrossRef]

Ewart, R.

Fejer, M. M.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

W. M. Tulloch, T. S. Rutherford, E. H. Huntington, R. Ewart, C. C. Harb, B. Willke, E. K. Gustafson, M. M. Fejer, R. L. Byer, S. Rowan, and J. Hough, "Quantum noise in a continuous-wave laser-diode-pumped Nd:YAG linear optical amplifier," Opt. Lett. 23, 1852-1854 (1998).
[CrossRef]

N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, "Modeling of efficient mode-matching and thermal lensing effect on a laser-beam coupling into a mode-cleaner cavity," in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukhand and S. Basu, eds., Proc. SPIE 2989, 57-69 (1997).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Goodno, G. D.

G. D. Goodno, S. Palese, J. Harkenrider, and H. Injeyan, "High average-power Yb:YAG end-pumped zig-zag slab laser," in Advanced Solid-State Lasers, C. Marshall, ed., Vol. 50 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2-4.

Gustafson, E. K.

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Harb, C. C.

Harkenrider, J.

G. D. Goodno, S. Palese, J. Harkenrider, and H. Injeyan, "High average-power Yb:YAG end-pumped zig-zag slab laser," in Advanced Solid-State Lasers, C. Marshall, ed., Vol. 50 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2-4.

Harry, G. M.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

Hough, J.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

W. M. Tulloch, T. S. Rutherford, E. H. Huntington, R. Ewart, C. C. Harb, B. Willke, E. K. Gustafson, M. M. Fejer, R. L. Byer, S. Rowan, and J. Hough, "Quantum noise in a continuous-wave laser-diode-pumped Nd:YAG linear optical amplifier," Opt. Lett. 23, 1852-1854 (1998).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Huntington, E. H.

Injeyan, H.

G. D. Goodno, S. Palese, J. Harkenrider, and H. Injeyan, "High average-power Yb:YAG end-pumped zig-zag slab laser," in Advanced Solid-State Lasers, C. Marshall, ed., Vol. 50 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2-4.

Ippen, E. P.

H. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, "Astigmatically compensated cavities for CW dye lasers," IEEE J. Quantum Electron. 8, 373-379 (1972).
[CrossRef]

Kane, T. J.

T. J. Kane and R. L. Byer, "Monolithic, unidirectional single-mode Nd:YAG ring laser," Opt. Lett. 10, 65-67 (1985).
[CrossRef] [PubMed]

J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser. Part 1. Theory," IEEE J. Quantum Electron. 20, 289-301 (1984).
[CrossRef]

Kawalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

King, P.

Kogelnik, H.

H. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, "Astigmatically compensated cavities for CW dye lasers," IEEE J. Quantum Electron. 8, 373-379 (1972).
[CrossRef]

Kuhn, K.

J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser. Part 1. Theory," IEEE J. Quantum Electron. 20, 289-301 (1984).
[CrossRef]

Meng, L. S.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Neumann, D. K.

Palese, S.

G. D. Goodno, S. Palese, J. Harkenrider, and H. Injeyan, "High average-power Yb:YAG end-pumped zig-zag slab laser," in Advanced Solid-State Lasers, C. Marshall, ed., Vol. 50 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2-4.

Penn, S. D.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

Route, R.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

Rowan, S.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

W. M. Tulloch, T. S. Rutherford, E. H. Huntington, R. Ewart, C. C. Harb, B. Willke, E. K. Gustafson, M. M. Fejer, R. L. Byer, S. Rowan, and J. Hough, "Quantum noise in a continuous-wave laser-diode-pumped Nd:YAG linear optical amplifier," Opt. Lett. 23, 1852-1854 (1998).
[CrossRef]

Rutherford, T. S.

Saraf, S.

Savage, R. L.

Seel, S.

Shank, C. V.

H. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, "Astigmatically compensated cavities for CW dye lasers," IEEE J. Quantum Electron. 8, 373-379 (1972).
[CrossRef]

Sneddon, P.

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

Tulloch, W. M.

Ueda, K.

Uehara, N.

Unternahrer, J.

J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser. Part 1. Theory," IEEE J. Quantum Electron. 20, 289-301 (1984).
[CrossRef]

Urbanek, K.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Weiss, R.

B. C. Barish and R. Weiss, "LIGO and the detection of gravitational waves," Phys. Today 52(10), 44-50 (1999).
[CrossRef]

Willke, B.

Appl. Opt. (1)

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kawalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser. Part 1. Theory," IEEE J. Quantum Electron. 20, 289-301 (1984).
[CrossRef]

H. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, "Astigmatically compensated cavities for CW dye lasers," IEEE J. Quantum Electron. 8, 373-379 (1972).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Today (1)

B. C. Barish and R. Weiss, "LIGO and the detection of gravitational waves," Phys. Today 52(10), 44-50 (1999).
[CrossRef]

Proc. SPIE (2)

G. M. Harry, H. Armandula, E. Black, D. R. M. Crooks, G. Cagnoli, M. M. Fejer, J. Hough, S. D. Penn, S. Rowan, R. Route, and P. Sneddon, "Optical coatings for gravitational wave detection," in Advances in Thin Film Coatings for Optical Applications, J. D. T. Kruschwitz and J. B. Oliver, eds., Proc. SPIE 5527, 33-40 (2004).
[CrossRef]

N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, "Modeling of efficient mode-matching and thermal lensing effect on a laser-beam coupling into a mode-cleaner cavity," in Modeling and Simulation of Higher-Power Laser Systems IV, U. O. Farrukhand and S. Basu, eds., Proc. SPIE 2989, 57-69 (1997).
[CrossRef]

Other (2)

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

G. D. Goodno, S. Palese, J. Harkenrider, and H. Injeyan, "High average-power Yb:YAG end-pumped zig-zag slab laser," in Advanced Solid-State Lasers, C. Marshall, ed., Vol. 50 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. 2-4.

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Figures (6)

Fig. 1
Fig. 1

(Color online) (a) Three-mirror Fabry–Perot cavity referred to as a mode cleaner by LIGO. The cavity is a spatial filter, a spectral filter, and a resonant polarizer integrated into one device. (b) Staggered resonances and calculated transmission for the two polarizations inside the 42 cm mode cleaner with an odd number of mirrors and an angle of incidence less than the polarization angle at all mirrors. Interferometer length for p-polarization resonance falls exactly midway between the lengths for s-polarization resonance. The finesse for p- and s-polarization is 670 and 3825, respectively. The extinction for s-polarization when the mode cleaner is locked to p-polarized light is calculated to be > 52 d B , while the extinction for p-polarization when the mode cleaner is locked to s-polarized light is calculated to be > 67 d B .

Fig. 2
Fig. 2

(Color online) Experimental setup to measure the polarization extinction of a resonant three-mirror cavity. The output of a NPRO is polarized using a pair of precision passive polarizers in order to control the polarization state of the incident light on the mode cleaner to a high degree of fidelity. The extinction ratio of the resonant cavity polarizer is measured using a set of precision polarizers to separate the s- and p-components of the leakage light from the back mirror of the mode cleaner. Lock-in techniques are used to measure the polarization state of the cavity output by dithering the laser intensity at a frequency outside the range of the locking servo.

Fig. 3
Fig. 3

(Color online) Modeled performance of resonant cavity polarizers with increasing cavity finesse. Using ion-beam sputtered superpolished mirrors with R > 99.9999 % , > 125 d B polarization extinction ratios can be achieved.

Fig. 4
Fig. 4

(a) Layout of the quantum-noise measuring system of a Nd:YAG free-space saturated amplifier. The high-power beam saturates the gain of the 100 W class slab amplifier and is separated from the precisely overlapped probe beam after the amplifier. The three Fabry–Perot cavities in the setup function as spatial and spectral filters and resonant polarizers. This allows generation of a single-spatial-mode and single-polarization shot-noise-limited probe beam, precision overlap of the high power and probe beam, and finally, precision separation of the beams after amplification. (b) The quantum noise versus power gain plotted for different input intensities of the high-power saturating beam. The theory curve is a plot of the quantum noise Eq. (8).

Fig. 5
Fig. 5

(Color online) (a) Optical parameters of the short low-finesse mode cleaner used as a precision filter. The free-spectral range of the cavity is 3 G H z , which sets the frequency offset of 750 MHz between the probe and the high-power beam for optimum filtering. (b) Cavity action on the constituent beams at the output of the power amplifier results in transmission of the s-polarized probe beam with the added quantum noise due to the amplifier and rejection of other components caused by polarizer leakage and amplifier birefringence. The rejection of the probe in the wrong polarization is due to resonant polarizer action while the rejection of the residual high-power beam is due to resonant polarizer action combined with spectral filtering in the same cavity.

Fig. 6
Fig. 6

(Color online) Four-mirror mode cleaner with overlapping s- and p-resonances. A tightly focused beam into a Brewster-cut nonlinear crystal like LBO would produce green light for LIGO without astigmatism. The spatial mode does not see any inversion in this configuration.

Equations (12)

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

r s = sin ( θ i θ t ) sin ( θ i + θ t ) ,
r p = tan ( θ i θ t ) tan ( θ i + θ t ) ,
θ p = tan 1 ( n t / n i ) .
φ p φ s = π ,
L p res = 2 π n c / ω p in ,
L s res = 2 π n c / ω s in + π c / ω s in ,
ω s in = ω p in = ω in ,
L s res L p res = π c / ω in .
L s res L p res = Δ L FSR / 2 .
H ( ν Δ ) = 1 1 + ( 2 F π ) 2 sin 2 ( π ν Δ Δ ν FSR ) ,
σ det 2 = σ shot 2 [ 1 + 2 f sp η ( G sat 1 ) ] ,
f sp = 1 + α l ln ( G ) ,

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