Abstract

The design of a high finesse optical cavity made from two prism retroreflectors is fully described. Optical beam propagation calculations to determine the specification of prism angles and relative dimensions, the size of the astigmatic TEM00 beam as it propagates in the cavity, and the sensitivity of the optic axis to changes in prism alignment and fabrication errors are presented. The effects of material dispersion are also quantified for three different materials: fused silica, calcium fluoride, and barium fluoride. The predictions made are found to be in good agreement with experimental results obtained from prisms we had made from fused silica. Prisms made of CaF2 and BaF2 are predicted to be useful for applications in the UV and mid-IR spectral regions, respectively.

© 2009 Optical Society of America

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2008 (2)

2007 (2)

M. J. Thorpe, D. D. Hudson, K. D. Moll, J. Lasri, and J. Ye, “Cavity-ringdown molecular spectroscopy based on an optical frequency comb at 1.45-1.65 μ,” Opt. Lett. 32, 307-309(2007).
[CrossRef]

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[CrossRef]

2006 (1)

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595-1599(2006).
[CrossRef]

2004 (1)

P. B. Tarsa, A. D. Wist, P. Rabinowitz, and K. K. Lehmann, “Single-cell detection by cavity ring-down spectroscopy,” Appl. Phys. Lett. 85, 4523-4525 (2004).
[CrossRef]

2003 (2)

S. L. Logunov and S. A. Kuchinsky, “Scattering losses in fused silica and CaF2 for DUV applications,” Proc. SPIE 5040, 1396-1407 (2003).

S. S. Brown, “Absorption spectroscopy in high-finesse cavities for atmospheric studies,” Chem. Rev. 103, 5219-5238 (2003).
[CrossRef]

2002 (1)

2000 (2)

1999 (1)

E. R. Crosson, P. Haar, G. A. Marcus, H. A. Schwettman, B. A. Paldus, T. G. Spence, and R. N. Zare, “Pulse-stacked cavity ring-down spectroscopy,” Rev. Sci. Instrum. 70, 4-10(1999).
[CrossRef]

1998 (3)

R. Engeln, G. Berden, R. Peeters, and G. Meijer, “Cavity enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763-3769 (1998).
[CrossRef]

A. O'Keefe, “Integrated cavity output analysis of ultra-weak absorption,” Chem. Phys. Lett. 293, 331-336 (1998).
[CrossRef]

H. Moosmuller, “Brewster's angle Porro prism: a different use for a Pellin-Broca prism,” Appl. Opt. 37, 8140-8142 (1998).

1997 (2)

J. J. Scherer, J. B. Paul, A. O'Keefe, and R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25-51 (1997).
[CrossRef]

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, “Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity,” Rev. Sci. Instrum. 68, 2978-2989(1997).
[CrossRef]

1996 (1)

1992 (1)

1988 (1)

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption-measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

1983 (2)

1968 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic,2001).

Balslev-Clausen, D.

Bennett, J. M.

Berden, G.

R. Engeln, G. Berden, R. Peeters, and G. Meijer, “Cavity enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763-3769 (1998).
[CrossRef]

Borrelli, N. F.

Brown, S. S.

S. S. Brown, “Absorption spectroscopy in high-finesse cavities for atmospheric studies,” Chem. Rev. 103, 5219-5238 (2003).
[CrossRef]

Crosson, E. R.

E. R. Crosson, P. Haar, G. A. Marcus, H. A. Schwettman, B. A. Paldus, T. G. Spence, and R. N. Zare, “Pulse-stacked cavity ring-down spectroscopy,” Rev. Sci. Instrum. 70, 4-10(1999).
[CrossRef]

Deacon, D. A. G.

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption-measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

Dudek, J. B.

G. Engel, W. B. Yan, J. B. Dudek, K. K. Lehmann, and P. Rabinowitz, “Ring-down spectroscopy with a Brewster's angle prism resonator,” in Laser Spectroscopy XIV International Conference, R. Blatt, J. Eschner, D. Leibfried, and F. Schmidt-Kaler, eds. (World Scientific, 1999), pp. 314-315.

Elson, J. M.

Engel, G.

G. Engel, W. B. Yan, J. B. Dudek, K. K. Lehmann, and P. Rabinowitz, “Ring-down spectroscopy with a Brewster's angle prism resonator,” in Laser Spectroscopy XIV International Conference, R. Blatt, J. Eschner, D. Leibfried, and F. Schmidt-Kaler, eds. (World Scientific, 1999), pp. 314-315.

Engeln, R.

R. Engeln, G. Berden, R. Peeters, and G. Meijer, “Cavity enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763-3769 (1998).
[CrossRef]

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart and Winston, 1975), p. 328.

Gherman, T.

Gohle, C.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[CrossRef]

Haar, P.

E. R. Crosson, P. Haar, G. A. Marcus, H. A. Schwettman, B. A. Paldus, T. G. Spence, and R. N. Zare, “Pulse-stacked cavity ring-down spectroscopy,” Rev. Sci. Instrum. 70, 4-10(1999).
[CrossRef]

Hall, J. L.

Hansch, T. W.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[CrossRef]

Hudgens, J. W.

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, “Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity,” Rev. Sci. Instrum. 68, 2978-2989(1997).
[CrossRef]

Hudson, D. D.

Huie, R. E.

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, “Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity,” Rev. Sci. Instrum. 68, 2978-2989(1997).
[CrossRef]

Jeffries, J. B.

A. McIlroy and J. B. Jeffries, “Cavity ringdown spectroscopy for concentration measurements,” in Applied Combustion Diagnostics, K. Kohse-Hoinghaus and J. B. Jeffries, eds. (Taylor & Francis, 2002), pp. 98-127.

Johnston, P. S.

Jones, R. J.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595-1599(2006).
[CrossRef]

Kimble, H. J.

Kirchner, M. S.

Kuchinsky, S. A.

S. L. Logunov and S. A. Kuchinsky, “Scattering losses in fused silica and CaF2 for DUV applications,” Proc. SPIE 5040, 1396-1407 (2003).

Lalezari, R.

Lasri, J.

Lehmann, K. K.

P. S. Johnston and K. K. Lehmann, “Cavity enhanced absorption spectroscopy using a broadband prism cavity and a supercontinuum source,” Opt. Express 16, 15013-15023(2008).
[CrossRef]

P. B. Tarsa, A. D. Wist, P. Rabinowitz, and K. K. Lehmann, “Single-cell detection by cavity ring-down spectroscopy,” Appl. Phys. Lett. 85, 4523-4525 (2004).
[CrossRef]

K. K. Lehmann, “Mathcad prism cavity analysis” (2007).

G. Engel, W. B. Yan, J. B. Dudek, K. K. Lehmann, and P. Rabinowitz, “Ring-down spectroscopy with a Brewster's angle prism resonator,” in Laser Spectroscopy XIV International Conference, R. Blatt, J. Eschner, D. Leibfried, and F. Schmidt-Kaler, eds. (World Scientific, 1999), pp. 314-315.

K. K. Lehmann and P. Rabinowitz, “High-finesse optical resonator for cavity ring-down spectroscopy based upon Brewster's angle prism retroreflectors,” U.S. patent 5973864 (October 1999).

Logunov, S. L.

S. L. Logunov and S. A. Kuchinsky, “Scattering losses in fused silica and CaF2 for DUV applications,” Proc. SPIE 5040, 1396-1407 (2003).

Ma, L. S.

Marcus, G. A.

E. R. Crosson, P. Haar, G. A. Marcus, H. A. Schwettman, B. A. Paldus, T. G. Spence, and R. N. Zare, “Pulse-stacked cavity ring-down spectroscopy,” Rev. Sci. Instrum. 70, 4-10(1999).
[CrossRef]

McIlroy, A.

A. McIlroy and J. B. Jeffries, “Cavity ringdown spectroscopy for concentration measurements,” in Applied Combustion Diagnostics, K. Kohse-Hoinghaus and J. B. Jeffries, eds. (Taylor & Francis, 2002), pp. 98-127.

Meijer, G.

R. Engeln, G. Berden, R. Peeters, and G. Meijer, “Cavity enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763-3769 (1998).
[CrossRef]

Miller, R. A.

Moll, K. D.

M. J. Thorpe, D. D. Hudson, K. D. Moll, J. Lasri, and J. Ye, “Cavity-ringdown molecular spectroscopy based on an optical frequency comb at 1.45-1.65 μ,” Opt. Lett. 32, 307-309(2007).
[CrossRef]

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595-1599(2006).
[CrossRef]

Moosmuller, H.

O'Keefe, A.

A. O'Keefe, “Integrated cavity output analysis of ultra-weak absorption,” Chem. Phys. Lett. 293, 331-336 (1998).
[CrossRef]

J. J. Scherer, J. B. Paul, A. O'Keefe, and R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25-51 (1997).
[CrossRef]

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption-measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

Osterberg, U. L.

U. L. Osterberg, “Optical fiber, cable, and connectors,” in Handbook of Fiber Optic Data Communication, C. DeCusatis, ed. (Academic, 2002).

Paldus, B. A.

E. R. Crosson, P. Haar, G. A. Marcus, H. A. Schwettman, B. A. Paldus, T. G. Spence, and R. N. Zare, “Pulse-stacked cavity ring-down spectroscopy,” Rev. Sci. Instrum. 70, 4-10(1999).
[CrossRef]

Paul, J. B.

J. J. Scherer, J. B. Paul, A. O'Keefe, and R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25-51 (1997).
[CrossRef]

Peeters, R.

R. Engeln, G. Berden, R. Peeters, and G. Meijer, “Cavity enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763-3769 (1998).
[CrossRef]

Pipino, A. C. R.

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, “Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity,” Rev. Sci. Instrum. 68, 2978-2989(1997).
[CrossRef]

Rabinowitz, P.

P. B. Tarsa, A. D. Wist, P. Rabinowitz, and K. K. Lehmann, “Single-cell detection by cavity ring-down spectroscopy,” Appl. Phys. Lett. 85, 4523-4525 (2004).
[CrossRef]

K. K. Lehmann and P. Rabinowitz, “High-finesse optical resonator for cavity ring-down spectroscopy based upon Brewster's angle prism retroreflectors,” U.S. patent 5973864 (October 1999).

G. Engel, W. B. Yan, J. B. Dudek, K. K. Lehmann, and P. Rabinowitz, “Ring-down spectroscopy with a Brewster's angle prism resonator,” in Laser Spectroscopy XIV International Conference, R. Blatt, J. Eschner, D. Leibfried, and F. Schmidt-Kaler, eds. (World Scientific, 1999), pp. 314-315.

Rahn, J. P.

Ranka, J. K.

Rempe, G.

Romanini, D.

Safdi, B.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595-1599(2006).
[CrossRef]

Saykally, R. J.

J. J. Scherer, J. B. Paul, A. O'Keefe, and R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25-51 (1997).
[CrossRef]

Scherer, J. J.

J. J. Scherer, J. B. Paul, A. O'Keefe, and R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25-51 (1997).
[CrossRef]

Schliesser, A.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[CrossRef]

Schwettman, H. A.

E. R. Crosson, P. Haar, G. A. Marcus, H. A. Schwettman, B. A. Paldus, T. G. Spence, and R. N. Zare, “Pulse-stacked cavity ring-down spectroscopy,” Rev. Sci. Instrum. 70, 4-10(1999).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986), p. 1283.

A. E. Siegman, “Errata list for LASERS,” http://www.stanford.edu/~siegman/lasers_book_errata.pdf (17 June 2008), retrieved 09/23/2008.

Spence, T. G.

E. R. Crosson, P. Haar, G. A. Marcus, H. A. Schwettman, B. A. Paldus, T. G. Spence, and R. N. Zare, “Pulse-stacked cavity ring-down spectroscopy,” Rev. Sci. Instrum. 70, 4-10(1999).
[CrossRef]

Stein, B.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[CrossRef]

Stentz, A. J.

Tarsa, P. B.

P. B. Tarsa, A. D. Wist, P. Rabinowitz, and K. K. Lehmann, “Single-cell detection by cavity ring-down spectroscopy,” Appl. Phys. Lett. 85, 4523-4525 (2004).
[CrossRef]

Thompson, R. J.

Thorpe, M. J.

Toyoda, T.

T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D 16, L97-L100 (1983).

Udem, T.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[CrossRef]

Windeler, R. S.

Wist, A. D.

P. B. Tarsa, A. D. Wist, P. Rabinowitz, and K. K. Lehmann, “Single-cell detection by cavity ring-down spectroscopy,” Appl. Phys. Lett. 85, 4523-4525 (2004).
[CrossRef]

Yabe, M.

T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D 16, L97-L100 (1983).

Yan, W. B.

G. Engel, W. B. Yan, J. B. Dudek, K. K. Lehmann, and P. Rabinowitz, “Ring-down spectroscopy with a Brewster's angle prism resonator,” in Laser Spectroscopy XIV International Conference, R. Blatt, J. Eschner, D. Leibfried, and F. Schmidt-Kaler, eds. (World Scientific, 1999), pp. 314-315.

Ye, J.

Zare, R. N.

E. R. Crosson, P. Haar, G. A. Marcus, H. A. Schwettman, B. A. Paldus, T. G. Spence, and R. N. Zare, “Pulse-stacked cavity ring-down spectroscopy,” Rev. Sci. Instrum. 70, 4-10(1999).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

P. B. Tarsa, A. D. Wist, P. Rabinowitz, and K. K. Lehmann, “Single-cell detection by cavity ring-down spectroscopy,” Appl. Phys. Lett. 85, 4523-4525 (2004).
[CrossRef]

Chem. Phys. Lett. (1)

A. O'Keefe, “Integrated cavity output analysis of ultra-weak absorption,” Chem. Phys. Lett. 293, 331-336 (1998).
[CrossRef]

Chem. Rev. (2)

J. J. Scherer, J. B. Paul, A. O'Keefe, and R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25-51 (1997).
[CrossRef]

S. S. Brown, “Absorption spectroscopy in high-finesse cavities for atmospheric studies,” Chem. Rev. 103, 5219-5238 (2003).
[CrossRef]

J. Phys. D (1)

T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D 16, L97-L100 (1983).

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hansch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[CrossRef]

Proc. SPIE (1)

S. L. Logunov and S. A. Kuchinsky, “Scattering losses in fused silica and CaF2 for DUV applications,” Proc. SPIE 5040, 1396-1407 (2003).

Rev. Sci. Instrum. (4)

E. R. Crosson, P. Haar, G. A. Marcus, H. A. Schwettman, B. A. Paldus, T. G. Spence, and R. N. Zare, “Pulse-stacked cavity ring-down spectroscopy,” Rev. Sci. Instrum. 70, 4-10(1999).
[CrossRef]

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption-measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

R. Engeln, G. Berden, R. Peeters, and G. Meijer, “Cavity enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763-3769 (1998).
[CrossRef]

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, “Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity,” Rev. Sci. Instrum. 68, 2978-2989(1997).
[CrossRef]

Science (1)

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595-1599(2006).
[CrossRef]

Other (11)

A. E. Siegman, Lasers (University Science, 1986), p. 1283.

A. E. Siegman, “Errata list for LASERS,” http://www.stanford.edu/~siegman/lasers_book_errata.pdf (17 June 2008), retrieved 09/23/2008.

M.Bass, ed., Handbook of Optics Volume II--Devices, Measurements, and Properties, 2nd ed. (McGraw-Hill, ), Vol. 2.

“BaF2 specifications” (Fairfield Crystal Technology), http://www.fairfieldcrystal.com/, retrieved 2 December 2008.

U. L. Osterberg, “Optical fiber, cable, and connectors,” in Handbook of Fiber Optic Data Communication, C. DeCusatis, ed. (Academic, 2002).

G. Engel, W. B. Yan, J. B. Dudek, K. K. Lehmann, and P. Rabinowitz, “Ring-down spectroscopy with a Brewster's angle prism resonator,” in Laser Spectroscopy XIV International Conference, R. Blatt, J. Eschner, D. Leibfried, and F. Schmidt-Kaler, eds. (World Scientific, 1999), pp. 314-315.

K. K. Lehmann and P. Rabinowitz, “High-finesse optical resonator for cavity ring-down spectroscopy based upon Brewster's angle prism retroreflectors,” U.S. patent 5973864 (October 1999).

A. McIlroy and J. B. Jeffries, “Cavity ringdown spectroscopy for concentration measurements,” in Applied Combustion Diagnostics, K. Kohse-Hoinghaus and J. B. Jeffries, eds. (Taylor & Francis, 2002), pp. 98-127.

G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart and Winston, 1975), p. 328.

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K. K. Lehmann, “Mathcad prism cavity analysis” (2007).

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Figures (10)

Fig. 1
Fig. 1

Schematic of the Brewster angle retroreflector based ring cavity showing the optical beam path. Light is coupled into the cavity at R 3 and coupled out at R 0 . All surfaces are flat with exception to EF, which has a 6 m convex curve. Labels are referred to in the text along with prism dimensions and angles. The size of the prisms relative to their displacement is not to scale.

Fig. 2
Fig. 2

Brewster’s angle for fused silica. Critical angle for fused silica.

Fig. 3
Fig. 3

Brewster’s angle for CaF 2 . Critical angle for CaF 2 .

Fig. 4
Fig. 4

Brewster’s angle for BaF 2 . Critical angle for BaF 2 .

Fig. 5
Fig. 5

Fresnel loss per surface in parts per million for fused silica when aligned for Brewster’s angle at 1 μm .

Fig. 6
Fig. 6

Fresnel loss per surface in parts per million for CaF 2 when aligned for Brewster’s angle at 300 nm.

Fig. 7
Fig. 7

Fresnel loss per surface in parts per million for BaF 2 when aligned for Brewster’s angle at 3.0 μm .

Fig. 8
Fig. 8

Effect of dispersion in fused silica on the prism cavity free spectral range. Rate of change of the free spectral range with respect to frequency in the fused silica prism cavity.

Fig. 9
Fig. 9

Effect of dispersion in CaF 2 on the prism cavity free spectral range. Rate of change of the free spectral range with respect to the frequency in the CaF 2 prism cavity.

Fig. 10
Fig. 10

Effect of dispersion in BaF 2 on the prism cavity free spectral range. Rate of change of the free spectral range with respect to the frequency in the BaF 2 prism cavity.

Tables (3)

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Table 1 Coordinates and Beam Radii of Cavity Axis Points (in mm) a

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Table 2 Displacements of Optic Axis Points due to Misalignments a

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Table 3 Displacements of the Optic Axis Points due to Errors in the Prism Fabrication a

Equations (23)

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a sin ( 45 ° ) 2 sin ( θ B ) = a 1 + n 2 2 2 n .
a 2 sin ( 135 ° θ B ) sin ( θ B ) = a 2 2 ( 1 + 1 n ) .
3 ( R 0 R 1 ) ( R 1 R 2 ) = a 2 2 ( 1 + 3 n ) .
4 R 0 A = 2 a 2 sin ( θ ) = 2 a 1 + n 2 2 n .
BC = AD sin ( 135 ° θ B ) [ a AD sin ( 135 ° θ B ) ] ctn ( 225 ° 3 θ B ) = a 5 + 3 n + n 2 n 3 ( 1 + n ) ( 4 n n 2 1 ) ,
CD = a AD cos ( 135 ° θ B ) sin ( 225 ° 3 θ B ) = a [ 2 ( 1 + n 2 ) 3 / 2 n ( n + 1 ) ( 4 n n 2 1 ) ] .
R c 2 2 n 3 ,
R c 2 n ,
L g < R c 2 L p 2 n 3 .
x = R m 4 ( 1 R t 1 R s ) .
( 2 π σ λ 0 n 2 1 n 2 + 1 ) 2 .
( n 4 1 ) 2 4 n 6 δ θ 2
σ ( θ ) = λ 2 π ω 0 = 0.02 ° ,
d θ B d T = ( 1 + n 2 ) 1 ( d n d T ) 40 μrad / K
R = R y 0 + ( d R y 0 · n k · n ) k .
s = k · ( Ry 0 R c ) ± [ k · ( Ry 0 R c ) ] 2 k 2 ( | Ry 0 R c | 2 R s 3 ) k 2 ,
k t = k + [ 1 + k 2 ( n r 2 1 ) ( k · n ) 2 1 ] ( k · n ) n ,
FSR ( λ ) = c [ L 0 2 λ ( d n d λ ) ( L p + d L p d n + d L g d n ) ] ,
Δ ν c = 2 · FSR · L r t π | ( d FSR d ν ) | ,
( d FSR d ν ) = λ 2 c ( d FSR d λ ) = λ 3 c 2 FSR 2 [ ( d 2 n d λ 2 ) ( d L 0 d n ) + ( d n d λ ) 2 ( d 2 L 0 d n 2 ) ] .
Δ ν d = Δ ν c 2 8 · FSR | ( d FSR d ν ) | 1 .
( d 2 FSR d ν 2 ) = λ 3 c 2 [ 2 ( d FSR d λ ) + λ ( d 2 FSR d λ 2 ) ] ( d 2 FSR d λ 2 ) = 2 FSR ( d FSR d λ ) 2 1 λ ( d FSR d λ ) λ · FSR 2 c [ ( d 3 n d λ 3 ) ( d L 0 d n ) + 3 ( d 2 n d λ 2 ) ( d n d λ ) ( d 2 L 0 d n 2 ) + ( d n d λ ) 3 ( d 3 L 0 d n 3 ) ] .
Δ ν c = [ 48 π L r t · FSR 2 · | ( d 2 FSR d ν 2 ) | 1 ] 1 / 3 .

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