Abstract

A complete theory describing the transmission of atomic vapor Faraday filters is developed. The dependence of the filter transmission on atomic density and external magnetic field strength, as well as the frequency dependence of transmission, are explained in physical terms. As examples, applications of the computed results to ongoing research to suppress sky background, thus allowing Na lidar operation under sunlit conditions, and to enable measurement of the density of mesospheric oxygen atoms are briefly discussed.

© 2009 Optical Society of America

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    [CrossRef]
  26. W. A. Van Wijngaarden and J. Li, “Measurement of hyperfine structure of sodium 3P1/2,3/2 states using optical spectroscopy,” Z. Phys. D: At., Mol. Clusters 32, 67-71 (1994).
    [CrossRef]
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    [CrossRef]
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2009 (1)

2008 (1)

Yu. Ralchenko, A. E. Kramida, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database” (National Institute of Standards and Technology, Gaithersburg, MD, 2008), version 3.1.4, ⟨http://physics.nist.gov/asd3⟩.

2006 (1)

S. Falke, E. Tiemann, and C. Lisdat, “Transition frequencies of the D lines of K39, K40, and K41 measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
[CrossRef]

2005 (2)

N. J. Stone, “Table of nuclear magnetic dipole and electric quadrupole moments,” At. Data Nucl. Data Tables 90, 75-176 (2005).
[CrossRef]

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

2004 (1)

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

2001 (1)

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristics of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).

1998 (2)

Y. P. Gangrsky, D. V. Karaivanov, K. P. Marinova, B. N. Markov, L. M. Melnikova, G. V. Mishinsky, S. G. Zemlyanoi, and V. I. Zhemenik, “Hyperfine splitting and isotope shift in the atomic D2 line of Na22,23 and the quadrupole moment of Na22,” Eur. Phys. J. A 3, 313-318 (1998).
[CrossRef]

Z. Hu, X. Sun, Y. Liu, L. Fu, and X. Zeng, “Temperature properties of Na dispersive Faraday optical filter at D1 and D2 line,” Opt. Commun. 156, 289-293 (1998).
[CrossRef]

1996 (3)

1994 (2)

J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994), Revised Ed., pp. 176-181.

W. A. Van Wijngaarden and J. Li, “Measurement of hyperfine structure of sodium 3P1/2,3/2 states using optical spectroscopy,” Z. Phys. D: At., Mol. Clusters 32, 67-71 (1994).
[CrossRef]

1993 (2)

Y. C. Chan and J. A. Gelbwachs, “A Fraunhofer-wavelength magnetooptic atomic filter at 422.7 nm,” IEEE J. Quantum Electron. 29, 2379-2384 (1993).

H. Chen, C. Y. She, P. Searcy, and E. Korevaar, “Sodium-vapor dispersive Faraday filter,” Opt. Lett. 18, 1019-1021 (1993).
[CrossRef] [PubMed]

1992 (1)

F. Schreier, “The Voigt and complex error function: A comparison of computational methods,” J. Quant. Spectrosc. Radiat. Transf. 48, 743-762 (1992).
[CrossRef]

1991 (3)

1988 (1)

K. S. Krane, Introductory Nuclear Physics (Wiley, 1988), pp. 602-651.

1982 (1)

1977 (2)

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms,” Rev. Mod. Phys. 49, 31-75 (1977).
[CrossRef]

A. Corney, Atomic and Laser Spectroscopy (Clarendon Press, 1977), pp. 667-674.

1975 (1)

G. Agnelli, A. Cacciani, and M. Fofi, “The magneto-optical filter I,” Sol. Phys. 44, 509-518 (1975).
[CrossRef]

1969 (1)

R. E. Honig and D. A. Kramer, “Vapor pressure data for the solid and liquid elements,” RCA Rev. 30, 285-305 (1969).

1957 (1)

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, 1957), pp. 75-76.

1956 (1)

Y. Ohman, “On some new auxiliary instruments in astrophysical research VI. A tentative monochromator for solar work based on the principle of selective magnetic rotation,” Stockholms Obs. Ann. 19(4), 9-11 (1956).

Acott, P.

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

Agnelli, G.

G. Agnelli, A. Cacciani, and M. Fofi, “The magneto-optical filter I,” Sol. Phys. 44, 509-518 (1975).
[CrossRef]

Allende Prieto, C.

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

Arimondo, E.

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms,” Rev. Mod. Phys. 49, 31-75 (1977).
[CrossRef]

Benson, K.

Billmers, R. I.

Bloom, S. H.

Cacciani, A.

G. Agnelli, A. Cacciani, and M. Fofi, “The magneto-optical filter I,” Sol. Phys. 44, 509-518 (1975).
[CrossRef]

Chan, Y. C.

Y. C. Chan and J. A. Gelbwachs, “A Fraunhofer-wavelength magnetooptic atomic filter at 422.7 nm,” IEEE J. Quantum Electron. 29, 2379-2384 (1993).

Chen, H.

Chu, X.

Collins, R. L.

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

Corney, A.

A. Corney, Atomic and Laser Spectroscopy (Clarendon Press, 1977), pp. 667-674.

Cosby, P. C.

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

Dick, D. J.

Dressler, E. T.

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, 1957), pp. 75-76.

Falke, S.

S. Falke, E. Tiemann, and C. Lisdat, “Transition frequencies of the D lines of K39, K40, and K41 measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
[CrossRef]

Fofi, M.

G. Agnelli, A. Cacciani, and M. Fofi, “The magneto-optical filter I,” Sol. Phys. 44, 509-518 (1975).
[CrossRef]

Fu, L.

Z. Hu, X. Sun, Y. Liu, L. Fu, and X. Zeng, “Temperature properties of Na dispersive Faraday optical filter at D1 and D2 line,” Opt. Commun. 156, 289-293 (1998).
[CrossRef]

Gangrsky, Y. P.

Y. P. Gangrsky, D. V. Karaivanov, K. P. Marinova, B. N. Markov, L. M. Melnikova, G. V. Mishinsky, S. G. Zemlyanoi, and V. I. Zhemenik, “Hyperfine splitting and isotope shift in the atomic D2 line of Na22,23 and the quadrupole moment of Na22,” Eur. Phys. J. A 3, 313-318 (1998).
[CrossRef]

Gelbwachs, J. A.

Y. C. Chan and J. A. Gelbwachs, “A Fraunhofer-wavelength magnetooptic atomic filter at 422.7 nm,” IEEE J. Quantum Electron. 29, 2379-2384 (1993).

Hagan, M. E.

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

Harrell, S. D.

Honig, R. E.

R. E. Honig and D. A. Kramer, “Vapor pressure data for the solid and liquid elements,” RCA Rev. 30, 285-305 (1969).

Hu, Z.

Z. Hu, X. Sun, Y. Liu, L. Fu, and X. Zeng, “Temperature properties of Na dispersive Faraday optical filter at D1 and D2 line,” Opt. Commun. 156, 289-293 (1998).
[CrossRef]

Huang, W.

Huestis, D. L.

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

Inguscio, M.

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms,” Rev. Mod. Phys. 49, 31-75 (1977).
[CrossRef]

Jenniskens, P.

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

Jia, X.

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristics of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).

Karaivanov, D. V.

Y. P. Gangrsky, D. V. Karaivanov, K. P. Marinova, B. N. Markov, L. M. Melnikova, G. V. Mishinsky, S. G. Zemlyanoi, and V. I. Zhemenik, “Hyperfine splitting and isotope shift in the atomic D2 line of Na22,23 and the quadrupole moment of Na22,” Eur. Phys. J. A 3, 313-318 (1998).
[CrossRef]

Kawahara, T. D.

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

Korevaar, E.

Kramer, D. A.

R. E. Honig and D. A. Kramer, “Vapor pressure data for the solid and liquid elements,” RCA Rev. 30, 285-305 (1969).

Kramida, A. E.

Yu. Ralchenko, A. E. Kramida, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database” (National Institute of Standards and Technology, Gaithersburg, MD, 2008), version 3.1.4, ⟨http://physics.nist.gov/asd3⟩.

Krane, K. S.

K. S. Krane, Introductory Nuclear Physics (Wiley, 1988), pp. 602-651.

Krueger, D. A.

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

H. Chen, M. A. White, D. A. Krueger, and C. Y. She, “Daytime mesopause temperature measurements with a sodium-vapor dispersive Faraday filter in a lidar receiver,” Opt. Lett. 21, 1093-1095 (1996).
[CrossRef] [PubMed]

Laux, A. E.

Li, J.

W. A. Van Wijngaarden and J. Li, “Measurement of hyperfine structure of sodium 3P1/2,3/2 states using optical spectroscopy,” Z. Phys. D: At., Mol. Clusters 32, 67-71 (1994).
[CrossRef]

Li, T.

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

Lisdat, C.

S. Falke, E. Tiemann, and C. Lisdat, “Transition frequencies of the D lines of K39, K40, and K41 measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
[CrossRef]

Liu, C. S.

Liu, H.-L.

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

Liu, Y.

Z. Hu, X. Sun, Y. Liu, L. Fu, and X. Zeng, “Temperature properties of Na dispersive Faraday optical filter at D1 and D2 line,” Opt. Commun. 156, 289-293 (1998).
[CrossRef]

Ma, Z.

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristics of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).

Marinova, K. P.

Y. P. Gangrsky, D. V. Karaivanov, K. P. Marinova, B. N. Markov, L. M. Melnikova, G. V. Mishinsky, S. G. Zemlyanoi, and V. I. Zhemenik, “Hyperfine splitting and isotope shift in the atomic D2 line of Na22,23 and the quadrupole moment of Na22,” Eur. Phys. J. A 3, 313-318 (1998).
[CrossRef]

Markov, B. N.

Y. P. Gangrsky, D. V. Karaivanov, K. P. Marinova, B. N. Markov, L. M. Melnikova, G. V. Mishinsky, S. G. Zemlyanoi, and V. I. Zhemenik, “Hyperfine splitting and isotope shift in the atomic D2 line of Na22,23 and the quadrupole moment of Na22,” Eur. Phys. J. A 3, 313-318 (1998).
[CrossRef]

Martin-Torres, F. J.

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

Melnikova, L. M.

Y. P. Gangrsky, D. V. Karaivanov, K. P. Marinova, B. N. Markov, L. M. Melnikova, G. V. Mishinsky, S. G. Zemlyanoi, and V. I. Zhemenik, “Hyperfine splitting and isotope shift in the atomic D2 line of Na22,23 and the quadrupole moment of Na22,” Eur. Phys. J. A 3, 313-318 (1998).
[CrossRef]

Menders, J.

Miles, B. M.

W. L. Wiese, M. W. Smith, and B. M. Miles, “Atomic Transition Probabilities: Volume II, Sodium Through Calcium,” Nat. Stand. Ref. Data Ser., Nat. Bur. Stand. (U. S.), 22.

Mishinsky, G. V.

Y. P. Gangrsky, D. V. Karaivanov, K. P. Marinova, B. N. Markov, L. M. Melnikova, G. V. Mishinsky, S. G. Zemlyanoi, and V. I. Zhemenik, “Hyperfine splitting and isotope shift in the atomic D2 line of Na22,23 and the quadrupole moment of Na22,” Eur. Phys. J. A 3, 313-318 (1998).
[CrossRef]

Murray, B. J.

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

Ohman, Y.

Y. Ohman, “On some new auxiliary instruments in astrophysical research VI. A tentative monochromator for solar work based on the principle of selective magnetic rotation,” Stockholms Obs. Ann. 19(4), 9-11 (1956).

O'Sullivan, D. A.

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

Plane, J. M. C.

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

Ralchenko, Yu.

Yu. Ralchenko, A. E. Kramida, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database” (National Institute of Standards and Technology, Gaithersburg, MD, 2008), version 3.1.4, ⟨http://physics.nist.gov/asd3⟩.

Reader, J.

Yu. Ralchenko, A. E. Kramida, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database” (National Institute of Standards and Technology, Gaithersburg, MD, 2008), version 3.1.4, ⟨http://physics.nist.gov/asd3⟩.

Saiz-Lopez, A.

T. G. Slanger, P. C. Cosby, D. L. Huestis, A. Saiz-Lopez, B. J. Murray, D. A. O'Sullivan, J. M. C. Plane, C. Allende Prieto, F. J. Martin-Torres, and P. Jenniskens, “Variability of the mesospheric nightglow sodium D2/D1 ratio,” J. Geophys. Res. 110, D23302 (2005).
[CrossRef]

Sakurai, J. J.

J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994), Revised Ed., pp. 176-181.

Schreier, F.

F. Schreier, “The Voigt and complex error function: A comparison of computational methods,” J. Quant. Spectrosc. Radiat. Transf. 48, 743-762 (1992).
[CrossRef]

Searcy, P.

Shay, T. M.

She, C. Y.

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

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[CrossRef]

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Z. Hu, X. Sun, Y. Liu, L. Fu, and X. Zeng, “Temperature properties of Na dispersive Faraday optical filter at D1 and D2 line,” Opt. Commun. 156, 289-293 (1998).
[CrossRef]

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S. Falke, E. Tiemann, and C. Lisdat, “Transition frequencies of the D lines of K39, K40, and K41 measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
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[CrossRef]

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[CrossRef]

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C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

Yeh, P.

Yin, B.

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C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

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[CrossRef]

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Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristics of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).

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Y. P. Gangrsky, D. V. Karaivanov, K. P. Marinova, B. N. Markov, L. M. Melnikova, G. V. Mishinsky, S. G. Zemlyanoi, and V. I. Zhemenik, “Hyperfine splitting and isotope shift in the atomic D2 line of Na22,23 and the quadrupole moment of Na22,” Eur. Phys. J. A 3, 313-318 (1998).
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[CrossRef]

Appl. Opt. (1)

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[CrossRef]

Eur. Phys. J. A (1)

Y. P. Gangrsky, D. V. Karaivanov, K. P. Marinova, B. N. Markov, L. M. Melnikova, G. V. Mishinsky, S. G. Zemlyanoi, and V. I. Zhemenik, “Hyperfine splitting and isotope shift in the atomic D2 line of Na22,23 and the quadrupole moment of Na22,” Eur. Phys. J. A 3, 313-318 (1998).
[CrossRef]

Geophys. Res. Lett. (1)

C. Y. She, T. Li, R. L. Collins, T. Yuan, B. P. Williams, T. D. Kawahara, J. D. Vance, P. Acott, D. A. Krueger, H.-L. Liu, and M. E. Hagan, “Tidal perturbations and variability in the mesopause region over Fort Collins, CO (41 N, 105 W): Continuous multi-day temperature and wind lidar observations,” Geophys. Res. Lett. 31, L24111 (2004).
[CrossRef]

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Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristics of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).

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[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (1)

S. Falke, E. Tiemann, and C. Lisdat, “Transition frequencies of the D lines of K39, K40, and K41 measured with a femtosecond laser frequency comb,” Phys. Rev. A 74, 032503 (2006).
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[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of an atomic vapor Faraday filter, consisting of a vapor cell in an axial magnetic field between crossed polarizers.

Fig. 2
Fig. 2

Energy level diagram for Na showing the 3 P 3 2 2 excited states. (a) The single fine structure state, with a degeneracy of 16. (b) The hyperfine splitting case with no external magnetic field. The F eigenstate notation and degeneracies (in parentheses) are indicated to the right, and the scale in GHz is to the left. (c) The exact solution for the Zeeman structure for an external magnetic field of 2000G. The states are broken up into four closely spaced groups due to the different values for μ I and μ B . Each Zeeman state has a degeneracy of 1. The m I m J eigenstate notations are listed to the right, and the scale in GHz is to the left.

Fig. 3
Fig. 3

(a) D 2 and (b) D 1 transmission as a fraction of input linear polarization (solid) and Faraday rotation in units of π (dashed) vs. frequency (GHz) for a Na vapor Faraday filter optimized for D 2 . (c) and (d) are the same for a D 1 optimized filter. Filter parameters are listed in Table 3. The letters in (a) refer to the three cases described in the text.

Fig. 4
Fig. 4

Same as Fig. 3, except for K. Filter parameters are listed in Table 3.

Fig. 5
Fig. 5

χ and χ curves for (a) Na D 2 and (b) D 1 lines split by the Zeeman effect due to the 1850 Gauss external magnetic field. Solid gray curve is χ for σ , gray dashed curve is χ for σ , black solid curve is χ for σ + , and black dashed curve is χ for σ + .

Fig. 6
Fig. 6

Same as Fig. 5, only for K.

Tables (5)

Tables Icon

Table 1 Atomic Properties a

Tables Icon

Table 2 Linestrength a , Transition Vacuum Wavelength, and Linewidth

Tables Icon

Table 3 Filter Parameters used to Generate Figs. 2, 3, 4, 5, and ν 0 + and ν 0 Transition Frequencies

Tables Icon

Table 4 D 1 Allowed Transition F 1 Value and Polarization

Tables Icon

Table 5 D 2 Allowed Transitions F 1 and F 2 Values and Polarization

Equations (45)

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k = ω c ( 1 + χ ± + i χ ± ) ω c ( 1 + χ ± 2 + i χ 2 ) ,
x ̂ = + ̂ ̂ 2 , and y ̂ = i + ̂ + ̂ 2 .
E ( L , ω ) = E 0 2 [ exp ( i { ω c ( 1 + 0.5 χ + + 0.5 i χ + ) L } ) + ̂ exp ( i { ω c ( 1 + 0.5 χ + 0.5 i χ ) L } ) ̂ ] ,
F ( ν ) = E y ̂ 2 E 0 2 = 1 4 [ exp ( ω c χ + L ) + exp ( ω c χ L ) 2 exp ( ω c χ + + χ 2 L ) cos ( ω c χ + χ 2 L ) ] .
θ F = ω c χ + χ 4 L = π 2 λ ( χ + χ ) L = π λ ( Δ n ) L ,
d ρ α β ( t ) d t = 1 i { [ H 0 , ρ ( t ) ] α β + [ γ H I ( t ) , ρ ( t ) ] α β } + ρ α β t random = 1 i { ω α β ρ α β + [ γ H I ( t ) , ρ ( t ) ] α β } Γ α β ρ α β ( t ) ,
d ρ α β ( 1 ) ( t ) d t = 1 i { ω α β ρ α β ( 1 ) ( t ) + [ H I ( t ) , ρ ( 0 ) ] α β } Γ α β ρ α β ( 1 ) ( t ) .
ρ α β ( 1 ) ( t ) = 1 2 [ ρ α β ( 1 ) ( ω ) e i ω t + ρ α β ( 1 ) * ( ω ) e i ω t ] ,
ρ α β ( 1 ) ( ω ) = 1 k = x , y e ( r α β k ρ β β ( 0 ) ρ α α ( 0 ) r α β k ) E k ω ω α β + i Γ α β .
P ( t ) = N e r = N e Tr [ ρ ( 1 ) ( t ) r ] = 1 2 [ P ( ω ) e i ω t + P * ( ω ) e + i ω t ] .
P j ( ω ) = N e 2 α , β , k ( ρ β β ( 0 ) ρ α α ( 0 ) ) r β α j r α β k E k ( ω ) ω ω α β + i Γ α β .
P ± ( ω ) ε 0 χ ± ( 1 ) ( ω ) E ± ( ω ) χ ± ( 1 ) ( ω ) = N e 2 ε 0 α β ( ρ β β ( 0 ) ( r ± ) β α 2 ρ α α ( 0 ) ( r ± ) α β 2 ) ω ω α β ± + i Γ α β ± .
χ ± ( 1 ) ( ω ) = N e 2 ε 0 α g ρ g ( 0 ) r α g ± 2 ( 1 ω ω α g ± + i Γ α g ± 1 ω + ω α g ± + i Γ α g ± ) ,
χ ± ( 1 ) ( ω ) = N e 2 ε 0 α g ρ g ( 0 ) ( r ± ) α g 2 ( 2 ω α g ± 2 ω α g ± ( ω α g ± ω i Γ α g ± ) ) .
χ ± ( 1 ) ( ν ) = N 2 π ε 0 1 π u α g ρ α g ( 0 ) ( p ± ) α g 2 exp ( v 2 u 2 ) d v [ ν α g ± ( v λ ) ν i ( Γ α g ± 2 π ) ] ,
χ ± ( ν ) = N 2 π ε 0 1 π u α g ρ α g ( 0 ) ( p ± ) α g 2 ( ν α g ± ( v λ ) ν ) exp ( v 2 u 2 ) d v [ ( ν α g ± ( v λ ) ν ) 2 + ( Γ α g ± 2 π ) 2 ] ,
χ ± ( ν ) = N 2 π ε 0 1 π u α g ρ α g ( 0 ) ( p ± α g ) 2 ( Γ α g ± 2 π ) exp ( v 2 u 2 ) d v [ ( ν α g ± ( v λ ) ν ) 2 + ( Γ α g ± 2 π ) 2 ] .
Z = i = 1 N exp ( E i k B T ) ρ g ( 0 ) = N i N g = exp ( E i k B T ) Z ,
H = H 0 + H I
H I = H HFS + H Zeeman = A J ( I J ) + B J 2 I ( 2 I 1 ) J ( 2 J + 1 ) [ 3 ( I J ) 2 + 3 2 ( I J ) I ( I + 1 ) J ( J + 1 ) ] + g J μ B B 0 J g I μ N B 0 I ,
g J = 3 J ( J + 1 ) + S ( S + 1 ) L ( L + 1 ) 2 J ( J + 1 ) .
log 10 ( P Na ) = 71.899 9217.2 ( T res ) 1 + 40693000 ( T res ) 3 + 0.0061264 ( T res ) 9.6625 ln ( T res ) ,
log 10 ( P K ) = 69.53 10486 ( T res ) 1 + 1.8658 × 10 8 ( T res ) 3 + 0.0027286 ( T res ) 8.5732 ln ( T res ) ,
[ 3 2 1 2 1 3 2 1 2 2 1 2 1 2 3 1 2 1 2 4 1 2 1 2 5 1 2 1 2 6 3 2 1 2 7 3 2 1 2 8 ] ,
H ± 0 = g J μ B B 0 J z g I μ I B 0 I z + A J I z J z + B J 2 I ( I 1 ) J ( 2 J 1 ) [ 3 ( I z J z I z J z + 1 4 ( I + J I J + + I J + I + J ) ) + 3 2 I z J z I ( I + 1 ) J ( J + 1 ) ] ,
H ± 1 = A J 2 ( I + J + I J + ) + B J 2 I ( I 1 ) J ( 2 J 1 ) 3 2 [ I z J z ( I + J + I J + ) + ( I + J + I J + ) I z J z + 1 2 ( I + J + I J + ) ] ,
H ± 2 = B J 2 I ( I 1 ) J ( 2 J 1 ) 3 4 ( I + J I + J + I J + I J + ) .
H HFS = ( H 1 , 1 0 H 2 , 2 H 2 , 3 H 3 , 2 H 3 , 3 H 4 , 4 H 4 , 5 H 5 , 4 H 5 , 5 H 6 , 6 H 6 , 7 H 7 , 6 H 7 , 7 0 H 8.8 ) .
H 1 , 1 = 3 4 A J + 1 2 g J μ B B 0 3 2 g I μ n B 0 ,
H 6 , 6 = 1 4 A J 1 2 g J μ B B 0 + 1 2 g I μ n B 0 ,
H 2 , 2 = 3 4 A J 1 2 g J μ B B 0 3 2 g I μ n B 0 ,
H 7 , 7 = 3 4 A J + 1 2 g J μ B B 0 + 3 2 g I μ n B 0 ,
H 3 , 3 = 1 4 A J + 1 2 g J μ B B 0 1 2 g I μ n B 0 ,
H 8 , 8 = 3 4 A J 1 2 g J μ B B 0 + 3 2 g I μ n B 0 ,
H 4 , 4 = 1 4 A J 1 2 g J μ B B 0 1 2 g I μ n B 0 ,
H 2 , 3 = H 3 , 2 = H 6 , 7 = H 7 , 6 = 3 2 A J ,
H 5 , 5 = 1 4 A J + 1 2 g J μ B B 0 + 1 2 g I μ n B 0 ,
H 4 , 5 = H 5 , 4 = A J .
m I m J p ± m I m J 2 = a 2 b 2 ( 2 J + 1 ) ( 2 J + 1 ) ( J 1 J m J ± 1 m J ) 2 [ l J S J l 1 ] 2 S 0 = F 1 F 2 ( 2 J + 1 ) ( 2 J + 1 ) [ l J S J l 1 ] 2 S 0 ,
( J 1 J m J ± 1 m J )
[ l J S J l 1 ]
F 1 = a 2 b 2 ,
F 2 = ( J 1 J m J ± 1 m J ) 2 .
m I m J p ± m I m J 2 = F 1 F 2 2 3 S 0 ,
m I m J p ± m I m J 2 = F 1 F 2 4 3 S 0 ,

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