Abstract

We report the polarization dependence of the spectrum in modulation transfer spectroscopy for the transitions from the lower ground state (Fg = 1) of 87Rb atoms. We measured the spectra for the two polarization configurations where the carrier and probe beams were linearly polarized in parallel or perpendicular directions. The measured spectra were in excellent agreement with calculated results. The spectra were strongly dependent on the polarization configurations. In particular, the signal for parallel polarization configuration was generated via an incoherent process mediated by spontaneous emission.

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  1. W. Demtröder, Laser Spectroscopy (Springer, 1998).
  2. C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett.36(20), 1170–1173 (1976).
    [CrossRef]
  3. K. L. Corwin, Z. Lu, C. F. Hand, R. J. Epstein, and C. E. Wieman, “Frequency-stabilized diode laser with the Zeeman shift in an atomic vapor,” Appl. Opt.37(15), 3295–3298 (1998).
    [CrossRef]
  4. M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B41(8), 085401 (2008).
    [CrossRef]
  5. G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett.5(1), 15–17 (1980).
    [CrossRef] [PubMed]
  6. J. H. Shirley, “Modulation transfer processes in optical heterodyne saturation spectroscopy,” Opt. Lett.7(11), 537–539 (1982).
    [CrossRef] [PubMed]
  7. M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans. Instrum. Meas.44(2), 155–158 (1995).
    [CrossRef]
  8. E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
    [CrossRef]
  9. A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A25(5), 2606–2621 (1982).
    [CrossRef]
  10. E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun.120, 91–97 (1995).
    [CrossRef]
  11. F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas.50(2), 490–492 (2001).
    [CrossRef]
  12. J. Zhang, D. Wei, C. Xie, and K. Peng, “Characteristics of absorption and dispersion for rubidium D2 lines with the modulation transfer spectrum,” Opt. Express11(11), 1338–1344 (2003).
    [CrossRef] [PubMed]
  13. D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol.19(10), 105601 (2008).
    [CrossRef]
  14. L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B45(6), 065002 (2012).
    [CrossRef]
  15. V. Negnevitsky and L. D. Turner, “Wideband laser lockng to an atomic reference with modulation transfer spectroscopy,” Opt. Express21(3), 3103–3113 (2013).
    [CrossRef] [PubMed]
  16. L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn.80(7), 074301 (2011).
    [CrossRef]
  17. H. R. Noh, S. E. Park, L. Z. Li, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express19(23), 23444–23452 (2011).
    [CrossRef] [PubMed]
  18. J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1line,” J. Phys. B29(12), 2629–2643 (1996).
    [CrossRef]
  19. P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B41(15), 155004 (2008).
    [CrossRef]

2013 (1)

2012 (1)

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B45(6), 065002 (2012).
[CrossRef]

2011 (2)

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn.80(7), 074301 (2011).
[CrossRef]

H. R. Noh, S. E. Park, L. Z. Li, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express19(23), 23444–23452 (2011).
[CrossRef] [PubMed]

2008 (3)

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol.19(10), 105601 (2008).
[CrossRef]

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B41(8), 085401 (2008).
[CrossRef]

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B41(15), 155004 (2008).
[CrossRef]

2007 (1)

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

2003 (1)

2001 (1)

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas.50(2), 490–492 (2001).
[CrossRef]

1998 (1)

1996 (1)

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1line,” J. Phys. B29(12), 2629–2643 (1996).
[CrossRef]

1995 (2)

E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun.120, 91–97 (1995).
[CrossRef]

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans. Instrum. Meas.44(2), 155–158 (1995).
[CrossRef]

1982 (2)

J. H. Shirley, “Modulation transfer processes in optical heterodyne saturation spectroscopy,” Opt. Lett.7(11), 537–539 (1982).
[CrossRef] [PubMed]

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A25(5), 2606–2621 (1982).
[CrossRef]

1980 (1)

1976 (1)

C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett.36(20), 1170–1173 (1976).
[CrossRef]

Adams, C. S.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B41(15), 155004 (2008).
[CrossRef]

Bava, E.

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas.50(2), 490–492 (2001).
[CrossRef]

Bertinetto, F.

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas.50(2), 490–492 (2001).
[CrossRef]

Bjorklund, G. C.

Brewer, R. G.

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A25(5), 2606–2621 (1982).
[CrossRef]

Cho, C. H.

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn.80(7), 074301 (2011).
[CrossRef]

H. R. Noh, S. E. Park, L. Z. Li, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express19(23), 23444–23452 (2011).
[CrossRef] [PubMed]

Cho, H.

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

Cordiale, P.

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas.50(2), 490–492 (2001).
[CrossRef]

Cornish, S. L.

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B41(8), 085401 (2008).
[CrossRef]

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol.19(10), 105601 (2008).
[CrossRef]

Corwin, K. L.

Demtröder, W.

W. Demtröder, Laser Spectroscopy (Springer, 1998).

DeVoe, R. G.

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A25(5), 2606–2621 (1982).
[CrossRef]

Eickhoff, M. L.

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans. Instrum. Meas.44(2), 155–158 (1995).
[CrossRef]

Epstein, R. J.

Galzerano, G.

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas.50(2), 490–492 (2001).
[CrossRef]

Ge, C.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B41(15), 155004 (2008).
[CrossRef]

Goldwin, J.

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B45(6), 065002 (2012).
[CrossRef]

Hall, J. L.

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans. Instrum. Meas.44(2), 155–158 (1995).
[CrossRef]

Hand, C. F.

Hänsch, T. W.

C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett.36(20), 1170–1173 (1976).
[CrossRef]

Harris, M. L.

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B41(8), 085401 (2008).
[CrossRef]

Huennekens, J.

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1line,” J. Phys. B29(12), 2629–2643 (1996).
[CrossRef]

Hughes, I. G.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B41(15), 155004 (2008).
[CrossRef]

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B41(8), 085401 (2008).
[CrossRef]

Jaatinen, E.

E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun.120, 91–97 (1995).
[CrossRef]

Kim, E. B.

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

King, S. A.

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol.19(10), 105601 (2008).
[CrossRef]

Kwon, T. Y.

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

Lee, H. S.

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

Li, L. Z.

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn.80(7), 074301 (2011).
[CrossRef]

H. R. Noh, S. E. Park, L. Z. Li, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express19(23), 23444–23452 (2011).
[CrossRef] [PubMed]

Lu, Z.

McCarron, D. J.

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol.19(10), 105601 (2008).
[CrossRef]

Mudarikwa, L.

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B45(6), 065002 (2012).
[CrossRef]

Namiotka, R. K.

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1line,” J. Phys. B29(12), 2629–2643 (1996).
[CrossRef]

Negnevitsky, V.

Noh, H. R.

H. R. Noh, S. E. Park, L. Z. Li, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express19(23), 23444–23452 (2011).
[CrossRef] [PubMed]

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn.80(7), 074301 (2011).
[CrossRef]

Pahwa, K.

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B45(6), 065002 (2012).
[CrossRef]

Park, C. Y.

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

Park, J. D.

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn.80(7), 074301 (2011).
[CrossRef]

H. R. Noh, S. E. Park, L. Z. Li, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express19(23), 23444–23452 (2011).
[CrossRef] [PubMed]

Park, S. E.

H. R. Noh, S. E. Park, L. Z. Li, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for 87Rb atoms: theory and experiment,” Opt. Express19(23), 23444–23452 (2011).
[CrossRef] [PubMed]

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn.80(7), 074301 (2011).
[CrossRef]

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

Park, Y. H.

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

Peng, K.

Sagle, J.

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1line,” J. Phys. B29(12), 2629–2643 (1996).
[CrossRef]

Schenzle, A.

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A25(5), 2606–2621 (1982).
[CrossRef]

Shirley, J. H.

Siddons, P.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B41(15), 155004 (2008).
[CrossRef]

Tripathi, A.

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B41(8), 085401 (2008).
[CrossRef]

Turner, L. D.

Wei, D.

Wieman, C.

C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett.36(20), 1170–1173 (1976).
[CrossRef]

Wieman, C. E.

Xie, C.

Yee, D.-S.

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

Zhang, J.

Appl. Opt. (1)

IEEE Trans. Instrum. Meas. (3)

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans. Instrum. Meas.44(2), 155–158 (1995).
[CrossRef]

E. B. Kim, S. E. Park, C. Y. Park, Y. H. Park, D.-S. Yee, T. Y. Kwon, H. S. Lee, and H. Cho, “Absolute frequency measurement of F= 4 → F′= 5 transition line of cesium using amplified optical frequency comb,” IEEE Trans. Instrum. Meas.56(2), 448–452 (2007).
[CrossRef]

F. Bertinetto, P. Cordiale, G. Galzerano, and E. Bava, “Frequency stabilization of DBR diode laser against Cs absorption lines at 852 nm using the modulation transfer method,” IEEE Trans. Instrum. Meas.50(2), 490–492 (2001).
[CrossRef]

J. Phys. B (4)

L. Mudarikwa, K. Pahwa, and J. Goldwin, “Sub-Doppler modulation spectroscopy of potassium for laser stabilization,” J. Phys. B45(6), 065002 (2012).
[CrossRef]

M. L. Harris, S. L. Cornish, A. Tripathi, and I. G. Hughes, “Optimization of sub-Doppler DAVLL on the rubidium D2 line,” J. Phys. B41(8), 085401 (2008).
[CrossRef]

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1line,” J. Phys. B29(12), 2629–2643 (1996).
[CrossRef]

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B41(15), 155004 (2008).
[CrossRef]

J. Phys. Soc. Jpn. (1)

L. Z. Li, S. E. Park, H. R. Noh, J. D. Park, and C. H. Cho, “Modulation transfer spectroscopy for a two-level atomic system with a non-cycling transition,” J. Phys. Soc. Jpn.80(7), 074301 (2011).
[CrossRef]

Meas. Sci. Technol. (1)

D. J. McCarron, S. A. King, and S. L. Cornish, “Modulation transfer spectroscopy in atomic rubidium,” Meas. Sci. Technol.19(10), 105601 (2008).
[CrossRef]

Opt. Commun. (1)

E. Jaatinen, “Theoretical determination of maximum signal levels obtainable with modulation transfer spectroscopy,” Opt. Commun.120, 91–97 (1995).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (1)

A. Schenzle, R. G. DeVoe, and R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A25(5), 2606–2621 (1982).
[CrossRef]

Phys. Rev. Lett. (1)

C. Wieman and T. W. Hänsch, “Doppler-free laser polarization spectroscopy,” Phys. Rev. Lett.36(20), 1170–1173 (1976).
[CrossRef]

Other (1)

W. Demtröder, Laser Spectroscopy (Springer, 1998).

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Figures (6)

Fig. 1
Fig. 1

(a) Energy level diagram of 87Rb atoms. (b) Schematic diagram of the MTS. (c) Simple energy level diagrams for the parallel and perpendicular polarization configuration.

Fig. 2
Fig. 2

(a) Experimental and (b) calculated results for the parallel polarization configuration.

Fig. 3
Fig. 3

(a) Experimental and (b) calculated results for the perpendicular polarization configuration.

Fig. 4
Fig. 4

(a) Decomposition of the calculated MTS spectrum for the parallel polarization configuration. (b) Energy level diagrams responsible for the crossover signal CO10.

Fig. 5
Fig. 5

(a) Decomposition of the calculated MTS spectrum for the perpendicular polarization configuration. (b) Energy level diagrams responsible for the resonance signals S1 and S0. (c) Energy level diagrams for the crossover signal CO10 for both polarization configurations.

Fig. 6
Fig. 6

(a) An energy level diagram for simple four-level model. (b) Calculated in-phase MTS signals for various values of the branching ratios, b1 and b2.

Equations (5)

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

ε ^ p = b ε ^ + b 0 ε ^ 0 + b + ε ^ + ,
σ j j = p j j ( 1 ) + ( p j j ( 2 ) + i p j j ( 3 ) ) e i Ω t + ( p j j ( 2 ) i p j j ( 3 ) ) e i Ω t ,
I 0 = q = 1 1 b q i j C i j ( s i j ( 2 ) + s i j ( 1 ) ) , Q 0 = q = 1 1 b q i j C i j ( r i j ( 2 ) r i j ( 1 ) ) ,
I = 1 t av 0 t av d t d v e ( v / u ) 2 π u I 0 , Q = 1 t av 0 t av d t d v e ( v / u ) 2 π u Q 0 ,
I cos ϕ + Q sin ϕ ,

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