Abstract

Small amounts of ellipticity in the nominally linearly polarized light used in magnetic rotation spectroscopy play an important role in determining the character of the signals developed in these experiments. For example, ellipticity introduced by stress-induced birefringence can easily influence such signals more than does a nonzero polarizer extinction ratio. In addition, for nearly-crossed polarizers, an initial ellipticity allows one to probe magnetic circular dichroism instead of the more commonly investigated magnetic circular birefringence. A general expression for the magnetic rotation spectroscopy signal is derived and compared to experimental results. An expression for the detection sensitivity is developed by taking shot noise and rms laser power fluctuations to be the dominant noise sources.

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References

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  1. G. Litfin, C. R. Pollock, R. F. Curl, Jr. and F. K. Tittel, "Sensitivity enhancement of laser absorption spectroscopy by magnetic rotation effect," J. Chem. Phys. 72, 6602-6605 (1980).
    [CrossRef]
  2. M. C. McCarthy and R. W. Field, "The use of magnetic rotation spectroscopy to simplify and presort spectra: An application to NiH and CeF," J. Chem. Phys. 96, 7237-7243 (1992).
    [CrossRef]
  3. A. D. Buckingham and P. J. Stephens, "Magnetic Optical Activity," Ann. Rev. Phys. Chem. 17, 399-432 (1966).
    [CrossRef]
  4. J.D. Jackson, Classical Electrodynamics 3rd ed. (Wiley, New York 1999), pp. 333-335.
  5. M. O. Scully, "Enhancement of the index of refraction via quantum coherence," Phys. Rev. Lett. 67, 1855-1858 (1991).
    [CrossRef] [PubMed]
  6. R. J. Brecha, L. M. Pedrotti and D. Krause, "Magnetic rotation spectroscopy of molecular oxygen with a diode laser," J. Opt. Soc. B 14, 1921-1930 (1997).
    [CrossRef]
  7. M. Yamamoto and S. Murayama, "Analysis of resonant Voigt effect," J. Opt. Soc. Am. 69, 781-786 (1979).
    [CrossRef]
  8. Y. Takubo, K. Muroo, S. Miwa, K. Yamamoto, K. Suzuki and M. Yamamoto, "Resonant magneto-optic spectra of the b 1 _ + g _ X 3 _ _ g transition of oxygen molecules," J. Mol. Spect. 178, 31-39 (1996) and Y. Takubo, K. Muroo, S. Miwa, K. Yamamoto and M. Yamamoto, "Detection of the atmospheric band b 1 _ + g _ X 3 _ _ g by the laser-probed resonant Voigt-effect," J. Spectrosc. Soc. Japan 43, 150-155 (1994).
    [CrossRef]
  9. M. Yamamoto, Y. Takubo, and S. Murayama, "Detection limit of resonant magnetooptic spectroscopy," Jpn. J. Appl. Phys. 23, 783 (1984) and K. Muroo, S. Nakamura, H. Ishizaka, Y. Takubo and M. Yamamoto, "Limit of sensitivity in the detection of sodium atoms in a flame with the resonant Voigt effect," J. Opt. Soc. B 11, 5-8 (1995).
    [CrossRef]
  10. J. Pfeiffer, D. Kirsten, P. Kalkert and W. Urban, "Sensitive magnetic rotation spectroscopy of the OH free radical fundamental band with a colour centre laser," Appl. Phys. B 26, 173-177 (1981).
    [CrossRef]
  11. T. A. Blake, C. Chackerian, Jr. and J. R. Podolske, "Prognosis for a mid-infrared magnetic rotation spectrometer for the in situ detection of atmospheric free radicals," Appl. Opt. 35, 973-985 (1996).
    [CrossRef] [PubMed]
  12. M. C. McCarthy, J. C. Bloch and R. W. Field, "Frequency-modulation enhanced magnetic rotation spectroscopy: A sensitive and selective absorption scheme for paramagnetic molecules," J. Chem. Phys. 100, 6331-6346 (1994).
    [CrossRef]
  13. C. Wieman and T. W. Hansch, "Doppler-free polarization spectroscopy," Phys. Rev. Lett. 36, 1170-1173 (1976).
    [CrossRef]

Other

G. Litfin, C. R. Pollock, R. F. Curl, Jr. and F. K. Tittel, "Sensitivity enhancement of laser absorption spectroscopy by magnetic rotation effect," J. Chem. Phys. 72, 6602-6605 (1980).
[CrossRef]

M. C. McCarthy and R. W. Field, "The use of magnetic rotation spectroscopy to simplify and presort spectra: An application to NiH and CeF," J. Chem. Phys. 96, 7237-7243 (1992).
[CrossRef]

A. D. Buckingham and P. J. Stephens, "Magnetic Optical Activity," Ann. Rev. Phys. Chem. 17, 399-432 (1966).
[CrossRef]

J.D. Jackson, Classical Electrodynamics 3rd ed. (Wiley, New York 1999), pp. 333-335.

M. O. Scully, "Enhancement of the index of refraction via quantum coherence," Phys. Rev. Lett. 67, 1855-1858 (1991).
[CrossRef] [PubMed]

R. J. Brecha, L. M. Pedrotti and D. Krause, "Magnetic rotation spectroscopy of molecular oxygen with a diode laser," J. Opt. Soc. B 14, 1921-1930 (1997).
[CrossRef]

M. Yamamoto and S. Murayama, "Analysis of resonant Voigt effect," J. Opt. Soc. Am. 69, 781-786 (1979).
[CrossRef]

Y. Takubo, K. Muroo, S. Miwa, K. Yamamoto, K. Suzuki and M. Yamamoto, "Resonant magneto-optic spectra of the b 1 _ + g _ X 3 _ _ g transition of oxygen molecules," J. Mol. Spect. 178, 31-39 (1996) and Y. Takubo, K. Muroo, S. Miwa, K. Yamamoto and M. Yamamoto, "Detection of the atmospheric band b 1 _ + g _ X 3 _ _ g by the laser-probed resonant Voigt-effect," J. Spectrosc. Soc. Japan 43, 150-155 (1994).
[CrossRef]

M. Yamamoto, Y. Takubo, and S. Murayama, "Detection limit of resonant magnetooptic spectroscopy," Jpn. J. Appl. Phys. 23, 783 (1984) and K. Muroo, S. Nakamura, H. Ishizaka, Y. Takubo and M. Yamamoto, "Limit of sensitivity in the detection of sodium atoms in a flame with the resonant Voigt effect," J. Opt. Soc. B 11, 5-8 (1995).
[CrossRef]

J. Pfeiffer, D. Kirsten, P. Kalkert and W. Urban, "Sensitive magnetic rotation spectroscopy of the OH free radical fundamental band with a colour centre laser," Appl. Phys. B 26, 173-177 (1981).
[CrossRef]

T. A. Blake, C. Chackerian, Jr. and J. R. Podolske, "Prognosis for a mid-infrared magnetic rotation spectrometer for the in situ detection of atmospheric free radicals," Appl. Opt. 35, 973-985 (1996).
[CrossRef] [PubMed]

M. C. McCarthy, J. C. Bloch and R. W. Field, "Frequency-modulation enhanced magnetic rotation spectroscopy: A sensitive and selective absorption scheme for paramagnetic molecules," J. Chem. Phys. 100, 6331-6346 (1994).
[CrossRef]

C. Wieman and T. W. Hansch, "Doppler-free polarization spectroscopy," Phys. Rev. Lett. 36, 1170-1173 (1976).
[CrossRef]

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Figures (5)

Figure 1.
Figure 1.

Plot of magnetic rotation signal as a function of laser frequency (in cm-1) for δ=0.02. The various curves are for different values of the analyzer offset angle θ: green - 0.0°; blue - 0.5°; black - 2.0°; red - 3.0°

Figure 2.
Figure 2.

Plot of the Signal-to-noise ratio (SNR) as a function of analyzer offset angle, with only the MCB contribution being taken into account. The red curve represents the limit in which excess laser noise can be ignored, the green curve is the opposite limit in which shot noise is neglected, and the blue curve shows the result when both contributions are present

Figure 3.
Figure 3.

Plot of the Signal-to-noise ratio (SNR) as a function of the initial field ellipticity δ, considering only the MCD contribution to the signal. The red curve represents the limit in which excess laser noise can be ignored, the green curve is the opposite limit in which shot noise is neglected, and the blue curve shows the result for both contributions present

Figure 4.
Figure 4.

Schematic of the experiment. The quarter-wave plate (QWP) is used to set any initial ellipticity in the incident field. For the experiments results to be shown here, the “sample” is simply atmospheric oxygen.

Figure 5.
Figure 5.

Plot of magnetic rotation signal as a function of laser frequency (in GHz). The various curves are for different values of the analyzer offset angle θ: green - 0.0°; blue - 0.5°; black - 2.0°; red - 4.0°

Equations (22)

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E = E 0 2 e ̂ R ( 1 + δ ) exp ( i ( k z ω t ) ) + E 0 2 e ̂ L ( 1 δ ) exp ( i ( k z ω t ) )
P ( θ ) = ( β cos 2 θ + α sin 2 θ β cos θ sin θ + α sin θ cos θ β cos θ sin θ + α sin θ cos θ β sin 2 θ + α cos 2 θ )
E t = E 0 2 e i ω t ( 1 + δ ) e i k R l ( β cos 2 θ + α sin 2 θ + i ( α β ) sin θ cos θ ( α β ) cos θ sin θ + i ( β sin 2 θ + α cos 2 θ ) )
+ E 0 2 e i ω t ( 1 δ ) e i k L l ( β cos 2 θ + α sin 2 θ i ( α β ) sin θ cos θ ( α β ) cos θ sin θ i ( β sin 2 θ + α cos 2 θ ) )
I t I 0 = e 2 Ξ { 1 2 α 2 cosh 2 Φ 1 2 α 2 cos ( 2 θ 2 Θ ) } ( α 2 + β 2 ) δ e 2 Ξ sin 2 Φ
+ ( β 2 + δ 2 α 2 ) e 2 Ξ { 1 2 cosh 2 Φ + 1 2 cos ( 2 θ 2 Θ ) }
+ δ 2 β 2 e 2 Ξ { 1 2 cosh 2 Φ 1 2 cos ( 2 θ 2 Θ ) }
I t I 0 = 1 2 e 2 Ξ { cosh 2 Φ cos ( 2 θ 2 Θ ) 2 δ sinh 2 Φ }
+ 1 2 e 2 Ξ ( β 2 + δ 2 ) { cosh 2 Φ + cos ( 2 θ 2 Θ ) } .
I t , β I 0 = 1 2 e 2 Ξ [ cosh 2 Φ cos ( 2 θ 2 Θ ) + β 2 ( cosh 2 Φ + cos ( 2 θ 2 Θ ) ) ]
= 1 2 e 2 Ξ [ cosh 2 Φ cos ( 2 θ 2 Θ ) + ξ ]
1 2 [ ( 1 cos 2 θ ) 2 Θ sin 2 θ + ξ ]
I t = I 0 ( Φ 2 + Θ 2 + θ 2 + β 2 + δ 2 2 Θ θ 2 δ Φ )
N = N 0 [ sin 2 ( θ Θ ) + ( β 2 + δ 2 ) cos 2 ( θ Θ ) ] .
δ Θ = δ N ( N Θ ) = δ N shot noise 2 + δ N laser power 2 ( 1 β 2 ) ( 1 δ 2 ) sin ( 2 θ 2 Θ ) .
δNshot noise2
δNlaser power2
S N R Θ δ Θ = Θ sin ( 2 θ 2 Θ ) γ 2 ( N 2 N 0 2 ) + N N 0 2
S N R = 2 Θ ( θ Θ ) γ ( β 2 + δ 2 + ( θ Θ ) 2 ) .
S N R max = Θ γ δ 2 + β 2
S N R max = 2 Θ N 0
S N R γ = 0 , δ β = 2 Φ N 0

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