Abstract

We discuss the theory and error analysis for an ultrasensitive refractive index detector based on the two-frequency Zeeman effect laser. Experimental measurements on gases agree fairly well with predictions. With a 5-cm pathlength, the typical interferometry stability is Δn = 8 × 10−9/h. Resolution is Δn = 1 × 10−9.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. J. Bornhop, T. G. Nolan, N. J. Dovichi, “Subnanoliter Laser-Based Refractive Index Detector for 0.25-mm I.D. Microbore Liquid Chromatography,” J. Chromatog. 384, 181–187 (1987).
    [CrossRef]
  2. R. G. Johnston, “Rapid, Differential Microthermometry Using Zeeman Interferometry,” Appl. Phys. Lett. 54, 289–291 (1989).
    [CrossRef]
  3. R. G. Johnston, “Zeeman Interferometry,” in Laser Interferometry, Proc. Soc. Photo-Opt. Instrum. Eng. 1162, 344–350 (1989).
  4. R. G. Johnston, S. B. Singham, G. C. Salzman, “Phase Differential Scattering from Microspheres,” Appl. Opt. 25, 3566–3572 (1986).
    [CrossRef] [PubMed]
  5. Optra, Inc., Peabody, MA.
  6. W. A. Shurcliff, Polarized Light (Harvard U.P., Cambridge, 1962).
  7. J. C. Cheng, L. A. Nafie, S. D. Allen, A. I. Braunstein, “Photoelastic Modulator for the 0.55–13-μm Range,” Appl. Opt. 15, 1960–1965 (1976).
    [CrossRef] [PubMed]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 87–90.
  9. L’Air Liquide Division Scientifique, Gas Encyclopedia (Elsevier, New York, 1976), pp. 109 and 1046.
  10. E. W. Washburn, Ed., International Critical Tables of Numerical Data, Physics, Chemistry, and Technology (McGraw-Hill, New York, 1930), pp. 3–7.
  11. H. Horvath, “The Refractive Index of Freon 12,” Appl. Opt. 6, 1140–1141 (1967).
    [CrossRef] [PubMed]

1989 (2)

R. G. Johnston, “Rapid, Differential Microthermometry Using Zeeman Interferometry,” Appl. Phys. Lett. 54, 289–291 (1989).
[CrossRef]

R. G. Johnston, “Zeeman Interferometry,” in Laser Interferometry, Proc. Soc. Photo-Opt. Instrum. Eng. 1162, 344–350 (1989).

1987 (1)

D. J. Bornhop, T. G. Nolan, N. J. Dovichi, “Subnanoliter Laser-Based Refractive Index Detector for 0.25-mm I.D. Microbore Liquid Chromatography,” J. Chromatog. 384, 181–187 (1987).
[CrossRef]

1986 (1)

1976 (1)

1967 (1)

Allen, S. D.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 87–90.

Bornhop, D. J.

D. J. Bornhop, T. G. Nolan, N. J. Dovichi, “Subnanoliter Laser-Based Refractive Index Detector for 0.25-mm I.D. Microbore Liquid Chromatography,” J. Chromatog. 384, 181–187 (1987).
[CrossRef]

Braunstein, A. I.

Cheng, J. C.

Dovichi, N. J.

D. J. Bornhop, T. G. Nolan, N. J. Dovichi, “Subnanoliter Laser-Based Refractive Index Detector for 0.25-mm I.D. Microbore Liquid Chromatography,” J. Chromatog. 384, 181–187 (1987).
[CrossRef]

Horvath, H.

Johnston, R. G.

R. G. Johnston, “Rapid, Differential Microthermometry Using Zeeman Interferometry,” Appl. Phys. Lett. 54, 289–291 (1989).
[CrossRef]

R. G. Johnston, “Zeeman Interferometry,” in Laser Interferometry, Proc. Soc. Photo-Opt. Instrum. Eng. 1162, 344–350 (1989).

R. G. Johnston, S. B. Singham, G. C. Salzman, “Phase Differential Scattering from Microspheres,” Appl. Opt. 25, 3566–3572 (1986).
[CrossRef] [PubMed]

Nafie, L. A.

Nolan, T. G.

D. J. Bornhop, T. G. Nolan, N. J. Dovichi, “Subnanoliter Laser-Based Refractive Index Detector for 0.25-mm I.D. Microbore Liquid Chromatography,” J. Chromatog. 384, 181–187 (1987).
[CrossRef]

Salzman, G. C.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U.P., Cambridge, 1962).

Singham, S. B.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 87–90.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. G. Johnston, “Rapid, Differential Microthermometry Using Zeeman Interferometry,” Appl. Phys. Lett. 54, 289–291 (1989).
[CrossRef]

J. Chromatog. (1)

D. J. Bornhop, T. G. Nolan, N. J. Dovichi, “Subnanoliter Laser-Based Refractive Index Detector for 0.25-mm I.D. Microbore Liquid Chromatography,” J. Chromatog. 384, 181–187 (1987).
[CrossRef]

Laser Interferometry (1)

R. G. Johnston, “Zeeman Interferometry,” in Laser Interferometry, Proc. Soc. Photo-Opt. Instrum. Eng. 1162, 344–350 (1989).

Other (5)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 87–90.

L’Air Liquide Division Scientifique, Gas Encyclopedia (Elsevier, New York, 1976), pp. 109 and 1046.

E. W. Washburn, Ed., International Critical Tables of Numerical Data, Physics, Chemistry, and Technology (McGraw-Hill, New York, 1930), pp. 3–7.

Optra, Inc., Peabody, MA.

W. A. Shurcliff, Polarized Light (Harvard U.P., Cambridge, 1962).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Zeeman interferometer. ZEL = Zeeman effect laser. CBD1 = CBD2 = calcite beam displacers. CELL = tandem cell containing two separate chambers for the sample and reference. POL = analyzing polarizer with transmission axis at 45°. PD = photodiode. LOCKIN = lock-in amplifier used to measure the relative phase of the 250-kHz beat frequency signal (SIG) on the PD relative to the reference 250-kHz sine wave (REF) generated within the ZEL. The phase depends on the optical pathlength difference for the vertical (v) polarization compared to the horizontal (h) polarization.

Fig. 2
Fig. 2

Excellent stability is possible. The relative phase of the 250-kHz beat frequency is shown plotted as a function of time for 6 h. One phase reading was made every 30 s with a Δϕ phase resolution of 0.1°. Room air was flowing through both chambers at a rate of 300 mliter/min. The air first entered one chamber then immediately the other. As a result, variations in air pressure and temperature would not cause phase changes that could be misinterpreted as interferometer drift. Similar stability was possible with zero air flow.

Fig. 3
Fig. 3

Phase shift for N2 vs dry air. Dry air initially flowed into the sample chamber at 300 mliter/min. At 120 seconds, the flowing gas sample was switched to N2 at the same pressure and flow rate. The phase of the 250-kHz beat frequency changed due to the higher RI of N2 At 240 seconds, the sample was switched back to dry air and the phase returned to 0°. Two overlapping replicate runs are plotted, but cannot be distinguished on this scale. Two phase readings were made per second.

Fig. 4
Fig. 4

Detecting Δn = −7.7 × 10−8 for N2 vs N2 doped with 488-ppm neon. The doped sample passed through the interferometer between time = 120 and 240 s. Two replicate runs are plotted.

Fig. 5
Fig. 5

Detecting Δn = −4 × 10−9. Two different sources of N2 gas were used. A phase shift of |Δϕ| = 0.12° was found consistently when switching between these two particular N2 sources (at 120 and 240 s in the figure). |Δϕ| was zero when switching between other N2 gas samples.

Tables (2)

Tables Icon

Table I Calculated Values of Refractive Index (RI) for the Sample Gases Under the Experimental Conditions Appropriate for This Work: λ = 632.8 nm, T = 35.10°C, P = 0.773 atm

Tables Icon

Table II Comparison of Experimental and Theoretical Results for the Phase Shift for Various Pairs of Gases

Equations (15)

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

E cav = 2 2 { A exp [ i ( k - ω 1 t ) ] - i A exp [ i ( k - ω 1 t ) ] } + 2 2 { B exp [ i ( k - ω 2 t ) ] i B exp [ i ( k - ω 2 t ) ] } ,
QWP = 1 2 ( 1 i i 1 ) .
E out = { A exp [ i ( k - ω 1 t ) ] i B exp [ i ( k - ω 2 t ) ] } ,
CBD 1 = [ exp ( - i ψ 1 ) 0 0 exp ( - i ψ 2 ) ] .
CELL = [ exp ( - i ϕ 1 ) 0 0 exp ( - i ϕ 2 ) ] .
CBD 2 = [ exp ( - i ζ 1 ) 0 0 exp ( - i ζ 2 ) ] .
POL = 1 2 [ 1 1 1 1 ] .
I = A 2 + B 2 + 2 A B sin ( 2 π f t + ϕ + ψ + ζ ) ,
ϕ = 2 π ( L λ ) ( n 2 - n 1 ) .
Δ ϕ = 360 ° ( L λ ) Δ n ,
E out = { ( 1 - i δ 2 ) A exp [ i ( k - ω 1 t ) ] - δ 2 B exp [ i ( k - ω 2 t ) ] ( i + δ 2 ) B exp [ i ( k - ω 2 t ) ] + i δ 2 A exp [ i ( k - ω 1 t ) ] } .
CBD 1 = [ G exp ( - i ψ 1 ) g exp ( - i ψ 1 ) h exp ( - i ψ 2 ) H exp ( - i ψ 2 ) ] ,
I ( t ) = 2 ABGH sin ( 2 π f t + ϕ + ψ + ζ ) + 2 AB ( G g + H h ) sin ( 2 π f t ) + δ AB ( H 2 - G 2 ) cos ( 2 π f t ) .
I ( t ) = A sin ( 2 π f t + ϕ + ψ + ζ ) ,
A = R T P n 2 - 1 n 2 + 2 ,

Metrics