Abstract

It is shown theoretically and experimentally that a Fizeau wedge wavemeter typically used to measure laser wavelength can also be used to measure the linewidth of a pulsed or cw laser. Linewidths as small as a few hundred megahertz can be measured by choosing the thickness of the wedge properly.

© 1988 Optical Society of America

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References

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  1. C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer 25, 151 (1981).
    [CrossRef]
  2. J. H. Zhang, B. R. Hity, H. A. Schuessler, Appl. Opt. 21, 3065 (1982).
    [CrossRef] [PubMed]
  3. A. Fischer, R. Kullmer, W. Demtröder, Opt. Commun. 39, 277 (1981).
    [CrossRef]
  4. M. B. Morris, T. J. McIlrath, J. J. Snyder, Appl. Opt. 23, 3862 (1984).
    [CrossRef] [PubMed]
  5. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), pp. 407, 480.
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 335.
  7. J. J. Snyder, Proc. Soc. Photo-Opt. Instrum. Eng. 288, 258 (1981).
  8. J. J. Snyder, Appl. Opt. 19, 1223 (1980).
    [CrossRef] [PubMed]
  9. P. Flamant, Appl. Opt. 17, 955 (1978).
    [CrossRef] [PubMed]
  10. K. H. Fricke, U. Von Zahn, J. Atmos. Terr. Phys. 47, 499 (1985).
    [CrossRef]
  11. C. Reiser, Proc. Soc. Photo-Opt. Instrum. Eng. 912, 214 (1988).
  12. C. Reiser, R. B. Lopert, “Laser wavemeter with solid Fizeau wedge interferometer,” Appl. Opt. (to be published).

1988 (1)

C. Reiser, Proc. Soc. Photo-Opt. Instrum. Eng. 912, 214 (1988).

1985 (1)

K. H. Fricke, U. Von Zahn, J. Atmos. Terr. Phys. 47, 499 (1985).
[CrossRef]

1984 (1)

1982 (1)

1981 (3)

C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer 25, 151 (1981).
[CrossRef]

A. Fischer, R. Kullmer, W. Demtröder, Opt. Commun. 39, 277 (1981).
[CrossRef]

J. J. Snyder, Proc. Soc. Photo-Opt. Instrum. Eng. 288, 258 (1981).

1980 (1)

1978 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 335.

Cahen, C.

C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer 25, 151 (1981).
[CrossRef]

Demtröder, W.

A. Fischer, R. Kullmer, W. Demtröder, Opt. Commun. 39, 277 (1981).
[CrossRef]

Fischer, A.

A. Fischer, R. Kullmer, W. Demtröder, Opt. Commun. 39, 277 (1981).
[CrossRef]

Flamant, P.

Fricke, K. H.

K. H. Fricke, U. Von Zahn, J. Atmos. Terr. Phys. 47, 499 (1985).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), pp. 407, 480.

Hity, B. R.

Kullmer, R.

A. Fischer, R. Kullmer, W. Demtröder, Opt. Commun. 39, 277 (1981).
[CrossRef]

Lopert, R. B.

C. Reiser, R. B. Lopert, “Laser wavemeter with solid Fizeau wedge interferometer,” Appl. Opt. (to be published).

McIlrath, T. J.

Megie, G.

C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer 25, 151 (1981).
[CrossRef]

Morris, M. B.

Reiser, C.

C. Reiser, Proc. Soc. Photo-Opt. Instrum. Eng. 912, 214 (1988).

C. Reiser, R. B. Lopert, “Laser wavemeter with solid Fizeau wedge interferometer,” Appl. Opt. (to be published).

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), pp. 407, 480.

Schuessler, H. A.

Snyder, J. J.

Von Zahn, U.

K. H. Fricke, U. Von Zahn, J. Atmos. Terr. Phys. 47, 499 (1985).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 335.

Zhang, J. H.

Appl. Opt. (4)

J. Atmos. Terr. Phys. (1)

K. H. Fricke, U. Von Zahn, J. Atmos. Terr. Phys. 47, 499 (1985).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer 25, 151 (1981).
[CrossRef]

Opt. Commun. (1)

A. Fischer, R. Kullmer, W. Demtröder, Opt. Commun. 39, 277 (1981).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

C. Reiser, Proc. Soc. Photo-Opt. Instrum. Eng. 912, 214 (1988).

J. J. Snyder, Proc. Soc. Photo-Opt. Instrum. Eng. 288, 258 (1981).

Other (3)

C. Reiser, R. B. Lopert, “Laser wavemeter with solid Fizeau wedge interferometer,” Appl. Opt. (to be published).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), pp. 407, 480.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 335.

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Figures (4)

Fig. 1
Fig. 1

Fringes captured by a photodiode array from a Kr-ion laser beam with 150-MHz linewidth (solid line) have excellent contrast, whereas a 2.5-GHz Kr-ion laser beam (dashed line) produces diminished contrast. The solid fused silica wedge was 25.4 mm thick with a 2′ angle.

Fig. 2
Fig. 2

Calculated results of linewidth determinations as measured by a Fizeau wavemeter having a 3′ wedge that is (a) 10 mm thick and (b) 1 mm thick. Circles, Gaussian distribution and Gaussian analysis; triangles, Lorentzian distribution and Lorentzian analysis. Solid lines with slope of unity have been added for reference.

Fig. 3
Fig. 3

Spectral distribution of the 2.5-GHz beam measured by a 10-GHz scanning Fabry–Perot étalon (solid curve) and a best-fitted Gaussian (dashed curve).

Fig. 4
Fig. 4

Experimental results using a Kr-ion laser and a solid Fizeau wedge (FW) wavemeter plotted as linewidth measured by a Fizeau wedge versus the linewidth measured with a 10-GHz scanning Fabry–Perot étalon (SFP). Gaussian distribution was used [relation (6)]. Wedge thicknesses: circles, 9.9 mm; triangles and squares, 12.7 mm; diamonds, 25.4 mm. A solid line with slope of unity has been added for reference.

Equations (10)

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I ( x ) = I 0 { 1 - cos [ 2 π ( L + 2 x tan α ) ν 0 ] } / 2 ,
I ( k , ν 0 ) = I 0 2 b π 0 exp [ - ( ν - ν 0 ) 2 b 2 ] [ 1 - cos ( 2 π k ν ) ] d ν ,
I ( k , ν 0 ) = I 0 2 a π 0 1 1 + ( ν - ν 0 ) 2 / a 2 [ 1 - cos ( 2 π k ν ) ] d ν .
I ( k , ν 0 ) = I 0 { 1 - exp [ - ( π k b ) 2 ] cos ( 2 π k ν 0 ) } / 2 ,
I ( k , ν 0 ) = I 0 [ 1 - exp ( - 2 π k a ) cos ( 2 π k ν 0 ) ] / 2.
FWHM Gaussian = 1.665 π k ( - ln C ) 1 / 2 1.665 π k ( 2 I v I p ) 1 / 2             for small I v ,
FWHM Lorentzian = - ln C π k 2 I v π k I p             for small I v ,
C = I p - I v I p + I v .
I v = I δ - ( I p - I δ ) [ 1 - cos ( 2 π δ / Λ ) ] / 2 ,
Lorentzian FWHM min 0.03 10 2 π k .

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