Abstract

The importance of flatness, parallelism, and equality in thickness of the elements and spacers of a resonant reflector is discussed. Using the matrix method, the reflectivity vs wavelength is computed for several types of resonators, the thicknesses of whose elements were subject to variations. For a two-element device, the exact mechanical thickness of the spacer is not important, but the equality of thickness of the dielectric elements is critical. For a three- or four-element device, the exact thickness of the center element is least important to reflectivity, but the reflectivity decreases if the total error in orders on either side of the center approaches ½. The results indicate that it is extremely difficult to produce a practical device of this complexity. Pressure and temperature scanning is discussed. Experimental results were obtained for two-element devices showing the importance in equality of thickness and the sensitivity to nonparallelism of the spacer. The relative electric field strengths within the reflector were mapped to investigate susceptibility to radiation damage. The amplitude of the field and the position in the resonator where damage would first occur depends upon the reflectivity at the wavelength used.

© 1971 Optical Society of America

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References

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  1. M. Hercher, Appl. Phys. Lett. 7, 39 (1965).
    [Crossref]
  2. G. Magyar, Rev. Sci. Instrum. 38, 517 (1967).
    [Crossref]
  3. A. L. Flamholz, MS Thesis, Cornell University, September1966.
  4. R. M. Schotland, Appl. Opt. 9, 1210 (1970).
    [Crossref]
  5. J. K. Watts, Appl. Opt. 7, 1621 (1968).
    [Crossref] [PubMed]
  6. Laser Optics, Danbury, Conn.
  7. J. Stone, Radiation and Optics (McGraw-Hill, New York, 1963).
  8. D. H. Rank, J. N. Shearer, J. Opt. Soc. Amer. 46, 463 (1956).
    [Crossref]
  9. Supplied by J. Larin, Laser Optics whom we thank for the use of these plates.
  10. T. A. Wiggins, T. T. Saito, L. M. Peterson, D. H. Rank, Appl. Opt. 9, 2177 (1970).
    [Crossref] [PubMed]
  11. B. Brixner, J. Opt. Soc. Amer. 57, 674 (1967).
    [Crossref]
  12. W. E. Williams, Applications of Interferometry (Dutton & Co., New York, 1928).
  13. Single etalons have been treated by V. N. Delpiano, A. F. Quesada in Appl. Opt. 4, 1386 (1965) and by D. G. Peterson, A. Yariv in Appl. Opt. 5, 985 (1966).
    [Crossref] [PubMed]

1970 (2)

1968 (1)

1967 (2)

G. Magyar, Rev. Sci. Instrum. 38, 517 (1967).
[Crossref]

B. Brixner, J. Opt. Soc. Amer. 57, 674 (1967).
[Crossref]

1965 (2)

1956 (1)

D. H. Rank, J. N. Shearer, J. Opt. Soc. Amer. 46, 463 (1956).
[Crossref]

Brixner, B.

B. Brixner, J. Opt. Soc. Amer. 57, 674 (1967).
[Crossref]

Delpiano, V. N.

Flamholz, A. L.

A. L. Flamholz, MS Thesis, Cornell University, September1966.

Hercher, M.

M. Hercher, Appl. Phys. Lett. 7, 39 (1965).
[Crossref]

Magyar, G.

G. Magyar, Rev. Sci. Instrum. 38, 517 (1967).
[Crossref]

Peterson, L. M.

Quesada, A. F.

Rank, D. H.

Saito, T. T.

Schotland, R. M.

Shearer, J. N.

D. H. Rank, J. N. Shearer, J. Opt. Soc. Amer. 46, 463 (1956).
[Crossref]

Stone, J.

J. Stone, Radiation and Optics (McGraw-Hill, New York, 1963).

Watts, J. K.

Wiggins, T. A.

Williams, W. E.

W. E. Williams, Applications of Interferometry (Dutton & Co., New York, 1928).

Appl. Opt. (4)

Appl. Phys. Lett. (1)

M. Hercher, Appl. Phys. Lett. 7, 39 (1965).
[Crossref]

J. Opt. Soc. Amer. (2)

D. H. Rank, J. N. Shearer, J. Opt. Soc. Amer. 46, 463 (1956).
[Crossref]

B. Brixner, J. Opt. Soc. Amer. 57, 674 (1967).
[Crossref]

Rev. Sci. Instrum. (1)

G. Magyar, Rev. Sci. Instrum. 38, 517 (1967).
[Crossref]

Other (5)

A. L. Flamholz, MS Thesis, Cornell University, September1966.

Supplied by J. Larin, Laser Optics whom we thank for the use of these plates.

Laser Optics, Danbury, Conn.

J. Stone, Radiation and Optics (McGraw-Hill, New York, 1963).

W. E. Williams, Applications of Interferometry (Dutton & Co., New York, 1928).

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Figures (6)

Fig. 1
Fig. 1

Reflectivity vs reciprocal wavelength for several two-element reflectors with air spacer of equal mechanical thickness. Trace A shows the calculated reflectivity when all elements and spacers are exactly tuned for the wavenumber marked T. Trace B is the calculated reflectivity when the air spacer has been increased by a thickness corresponding to a half order of interference. The trace has been translated by 1.17 cm−1 to emphasize the similarity with Trace A. Trace C shows the calculated reflectivity when the thickness of one of the dielectric elements is increased by an amount corresponding to one-half order.

Fig. 2
Fig. 2

The reciprocal wavelength at which the peak reflectivity occurs plotted as a function of the order of interference of the air space for a two-element device having equal optical thicknesses. The numbers on the lines indicate the magnitude of the reflectivity.

Fig. 3
Fig. 3

Experimental arrangement for measurement of the reflectivity of resonant reflectors.

Fig. 4
Fig. 4

Densitometer traces of plates taken in (A) fifth order at 7850 Å and (B) seventh order at 5600 Å using a two-element device with equal optical thicknesses. The dispersions are in the ratio of 7:5.

Fig. 5
Fig. 5

Densitometer traces of plates taken at 7850 Å of a two-element device of essentially equal mechanical thicknesses. Trace A is for a perfect alignment of the elements. Trace B shows the result for a misalignment of one half of an order over the aperture used. Trace C shows the Edser-Butler fringes from a single element for comparison.

Fig. 6
Fig. 6

Computed relative electric field amplitudes at various positions in a two-element device with index unity on both sides of the device. A shows the field amplitude for a perfect device at the tuned wavelength and B shows the amplitude for a wavelength at which the reflectivity is nearly zero. C shows the amplitude at a wavelength of maximum reflectivity for a device in which the thickness of the air spacer has been increased by an amount corresponding to a half order.

Equations (2)

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[ X ν Y ν ] = ν = ν + 1 k [ cos β ν i μ ν sin β ν i μ ν sin β ν cos β ν ] × [ τ k + 1 - μ τ k + 1 ] = [ A B C D ] [ τ k + 1 - μ τ k + 1 ]
E ( Z , ν ) = ( μ 0 τ 0 / μ ν ) e - i w t ( μ 0 A 0 + μ D 0 - μ 0 μ B 0 - C 0 ) × { ( μ ν A + μ D - μ ν μ B - C ) e i β ν + ( μ ν A - μ D - μ ν μ B + C ) e - i β }

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