Abstract

The shapes of the reflected and transmitted fringes of an interferential wedge are studied theoretically and experimentally. It is shown that, for high reflectivities of wedge coatings, interesting interference patterns are obtained, such as bright narrow fringes in reflection. The fringe profiles are computed for different wedge geometries, coating reflectivities, and incidence angles in the cases of equal and unequal coating reflectivities. The localization of the fringes is studied in relation to the focusing effect that is due to the wedge. The interferential wedge properties of frequency selectivity and tunability are discussed briefly with regard to applications to spectroscopy and laser technology.

© 1981 Optical Society of America

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  1. H. Fizeau, "Recherches sur les modifications que subit la vitesse de la lumière dans le verre sous l'influence de la chaleur," Ann. Chim. Phys. 66, 429–482 (1862).
  2. M. Hamy, "Sur les franges de reflexion des lames argentées," J. Phys. 5, 789–809 (1906).
  3. J. Holden, "Multiple-beam interferometry: intensity distribution in the reflected system," Proc. Phys. Soc. London 62, 405–417 (1949).
  4. J. Brossel, "Multiple-beam localized fringes. Part I. Intensity distribution and localization," Proc. Phys. Soc. London 59, 224–234 (1947).
  5. K. Kinosita, "Numerical evaluation of the intensity curve of a multiple-beam Fizeau fringe," J. Phys. Soc. Jpn. 8, 215–225 (1953).
  6. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).
  7. A. R. Cownie, "Formation of transmissionlike reflection fringes," J. Opt. Soc. Am. 53, 425–428 (1963).
  8. D. Sen and P. N. Puntambekar, "An inverting Fizeau interferometer," Opt. Acta 12, 137–149 (1965).
  9. N. Barakat and F. G. Abouzakhm, "Phase modulation of the first beam in reflected multiple beam interference fringes," Opt. Acta 12, 321–332 (1965).
  10. H. Dupoisot, "Mesure de l’épaisseur des couches minces par microscopie interferentielle à ondes multiples," Thesis, University of Paris (1965); Ann. Phys. 3, 369–390 (1968).
  11. J. Pastor and P. H. Lee, "Transmission fringes in reflection multiple-beam interferometry," J. Opt. Soc. Am. 58, 149–153 (1968).
  12. N. Aebischer, "Etude d’interférences en ondes multiples par diagramme complexe pour visualiser les franges en réflexion," Thesis, University of Besançon (1969); Nouv. Rev. Opt. Appl. 1, 233–248 (1970).
  13. F. Spiegelhalter, R. Bunnagel, and J. Moser, "Intensitätsverteilung von Fizeau-Streigen in reflektierten Licht bei Vielstrahl-interferenz," Optik 31, 535–552 (1970).
  14. J. J. Snyder, "Fizeau wavelength meter," in Laser Spectroscopy III (Springer-Verlag, Berlin, 1977), pp. 419–420; "Compact static wavelength meter for both pulsed and cw lasers," Sov. J. Quantum Electron. 8, 959–960 (1979); C. Cahen, J. P. Jegou, J. Pelon, P. Gildwarg, and J. Porteneuve, "Wavelength stabilization and control of the emission of pulsed dye lasers by means of a multibeam Fizeau interferometer," Rev. Phys. Appl. 16, 353–358 (1981).
  15. V. I. Tomin, B. A. Bushuk, and A. N. Rubinov, "Study of the gain curve and the triplet-triplet absorption in a rhodamine 6G solution laser," Opt. Spectrosc. 32, 527–529 (1972); A. N. Rubinov and V. I. Nikolaev, "Stabilization and control of monopulse radiation spectrum of ruby laser," Dokl. Akad. Nauk B. SSR 14, 20–24 (1970).
  16. Spectra-Physics, Laser Instruments Division, 1250 W. Middlefield Road, Mountain View, Calif. 94042.
  17. Y. H. Meyer and M. N. Nenchev, "Tuning of dye lasers with a reflecting Fizeau wedge," Opt. Commun. 35, 115–119 (1980); "Single-mode dye laser with a double-action Fizeau interferometer," Opt. Lett. 6, 119–121 (1981).
  18. D. Malacara, Optical Shop Testing (Wiley, New York, 1978) Sec. 6.3.

1980 (1)

Y. H. Meyer and M. N. Nenchev, "Tuning of dye lasers with a reflecting Fizeau wedge," Opt. Commun. 35, 115–119 (1980); "Single-mode dye laser with a double-action Fizeau interferometer," Opt. Lett. 6, 119–121 (1981).

1972 (1)

V. I. Tomin, B. A. Bushuk, and A. N. Rubinov, "Study of the gain curve and the triplet-triplet absorption in a rhodamine 6G solution laser," Opt. Spectrosc. 32, 527–529 (1972); A. N. Rubinov and V. I. Nikolaev, "Stabilization and control of monopulse radiation spectrum of ruby laser," Dokl. Akad. Nauk B. SSR 14, 20–24 (1970).

1970 (1)

F. Spiegelhalter, R. Bunnagel, and J. Moser, "Intensitätsverteilung von Fizeau-Streigen in reflektierten Licht bei Vielstrahl-interferenz," Optik 31, 535–552 (1970).

1968 (1)

1965 (2)

D. Sen and P. N. Puntambekar, "An inverting Fizeau interferometer," Opt. Acta 12, 137–149 (1965).

N. Barakat and F. G. Abouzakhm, "Phase modulation of the first beam in reflected multiple beam interference fringes," Opt. Acta 12, 321–332 (1965).

1963 (1)

1953 (1)

K. Kinosita, "Numerical evaluation of the intensity curve of a multiple-beam Fizeau fringe," J. Phys. Soc. Jpn. 8, 215–225 (1953).

1949 (1)

J. Holden, "Multiple-beam interferometry: intensity distribution in the reflected system," Proc. Phys. Soc. London 62, 405–417 (1949).

1947 (1)

J. Brossel, "Multiple-beam localized fringes. Part I. Intensity distribution and localization," Proc. Phys. Soc. London 59, 224–234 (1947).

1906 (1)

M. Hamy, "Sur les franges de reflexion des lames argentées," J. Phys. 5, 789–809 (1906).

1862 (1)

H. Fizeau, "Recherches sur les modifications que subit la vitesse de la lumière dans le verre sous l'influence de la chaleur," Ann. Chim. Phys. 66, 429–482 (1862).

Abouzakhm, F. G.

N. Barakat and F. G. Abouzakhm, "Phase modulation of the first beam in reflected multiple beam interference fringes," Opt. Acta 12, 321–332 (1965).

Aebischer, N.

N. Aebischer, "Etude d’interférences en ondes multiples par diagramme complexe pour visualiser les franges en réflexion," Thesis, University of Besançon (1969); Nouv. Rev. Opt. Appl. 1, 233–248 (1970).

Barakat, N.

N. Barakat and F. G. Abouzakhm, "Phase modulation of the first beam in reflected multiple beam interference fringes," Opt. Acta 12, 321–332 (1965).

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Brossel, J.

J. Brossel, "Multiple-beam localized fringes. Part I. Intensity distribution and localization," Proc. Phys. Soc. London 59, 224–234 (1947).

Bunnagel, R.

F. Spiegelhalter, R. Bunnagel, and J. Moser, "Intensitätsverteilung von Fizeau-Streigen in reflektierten Licht bei Vielstrahl-interferenz," Optik 31, 535–552 (1970).

Bushuk, B. A.

V. I. Tomin, B. A. Bushuk, and A. N. Rubinov, "Study of the gain curve and the triplet-triplet absorption in a rhodamine 6G solution laser," Opt. Spectrosc. 32, 527–529 (1972); A. N. Rubinov and V. I. Nikolaev, "Stabilization and control of monopulse radiation spectrum of ruby laser," Dokl. Akad. Nauk B. SSR 14, 20–24 (1970).

Cownie, A. R.

Dupoisot, H.

H. Dupoisot, "Mesure de l’épaisseur des couches minces par microscopie interferentielle à ondes multiples," Thesis, University of Paris (1965); Ann. Phys. 3, 369–390 (1968).

Fizeau, H.

H. Fizeau, "Recherches sur les modifications que subit la vitesse de la lumière dans le verre sous l'influence de la chaleur," Ann. Chim. Phys. 66, 429–482 (1862).

Hamy, M.

M. Hamy, "Sur les franges de reflexion des lames argentées," J. Phys. 5, 789–809 (1906).

Holden, J.

J. Holden, "Multiple-beam interferometry: intensity distribution in the reflected system," Proc. Phys. Soc. London 62, 405–417 (1949).

Kinosita, K.

K. Kinosita, "Numerical evaluation of the intensity curve of a multiple-beam Fizeau fringe," J. Phys. Soc. Jpn. 8, 215–225 (1953).

Lee, P. H.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978) Sec. 6.3.

Meyer, Y. H.

Y. H. Meyer and M. N. Nenchev, "Tuning of dye lasers with a reflecting Fizeau wedge," Opt. Commun. 35, 115–119 (1980); "Single-mode dye laser with a double-action Fizeau interferometer," Opt. Lett. 6, 119–121 (1981).

Moser, J.

F. Spiegelhalter, R. Bunnagel, and J. Moser, "Intensitätsverteilung von Fizeau-Streigen in reflektierten Licht bei Vielstrahl-interferenz," Optik 31, 535–552 (1970).

Nenchev, M. N.

Y. H. Meyer and M. N. Nenchev, "Tuning of dye lasers with a reflecting Fizeau wedge," Opt. Commun. 35, 115–119 (1980); "Single-mode dye laser with a double-action Fizeau interferometer," Opt. Lett. 6, 119–121 (1981).

Pastor, J.

Puntambekar, P. N.

D. Sen and P. N. Puntambekar, "An inverting Fizeau interferometer," Opt. Acta 12, 137–149 (1965).

Rubinov, A. N.

V. I. Tomin, B. A. Bushuk, and A. N. Rubinov, "Study of the gain curve and the triplet-triplet absorption in a rhodamine 6G solution laser," Opt. Spectrosc. 32, 527–529 (1972); A. N. Rubinov and V. I. Nikolaev, "Stabilization and control of monopulse radiation spectrum of ruby laser," Dokl. Akad. Nauk B. SSR 14, 20–24 (1970).

Sen, D.

D. Sen and P. N. Puntambekar, "An inverting Fizeau interferometer," Opt. Acta 12, 137–149 (1965).

Snyder, J. J.

J. J. Snyder, "Fizeau wavelength meter," in Laser Spectroscopy III (Springer-Verlag, Berlin, 1977), pp. 419–420; "Compact static wavelength meter for both pulsed and cw lasers," Sov. J. Quantum Electron. 8, 959–960 (1979); C. Cahen, J. P. Jegou, J. Pelon, P. Gildwarg, and J. Porteneuve, "Wavelength stabilization and control of the emission of pulsed dye lasers by means of a multibeam Fizeau interferometer," Rev. Phys. Appl. 16, 353–358 (1981).

Spiegelhalter, F.

F. Spiegelhalter, R. Bunnagel, and J. Moser, "Intensitätsverteilung von Fizeau-Streigen in reflektierten Licht bei Vielstrahl-interferenz," Optik 31, 535–552 (1970).

Tomin, V. I.

V. I. Tomin, B. A. Bushuk, and A. N. Rubinov, "Study of the gain curve and the triplet-triplet absorption in a rhodamine 6G solution laser," Opt. Spectrosc. 32, 527–529 (1972); A. N. Rubinov and V. I. Nikolaev, "Stabilization and control of monopulse radiation spectrum of ruby laser," Dokl. Akad. Nauk B. SSR 14, 20–24 (1970).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Ann. Chim. Phys. (1)

H. Fizeau, "Recherches sur les modifications que subit la vitesse de la lumière dans le verre sous l'influence de la chaleur," Ann. Chim. Phys. 66, 429–482 (1862).

J. Opt. Soc. Am. (2)

J. Phys. (1)

M. Hamy, "Sur les franges de reflexion des lames argentées," J. Phys. 5, 789–809 (1906).

J. Phys. Soc. Jpn. (1)

K. Kinosita, "Numerical evaluation of the intensity curve of a multiple-beam Fizeau fringe," J. Phys. Soc. Jpn. 8, 215–225 (1953).

Opt. Acta (2)

D. Sen and P. N. Puntambekar, "An inverting Fizeau interferometer," Opt. Acta 12, 137–149 (1965).

N. Barakat and F. G. Abouzakhm, "Phase modulation of the first beam in reflected multiple beam interference fringes," Opt. Acta 12, 321–332 (1965).

Opt. Commun. (1)

Y. H. Meyer and M. N. Nenchev, "Tuning of dye lasers with a reflecting Fizeau wedge," Opt. Commun. 35, 115–119 (1980); "Single-mode dye laser with a double-action Fizeau interferometer," Opt. Lett. 6, 119–121 (1981).

Opt. Spectrosc. (1)

V. I. Tomin, B. A. Bushuk, and A. N. Rubinov, "Study of the gain curve and the triplet-triplet absorption in a rhodamine 6G solution laser," Opt. Spectrosc. 32, 527–529 (1972); A. N. Rubinov and V. I. Nikolaev, "Stabilization and control of monopulse radiation spectrum of ruby laser," Dokl. Akad. Nauk B. SSR 14, 20–24 (1970).

Optik (1)

F. Spiegelhalter, R. Bunnagel, and J. Moser, "Intensitätsverteilung von Fizeau-Streigen in reflektierten Licht bei Vielstrahl-interferenz," Optik 31, 535–552 (1970).

Proc. Phys. Soc. London (2)

J. Holden, "Multiple-beam interferometry: intensity distribution in the reflected system," Proc. Phys. Soc. London 62, 405–417 (1949).

J. Brossel, "Multiple-beam localized fringes. Part I. Intensity distribution and localization," Proc. Phys. Soc. London 59, 224–234 (1947).

Other (6)

H. Dupoisot, "Mesure de l’épaisseur des couches minces par microscopie interferentielle à ondes multiples," Thesis, University of Paris (1965); Ann. Phys. 3, 369–390 (1968).

J. J. Snyder, "Fizeau wavelength meter," in Laser Spectroscopy III (Springer-Verlag, Berlin, 1977), pp. 419–420; "Compact static wavelength meter for both pulsed and cw lasers," Sov. J. Quantum Electron. 8, 959–960 (1979); C. Cahen, J. P. Jegou, J. Pelon, P. Gildwarg, and J. Porteneuve, "Wavelength stabilization and control of the emission of pulsed dye lasers by means of a multibeam Fizeau interferometer," Rev. Phys. Appl. 16, 353–358 (1981).

Spectra-Physics, Laser Instruments Division, 1250 W. Middlefield Road, Mountain View, Calif. 94042.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

N. Aebischer, "Etude d’interférences en ondes multiples par diagramme complexe pour visualiser les franges en réflexion," Thesis, University of Besançon (1969); Nouv. Rev. Opt. Appl. 1, 233–248 (1970).

D. Malacara, Optical Shop Testing (Wiley, New York, 1978) Sec. 6.3.

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