Abstract

Interferometric methods for array generation offer various advantages over diffractive methods. Use of polarizing elements in an interferometric array illuminator results in interesting properties in addition to improving the efficiency considerably from low levels. The array pattern appears as nonobservable fringes that can be observed only with a polarizer, and the interferometer is insensitive to one of the tilt components. A thorough analysis of such an interferometric array illuminator is presented in this paper. Several possible applications of such an interferometer in addition to use as an array illuminator are proposed.

© 1999 Optical Society of America

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References

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  1. N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
    [CrossRef]
  2. A. W. Lohmann, “Array illuminators and complexity theory,” Opt. Commun. 89, 167–172 (1992).
    [CrossRef]
  3. Shanti Battacharya, V. V. Rao, R. S. Sirohi, “Array illuminators: a review,” J. Opt. (India) 25, 203–221 (1996).
  4. P. Senthilkumaran, K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Array generation using double wedge plate interferometer,” J. Mod. Opt. 41, 481–489 (1994).
    [CrossRef]
  5. P. Senthilkumaran, R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105, 158–160 (1994).
    [CrossRef]
  6. Shanti Bhattacharya, P. Senthilkumaran, J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Holographic array illuminator using Michelson interferometers in tandem: fabrication and analysis,” J. Mod. Opt. 42, 2275–2283 (1995).
    [CrossRef]
  7. J. S. Darlin, P. Senthilkumaran, Shanti Bhattacharya, M. P. Kothiyal, R. S. Sirohi, “Fabrication of array generators using Michelson interferometers in tandem,” Opt. Commun. 123, 1–4 (1996).
    [CrossRef]
  8. P. Senthilkumaran, “An interferometric array generator with polarizing elements,” Opt. Lasers Eng. 28, 457–461 (1997).
    [CrossRef]
  9. J. L. Garcia-Marques, D. Malacara-Hernandez, D. Malacara-Boblado, “Interferometers without observable fringes,” Opt. Eng. 36, 2863–2867 (1997).
    [CrossRef]
  10. C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
    [CrossRef] [PubMed]
  11. J. K. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by the dipole force of resonance radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
    [CrossRef]
  12. V. I. Balykin, V. S. Letokhov, V. G. Minogin, Yu. V. Rozhdestvensky, A. I. Sidorov, “Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser radiation pressure,” J. Opt. Soc. Am. B 22, 1776–1983 (1985).
    [CrossRef]
  13. S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
    [CrossRef] [PubMed]
  14. V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
    [CrossRef]
  15. B. G. Turukhano, N. Turukhano, Yu. M. Lavrov, “Methods for producing two coordinate holographic diffraction gratings,” Opt. Laser Technol. 28, 251–254 (1996).
    [CrossRef]

1997

P. Senthilkumaran, “An interferometric array generator with polarizing elements,” Opt. Lasers Eng. 28, 457–461 (1997).
[CrossRef]

J. L. Garcia-Marques, D. Malacara-Hernandez, D. Malacara-Boblado, “Interferometers without observable fringes,” Opt. Eng. 36, 2863–2867 (1997).
[CrossRef]

V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
[CrossRef]

1996

B. G. Turukhano, N. Turukhano, Yu. M. Lavrov, “Methods for producing two coordinate holographic diffraction gratings,” Opt. Laser Technol. 28, 251–254 (1996).
[CrossRef]

J. S. Darlin, P. Senthilkumaran, Shanti Bhattacharya, M. P. Kothiyal, R. S. Sirohi, “Fabrication of array generators using Michelson interferometers in tandem,” Opt. Commun. 123, 1–4 (1996).
[CrossRef]

Shanti Battacharya, V. V. Rao, R. S. Sirohi, “Array illuminators: a review,” J. Opt. (India) 25, 203–221 (1996).

1995

Shanti Bhattacharya, P. Senthilkumaran, J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Holographic array illuminator using Michelson interferometers in tandem: fabrication and analysis,” J. Mod. Opt. 42, 2275–2283 (1995).
[CrossRef]

1994

P. Senthilkumaran, K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Array generation using double wedge plate interferometer,” J. Mod. Opt. 41, 481–489 (1994).
[CrossRef]

P. Senthilkumaran, R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105, 158–160 (1994).
[CrossRef]

1992

A. W. Lohmann, “Array illuminators and complexity theory,” Opt. Commun. 89, 167–172 (1992).
[CrossRef]

1989

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

1987

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

1986

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

1985

V. I. Balykin, V. S. Letokhov, V. G. Minogin, Yu. V. Rozhdestvensky, A. I. Sidorov, “Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser radiation pressure,” J. Opt. Soc. Am. B 22, 1776–1983 (1985).
[CrossRef]

1978

J. K. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by the dipole force of resonance radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

Ashkin, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

J. K. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by the dipole force of resonance radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

Aspect, A.

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

Balykin, V. I.

V. I. Balykin, V. S. Letokhov, V. G. Minogin, Yu. V. Rozhdestvensky, A. I. Sidorov, “Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser radiation pressure,” J. Opt. Soc. Am. B 22, 1776–1983 (1985).
[CrossRef]

Battacharya, Shanti

Shanti Battacharya, V. V. Rao, R. S. Sirohi, “Array illuminators: a review,” J. Opt. (India) 25, 203–221 (1996).

Bhattacharya, Shanti

J. S. Darlin, P. Senthilkumaran, Shanti Bhattacharya, M. P. Kothiyal, R. S. Sirohi, “Fabrication of array generators using Michelson interferometers in tandem,” Opt. Commun. 123, 1–4 (1996).
[CrossRef]

Shanti Bhattacharya, P. Senthilkumaran, J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Holographic array illuminator using Michelson interferometers in tandem: fabrication and analysis,” J. Mod. Opt. 42, 2275–2283 (1995).
[CrossRef]

Bjorkholm, J. E.

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

Bjorkholm, J. K.

J. K. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by the dipole force of resonance radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

Brezger, B.

V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
[CrossRef]

Cable, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

Chu, S.

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

Cohen-Tannoudji, C.

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

Dalibard, J.

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

Darlin, J. S.

J. S. Darlin, P. Senthilkumaran, Shanti Bhattacharya, M. P. Kothiyal, R. S. Sirohi, “Fabrication of array generators using Michelson interferometers in tandem,” Opt. Commun. 123, 1–4 (1996).
[CrossRef]

Shanti Bhattacharya, P. Senthilkumaran, J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Holographic array illuminator using Michelson interferometers in tandem: fabrication and analysis,” J. Mod. Opt. 42, 2275–2283 (1995).
[CrossRef]

Drewsen, M.

V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
[CrossRef]

Drodofsky, U.

V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
[CrossRef]

Freeman, R. R.

J. K. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by the dipole force of resonance radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

Garcia-Marques, J. L.

J. L. Garcia-Marques, D. Malacara-Hernandez, D. Malacara-Boblado, “Interferometers without observable fringes,” Opt. Eng. 36, 2863–2867 (1997).
[CrossRef]

Kothiyal, M. P.

J. S. Darlin, P. Senthilkumaran, Shanti Bhattacharya, M. P. Kothiyal, R. S. Sirohi, “Fabrication of array generators using Michelson interferometers in tandem,” Opt. Commun. 123, 1–4 (1996).
[CrossRef]

Shanti Bhattacharya, P. Senthilkumaran, J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Holographic array illuminator using Michelson interferometers in tandem: fabrication and analysis,” J. Mod. Opt. 42, 2275–2283 (1995).
[CrossRef]

P. Senthilkumaran, K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Array generation using double wedge plate interferometer,” J. Mod. Opt. 41, 481–489 (1994).
[CrossRef]

Lavrov, Yu. M.

B. G. Turukhano, N. Turukhano, Yu. M. Lavrov, “Methods for producing two coordinate holographic diffraction gratings,” Opt. Laser Technol. 28, 251–254 (1996).
[CrossRef]

Letokhov, V. S.

V. I. Balykin, V. S. Letokhov, V. G. Minogin, Yu. V. Rozhdestvensky, A. I. Sidorov, “Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser radiation pressure,” J. Opt. Soc. Am. B 22, 1776–1983 (1985).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, “Array illuminators and complexity theory,” Opt. Commun. 89, 167–172 (1992).
[CrossRef]

Malacara-Boblado, D.

J. L. Garcia-Marques, D. Malacara-Hernandez, D. Malacara-Boblado, “Interferometers without observable fringes,” Opt. Eng. 36, 2863–2867 (1997).
[CrossRef]

Malacara-Hernandez, D.

J. L. Garcia-Marques, D. Malacara-Hernandez, D. Malacara-Boblado, “Interferometers without observable fringes,” Opt. Eng. 36, 2863–2867 (1997).
[CrossRef]

Metcalf, H.

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

Minogin, V. G.

V. I. Balykin, V. S. Letokhov, V. G. Minogin, Yu. V. Rozhdestvensky, A. I. Sidorov, “Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser radiation pressure,” J. Opt. Soc. Am. B 22, 1776–1983 (1985).
[CrossRef]

Mlynek, J.

V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
[CrossRef]

Pearson, D. B.

J. K. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by the dipole force of resonance radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

Pfau, T.

V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
[CrossRef]

Rao, V. V.

Shanti Battacharya, V. V. Rao, R. S. Sirohi, “Array illuminators: a review,” J. Opt. (India) 25, 203–221 (1996).

Rozhdestvensky, Yu. V.

V. I. Balykin, V. S. Letokhov, V. G. Minogin, Yu. V. Rozhdestvensky, A. I. Sidorov, “Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser radiation pressure,” J. Opt. Soc. Am. B 22, 1776–1983 (1985).
[CrossRef]

Salomon, C.

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

Sandoghdar, V.

V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
[CrossRef]

Schulze, TH.

V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
[CrossRef]

Senthilkumaran, P.

P. Senthilkumaran, “An interferometric array generator with polarizing elements,” Opt. Lasers Eng. 28, 457–461 (1997).
[CrossRef]

J. S. Darlin, P. Senthilkumaran, Shanti Bhattacharya, M. P. Kothiyal, R. S. Sirohi, “Fabrication of array generators using Michelson interferometers in tandem,” Opt. Commun. 123, 1–4 (1996).
[CrossRef]

Shanti Bhattacharya, P. Senthilkumaran, J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Holographic array illuminator using Michelson interferometers in tandem: fabrication and analysis,” J. Mod. Opt. 42, 2275–2283 (1995).
[CrossRef]

P. Senthilkumaran, K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Array generation using double wedge plate interferometer,” J. Mod. Opt. 41, 481–489 (1994).
[CrossRef]

P. Senthilkumaran, R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105, 158–160 (1994).
[CrossRef]

Sidorov, A. I.

V. I. Balykin, V. S. Letokhov, V. G. Minogin, Yu. V. Rozhdestvensky, A. I. Sidorov, “Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser radiation pressure,” J. Opt. Soc. Am. B 22, 1776–1983 (1985).
[CrossRef]

Sirohi, R. S.

J. S. Darlin, P. Senthilkumaran, Shanti Bhattacharya, M. P. Kothiyal, R. S. Sirohi, “Fabrication of array generators using Michelson interferometers in tandem,” Opt. Commun. 123, 1–4 (1996).
[CrossRef]

Shanti Battacharya, V. V. Rao, R. S. Sirohi, “Array illuminators: a review,” J. Opt. (India) 25, 203–221 (1996).

Shanti Bhattacharya, P. Senthilkumaran, J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Holographic array illuminator using Michelson interferometers in tandem: fabrication and analysis,” J. Mod. Opt. 42, 2275–2283 (1995).
[CrossRef]

P. Senthilkumaran, K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Array generation using double wedge plate interferometer,” J. Mod. Opt. 41, 481–489 (1994).
[CrossRef]

P. Senthilkumaran, R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105, 158–160 (1994).
[CrossRef]

Sriram, K. V.

P. Senthilkumaran, K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Array generation using double wedge plate interferometer,” J. Mod. Opt. 41, 481–489 (1994).
[CrossRef]

Streibl, N.

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

Turukhano, B. G.

B. G. Turukhano, N. Turukhano, Yu. M. Lavrov, “Methods for producing two coordinate holographic diffraction gratings,” Opt. Laser Technol. 28, 251–254 (1996).
[CrossRef]

Turukhano, N.

B. G. Turukhano, N. Turukhano, Yu. M. Lavrov, “Methods for producing two coordinate holographic diffraction gratings,” Opt. Laser Technol. 28, 251–254 (1996).
[CrossRef]

J. Mod. Opt.

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

P. Senthilkumaran, K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Array generation using double wedge plate interferometer,” J. Mod. Opt. 41, 481–489 (1994).
[CrossRef]

Shanti Bhattacharya, P. Senthilkumaran, J. S. Darlin, M. P. Kothiyal, R. S. Sirohi, “Holographic array illuminator using Michelson interferometers in tandem: fabrication and analysis,” J. Mod. Opt. 42, 2275–2283 (1995).
[CrossRef]

V. Sandoghdar, U. Drodofsky, TH. Schulze, B. Brezger, M. Drewsen, T. Pfau, J. Mlynek, “Lithography using nano-lens arrays made of light,” J. Mod. Opt. 44, 1883–1898 (1997).
[CrossRef]

J. Opt. (India)

Shanti Battacharya, V. V. Rao, R. S. Sirohi, “Array illuminators: a review,” J. Opt. (India) 25, 203–221 (1996).

J. Opt. Soc. Am. B

V. I. Balykin, V. S. Letokhov, V. G. Minogin, Yu. V. Rozhdestvensky, A. I. Sidorov, “Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser radiation pressure,” J. Opt. Soc. Am. B 22, 1776–1983 (1985).
[CrossRef]

Opt. Commun.

J. S. Darlin, P. Senthilkumaran, Shanti Bhattacharya, M. P. Kothiyal, R. S. Sirohi, “Fabrication of array generators using Michelson interferometers in tandem,” Opt. Commun. 123, 1–4 (1996).
[CrossRef]

P. Senthilkumaran, R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105, 158–160 (1994).
[CrossRef]

A. W. Lohmann, “Array illuminators and complexity theory,” Opt. Commun. 89, 167–172 (1992).
[CrossRef]

Opt. Eng.

J. L. Garcia-Marques, D. Malacara-Hernandez, D. Malacara-Boblado, “Interferometers without observable fringes,” Opt. Eng. 36, 2863–2867 (1997).
[CrossRef]

Opt. Laser Technol.

B. G. Turukhano, N. Turukhano, Yu. M. Lavrov, “Methods for producing two coordinate holographic diffraction gratings,” Opt. Laser Technol. 28, 251–254 (1996).
[CrossRef]

Opt. Lasers Eng.

P. Senthilkumaran, “An interferometric array generator with polarizing elements,” Opt. Lasers Eng. 28, 457–461 (1997).
[CrossRef]

Phys. Rev. Lett.

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

J. K. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, “Observation of focusing of neutral atoms by the dipole force of resonance radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[CrossRef]

S. Chu, J. E. Bjorkholm, A. Ashkin, A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Michelson interferometers in tandem setup with polarizing elements for array generation. M1, M2, M3, and M4 are mirrors. Q1, Q2, Q3, Q4, and Q5 are quarter-wave plates. P is a polarizer. PBS1 and PBS2 are polarizing beam splitters.

Fig. 2
Fig. 2

Array pattern when the polarizer P in Fig. (1) is aligned at 45°.

Fig. 3
Fig. 3

Polarization plane of the four beams and of the four particular orientations of the polarizer.

Fig. 4
Fig. 4

Polarization state of the vertical fringes when the polarizer P in Fig. (1) is aligned horizontally, i.e., along OC in Fig. (3).

Fig. 5
Fig. 5

Polarization state of the vertical fringes when the polarizer P in Fig. (1) is aligned vertically, i.e., along OA in Fig. (3).

Fig. 6
Fig. 6

Integration of the interferometric array generator given in Fig. (1). Each element can be identified by comparison with Fig. (1).

Fig. 7
Fig. 7

Array pattern in a different state of elliptical polarization can be produced if a retarder is inserted after a polarizer that is aligned at 45°.

Tables (1)

Tables Icon

Table 1 Tracing of the Polarization States of the Interfering Beams

Equations (4)

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

I12x, y=a4+a4exp-j2πμx2=a281+cos2πμx,
I34x, y=a4exp-j2πνy+a4exp-j2π×μx+νy2=a281+cos2πμx.
Ix, y=a2/81+cos2πμx1+cos2πνy.
Ix, y=a2/81+cos2πμx×1+sin2ϕ0cos2πνy.

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