Abstract

The theory of boundary diffraction waves (BDWs) is gaining importance due to its simplicity and physically appealing nature. The present work reports formation of circular fringes far away from the geometrically illuminated region by interference of two BDWs. One BDW is reconstructed from the hologram while the second is coming directly from the knife-edge. The uniqueness of the fringes is that their position can be controlled on the screen at will and fringes can be produced with bright as well as dark central fringe. These results could play an important role in understanding the nature of diffraction of light.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).
  2. A. Rubinowicz, “Thomas Young and the theory of diffraction,” Nature 180, 160–162 (1957).
    [CrossRef]
  3. K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz theory of the boundary diffraction wave—part I,” J. Opt. Soc. Am. 52, 615–622 (1962).
    [CrossRef]
  4. K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz theory of the boundary diffraction wave—part II,” J. Opt. Soc. Am. 52, 626–636 (1962).
    [CrossRef]
  5. A. I. Khizhnyak, S. P. Anokhov, R. A. Lymarenko, M. S. Soskin, and M. V. Vasnetsov, “Structure of an edge-dislocation wave originating in plane-wave diffraction by a half-plane,” J. Opt. Soc. Am. A 17, 2199–2207 (2000).
    [CrossRef]
  6. R. Kumar, “Structure of boundary diffraction wave revisited,” Appl. Phys. B 90, 379–382 (2008).
    [CrossRef]
  7. Y. Z. Umul, “The theory of the boundary diffraction wave,” in Advances in Imaging and Electron Physics (Academic, 2011), Vol. 165, Chap. 6.
  8. C. K. G. Piyadasa, “Detection of a cylindrical boundary diffraction wave emanating from a straight edge by light interaction,” Opt. Commun. 285, 4878–4883 (2012).
    [CrossRef]
  9. S. Kimura and C. Munakata, “Method for measuring the spot size of a laser beam using a boundary-diffraction wave,” Opt. Lett. 12, 552–554 (1987).
    [CrossRef]
  10. Raj Kumar, D. P. Chhachhia, and A. K. Aggarwal, “Folding mirror schlieren diffraction interferometer,” Appl. Opt. 45, 6708–6711 (2006).
    [CrossRef]
  11. P. Janpugdee, P. H. Pathak, and R. J. Burkholder, “On the boundary diffraction wave method for the analytical prediction of the radiation from large planar phased array antennas,” Radio Sci. 42, RS6S26 (2007).
    [CrossRef]
  12. P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
    [CrossRef]
  13. Raj Kumar, “Diffraction Lloyd mirror interferometer,” J. Opt. (India) 39, 90–101 (2010).
    [CrossRef]
  14. G. E. Sommargren, “Phase shifting diffraction interferometry for measuring extreme ultraviolet optics,” in Extreme Ultraviolet Lithography, G. D. Kubiak and D. R. Kania, eds., Vol. 4 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 108–112.
  15. J. E. Greivenkamp, “Interference,” in OSA Handbook of Optics (OSA, 1995), Vol. 1.
  16. N. L. Hecht, J. E. Minardi, D. Lewis, and R. L. Fusek, “Quantitative theory for predicting fringe pattern formation in holographic interferometry,” Appl. Opt. 12, 2665–2676 (1973).
    [CrossRef]
  17. A. Sommerfeld, Optics (Academic, 1954).
  18. Y. Z. Umul, “Fictitious diffracted waves in the diffraction theory of Kirchhoff,” J. Opt. Soc. Am. A 27, 109–115 (2010).
    [CrossRef]
  19. Raj Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Direct visualization of Young’s boundary diffraction wave,” Opt. Commun. 276, 54–57 (2007).
    [CrossRef]
  20. S. Ganci, “On the physical reality of edge sources,” Optik 123, 100–103 (2012).
    [CrossRef]

2012

C. K. G. Piyadasa, “Detection of a cylindrical boundary diffraction wave emanating from a straight edge by light interaction,” Opt. Commun. 285, 4878–4883 (2012).
[CrossRef]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

S. Ganci, “On the physical reality of edge sources,” Optik 123, 100–103 (2012).
[CrossRef]

2010

2008

R. Kumar, “Structure of boundary diffraction wave revisited,” Appl. Phys. B 90, 379–382 (2008).
[CrossRef]

2007

Raj Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Direct visualization of Young’s boundary diffraction wave,” Opt. Commun. 276, 54–57 (2007).
[CrossRef]

P. Janpugdee, P. H. Pathak, and R. J. Burkholder, “On the boundary diffraction wave method for the analytical prediction of the radiation from large planar phased array antennas,” Radio Sci. 42, RS6S26 (2007).
[CrossRef]

2006

2000

1987

1973

1962

1957

A. Rubinowicz, “Thomas Young and the theory of diffraction,” Nature 180, 160–162 (1957).
[CrossRef]

Aggarwal, A. K.

Raj Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Direct visualization of Young’s boundary diffraction wave,” Opt. Commun. 276, 54–57 (2007).
[CrossRef]

Raj Kumar, D. P. Chhachhia, and A. K. Aggarwal, “Folding mirror schlieren diffraction interferometer,” Appl. Opt. 45, 6708–6711 (2006).
[CrossRef]

Anokhov, S. P.

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Bowlan, P.

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

Burkholder, R. J.

P. Janpugdee, P. H. Pathak, and R. J. Burkholder, “On the boundary diffraction wave method for the analytical prediction of the radiation from large planar phased array antennas,” Radio Sci. 42, RS6S26 (2007).
[CrossRef]

Chhachhia, D. P.

Raj Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Direct visualization of Young’s boundary diffraction wave,” Opt. Commun. 276, 54–57 (2007).
[CrossRef]

Raj Kumar, D. P. Chhachhia, and A. K. Aggarwal, “Folding mirror schlieren diffraction interferometer,” Appl. Opt. 45, 6708–6711 (2006).
[CrossRef]

Fusek, R. L.

Ganci, S.

S. Ganci, “On the physical reality of edge sources,” Optik 123, 100–103 (2012).
[CrossRef]

Greivenkamp, J. E.

J. E. Greivenkamp, “Interference,” in OSA Handbook of Optics (OSA, 1995), Vol. 1.

Hecht, N. L.

Janpugdee, P.

P. Janpugdee, P. H. Pathak, and R. J. Burkholder, “On the boundary diffraction wave method for the analytical prediction of the radiation from large planar phased array antennas,” Radio Sci. 42, RS6S26 (2007).
[CrossRef]

Kaura, S. K.

Raj Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Direct visualization of Young’s boundary diffraction wave,” Opt. Commun. 276, 54–57 (2007).
[CrossRef]

Khizhnyak, A. I.

Kimura, S.

Kumar, R.

R. Kumar, “Structure of boundary diffraction wave revisited,” Appl. Phys. B 90, 379–382 (2008).
[CrossRef]

Kumar, Raj

Raj Kumar, “Diffraction Lloyd mirror interferometer,” J. Opt. (India) 39, 90–101 (2010).
[CrossRef]

Raj Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Direct visualization of Young’s boundary diffraction wave,” Opt. Commun. 276, 54–57 (2007).
[CrossRef]

Raj Kumar, D. P. Chhachhia, and A. K. Aggarwal, “Folding mirror schlieren diffraction interferometer,” Appl. Opt. 45, 6708–6711 (2006).
[CrossRef]

Lewis, D.

Lõhmus, M.

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

Lymarenko, R. A.

Minardi, J. E.

Miyamoto, K.

Munakata, C.

Pathak, P. H.

P. Janpugdee, P. H. Pathak, and R. J. Burkholder, “On the boundary diffraction wave method for the analytical prediction of the radiation from large planar phased array antennas,” Radio Sci. 42, RS6S26 (2007).
[CrossRef]

Piksarv, P.

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

Piyadasa, C. K. G.

C. K. G. Piyadasa, “Detection of a cylindrical boundary diffraction wave emanating from a straight edge by light interaction,” Opt. Commun. 285, 4878–4883 (2012).
[CrossRef]

Rubinowicz, A.

A. Rubinowicz, “Thomas Young and the theory of diffraction,” Nature 180, 160–162 (1957).
[CrossRef]

Saari, P.

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

Sommargren, G. E.

G. E. Sommargren, “Phase shifting diffraction interferometry for measuring extreme ultraviolet optics,” in Extreme Ultraviolet Lithography, G. D. Kubiak and D. R. Kania, eds., Vol. 4 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 108–112.

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, 1954).

Soskin, M. S.

Trebino, R.

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

Umul, Y. Z.

Y. Z. Umul, “Fictitious diffracted waves in the diffraction theory of Kirchhoff,” J. Opt. Soc. Am. A 27, 109–115 (2010).
[CrossRef]

Y. Z. Umul, “The theory of the boundary diffraction wave,” in Advances in Imaging and Electron Physics (Academic, 2011), Vol. 165, Chap. 6.

Valtna-Lukner, H.

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

Vasnetsov, M. V.

Wolf, E.

Appl. Opt.

Appl. Phys. B

R. Kumar, “Structure of boundary diffraction wave revisited,” Appl. Phys. B 90, 379–382 (2008).
[CrossRef]

J. Opt.

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

J. Opt. (India)

Raj Kumar, “Diffraction Lloyd mirror interferometer,” J. Opt. (India) 39, 90–101 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature

A. Rubinowicz, “Thomas Young and the theory of diffraction,” Nature 180, 160–162 (1957).
[CrossRef]

Opt. Commun.

C. K. G. Piyadasa, “Detection of a cylindrical boundary diffraction wave emanating from a straight edge by light interaction,” Opt. Commun. 285, 4878–4883 (2012).
[CrossRef]

Raj Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Direct visualization of Young’s boundary diffraction wave,” Opt. Commun. 276, 54–57 (2007).
[CrossRef]

Opt. Lett.

Optik

S. Ganci, “On the physical reality of edge sources,” Optik 123, 100–103 (2012).
[CrossRef]

Radio Sci.

P. Janpugdee, P. H. Pathak, and R. J. Burkholder, “On the boundary diffraction wave method for the analytical prediction of the radiation from large planar phased array antennas,” Radio Sci. 42, RS6S26 (2007).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Y. Z. Umul, “The theory of the boundary diffraction wave,” in Advances in Imaging and Electron Physics (Academic, 2011), Vol. 165, Chap. 6.

G. E. Sommargren, “Phase shifting diffraction interferometry for measuring extreme ultraviolet optics,” in Extreme Ultraviolet Lithography, G. D. Kubiak and D. R. Kania, eds., Vol. 4 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 108–112.

J. E. Greivenkamp, “Interference,” in OSA Handbook of Optics (OSA, 1995), Vol. 1.

A. Sommerfeld, Optics (Academic, 1954).

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.

Schematic representation of the generation of circular fringe pattern by superposition of two BDWs. (a) Change in position of the fringe pattern due to change in the position of hologram and (b) change in optical path length between two sources of BDWs (knife-edge K and its virtual image K or K) by change in position of the hologram during reconstruction.

Fig. 2.
Fig. 2.

Schematic of the experimental setup for recording the hologram of BDW.

Fig. 3.
Fig. 3.

Experimental results showing a geometrical patch of light (left) and a circular fringe pattern formed by superposition of BDWs.

Fig. 4.
Fig. 4.

Photographs of circular fringes due to the interference of two BDWs with (a) bright central fringe and (b) dark central fringe.

Fig. 5.
Fig. 5.

Experimental results showing control over the position of circular fringes in the observation plane at will.

Equations (9)

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

A(x,y)=A0r1exp(jkr1),
O(x,y)=Ug(x,y)+Ud(x,y).
R(x,y)=R0exp(jkxsinη),
I(x,y)=|O(x,y)+R(x,y)|2.
U=(R+O)tR|O|2+R|R|2+O|R|2+O*R2+O|O|2+O|R|2+O2R*+R|O|2,
δ=d(ρ2d2r2)
Δφ=2πλ(dρ2d2r2),
h=dcosα.
2πλ(dρ2d2r2)=2mπ,ρm=2r2(1mλ/d).

Metrics