Abstract

It is shown for the first time, to our knowledge, that when a plane wave illuminates a certain type of bicomponent optical system, consisting of two plane screens with circular apertures on a given optical axis, a multifocal diffractive focusing effect can appear. Here the diffraction picture in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by 6–10 times the value of the incident-wave intensity. The detected optical effect is observed across a wide range of wavelengths, λ = 0.4–103 µm, and ratios of the aperture diameters d 1 ≥ 2d 2 = 25–1000λ, and it is also insensitive to changes in the medium of the wave propagation. For the large diameters of input holes, d 1 = 2d 2 > 100λ, or for wavelengths in the radio-frequency region of the spectrum, the bicomponent diffraction system acts as a long-focus lens with a high-intensity Gaussian distribution of radiation, at times exceeding the initial intensity, persisting at large distances (z = 1–100 cm) from the diffraction system.

© 2000 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1968).
  2. Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
    [CrossRef]
  3. V. N. Mahajan, “Axial irradiance and optimal focusing of laser beams,” Appl. Opt. 22, 3042–3053 (1983).
    [CrossRef]
  4. M. Martinez-Corral, V. Climent, “Focal switch: a new effect in low-Fresnel-number systems,” Appl. Opt. 35, 24–27 (1996).
    [CrossRef] [PubMed]
  5. V. I. Igoshin, R. R. Letfullin, “Diffractive focusing of an input pulse and giant energy gain in a laser based on an auto-wave photon-branched chain reaction,” Quantum Electron. 29, 37–42 (1999).
    [CrossRef]
  6. V. I. Igoshin, R. R. Letfullin, “High-power laser amplifier based on an auto-wave photon-branched chain reaction in an unstable telescopic cavity,” Quantum Electron. 27, 487–491 (1997).
    [CrossRef]
  7. R. R. Letfullin, V. I. Igoshin, “Multipass optical reactor for laser processing of disperse materials,” Quantum Electron. 25, 684–689 (1995).
    [CrossRef]
  8. N. N. Rikalin, A. A. Uglov, I. V. Zuev, A. N. Kokora, Laser and Electron-Beam Processing of Materials (Mashinostroenie, Moscow, 1985).
  9. R. R. Letfullin, V. I. Igoshin, A. N. Bekrenev “Thermal calculation of bone-tissue slash modes by laser radiation,” in Cell and Biotissue Optics: Applications in Laser Diagnostics and Therapy, V. V. Tuchin, ed., Proc. SPIE2100, 272–275 (1993).
  10. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  11. R. R. Letfullin, Laser Diagnostics of Aerosol (Preprint of Lebedev Physics Institute, Russian Academy of Sciences, N9, Moscow, 1998).

1999

V. I. Igoshin, R. R. Letfullin, “Diffractive focusing of an input pulse and giant energy gain in a laser based on an auto-wave photon-branched chain reaction,” Quantum Electron. 29, 37–42 (1999).
[CrossRef]

1997

V. I. Igoshin, R. R. Letfullin, “High-power laser amplifier based on an auto-wave photon-branched chain reaction in an unstable telescopic cavity,” Quantum Electron. 27, 487–491 (1997).
[CrossRef]

1996

1995

R. R. Letfullin, V. I. Igoshin, “Multipass optical reactor for laser processing of disperse materials,” Quantum Electron. 25, 684–689 (1995).
[CrossRef]

1983

1981

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Bekrenev, A. N.

R. R. Letfullin, V. I. Igoshin, A. N. Bekrenev “Thermal calculation of bone-tissue slash modes by laser radiation,” in Cell and Biotissue Optics: Applications in Laser Diagnostics and Therapy, V. V. Tuchin, ed., Proc. SPIE2100, 272–275 (1993).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1968).

Climent, V.

Igoshin, V. I.

V. I. Igoshin, R. R. Letfullin, “Diffractive focusing of an input pulse and giant energy gain in a laser based on an auto-wave photon-branched chain reaction,” Quantum Electron. 29, 37–42 (1999).
[CrossRef]

V. I. Igoshin, R. R. Letfullin, “High-power laser amplifier based on an auto-wave photon-branched chain reaction in an unstable telescopic cavity,” Quantum Electron. 27, 487–491 (1997).
[CrossRef]

R. R. Letfullin, V. I. Igoshin, “Multipass optical reactor for laser processing of disperse materials,” Quantum Electron. 25, 684–689 (1995).
[CrossRef]

R. R. Letfullin, V. I. Igoshin, A. N. Bekrenev “Thermal calculation of bone-tissue slash modes by laser radiation,” in Cell and Biotissue Optics: Applications in Laser Diagnostics and Therapy, V. V. Tuchin, ed., Proc. SPIE2100, 272–275 (1993).

Kokora, A. N.

N. N. Rikalin, A. A. Uglov, I. V. Zuev, A. N. Kokora, Laser and Electron-Beam Processing of Materials (Mashinostroenie, Moscow, 1985).

Letfullin, R. R.

V. I. Igoshin, R. R. Letfullin, “Diffractive focusing of an input pulse and giant energy gain in a laser based on an auto-wave photon-branched chain reaction,” Quantum Electron. 29, 37–42 (1999).
[CrossRef]

V. I. Igoshin, R. R. Letfullin, “High-power laser amplifier based on an auto-wave photon-branched chain reaction in an unstable telescopic cavity,” Quantum Electron. 27, 487–491 (1997).
[CrossRef]

R. R. Letfullin, V. I. Igoshin, “Multipass optical reactor for laser processing of disperse materials,” Quantum Electron. 25, 684–689 (1995).
[CrossRef]

R. R. Letfullin, V. I. Igoshin, A. N. Bekrenev “Thermal calculation of bone-tissue slash modes by laser radiation,” in Cell and Biotissue Optics: Applications in Laser Diagnostics and Therapy, V. V. Tuchin, ed., Proc. SPIE2100, 272–275 (1993).

R. R. Letfullin, Laser Diagnostics of Aerosol (Preprint of Lebedev Physics Institute, Russian Academy of Sciences, N9, Moscow, 1998).

Li, Y.

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Mahajan, V. N.

Martinez-Corral, M.

Rikalin, N. N.

N. N. Rikalin, A. A. Uglov, I. V. Zuev, A. N. Kokora, Laser and Electron-Beam Processing of Materials (Mashinostroenie, Moscow, 1985).

Uglov, A. A.

N. N. Rikalin, A. A. Uglov, I. V. Zuev, A. N. Kokora, Laser and Electron-Beam Processing of Materials (Mashinostroenie, Moscow, 1985).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wolf, E.

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1968).

Zuev, I. V.

N. N. Rikalin, A. A. Uglov, I. V. Zuev, A. N. Kokora, Laser and Electron-Beam Processing of Materials (Mashinostroenie, Moscow, 1985).

Appl. Opt.

Opt. Commun.

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Quantum Electron.

V. I. Igoshin, R. R. Letfullin, “Diffractive focusing of an input pulse and giant energy gain in a laser based on an auto-wave photon-branched chain reaction,” Quantum Electron. 29, 37–42 (1999).
[CrossRef]

V. I. Igoshin, R. R. Letfullin, “High-power laser amplifier based on an auto-wave photon-branched chain reaction in an unstable telescopic cavity,” Quantum Electron. 27, 487–491 (1997).
[CrossRef]

R. R. Letfullin, V. I. Igoshin, “Multipass optical reactor for laser processing of disperse materials,” Quantum Electron. 25, 684–689 (1995).
[CrossRef]

Other

N. N. Rikalin, A. A. Uglov, I. V. Zuev, A. N. Kokora, Laser and Electron-Beam Processing of Materials (Mashinostroenie, Moscow, 1985).

R. R. Letfullin, V. I. Igoshin, A. N. Bekrenev “Thermal calculation of bone-tissue slash modes by laser radiation,” in Cell and Biotissue Optics: Applications in Laser Diagnostics and Therapy, V. V. Tuchin, ed., Proc. SPIE2100, 272–275 (1993).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

R. R. Letfullin, Laser Diagnostics of Aerosol (Preprint of Lebedev Physics Institute, Russian Academy of Sciences, N9, Moscow, 1998).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1968).

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Figures (3)

Fig. 1
Fig. 1

Geometry of (a) the wave-diffraction system with a circular aperture and (b) the bicomponent diffracting system with circular apertures with diameters d 1 and d 2.

Fig. 2
Fig. 2

Fresnel diffraction of (a) a plane wave with wavelength λ = 3.3 µm by a circular aperture of diameter d 1 = 100 λ, (b)–(f) calculated for various distances z along the optical axis.

Fig. 3
Fig. 3

Diffractive focusing of (a) a conical wave by a second circular aperture of diameter d 2 = 50λ, (b)–(f) calculated for various distances z from the aperture along the optical axis.

Tables (1)

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Table 1 Multifocal Focusing Observed in a Bicomponent Diffraction System for Various Ratios of Aperture Diameters and Wavelengths of Input Radiation

Equations (15)

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Ar, z, t=Er, zexpiw0t.
ΔEr, z+k02m2Er, z=0,
Δ=2x2+2y2+2z2
k0m Ez  2Ez2.
2ik0m Ez+1rrr Er=0.
Er, z|z=0=E0R1r,  Er, z||z|=Er, z||r|=0,  R1r||r|<d1/2=1,
R1r=exp-r-rS/rS,
Ir, z=cm4π E*r, zEr, z,
Er, z|z=L=Er, LR2r,  Er, z||z|=Er, z||r|=0,  R2r||r|<d2/2=1.
m˜=1-iS02πNk-3,
S0=12l=12l+1al+bl
al=ψlyψlρ-m˜ψlyψlρψlyξlρ-m˜ψlyξlρ,  bl=m˜ψlyψlρ-ψlyψlρm˜ψlyξlρ-ψlyξlρ.
2ikˆm˜Er, zz+1rrr Er, zr=0,
kˆm˜=km˜=i2πNS0m˜-11/3.
ψl+1yψl+1y=-1ψly/ψly-l+1/y+l+1y

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