Abstract

A diffractive optics design method based on a phase retrieval algorithm and carrier grating coding is modified to enable designing of photonic bandgap reflectances. Discrete and continuous signals are designed for a fiber grating to demonstrate the capability of the approach. The method is proved a versatile tool for synthesizing reflectance spectra of periodic structures.

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. R. Kashyap, Fiber Bragg Gratings (Academic Press, San Diego, 2010).
  5. H. Nishihara, M. Haruna, and T. Suhara, Integrated Optical Circuits (McGraw-Hill, New York, 1989).
  6. T. Aalto, S. Yliniemi, P. Heimala, P. Pekko, J. Simonen, and M. Kuittinen, “Integrated Bragg gratings in silicon-on-insulator waveguides,” in Integrated Optics: Devices, Materials, and Technologies VI, Y. S. Sidorin and A. Tervonen, eds., Proc SPIE4640, 117–124 (2002).
    [CrossRef]
  7. R. Kashyap, “Design of step-chirped fibre Bragg gratings,” Opt. Commun.136, 461–469 (1997).
    [CrossRef]
  8. D. Wiesmann, R. Germann, G.-L. Bona, C. David, D. Erni, and H. Jäckel, “Add-drop filter based on apodized surface-corrugated gratings,” J. Opt. Soc. Am. B20, 417–423 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. T. Vallius, J. Konttinen, and P. Tuomisto, “An optical broadband filter and a device comprising the same,” EpiCrystals Inc., US Patent Application US61/491,007, (2011).
  12. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9, 919–933 (1973).
    [CrossRef]
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    [CrossRef]
  14. J. A. Armstrong, N. Bloembergen, J. Ducing, and P. S. Pershan, “Interactions between light waves in a nonlinear medium,” Phys. Rev.127, 1918–1939 (1962).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013

2003

1997

1996

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt.43, 1389–1398 (1996).

1993

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fibre by UV exposure through a phase mask,” Appl. Phys. Lett.62, 1035–1037 (1993).
[CrossRef]

1992

1991

F. Wyrowski and O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys.54, 1481–1571 (1991).
[CrossRef]

1990

F. Wyrowski, “Diffractive optical elements: Iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A7, 961–969 (1990).
[CrossRef]

K. A. Winick, “Design of corrugated waveguide filters by Fourier-transform techniques,” IEEE J. Quantum Electron.26, 1918–1929 (1990).
[CrossRef]

1989

1978

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photo-sensitivity in optical fiber waveguide: Application to reflection filter fabrication,” Appl. Phys. Lett.32, 647–649 (1978).
[CrossRef]

1973

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9, 919–933 (1973).
[CrossRef]

1972

H. Kogelnik and C. V. Shank, “Coupled-mode theory of distributed feedback lasers,” Appl. Phys.43, 2327–2335 (1972).
[CrossRef]

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik35, 237–246 (1972).

1967

1966

1962

J. A. Armstrong, N. Bloembergen, J. Ducing, and P. S. Pershan, “Interactions between light waves in a nonlinear medium,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Aagedal, H.

Aalto, T.

T. Aalto, S. Yliniemi, P. Heimala, P. Pekko, J. Simonen, and M. Kuittinen, “Integrated Bragg gratings in silicon-on-insulator waveguides,” in Integrated Optics: Devices, Materials, and Technologies VI, Y. S. Sidorin and A. Tervonen, eds., Proc SPIE4640, 117–124 (2002).
[CrossRef]

Albert, J.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fibre by UV exposure through a phase mask,” Appl. Phys. Lett.62, 1035–1037 (1993).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducing, and P. S. Pershan, “Interactions between light waves in a nonlinear medium,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Beth, T.

Bilodeau, F.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fibre by UV exposure through a phase mask,” Appl. Phys. Lett.62, 1035–1037 (1993).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducing, and P. S. Pershan, “Interactions between light waves in a nonlinear medium,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Bogaerts, W.

Bona, G.-L.

Brown, B. R.

Bryngdahl, O.

F. Wyrowski and O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys.54, 1481–1571 (1991).
[CrossRef]

Dänliker, R.

David, C.

Ducing, J.

J. A. Armstrong, N. Bloembergen, J. Ducing, and P. S. Pershan, “Interactions between light waves in a nonlinear medium,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Egner, S.

Erni, D.

Fienup, J. R.

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photo-sensitivity in optical fiber waveguide: Application to reflection filter fabrication,” Appl. Phys. Lett.32, 647–649 (1978).
[CrossRef]

Gale, M. T.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik35, 237–246 (1972).

Germann, R.

Glen, W. H.

Haruna, M.

H. Nishihara, M. Haruna, and T. Suhara, Integrated Optical Circuits (McGraw-Hill, New York, 1989).

Heimala, P.

T. Aalto, S. Yliniemi, P. Heimala, P. Pekko, J. Simonen, and M. Kuittinen, “Integrated Bragg gratings in silicon-on-insulator waveguides,” in Integrated Optics: Devices, Materials, and Technologies VI, Y. S. Sidorin and A. Tervonen, eds., Proc SPIE4640, 117–124 (2002).
[CrossRef]

Herzig, H. P.

Hill, K. O.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fibre by UV exposure through a phase mask,” Appl. Phys. Lett.62, 1035–1037 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photo-sensitivity in optical fiber waveguide: Application to reflection filter fabrication,” Appl. Phys. Lett.32, 647–649 (1978).
[CrossRef]

Honkanen, M.

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt.43, 1389–1398 (1996).

Jäckel, H.

Johnson, D. C.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fibre by UV exposure through a phase mask,” Appl. Phys. Lett.62, 1035–1037 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photo-sensitivity in optical fiber waveguide: Application to reflection filter fabrication,” Appl. Phys. Lett.32, 647–649 (1978).
[CrossRef]

Kashyap, R.

R. Kashyap, “Design of step-chirped fibre Bragg gratings,” Opt. Commun.136, 461–469 (1997).
[CrossRef]

R. Kashyap, Fiber Bragg Gratings (Academic Press, San Diego, 2010).

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photo-sensitivity in optical fiber waveguide: Application to reflection filter fabrication,” Appl. Phys. Lett.32, 647–649 (1978).
[CrossRef]

Kettunen, V.

Kogelnik, H.

H. Kogelnik and C. V. Shank, “Coupled-mode theory of distributed feedback lasers,” Appl. Phys.43, 2327–2335 (1972).
[CrossRef]

Konttinen, J.

T. Vallius, J. Konttinen, and P. Tuomisto, “An optical broadband filter and a device comprising the same,” EpiCrystals Inc., US Patent Application US61/491,007, (2011).

Kuittinen, M.

T. Aalto, S. Yliniemi, P. Heimala, P. Pekko, J. Simonen, and M. Kuittinen, “Integrated Bragg gratings in silicon-on-insulator waveguides,” in Integrated Optics: Devices, Materials, and Technologies VI, Y. S. Sidorin and A. Tervonen, eds., Proc SPIE4640, 117–124 (2002).
[CrossRef]

Lohmann, A. W.

Malo, B.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fibre by UV exposure through a phase mask,” Appl. Phys. Lett.62, 1035–1037 (1993).
[CrossRef]

Meltz, G.

Morey, W. W.

Müller-Quade, J.

Nishihara, H.

H. Nishihara, M. Haruna, and T. Suhara, Integrated Optical Circuits (McGraw-Hill, New York, 1989).

Noponen, E.

V. Kettunen, P. Vahimaa, J. Turunen, and E. Noponen, “Zeroth-order coding of complex amplitude in two dimensions,” J. Opt. Soc. Am. A14, 808–815 (1997).
[CrossRef]

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt.43, 1389–1398 (1996).

Paris, D. P.

Pekko, P.

T. Aalto, S. Yliniemi, P. Heimala, P. Pekko, J. Simonen, and M. Kuittinen, “Integrated Bragg gratings in silicon-on-insulator waveguides,” in Integrated Optics: Devices, Materials, and Technologies VI, Y. S. Sidorin and A. Tervonen, eds., Proc SPIE4640, 117–124 (2002).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducing, and P. S. Pershan, “Interactions between light waves in a nonlinear medium,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Prongu, D.

Salminen, O.

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt.43, 1389–1398 (1996).

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik35, 237–246 (1972).

Schmid, M.

Shank, C. V.

H. Kogelnik and C. V. Shank, “Coupled-mode theory of distributed feedback lasers,” Appl. Phys.43, 2327–2335 (1972).
[CrossRef]

Simonen, J.

T. Aalto, S. Yliniemi, P. Heimala, P. Pekko, J. Simonen, and M. Kuittinen, “Integrated Bragg gratings in silicon-on-insulator waveguides,” in Integrated Optics: Devices, Materials, and Technologies VI, Y. S. Sidorin and A. Tervonen, eds., Proc SPIE4640, 117–124 (2002).
[CrossRef]

Suhara, T.

H. Nishihara, M. Haruna, and T. Suhara, Integrated Optical Circuits (McGraw-Hill, New York, 1989).

Tuomisto, P.

T. Vallius, J. Konttinen, and P. Tuomisto, “An optical broadband filter and a device comprising the same,” EpiCrystals Inc., US Patent Application US61/491,007, (2011).

Turunen, J.

V. Kettunen, P. Vahimaa, J. Turunen, and E. Noponen, “Zeroth-order coding of complex amplitude in two dimensions,” J. Opt. Soc. Am. A14, 808–815 (1997).
[CrossRef]

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt.43, 1389–1398 (1996).

Vahimaa, P.

V. Kettunen, P. Vahimaa, J. Turunen, and E. Noponen, “Zeroth-order coding of complex amplitude in two dimensions,” J. Opt. Soc. Am. A14, 808–815 (1997).
[CrossRef]

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt.43, 1389–1398 (1996).

Vallius, T.

T. Vallius, J. Konttinen, and P. Tuomisto, “An optical broadband filter and a device comprising the same,” EpiCrystals Inc., US Patent Application US61/491,007, (2011).

Van Thourhout, D.

Verbist, M.

Wiesmann, D.

Winick, K. A.

K. A. Winick, “Design of corrugated waveguide filters by Fourier-transform techniques,” IEEE J. Quantum Electron.26, 1918–1929 (1990).
[CrossRef]

Wyrowski, F.

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9, 919–933 (1973).
[CrossRef]

Yliniemi, S.

T. Aalto, S. Yliniemi, P. Heimala, P. Pekko, J. Simonen, and M. Kuittinen, “Integrated Bragg gratings in silicon-on-insulator waveguides,” in Integrated Optics: Devices, Materials, and Technologies VI, Y. S. Sidorin and A. Tervonen, eds., Proc SPIE4640, 117–124 (2002).
[CrossRef]

Appl. Opt.

Appl. Phys.

H. Kogelnik and C. V. Shank, “Coupled-mode theory of distributed feedback lasers,” Appl. Phys.43, 2327–2335 (1972).
[CrossRef]

Appl. Phys. Lett.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fibre by UV exposure through a phase mask,” Appl. Phys. Lett.62, 1035–1037 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photo-sensitivity in optical fiber waveguide: Application to reflection filter fabrication,” Appl. Phys. Lett.32, 647–649 (1978).
[CrossRef]

IEEE J. Quantum Electron.

K. A. Winick, “Design of corrugated waveguide filters by Fourier-transform techniques,” IEEE J. Quantum Electron.26, 1918–1929 (1990).
[CrossRef]

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9, 919–933 (1973).
[CrossRef]

J. Mod. Opt.

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, “Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements,” J. Mod. Opt.43, 1389–1398 (1996).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

R. Kashyap, “Design of step-chirped fibre Bragg gratings,” Opt. Commun.136, 461–469 (1997).
[CrossRef]

Opt. Lett.

Optik

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik35, 237–246 (1972).

Phys. Rev.

J. A. Armstrong, N. Bloembergen, J. Ducing, and P. S. Pershan, “Interactions between light waves in a nonlinear medium,” Phys. Rev.127, 1918–1939 (1962).
[CrossRef]

Rep. Prog. Phys.

F. Wyrowski and O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys.54, 1481–1571 (1991).
[CrossRef]

Other

T. Vallius, J. Konttinen, and P. Tuomisto, “An optical broadband filter and a device comprising the same,” EpiCrystals Inc., US Patent Application US61/491,007, (2011).

R. Kashyap, Fiber Bragg Gratings (Academic Press, San Diego, 2010).

H. Nishihara, M. Haruna, and T. Suhara, Integrated Optical Circuits (McGraw-Hill, New York, 1989).

T. Aalto, S. Yliniemi, P. Heimala, P. Pekko, J. Simonen, and M. Kuittinen, “Integrated Bragg gratings in silicon-on-insulator waveguides,” in Integrated Optics: Devices, Materials, and Technologies VI, Y. S. Sidorin and A. Tervonen, eds., Proc SPIE4640, 117–124 (2002).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Phase distribution that produces nine uniform reflectance peaks.

Fig. 2
Fig. 2

Reflectance spectrum of the grating with uniform discrete wavelengths.

Fig. 3
Fig. 3

Phase distribution that produces nine modulated reflectance peaks.

Fig. 4
Fig. 4

Reflectance spectrum of the grating with modulated discrete wavelengths.

Fig. 5
Fig. 5

Phase (a) and amplitude (b) distribution that produces the continuous signal.

Fig. 6
Fig. 6

Reflectance of the non-periodic structure. Both target signal (green) and the realized reflectance (blue) are given using linear (a) and logarithmic (b) scales.

Equations (7)

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

d A ( z , Δ k ) d z = i κ ( z ) B ( z , Δ k ) exp ( i Δ k z )
d B ( z , Δ k ) d z = i κ ( z ) A ( z , Δ k ) exp ( i Δ k z ) ,
B ( Δ k ) = L 0 i κ ( z ) exp ( i Δ k z ) d z ,
κ ( z ) = 1 2 π i B ( Δ k ) exp ( i Δ k z ) d Δ k .
ϕ = Δ z Δ k
f = arcsin [ | κ ( z ) | ] π .
S ( λ ) = | exp [ ( λ λ 0 ) 4 / w 1 4 ] exp [ ( λ λ 0 ) 2 / w 2 2 ] / 2 | ,

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