Abstract

We present a simple and consistent technique for fabricating slow light structures in dye-doped polymer waveguides using the process of irreversible photobleaching. The slow light structures are moiré gratings. The gratings are holographically written into channel waveguides photobleached in side-chained PMMA∕DR1 films. The films are annealed during the photobleaching process in order to remove stresses in the films generated during the photobleaching process. These stresses have been observed to cause distortion and cracking of the film surface. The slowing factor for the moiré gratings is calculated from the reflectance spectrum of the waveguides using the Hilbert transform. Moiré gratings with slowing factors between 1.6 and 2.6 are demonstrated.

© 2007 Optical Society of America

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    [CrossRef]
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2007

F. Xia, L. Sekaric, and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

2006

M. Roussey, M. Bernal, N. Courjal, D. V. Labeke, F. I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

S. Dubovitsky and W. Steier, "Relationship between the slowing and loss in optical delay lines," IEEE J. Quantum Electron. 42, 372-377 (2006).
[CrossRef]

M. Herraez, K. Song, and L. Thevenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006).
[CrossRef]

2005

J. Khurgin, "Expanding the bandwidth of slow-light photonic devices based on coupled resonators," Opt. Lett. 30, 513-515 (2005).
[CrossRef] [PubMed]

E. McKenna, J. Xue, R. Fan, L. Bintz, R. Dinu, and A. Mickelson, "Wavelength dependence of irreversible photobleaching of dye-doped polymer waveguide materials," Appl. Opt. 44, 3063-3068 (2005).
[CrossRef] [PubMed]

M. Povinelli, S. Johnson, and J. Joannopoulos, "Slow-light, band-edge waveguides for tunable time delays," Opt. Express 13, 7145-7159 (2005).
[CrossRef] [PubMed]

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

D. Janner, G. Galzerano, G. D. Valle, P. Laporta, S. Longhi, and M. Belmonte, "Slow light in periodic superstructure Bragg gratings," Phys. Rev. E 72, 1-8 (2005).
[CrossRef]

M. Yanik and S. Fan, "Stopping and storing light coherently," Phys. Rev. A 71, 1-10 (2005).
[CrossRef]

2003

A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photon. News 14(11), 44-48 (2003).
[CrossRef]

2002

Y. Sugimoto, S. Lan, S. Nishikawa, N. Ikeda, H. Ishikawa, and K. Asakawa, "Design and fabrication of impurity band-based photonic crystal waveguides for optical delay lines," Appl. Phys. Lett. 81, 1946-1948 (2002).
[CrossRef]

2001

G. Lenz, B. Eggleton, C. Madsen, and R. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 1390-1402 (2001).
[CrossRef]

R. Williamson, "Sensitivity-bandwidth product for electro-optic modulators," Opt. Lett. 26, 1362-1363 (2001).
[CrossRef]

2000

J. B. Khurgin, "Light slowing down in moiré fiber gratings and its implications for nonlinear optics," Phys. Rev. A 62, 1212-1256 (2000).
[CrossRef]

1999

1997

1995

1991

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, and T. Georges, "Formation of moire grating in core of germanosilicate fibre by transverse holographic double exposure method," Electron. Lett. 27, 1945-1947 (1991).
[CrossRef]

1990

D. Reid, C. Ragdale, I. Bennion, D. Robbins, J. Buus, and W. Stewart, "Phase-shifted moiré grating fibre resonators," Electron. Lett. 26, 10-12 (1990).
[CrossRef]

1974

R. Burge, M. Fiddy, A. Greenaway, and G. Ross, "The application of dispersions relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

1972

1956

J. Toll, "Causality and the dispersion relation: logical foundations," Phys. Rev. 104, 1760-1770 (1956).
[CrossRef]

Asakawa, K.

Y. Sugimoto, S. Lan, S. Nishikawa, N. Ikeda, H. Ishikawa, and K. Asakawa, "Design and fabrication of impurity band-based photonic crystal waveguides for optical delay lines," Appl. Phys. Lett. 81, 1946-1948 (2002).
[CrossRef]

Baida, F. I.

M. Roussey, M. Bernal, N. Courjal, D. V. Labeke, F. I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Bayon, F.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, and T. Georges, "Formation of moire grating in core of germanosilicate fibre by transverse holographic double exposure method," Electron. Lett. 27, 1945-1947 (1991).
[CrossRef]

Belmonte, M.

D. Janner, G. Galzerano, G. D. Valle, P. Laporta, S. Longhi, and M. Belmonte, "Slow light in periodic superstructure Bragg gratings," Phys. Rev. E 72, 1-8 (2005).
[CrossRef]

Bennion, I.

D. Reid, C. Ragdale, I. Bennion, D. Robbins, J. Buus, and W. Stewart, "Phase-shifted moiré grating fibre resonators," Electron. Lett. 26, 10-12 (1990).
[CrossRef]

Bernage, P.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, and T. Georges, "Formation of moire grating in core of germanosilicate fibre by transverse holographic double exposure method," Electron. Lett. 27, 1945-1947 (1991).
[CrossRef]

Bernal, M.

M. Roussey, M. Bernal, N. Courjal, D. V. Labeke, F. I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Bintz, L.

Burge, R.

R. Burge, M. Fiddy, A. Greenaway, and G. Ross, "The application of dispersions relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Buus, J.

D. Reid, C. Ragdale, I. Bennion, D. Robbins, J. Buus, and W. Stewart, "Phase-shifted moiré grating fibre resonators," Electron. Lett. 26, 10-12 (1990).
[CrossRef]

Courjal, N.

M. Roussey, M. Bernal, N. Courjal, D. V. Labeke, F. I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Dinu, R.

Douay, M.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, and T. Georges, "Formation of moire grating in core of germanosilicate fibre by transverse holographic double exposure method," Electron. Lett. 27, 1945-1947 (1991).
[CrossRef]

Dubovitsky, S.

S. Dubovitsky and W. Steier, "Relationship between the slowing and loss in optical delay lines," IEEE J. Quantum Electron. 42, 372-377 (2006).
[CrossRef]

Eggleton, B.

G. Lenz, B. Eggleton, C. Madsen, and R. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 1390-1402 (2001).
[CrossRef]

Fan, R.

Fan, S.

M. Yanik and S. Fan, "Stopping and storing light coherently," Phys. Rev. A 71, 1-10 (2005).
[CrossRef]

Feng, W.

Fertein, E.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, and T. Georges, "Formation of moire grating in core of germanosilicate fibre by transverse holographic double exposure method," Electron. Lett. 27, 1945-1947 (1991).
[CrossRef]

Feuerstein, R.

Fiddy, M.

R. Burge, M. Fiddy, A. Greenaway, and G. Ross, "The application of dispersions relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Galzerano, G.

D. Janner, G. Galzerano, G. D. Valle, P. Laporta, S. Longhi, and M. Belmonte, "Slow light in periodic superstructure Bragg gratings," Phys. Rev. E 72, 1-8 (2005).
[CrossRef]

Georges, T.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, and T. Georges, "Formation of moire grating in core of germanosilicate fibre by transverse holographic double exposure method," Electron. Lett. 27, 1945-1947 (1991).
[CrossRef]

Greenaway, A.

R. Burge, M. Fiddy, A. Greenaway, and G. Ross, "The application of dispersions relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Hahn, S.

S. Hahn, Hilbert Transforms in the Transform and Applications Handbook, A. Poularikas, ed. (CRC, 1996).

Hamann, H. F.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Heaton, J.

N. Shaw, W. Stewart, J. Heaton, and D. Wight, "Optical slow-wave resonant modulation in electro-optic GaAs/AlGaAs modulators," Electron. Lett. 35, 1557-1558 (1999).
[CrossRef]

Herraez, M.

Hooker, B.

Hooker, R.

Ikeda, N.

Y. Sugimoto, S. Lan, S. Nishikawa, N. Ikeda, H. Ishikawa, and K. Asakawa, "Design and fabrication of impurity band-based photonic crystal waveguides for optical delay lines," Appl. Phys. Lett. 81, 1946-1948 (2002).
[CrossRef]

Ishikawa, H.

Y. Sugimoto, S. Lan, S. Nishikawa, N. Ikeda, H. Ishikawa, and K. Asakawa, "Design and fabrication of impurity band-based photonic crystal waveguides for optical delay lines," Appl. Phys. Lett. 81, 1946-1948 (2002).
[CrossRef]

Janner, D.

D. Janner, G. Galzerano, G. D. Valle, P. Laporta, S. Longhi, and M. Belmonte, "Slow light in periodic superstructure Bragg gratings," Phys. Rev. E 72, 1-8 (2005).
[CrossRef]

Joannopoulos, J.

Johnson, S.

Khurgin, J.

Khurgin, J. B.

J. B. Khurgin, "Light slowing down in moiré fiber gratings and its implications for nonlinear optics," Phys. Rev. A 62, 1212-1256 (2000).
[CrossRef]

Labeke, D. V.

M. Roussey, M. Bernal, N. Courjal, D. V. Labeke, F. I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Lan, S.

Y. Sugimoto, S. Lan, S. Nishikawa, N. Ikeda, H. Ishikawa, and K. Asakawa, "Design and fabrication of impurity band-based photonic crystal waveguides for optical delay lines," Appl. Phys. Lett. 81, 1946-1948 (2002).
[CrossRef]

Laporta, P.

D. Janner, G. Galzerano, G. D. Valle, P. Laporta, S. Longhi, and M. Belmonte, "Slow light in periodic superstructure Bragg gratings," Phys. Rev. E 72, 1-8 (2005).
[CrossRef]

Legoubin, S.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, and T. Georges, "Formation of moire grating in core of germanosilicate fibre by transverse holographic double exposure method," Electron. Lett. 27, 1945-1947 (1991).
[CrossRef]

Lenz, G.

G. Lenz, B. Eggleton, C. Madsen, and R. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 1390-1402 (2001).
[CrossRef]

Lin, S.

Longhi, S.

D. Janner, G. Galzerano, G. D. Valle, P. Laporta, S. Longhi, and M. Belmonte, "Slow light in periodic superstructure Bragg gratings," Phys. Rev. E 72, 1-8 (2005).
[CrossRef]

Ma, J.

Madsen, C.

G. Lenz, B. Eggleton, C. Madsen, and R. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 1390-1402 (2001).
[CrossRef]

Martin, R.

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photon. News 14(11), 44-48 (2003).
[CrossRef]

McKenna, E.

McNab, S. J.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Melloni, A.

A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photon. News 14(11), 44-48 (2003).
[CrossRef]

Mickelson, A.

Milloni, P.

P. Milloni, Fast Light, Slow Light and Left-Handed Light (Institute of Physics, 2005).

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photon. News 14(11), 44-48 (2003).
[CrossRef]

Niay, P.

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, and T. Georges, "Formation of moire grating in core of germanosilicate fibre by transverse holographic double exposure method," Electron. Lett. 27, 1945-1947 (1991).
[CrossRef]

Nishikawa, S.

Y. Sugimoto, S. Lan, S. Nishikawa, N. Ikeda, H. Ishikawa, and K. Asakawa, "Design and fabrication of impurity band-based photonic crystal waveguides for optical delay lines," Appl. Phys. Lett. 81, 1946-1948 (2002).
[CrossRef]

O'Boyle, M.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Poladian, L.

Povinelli, M.

Ragdale, C.

D. Reid, C. Ragdale, I. Bennion, D. Robbins, J. Buus, and W. Stewart, "Phase-shifted moiré grating fibre resonators," Electron. Lett. 26, 10-12 (1990).
[CrossRef]

Reid, D.

D. Reid, C. Ragdale, I. Bennion, D. Robbins, J. Buus, and W. Stewart, "Phase-shifted moiré grating fibre resonators," Electron. Lett. 26, 10-12 (1990).
[CrossRef]

Robbins, D.

D. Reid, C. Ragdale, I. Bennion, D. Robbins, J. Buus, and W. Stewart, "Phase-shifted moiré grating fibre resonators," Electron. Lett. 26, 10-12 (1990).
[CrossRef]

Ross, G.

R. Burge, M. Fiddy, A. Greenaway, and G. Ross, "The application of dispersions relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Roussey, M.

M. Roussey, M. Bernal, N. Courjal, D. V. Labeke, F. I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Salut, R.

M. Roussey, M. Bernal, N. Courjal, D. V. Labeke, F. I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Sekaric, L.

F. Xia, L. Sekaric, and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

Shaw, N.

N. Shaw, W. Stewart, J. Heaton, and D. Wight, "Optical slow-wave resonant modulation in electro-optic GaAs/AlGaAs modulators," Electron. Lett. 35, 1557-1558 (1999).
[CrossRef]

Slusher, R.

G. Lenz, B. Eggleton, C. Madsen, and R. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 1390-1402 (2001).
[CrossRef]

Smolinsky, G.

Song, K.

Steier, W.

S. Dubovitsky and W. Steier, "Relationship between the slowing and loss in optical delay lines," IEEE J. Quantum Electron. 42, 372-377 (2006).
[CrossRef]

Stewart, W.

N. Shaw, W. Stewart, J. Heaton, and D. Wight, "Optical slow-wave resonant modulation in electro-optic GaAs/AlGaAs modulators," Electron. Lett. 35, 1557-1558 (1999).
[CrossRef]

D. Reid, C. Ragdale, I. Bennion, D. Robbins, J. Buus, and W. Stewart, "Phase-shifted moiré grating fibre resonators," Electron. Lett. 26, 10-12 (1990).
[CrossRef]

Sugimoto, Y.

Y. Sugimoto, S. Lan, S. Nishikawa, N. Ikeda, H. Ishikawa, and K. Asakawa, "Design and fabrication of impurity band-based photonic crystal waveguides for optical delay lines," Appl. Phys. Lett. 81, 1946-1948 (2002).
[CrossRef]

Taylor, H.

Thevenaz, L.

Tien, P.

Toll, J.

J. Toll, "Causality and the dispersion relation: logical foundations," Phys. Rev. 104, 1760-1770 (1956).
[CrossRef]

Tomic, D.

Valle, G. D.

D. Janner, G. Galzerano, G. D. Valle, P. Laporta, S. Longhi, and M. Belmonte, "Slow light in periodic superstructure Bragg gratings," Phys. Rev. E 72, 1-8 (2005).
[CrossRef]

Vlasov, Y.

F. Xia, L. Sekaric, and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Wight, D.

N. Shaw, W. Stewart, J. Heaton, and D. Wight, "Optical slow-wave resonant modulation in electro-optic GaAs/AlGaAs modulators," Electron. Lett. 35, 1557-1558 (1999).
[CrossRef]

Williamson, R.

Xia, F.

F. Xia, L. Sekaric, and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007).
[CrossRef]

Xue, J.

Yanik, M.

M. Yanik and S. Fan, "Stopping and storing light coherently," Phys. Rev. A 71, 1-10 (2005).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Roussey, M. Bernal, N. Courjal, D. V. Labeke, F. I. Baida, and R. Salut, "Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons," Appl. Phys. Lett. 89, 241110 (2006).
[CrossRef]

Y. Sugimoto, S. Lan, S. Nishikawa, N. Ikeda, H. Ishikawa, and K. Asakawa, "Design and fabrication of impurity band-based photonic crystal waveguides for optical delay lines," Appl. Phys. Lett. 81, 1946-1948 (2002).
[CrossRef]

Electron. Lett.

N. Shaw, W. Stewart, J. Heaton, and D. Wight, "Optical slow-wave resonant modulation in electro-optic GaAs/AlGaAs modulators," Electron. Lett. 35, 1557-1558 (1999).
[CrossRef]

D. Reid, C. Ragdale, I. Bennion, D. Robbins, J. Buus, and W. Stewart, "Phase-shifted moiré grating fibre resonators," Electron. Lett. 26, 10-12 (1990).
[CrossRef]

S. Legoubin, E. Fertein, M. Douay, P. Bernage, P. Niay, F. Bayon, and T. Georges, "Formation of moire grating in core of germanosilicate fibre by transverse holographic double exposure method," Electron. Lett. 27, 1945-1947 (1991).
[CrossRef]

IEEE J. Quantum Electron.

G. Lenz, B. Eggleton, C. Madsen, and R. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 1390-1402 (2001).
[CrossRef]

S. Dubovitsky and W. Steier, "Relationship between the slowing and loss in optical delay lines," IEEE J. Quantum Electron. 42, 372-377 (2006).
[CrossRef]

J. Lightwave Technol.

J. Phys. D

R. Burge, M. Fiddy, A. Greenaway, and G. Ross, "The application of dispersions relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Nature

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Holographic writing setup for irreversibly photobleaching moiré gratings into waveguides.

Fig. 2
Fig. 2

Waveguide and moiré grating mode characterization and transmission measurement system.

Fig. 3
Fig. 3

Reflectance spectra for three 1 cm long moiré gratings written into PMMA∕DR1 channel waveguides.

Fig. 4
Fig. 4

Calculated delay spectra for three 1   cm long moiré gratings written into PMMA∕DR1 channel waveguides.

Tables (1)

Tables Icon

Table 1 Summarizing the Measured and Calculated Parameters for the Reflectance Spectra of the Moiré Gratings in PMMA∕DR1 Channel Waveguides

Equations (70)

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V π
τ max Δ ω const
τ max
n ( x ) = n 0 + Δ n cos ( 2 π Λ s x ) cos ( 2 π Λ B x ) ,
n 0
Δ n
Λ B
Λ s
4.5   μm
n = 1.501
1550   nm
n = 1.540
1550   nm
90   ° C
120   ° C
500 m W / c m 2
10   h
514   nm
1 10   mm
110   ° C
1   ( BS1 )
2 ( BS2 )
3 ( M3 )
4 ( M4 )
Λ s
M4
5   μm
λ 0
Λ Bragg = λ 0 2 n e f f .
n e f f = 1.522
λ 0 = 1550   nm
509   nm
λ B
θ = sin 1 ( λ B 2 Λ Bragg ) .
300 mW / cm 2
t ( ω ) = T ( ω ) e i ϕ ( ω ) ,
T ( ω )
ϕ ( ω ) = 1 π P log T ( ω ) ω ω d ω ,
τ = d ϕ ( ω ) d ω .
h ( i ) = 2 N sin 2 ( π i 2 ) cot ( π i N ) .
v g
v g = L τ ,
S = c v g ,
1.0   cm
1521.5 nm
143   mW / cm 2
143   mW / cm 2
1.24   mm
50.67   ps
50   ps
1   cm
50 mW / cm 2
25 mW / cm 2
1.13   mm
1.49   nm
2   nm
1.188   mm
50.67 ps
30   ps
1.1   mm
1.68   nm
2.2   nm
1.075   mm
80   ps
T g
Δ n
Δ n
1550   nm
Δ n
1   cm

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