Far-field scattering microscopy applied to analysis of slow light, power enhancement, and delay times in uniform Bragg waveguide gratings

W. C. L. Hopman; H. J. W. M. Hoekstra; R. Dekker; L. Zhuang; R .M. de Ridder

doi:10.1364/OE.15.001851

Far-field scattering microscopy applied to analysis of slow light, power enhancement, and delay times in uniform Bragg waveguide gratings

W. C. L. Hopman, H. J. W. M. Hoekstra, R. Dekker, L. Zhuang, and R .M. de Ridder

Optics Express
Vol. 15,
Issue 4,
pp. 1851-1870
(2007)
•doi: 10.1364/OE.15.001851

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W. C. L. Hopman, H. J. W. M. Hoekstra, R. Dekker, L. Zhuang, and R .M. de Ridder, "Far-field scattering microscopy applied to analysis of slow light, power enhancement, and delay times in uniform Bragg waveguide gratings," Opt. Express 15, 1851-1870 (2007)

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Abstract

A novel method is presented for determining the group index, intensity enhancement and delay times for waveguide gratings, based on (Rayleigh) scattering observations. This far-field scattering microscopy (FScM) method is compared with the phase shift method and a method that uses the transmission spectrum to quantify the slow wave properties. We find a minimum group velocity of 0.04c and a maximum intensity enhancement of ∼14.5 for a 1000-period grating and a maximum group delay of ∼80 ps for a 2000-period grating. Furthermore, we show that the FScM method can be used for both displaying the intensity distribution of the Bloch resonances and for investigating out of plane losses. Finally, an application is discussed for the slow-wave grating as index sensor able to detect a minimum cladding index change of 10^-8, assuming a transmission detection limit of 10^-4.

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J. F. Lepage, R. Massudi, G. Anctil, S. Gilbert, M. Piche, and N. McCarthy, “Apodizing holographic gratings for the modal control of semiconductor lasers,” Appl. Opt. 36,4993–4998 (1997).
[Crossref] [PubMed]
W. C. L. Hopman, P. Pottier, D. Yudistira, J. van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building-block for refractometric optical sensors,” IEEE J. Sel. Tops. Quantum Electron. 11,11–16 (2005).
[Crossref]
P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, “Waveguide distributed Bragg reflector laser arrays in erbium doped glass made by dry Ag film ion exchange,” Opt. Eng. 41,1084–1086 (2002).
[Crossref]
H. C. Wu, Z. M. Sheng, and J. Zhang, “Chirped pulse compression in nonuniform plasma Bragg gratings,” Appl. Phys. Lett. 87,201502/1–3 (2005).
[Crossref]
D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic-bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18,1326–1333 (2001).
[Crossref]
D. Faccio, F. Bragheri, and M. Cherchi, “Optical Bloch-mode-induced quasi phase matching of quadratic interactions in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 21,296–301 (2004).
[Crossref]
J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34,455–470 (2002).
[Crossref]
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[Crossref] [PubMed]
V. I. Kopp, B. Fan, H. K. M. Vithana, and A. Z. Genack, “Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals,” Opt. Lett. 23,1707–1709 (1998).
[Crossref]
A. Figotin and I. Vitebskiy, “Slow light in photonic crystals,” Waves Random Complex Media 16,293–382 (2006).
[Crossref]
H. J. W. M. Hoekstra, W. C. L. Hopman, J. Kautz, R. Dekker, and R. M. de Ridder, “A simple coupled mode model for near band-edge phenomena in grated waveguides,” accepted for publication in Opt. Quantum Electron. (2006).
W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. De Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18,1855–1857 (2006).
[Crossref]
J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53,4107–4121 (1996).
[Crossref]
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[Crossref] [PubMed]
C. E. Finlayson, F. Cattaneo, N. M. B. Perney, J. J. Baumberg, M. C. Netti, M. E. Zoorob, M. D. B. Charlton, and G. J. Parker, “Slow light and chromatic temporal dispersion in photonic crystal waveguides using femtosecond time of flight,” Phys. Rev. E 73,016619/1–10 (2006).
[Crossref]
R. S. Jacobsen, A. V. Lavrinenko, L. H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage-Pedersen, and P. I. Borel, “Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides,” Opt. Express. 13,7861–7871 (2005).
[Crossref] [PubMed]
M. C. Netti, C. E. Finlayson, J. J. Baumberg, M. D. B. Charlton, M. E. Zoorob, J. S. Wilkinson, and G. J. Parker, “Separation of photonic crystal waveguides modes using femtosecond time-of-flight,” Appl. Phys. Lett. 81,3927–3929 (2002).
[Crossref]
Y. A. Vlasov, S. Petit, G. Klein, B. Honerlage, and C. Hirlimann, “Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal,” Phys. Rev. E 60,1030–1035 (1999).
[Crossref]
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]
M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87,253902/1–4 (2001).
[Crossref] [PubMed]
X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor D′Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79,2312–2314 (2001).
[Crossref]
K. Daikoku and A. Sugimura, “Direct measurement of wavelength dispersion in optical fibres-difference method,” Electron. Lett. 14,149–151 (1978).
[Crossref]
K. Hosomi, T. Fukamachi, T. Katsuyama, and Y. Arakawa, “Group delay of a coupled-defect waveguide in a photonic crystal,” Opt. Rev. 11,300–302 (2004).
[Crossref]
S. Ryu, Y. Horiuchi, and K. Mochizuki, “Novel chromatic dispersion measurement method over continuous Gigahertz tuning range,” J. Lightwave Technol. 7,1177–1180 (1989).
[Crossref]
W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quantum Electron. 34,195–203 (2002).
[Crossref]
R. Ferrini, R. Houdre, H. Benisty, M. Qiu, and J. Moosburger, “Radiation losses in planar photonic crystals: two-dimensional representation of hole depth and shape by an imaginary dielectric constant,” J. Opt. Soc. Am. B 20,469–478 (2003).
[Crossref]
S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express. 11,2927–2939 (2003).
[Crossref] [PubMed]
M. Loncar, D. Nedeljkovic, T. P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D. C. Allan, “Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides,” Appl. Phys. Lett. 80,1689–1691 (2002).
[Crossref]
D. J. W. Klunder, F. S. Tan, T. Van der Veen, H. F. Bulthuis, G. Sengo, B. Docter, H. J. W. M. Hoekstra, and A. Driessen, “Experimental and numerical study of SiON microresonators with air and polymer cladding,” J. Lightwave Technol. 21,1099–1110 (2003).
[Crossref]
D. B. Hunter, M. E. Parker, and J. L. Dexter, “Demonstration of a continuously variable true-time delay beamformer using a multichannel chirped fiber grating,” IEEE Trans. Microwave Theory Tech. 54,861–867 (2006).
[Crossref]
J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol., B 20,2753–2757 (2002).
[Crossref]
J. F. Lepage and N. McCarthy, “Analysis of the diffractional properties of dual-period apodizing gratings: theoretical and experimental results,” Appl. Opt. 43,3504–3512 (2004).
[Crossref] [PubMed]
D. Wiesmann, C. David, R. Germann, D. Emi, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12,639–641 (2000).
[Crossref]
L. Xuhui, C. Xiangfei, Y. Yuzhe, and X. Shizhong, “A novel apodization technique of variable duty cycle for sampled grating,” Opt. Commun. 225,301–305 (2003).
[Crossref]
H. G. Winful, “The meaning of group delay in barrier tunnelling: A re-examination of superluminal group velocities,” New J. Phys. 8,101/1–16 (2006).
[Crossref]
Olympios, “OlympIOs Integrated Optics Software,” C2V, http://www.c2v.nl/software/.
C. De Angelis, F. Gringoli, M. Midrio, D. Modotto, J. S. Aitchison, and G. F. Nalesso, “Conversion efficiency for second-harmonic generation in photonic crystals,” J. Opt. Soc. Am. B 18,348–351 (2001).
[Crossref]
M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt. Express. 13,7145–7159 (2005).
[Crossref] [PubMed]
D. Yudistira, H. Hoekstra, M. Hammer, and D. Marpaung, “Slow light excitation in tapered 1D photonic crystals: Theory,” Opt. Quantum Electron. 38,161–176 (2006).
[Crossref]
P. V. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. 17,R93–R116 (2006).
[Crossref]

2006 (7)

A. Figotin and I. Vitebskiy, “Slow light in photonic crystals,” Waves Random Complex Media 16,293–382 (2006).
[Crossref]

W. C. L. Hopman, R. Dekker, D. Yudistira, W. F. A. Engbers, H. J. W. M. Hoekstra, and R. M. De Ridder, “Fabrication and characterization of high-quality uniform and apodized Si3N4 waveguide gratings using laser interference lithography,” IEEE Photon. Technol. Lett. 18,1855–1857 (2006).
[Crossref]

C. E. Finlayson, F. Cattaneo, N. M. B. Perney, J. J. Baumberg, M. C. Netti, M. E. Zoorob, M. D. B. Charlton, and G. J. Parker, “Slow light and chromatic temporal dispersion in photonic crystal waveguides using femtosecond time of flight,” Phys. Rev. E 73,016619/1–10 (2006).
[Crossref]

D. B. Hunter, M. E. Parker, and J. L. Dexter, “Demonstration of a continuously variable true-time delay beamformer using a multichannel chirped fiber grating,” IEEE Trans. Microwave Theory Tech. 54,861–867 (2006).
[Crossref]

H. G. Winful, “The meaning of group delay in barrier tunnelling: A re-examination of superluminal group velocities,” New J. Phys. 8,101/1–16 (2006).
[Crossref]

D. Yudistira, H. Hoekstra, M. Hammer, and D. Marpaung, “Slow light excitation in tapered 1D photonic crystals: Theory,” Opt. Quantum Electron. 38,161–176 (2006).
[Crossref]

P. V. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. 17,R93–R116 (2006).
[Crossref]

2005 (6)

M. L. Povinelli, S. G. Johnson, and J. D. 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]

R. S. Jacobsen, A. V. Lavrinenko, L. H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage-Pedersen, and P. I. Borel, “Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides,” Opt. Express. 13,7861–7871 (2005).
[Crossref] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys Rev Lett 94 (2005).
[Crossref] [PubMed]

W. C. L. Hopman, P. Pottier, D. Yudistira, J. van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building-block for refractometric optical sensors,” IEEE J. Sel. Tops. Quantum Electron. 11,11–16 (2005).
[Crossref]

H. C. Wu, Z. M. Sheng, and J. Zhang, “Chirped pulse compression in nonuniform plasma Bragg gratings,” Appl. Phys. Lett. 87,201502/1–3 (2005).
[Crossref]

2004 (4)

D. Faccio, F. Bragheri, and M. Cherchi, “Optical Bloch-mode-induced quasi phase matching of quadratic interactions in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 21,296–301 (2004).
[Crossref]

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3,211–219 (2004).
[Crossref] [PubMed]

K. Hosomi, T. Fukamachi, T. Katsuyama, and Y. Arakawa, “Group delay of a coupled-defect waveguide in a photonic crystal,” Opt. Rev. 11,300–302 (2004).
[Crossref]

J. F. Lepage and N. McCarthy, “Analysis of the diffractional properties of dual-period apodizing gratings: theoretical and experimental results,” Appl. Opt. 43,3504–3512 (2004).
[Crossref] [PubMed]

2003 (4)

D. J. W. Klunder, F. S. Tan, T. Van der Veen, H. F. Bulthuis, G. Sengo, B. Docter, H. J. W. M. Hoekstra, and A. Driessen, “Experimental and numerical study of SiON microresonators with air and polymer cladding,” J. Lightwave Technol. 21,1099–1110 (2003).
[Crossref]

R. Ferrini, R. Houdre, H. Benisty, M. Qiu, and J. Moosburger, “Radiation losses in planar photonic crystals: two-dimensional representation of hole depth and shape by an imaginary dielectric constant,” J. Opt. Soc. Am. B 20,469–478 (2003).
[Crossref]

S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express. 11,2927–2939 (2003).
[Crossref] [PubMed]

L. Xuhui, C. Xiangfei, Y. Yuzhe, and X. Shizhong, “A novel apodization technique of variable duty cycle for sampled grating,” Opt. Commun. 225,301–305 (2003).
[Crossref]

2002 (6)

M. Loncar, D. Nedeljkovic, T. P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D. C. Allan, “Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides,” Appl. Phys. Lett. 80,1689–1691 (2002).
[Crossref]

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quantum Electron. 34,195–203 (2002).
[Crossref]

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol., B 20,2753–2757 (2002).
[Crossref]

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, and R. M. De La Rue, “Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task,” Opt. Quantum Electron. 34,455–470 (2002).
[Crossref]

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, “Waveguide distributed Bragg reflector laser arrays in erbium doped glass made by dry Ag film ion exchange,” Opt. Eng. 41,1084–1086 (2002).
[Crossref]

M. C. Netti, C. E. Finlayson, J. J. Baumberg, M. D. B. Charlton, M. E. Zoorob, J. S. Wilkinson, and G. J. Parker, “Separation of photonic crystal waveguides modes using femtosecond time-of-flight,” Appl. Phys. Lett. 81,3927–3929 (2002).
[Crossref]

2001 (4)

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic-bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18,1326–1333 (2001).
[Crossref]

C. De Angelis, F. Gringoli, M. Midrio, D. Modotto, J. S. Aitchison, and G. F. Nalesso, “Conversion efficiency for second-harmonic generation in photonic crystals,” J. Opt. Soc. Am. B 18,348–351 (2001).
[Crossref]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87,253902/1–4 (2001).
[Crossref] [PubMed]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor D′Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79,2312–2314 (2001).
[Crossref]

2000 (1)

D. Wiesmann, C. David, R. Germann, D. Emi, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12,639–641 (2000).
[Crossref]

1999 (1)

Y. A. Vlasov, S. Petit, G. Klein, B. Honerlage, and C. Hirlimann, “Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal,” Phys. Rev. E 60,1030–1035 (1999).
[Crossref]

1998 (1)

V. I. Kopp, B. Fan, H. K. M. Vithana, and A. Z. Genack, “Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals,” Opt. Lett. 23,1707–1709 (1998).
[Crossref]

1997 (1)

J. F. Lepage, R. Massudi, G. Anctil, S. Gilbert, M. Piche, and N. McCarthy, “Apodizing holographic gratings for the modal control of semiconductor lasers,” Appl. Opt. 36,4993–4998 (1997).
[Crossref] [PubMed]

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53,4107–4121 (1996).
[Crossref]

1989 (1)

S. Ryu, Y. Horiuchi, and K. Mochizuki, “Novel chromatic dispersion measurement method over continuous Gigahertz tuning range,” J. Lightwave Technol. 7,1177–1180 (1989).
[Crossref]

1978 (1)

K. Daikoku and A. Sugimura, “Direct measurement of wavelength dispersion in optical fibres-difference method,” Electron. Lett. 14,149–151 (1978).
[Crossref]

Aitchison, J. S.

Allan, D. C.

Anctil, G.

Arakawa, Y.

K. Hosomi, T. Fukamachi, T. Katsuyama, and Y. Arakawa, “Group delay of a coupled-defect waveguide in a photonic crystal,” Opt. Rev. 11,300–302 (2004).
[Crossref]

Baets, R.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quantum Electron. 34,195–203 (2002).
[Crossref]

Baumberg, J. J.

Bendickson, J. M.

Benisty, H.

Bertolotti, M.

Bienstman, P.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quantum Electron. 34,195–203 (2002).
[Crossref]

Bloemer, M. J.

Bogaerts, W.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quantum Electron. 34,195–203 (2002).
[Crossref]

Bona, G. L.

D. Wiesmann, C. David, R. Germann, D. Emi, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12,639–641 (2000).
[Crossref]

Borel, P. I.

Bowden, C. M.

Bragheri, F.

Bulthuis, H. F.

Cassagne, D.

Cattaneo, F.

Charlton, M. D. B.

Cherchi, M.

Conti, G. N.

Ctyroky, J.

Daikoku, K.

K. Daikoku and A. Sugimura, “Direct measurement of wavelength dispersion in optical fibres-difference method,” Electron. Lett. 14,149–151 (1978).
[Crossref]

David, C.

D. Wiesmann, C. David, R. Germann, D. Emi, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12,639–641 (2000).
[Crossref]

De Angelis, C.

De La Rue, R. M.

De Ridder, R.

De Ridder, R. M.

H. J. W. M. Hoekstra, W. C. L. Hopman, J. Kautz, R. Dekker, and R. M. de Ridder, “A simple coupled mode model for near band-edge phenomena in grated waveguides,” accepted for publication in Opt. Quantum Electron. (2006).

De Zutter, D.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quantum Electron. 34,195–203 (2002).
[Crossref]

Dekker, R.

Dexter, J. L.

Docter, B.

Dowling, J. P.

Driessen, A.

Emi, D.

D. Wiesmann, C. David, R. Germann, D. Emi, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12,639–641 (2000).
[Crossref]

Engbers, W. F. A.

Engelen, R. J. P.

Faccio, D.

Fage-Pedersen, J.

Fan, B.

V. I. Kopp, B. Fan, H. K. M. Vithana, and A. Z. Genack, “Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals,” Opt. Lett. 23,1707–1709 (1998).
[Crossref]

Ferrini, R.

Figotin, A.

A. Figotin and I. Vitebskiy, “Slow light in photonic crystals,” Waves Random Complex Media 16,293–382 (2006).
[Crossref]

Finlayson, C. E.

Frandsen, L. H.

Fukamachi, T.

K. Hosomi, T. Fukamachi, T. Katsuyama, and Y. Arakawa, “Group delay of a coupled-defect waveguide in a photonic crystal,” Opt. Rev. 11,300–302 (2004).
[Crossref]

Genack, A. Z.

V. I. Kopp, B. Fan, H. K. M. Vithana, and A. Z. Genack, “Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals,” Opt. Lett. 23,1707–1709 (1998).
[Crossref]

Geraghty, D. F.

Germann, R.

D. Wiesmann, C. David, R. Germann, D. Emi, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12,639–641 (2000).
[Crossref]

Gersen, H.

Gilbert, S.

Goodberlet, J. G.

Grillet, C.

Gringoli, F.

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]

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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).
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L. Xuhui, C. Xiangfei, Y. Yuzhe, and X. Shizhong, “A novel apodization technique of variable duty cycle for sampled grating,” Opt. Commun. 225,301–305 (2003).
[Crossref]

Xuhui, L.

L. Xuhui, C. Xiangfei, Y. Yuzhe, and X. Shizhong, “A novel apodization technique of variable duty cycle for sampled grating,” Opt. Commun. 225,301–305 (2003).
[Crossref]

Yamada, K.

Yokohama, I.

Yudistira, D.

D. Yudistira, H. Hoekstra, M. Hammer, and D. Marpaung, “Slow light excitation in tapered 1D photonic crystals: Theory,” Opt. Quantum Electron. 38,161–176 (2006).
[Crossref]

Yuzhe, Y.

L. Xuhui, C. Xiangfei, Y. Yuzhe, and X. Shizhong, “A novel apodization technique of variable duty cycle for sampled grating,” Opt. Commun. 225,301–305 (2003).
[Crossref]

Zhang, J.

H. C. Wu, Z. M. Sheng, and J. Zhang, “Chirped pulse compression in nonuniform plasma Bragg gratings,” Appl. Phys. Lett. 87,201502/1–3 (2005).
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Zsigri, B.

Appl. Opt. (2)

Appl. Phys. Lett. (4)

H. C. Wu, Z. M. Sheng, and J. Zhang, “Chirped pulse compression in nonuniform plasma Bragg gratings,” Appl. Phys. Lett. 87,201502/1–3 (2005).
[Crossref]

Electron. Lett. (1)

K. Daikoku and A. Sugimura, “Direct measurement of wavelength dispersion in optical fibres-difference method,” Electron. Lett. 14,149–151 (1978).
[Crossref]

IEEE J. Sel. Tops. Quantum Electron. (1)

IEEE Photon. Technol. Lett. (2)

D. Wiesmann, C. David, R. Germann, D. Emi, and G. L. Bona, “Apodized surface-corrugated gratings with varying duty cycles,” IEEE Photon. Technol. Lett. 12,639–641 (2000).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

J. Lightwave Technol. (2)

S. Ryu, Y. Horiuchi, and K. Mochizuki, “Novel chromatic dispersion measurement method over continuous Gigahertz tuning range,” J. Lightwave Technol. 7,1177–1180 (1989).
[Crossref]

J. Opt. Soc. Am. B (4)

J. Vac. Sci. Technol., B (1)

Meas. Sci. Technol. (1)

P. V. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. 17,R93–R116 (2006).
[Crossref]

Nat. Mater. (1)

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3,211–219 (2004).
[Crossref] [PubMed]

Nature (1)

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]

New J. Phys. (1)

H. G. Winful, “The meaning of group delay in barrier tunnelling: A re-examination of superluminal group velocities,” New J. Phys. 8,101/1–16 (2006).
[Crossref]

Opt. Commun. (1)

L. Xuhui, C. Xiangfei, Y. Yuzhe, and X. Shizhong, “A novel apodization technique of variable duty cycle for sampled grating,” Opt. Commun. 225,301–305 (2003).
[Crossref]

Opt. Eng. (1)

Opt. Express. (3)

S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express. 11,2927–2939 (2003).
[Crossref] [PubMed]

M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt. Express. 13,7145–7159 (2005).
[Crossref] [PubMed]

Opt. Lett. (1)

V. I. Kopp, B. Fan, H. K. M. Vithana, and A. Z. Genack, “Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals,” Opt. Lett. 23,1707–1709 (1998).
[Crossref]

Opt. Quantum Electron. (3)

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. De Zutter, “Out-of-plane scattering in 1-D photonic crystal slabs,” Opt. Quantum Electron. 34,195–203 (2002).
[Crossref]

D. Yudistira, H. Hoekstra, M. Hammer, and D. Marpaung, “Slow light excitation in tapered 1D photonic crystals: Theory,” Opt. Quantum Electron. 38,161–176 (2006).
[Crossref]

Opt. Rev. (1)

K. Hosomi, T. Fukamachi, T. Katsuyama, and Y. Arakawa, “Group delay of a coupled-defect waveguide in a photonic crystal,” Opt. Rev. 11,300–302 (2004).
[Crossref]

Phys Rev Lett (1)

Phys. Rev. E (3)

Phys. Rev. Lett. (1)

Waves Random Complex Media (1)

A. Figotin and I. Vitebskiy, “Slow light in photonic crystals,” Waves Random Complex Media 16,293–382 (2006).
[Crossref]

Other (3)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: Molding the flow of light (Princeton University Press, 1995).

Olympios, “OlympIOs Integrated Optics Software,” C2V, http://www.c2v.nl/software/.

Supplementary Material (2)

» Media 1: AVI (5123 KB)

» Media 2: AVI (2737 KB)

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Figures (16)

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.
Fig. 16.

Fig. 1.

(a). Schematic 3D drawing of the WGG. (b) Top view SEM image of a zoomed in view of the 500-Period WGG, the small ridge of only 5 nm is not observed in the image.

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Fig. 2.

Schematic drawing of the dual-setup: NIR CCD-camera + end-fire detection.

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Fig. 3.

Power balance of the resonator (effective length L, effective cross-section A_r ) with input and output waveguides, and radiative coupling to free space (and substrate). The right traveling energy flux density S ₀ ⁺ in the input waveguide is partly back reflected (S ₀ ^-) and couples in part to the resonator (flux density S_i ) and in part to radiation modes S _s1 due to modal mismatch between waveguide mode and resonator mode. Inside the resonator, the net flux density S_r , which is composed of a right traveling flux density S_r ⁺ and a left traveling one S _r ^- is assumed to be constant along the cavity (neglecting S_sc ). At the interface to the output waveguide, an output flux density S_out remains after subtracting radiation loss S _s2 due to modal mismatch.

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Fig. 4.

The group index of a reference waveguide (dashed) and the normalized transmission T (blue) and group index (red) of a 350-period WGG obtained using a BEP method and Eq. (19).

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Fig. 5.

Intra-cavity grating resonance modes in the dielectric band obtained via BEP Simulations. (a)-(d) The top image shows the H-field amplitude in the cross-section of the WGG for the resonance wavelengths shown in Fig. 4. The x- and z-coordinates are defined in Fig. 2. The bottom graphs show the H-field amplitude along the center-line of the guiding layer.

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Fig. 6.

Field amplitude (H-field) of the grating resonances at both band edges (resonances I and −I) of a 100-period WGG. In the middle section of the periodic medium (the grating) we see the well known phenomena [8] (studied by overlaying the grating structure with the field-distributions): the field for the first resonance in the air band is concentrated in the grooves (low-index) and for the dielectric band in the teeth (high-index). There is a shift between both field distributions of half a period. At the transition between the grating and the waveguide we observe the same (in phase) field distribution.

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Fig. 7.

(a). Maximum field strength as function of the number of periods. (b) Maximum group index (N_g ) and Q versus the number of periods.

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Fig. 8.

Normalized transmission versus cladding index and wavelength for a 200-period WGG.

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Fig. 9.

Measurements on the 500-period waveguide grating. (a) Transmission spectrum of the WGG. (b) The scatter intensity (I_sc ) collected using the NIR camera. (c) Scatter image A is taken from the grating region without cladding at the wavelength in the stopband labeled A in the transmission and scatter graphs (panels (a) and (b), respectively) [Media 2]. A wavelength scaling factor has been used to account for the difference in cladding index, as explained further in the text. Only scattering from the input spot is observed for this wavelength. Image B is taken at the lowest-order resonance wavelength. The smoothed curve in graph B″ shows a single maximum. Images C and D show 2 and 3 intra-cavity maxima, respectively. The frames A to D can be clicked to start a movie (2.67 MB) of the transmission versus an increasing wavelength (6.82MB version).

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Fig. 10.

Measurements on the 1000-period grating. (a) Transmission spectrum of the WGG, showing a very sharp fringe with a FWHM of only 33 pm in the airband, which corresponds to a Q of 46000. (b) The scatter intensity (I_sc ) spectrum collected using the NIR camera.

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Fig. 11.

Relative group delay as a function of wavelength, directly measured using the phase shift method for the 1000-periods long grating.

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Fig. 12.

Transmission spectrum obtained from the 2000-periods grating, zoomed in on the left edge.

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Fig. 13.

Measurements on the 2000-periods long grating. (a) The scatter intensity spectrum (b) Relative group delay, directly measured using the phase shift method.

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Fig. 14.

(a). Experimentally derived relationship between η and Q. (b) Group delays calculated using various methods versus the directly measured group delay (t_d ).

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Fig. 15.

A BEP [37] simulation of the transmission (T), reflection (R) and loss of a 350 period WGG. The out of plane loss is calculated using the relation OPS = 1 − R − T.

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Fig. 16.

Measurement of the scattering observed at the input and output spots of the grating. A sum of both gives a figure for the total OPS.

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Equations (20)

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

v_{g} (ω) = \frac{d ω}{dk},

Q = ω_{0} \frac{U}{\frac{d U}{d t}},

Q = ω_{0} τ_{c} .

Q = \frac{λ_{0}}{Δ λ_{- 3 dB}},

U = W_{r} V = W_{r} A_{r} L .

\frac{d U}{d t} = S_{i} A_{r} .

S_{i} \approx S_{r} = W_{r} v_{g} .

Q = ω_{0} \frac{W_{r} V}{S_{r} A_{r}} = ω_{0} \frac{S_{r}}{S_{i}} \frac{L}{v_{g}} = ω_{0} \frac{L}{v_{g}} .

Q = 2 π \frac{L N_{g}}{λ_{0}} .

t_{d} (λ) = \frac{L}{c} N_{g} (λ) .

t_{q} = τ_{c} = \frac{Q λ_{0}}{2 π c} .

η (λ) = \frac{U}{U_{ref}} = \frac{W_{r} (λ) V}{W_{ref} (λ_{ref}) V} = \frac{S (λ) v_{g, ref} (λ_{ref})}{S_{ref} (λ_{ref}) v_{g} (λ)} = \frac{N_{g} (λ)}{N_{g, ref} (λ_{ref})} .

η (λ) = \frac{N_{g} (λ)}{N_{g, ref} (λ_{ref})} \approx \frac{I_{s c} (λ)}{I_{s c, r e f} (λ_{ref})} .

t_{s c} (λ) = \frac{L}{c} η (λ) N_{g, ref} (λ_{ref}) .

Q (λ_{0}) = η (λ_{0}) \frac{2 π L N_{g, ref} (λ_{ref})}{λ_{0}} .

Δ λ_{FSR} = \frac{λ_{0}^{2}}{2 N_{g} L} .

t_{FSR} = \frac{λ_{0}^{2}}{2 c Δ λ_{FSR}} .

t (ω) \equiv x (ω) + i y (ω) .

v_{g} = \frac{d ω}{d k} = L \frac{x^{2} + y^{2}}{x \frac{d y}{d ω} - y \frac{d x}{d ω}} .

Δ n_{cladding} \approx \frac{\partial n}{\partial λ} \frac{\partial λ}{\partial T} Δ T_{0}