Abstract

Photonic Wire Bragg Gratings, made by periodic insertion of lateral rectangular recesses into photonic wires in silicon-on-insulator, can provide large reflectivity with short device lengths because of their large index contrast. This type of design shows a counter-intuitive behaviour, as we demonstrate — using experimental and numerical data — that it can have low or null reflectance, even for large indentation values. We provide physical insight into this phenomenon by developing a model based on Bloch mode theory, and are able to find an analytical expression for the frequency at which the grating does not sustain the stop-band. Finally we demonstrate that the stop-band closing effect is a general phenomenon that may occur in various types of periodic device that can be modeled as transmission line structures.

© 2009 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. F. Fogli, N. Greco, P. Bassi, G. Bellanca, P. Aschieri, and P. Baldi, "Spatial harmonics modelling of planar periodic segmented waveguides," Opt. Quantum Electron. 33, 485-498 (2001).
    [CrossRef]
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    [CrossRef]

2009 (1)

A. S. Jugessur, J. Dou, S. Aitchison, R. M. De La Rue, and M. Gnan, "A photonic nano-Bragg grating device integrated with microfluidic channels for bio-sensing applications," Microelectron. Eng.(in press, 2009).
[CrossRef]

2008 (2)

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, "Fabrication of low-loss photonic wires in silicon-on-insulator using Hydrogen Silsesquioxane electron-beam resist," Electron. Lett. 44, 115-116 (2008).
[CrossRef]

A. R. Md Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, "Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI)," Opt. Express 16, 12084-12089 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (3)

2005 (1)

2001 (2)

F. Fogli, N. Greco, P. Bassi, G. Bellanca, P. Aschieri, and P. Baldi, "Spatial harmonics modelling of planar periodic segmented waveguides," Opt. Quantum Electron. 33, 485-498 (2001).
[CrossRef]

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

1996 (1)

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, "Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure," J. Mod. Opt. 43, 1035-1053 (1996).
[CrossRef]

Aitchison, S.

A. S. Jugessur, J. Dou, S. Aitchison, R. M. De La Rue, and M. Gnan, "A photonic nano-Bragg grating device integrated with microfluidic channels for bio-sensing applications," Microelectron. Eng.(in press, 2009).
[CrossRef]

Aschieri, P.

F. Fogli, N. Greco, P. Bassi, G. Bellanca, P. Aschieri, and P. Baldi, "Spatial harmonics modelling of planar periodic segmented waveguides," Opt. Quantum Electron. 33, 485-498 (2001).
[CrossRef]

Atkin, D. M.

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, "Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure," J. Mod. Opt. 43, 1035-1053 (1996).
[CrossRef]

Baets, R.

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Baldi, P.

F. Fogli, N. Greco, P. Bassi, G. Bellanca, P. Aschieri, and P. Baldi, "Spatial harmonics modelling of planar periodic segmented waveguides," Opt. Quantum Electron. 33, 485-498 (2001).
[CrossRef]

Bassi, P.

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, "Modelling of photonic wire Bragg gratings," Opt. Quantum Electron. 38, 133-148 (2006).
[CrossRef]

F. Fogli, N. Greco, P. Bassi, G. Bellanca, P. Aschieri, and P. Baldi, "Spatial harmonics modelling of planar periodic segmented waveguides," Opt. Quantum Electron. 33, 485-498 (2001).
[CrossRef]

Bellanca, G.

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, "Modelling of photonic wire Bragg gratings," Opt. Quantum Electron. 38, 133-148 (2006).
[CrossRef]

F. Fogli, N. Greco, P. Bassi, G. Bellanca, P. Aschieri, and P. Baldi, "Spatial harmonics modelling of planar periodic segmented waveguides," Opt. Quantum Electron. 33, 485-498 (2001).
[CrossRef]

Bettotti, P.

Bienstman, P.

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Birks, T. A.

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, "Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure," J. Mod. Opt. 43, 1035-1053 (1996).
[CrossRef]

Charvolin, T.

Chong, H.

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, "Modelling of photonic wire Bragg gratings," Opt. Quantum Electron. 38, 133-148 (2006).
[CrossRef]

De La Rue, R. M.

A. S. Jugessur, J. Dou, S. Aitchison, R. M. De La Rue, and M. Gnan, "A photonic nano-Bragg grating device integrated with microfluidic channels for bio-sensing applications," Microelectron. Eng.(in press, 2009).
[CrossRef]

A. R. Md Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, "Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI)," Opt. Express 16, 12084-12089 (2008).
[CrossRef] [PubMed]

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, "Fabrication of low-loss photonic wires in silicon-on-insulator using Hydrogen Silsesquioxane electron-beam resist," Electron. Lett. 44, 115-116 (2008).
[CrossRef]

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, "Modelling of photonic wire Bragg gratings," Opt. Quantum Electron. 38, 133-148 (2006).
[CrossRef]

Dou, J.

A. S. Jugessur, J. Dou, S. Aitchison, R. M. De La Rue, and M. Gnan, "A photonic nano-Bragg grating device integrated with microfluidic channels for bio-sensing applications," Microelectron. Eng.(in press, 2009).
[CrossRef]

Fathpour, S.

Fogli, F.

F. Fogli, N. Greco, P. Bassi, G. Bellanca, P. Aschieri, and P. Baldi, "Spatial harmonics modelling of planar periodic segmented waveguides," Opt. Quantum Electron. 33, 485-498 (2001).
[CrossRef]

Gnan, M.

A. S. Jugessur, J. Dou, S. Aitchison, R. M. De La Rue, and M. Gnan, "A photonic nano-Bragg grating device integrated with microfluidic channels for bio-sensing applications," Microelectron. Eng.(in press, 2009).
[CrossRef]

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, "Fabrication of low-loss photonic wires in silicon-on-insulator using Hydrogen Silsesquioxane electron-beam resist," Electron. Lett. 44, 115-116 (2008).
[CrossRef]

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, "Modelling of photonic wire Bragg gratings," Opt. Quantum Electron. 38, 133-148 (2006).
[CrossRef]

Greco, N.

F. Fogli, N. Greco, P. Bassi, G. Bellanca, P. Aschieri, and P. Baldi, "Spatial harmonics modelling of planar periodic segmented waveguides," Opt. Quantum Electron. 33, 485-498 (2001).
[CrossRef]

Hadji, E.

Jalali, B.

Johnson, N. P.

Jugessur, A. S.

A. S. Jugessur, J. Dou, S. Aitchison, R. M. De La Rue, and M. Gnan, "A photonic nano-Bragg grating device integrated with microfluidic channels for bio-sensing applications," Microelectron. Eng.(in press, 2009).
[CrossRef]

Lalanne, P.

Lipson, M.

Macintyre, D. S.

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, "Fabrication of low-loss photonic wires in silicon-on-insulator using Hydrogen Silsesquioxane electron-beam resist," Electron. Lett. 44, 115-116 (2008).
[CrossRef]

Md Zain, A. R.

Noda, S.

Pavesi, L.

Peyrade, D.

Picard, E.

Riboli, F.

Roberts, P. J.

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, "Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure," J. Mod. Opt. 43, 1035-1053 (1996).
[CrossRef]

Rodier, J. C.

Russell, P. S. J.

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, "Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure," J. Mod. Opt. 43, 1035-1053 (1996).
[CrossRef]

Sorel, M.

A. R. Md Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, "Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI)," Opt. Express 16, 12084-12089 (2008).
[CrossRef] [PubMed]

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, "Fabrication of low-loss photonic wires in silicon-on-insulator using Hydrogen Silsesquioxane electron-beam resist," Electron. Lett. 44, 115-116 (2008).
[CrossRef]

Thoms, S.

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, "Fabrication of low-loss photonic wires in silicon-on-insulator using Hydrogen Silsesquioxane electron-beam resist," Electron. Lett. 44, 115-116 (2008).
[CrossRef]

Velha, P.

Electron. Lett. (1)

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, "Fabrication of low-loss photonic wires in silicon-on-insulator using Hydrogen Silsesquioxane electron-beam resist," Electron. Lett. 44, 115-116 (2008).
[CrossRef]

J. Lightwave Technol. (3)

J. Mod. Opt. (1)

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, "Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure," J. Mod. Opt. 43, 1035-1053 (1996).
[CrossRef]

Microelectron. Eng. (1)

A. S. Jugessur, J. Dou, S. Aitchison, R. M. De La Rue, and M. Gnan, "A photonic nano-Bragg grating device integrated with microfluidic channels for bio-sensing applications," Microelectron. Eng.(in press, 2009).
[CrossRef]

Opt. Express (3)

Opt. Quantum Electron. (3)

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, "Modelling of photonic wire Bragg gratings," Opt. Quantum Electron. 38, 133-148 (2006).
[CrossRef]

F. Fogli, N. Greco, P. Bassi, G. Bellanca, P. Aschieri, and P. Baldi, "Spatial harmonics modelling of planar periodic segmented waveguides," Opt. Quantum Electron. 33, 485-498 (2001).
[CrossRef]

P. Bienstman and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
[CrossRef]

Other (1)

P. Yeh and A. Yariv, Optical Waves in Crystals, (Wiley, 1984).

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Figures (10)

Fig. 1.
Fig. 1.

Scanning electron micrograph giving a ‘bird’s-eye’ view of photonic wire Bragg grating fully etched into silicon waveguide core layer. Inset: top view, defining dimensions.

Fig. 2.
Fig. 2.

Experimental transmission curves for three recess depth (d) values (other dimensions are given in the main text). For recess depth d = 160 nm the main stop-band is centered at ≈ 1385 nm. The higher order stop-band is also visible at wavelengths smaller than 1320 nm (compare with Fig. 3). For d = 170 nm the main stop-band is not visible (the dotted line points to its expected centre). For d = 180 nm the stop-band is again visible centered approximately at 1340 nm. Also the higher order stop-band is shifted to smaller wavelengths and does not appear in the graph. Note that the overall slope of all the curves is mainly due to the characteristic of the light source employed.

Fig. 3.
Fig. 3.

Calculated Transmission (T) and Loss (L) spectra (obtained as L = 1 - (T + R), R standing for Reflectance) relevant to three geometrical configurations. For recess depth d = 160 nm, the stop-band disappears. Note the opposite slope of the loss curve within the stop-band region for d = 150 nm and d = 170 nm. The gratings are 16-periods long.

Fig. 4.
Fig. 4.

Positions of numerical (black filled circles) and experimental (red empty circles) transmission stop-band of PhWBG in dependence on the recess depth d. The reduction of stop bandwidth is consistent the reduction of numerical maximum reflectance (crossed diamonds)

Fig. 5.
Fig. 5.

Sketch of the steps of the theoretical model. (a) Semi-infinite interface. (b) 1D-stack grating. (c) Laterally confined 2D grating. (d) Photonic Wire Bragg Grating.

Fig. 6.
Fig. 6.

Band gap edges for TM (solid blue curves) and TE (dashed gray curves) polarization together with the (dashed red) line corresponding to Brewster’s condition. The insets show the normalised squared absolute value of the magnetic field |H|2 for TM polarization at 4 points around the gap-closing condition. Intensity distributions A and B are calculated for ky = 0.2855K, whereas C and D are calculated for ky = 0.3228K.

Fig. 7.
Fig. 7.

Stop-band edges of various orders in dependence of the grating thickness d, calculated with a two-wave approximation of the dispersion relation. The insets show the intensity maps (|Hx |2) for four points around the stop-band closing condition at dB ≈ 0.563 μm. Points A and B have d = 0.538 μm, whereas points C and D have d = 0.59 μm. The dashed horizontal line represents k 0B = 0.3191K evaluated by Eq. (3).

Fig. 8.
Fig. 8.

Dispersion curves and intensity plots (|Hx|2) at the stop-band edges for three values of recess depth d, around the configuration that results in the stop-band being closed (d = 184 nm) at k 0 = 0.288K. The intensity maps are calculated at kz = 0.4989K.

Fig. 9.
Fig. 9.

Three transmission line configurations that can result in stop-band closure.

Fig. 10.
Fig. 10.

Calculated transmittance (black) and dispersion curves (red) of the transmission line loaded by 10 short-circuit stubs as a function of the normalised stub length δ = l/(λ 0/4).

Equations (10)

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ρ=n2cos(α1)n1cos(α2)n1cos(α2)+n2cos(α1),
ky=k0(1n12+1n22)1k0nB,
k0B=πηnB,
tan(α1)=n2n1
tan(α1)=kykz1=kyk02n12ky2
f1Dk0kykzcos(Λkz)(A+D)2=0,
ATM=ejkz1a[cos(kz2b)+j12sin(kz2b)(n22n12kz1kz2+n12n22kz2kz1)]
DTM=ejkz1a[cos(kz2b)j12sin(kz2b)(n22n12kz1kz2+n12n22kz2kz1)],
ΛkzB=ηkyB+2,
k0B=π+2ηnB.

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