Abstract

We consider the spectral properties of dielectric waveguides with low refractive index cores and binary layered claddings, such as Bragg fibers and integrated-ARROWs. We show that the full, nontrivial, 2-D spectrum of Bloch bands (hence bandgaps) of such claddings correspond, in structure and topology, to the dispersion properties of both constituent layer types; quantitatively demonstrating an intimate relationship between the bandgap and antiresonance guidance mechanisms. The dispersion functions of these layers, and the interactions thereof, thus form what we coin the Stratified Planar Anti-Resonant Reflecting OpticalWaveguide (SPARROW) model, capable of quantitative, analytic, descriptions of many nontrivial bandgap and antiresonance properties. The SPARROW model is useful for the spectral analysis and design of Bragg fibers and integrated-ARROWs with cores of arbitrary refractive index (equal to or less than the lowest cladding index). Both waveguide types are of interest for sensing and microfluidic applications due to their natural ability to guide light within low-index cores, permitting low-loss guidance within a large range of gases and liquids. A liquid-core Bragg fiber is discussed as an example, demonstrating the applicability of the SPARROW model to realistic and important waveguide designs.

© 2008 Optical Society of America

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2008

2007

2006

2005

2004

2003

2002

2001

1999

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 19, 2039-2041 (1999).
[CrossRef]

1998

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

1993

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, "Loss calculations for antiresonant waveguides," J. Lightwave Technol. 11, 416-423 (1993).
[CrossRef]

1992

T. Baba and Y. Kokubun, "Dispersion and radiations loss characteristics of antiresonant reflecting optical waveguides - numerical results and analytical expressions," J. Quantum Electron. 28, 1689-1700 (1992).
[CrossRef]

1990

1986

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

1977

1971

Abeeluck, A. K.

Archambault, J. L.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, "Loss calculations for antiresonant waveguides," J. Lightwave Technol. 11, 416-423 (1993).
[CrossRef]

Argyros, A.

Baba, T.

T. Baba and Y. Kokubun, "Dispersion and radiations loss characteristics of antiresonant reflecting optical waveguides - numerical results and analytical expressions," J. Quantum Electron. 28, 1689-1700 (1992).
[CrossRef]

T. Baba and Y. Kokubun, "High efficiency light coupling from antiresonant reflecting optical waveguide to integrated photodetector using an antireflecting layer," Appl. Opt. 29, 2781-2792 (1990).
[CrossRef] [PubMed]

Barber, J. P.

Bassett, I. M.

Bayindir, M.

Benoit, G.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, "Hollow multilayer photonic bandgap fibers for NIR applications," Opt. Express 12, 1510-1517 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Bird, D. M.

Birks, T. A.

Bjarklev, A.

Black, R. J.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, "Loss calculations for antiresonant waveguides," J. Lightwave Technol. 11, 416-423 (1993).
[CrossRef]

Broeng, J.

Bures, J.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, "Loss calculations for antiresonant waveguides," J. Lightwave Technol. 11, 416-423 (1993).
[CrossRef]

Chen, C.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 19, 2039-2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Chiang, K. S.

Cucinotta, A.

de Sterke, C. M.

Deyerl, H.

Duguay, M. A.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Dunn, S. C.

Eggleton, B. J.

Engeness, T.

Fan, S.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 19, 2039-2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Finazzi, V.

Fink, Y.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, "Hollow multilayer photonic bandgap fibers for NIR applications," Opt. Express 12, 1510-1517 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 19, 2039-2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Foroni, M.

Hansen, T.

Hart, S. D.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, "Hollow multilayer photonic bandgap fibers for NIR applications," Opt. Express 12, 1510-1517 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Hawkins, A. R.

Headley, C.

Hong, C.

Hu, J. J.

Huang, Y.

Ibanescu, M.

Jakobsen, C.

Jensen, J.

Joannopoulos, J. D.

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, "Hollow multilayer photonic bandgap fibers for NIR applications," Opt. Express 12, 1510-1517 (2004).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 19, 2039-2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Johnson, S. G.

Katagiri, T.

Koch, T. L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Kokubun, Y.

T. Baba and Y. Kokubun, "Dispersion and radiations loss characteristics of antiresonant reflecting optical waveguides - numerical results and analytical expressions," J. Quantum Electron. 28, 1689-1700 (1992).
[CrossRef]

T. Baba and Y. Kokubun, "High efficiency light coupling from antiresonant reflecting optical waveguide to integrated photodetector using an antireflecting layer," Appl. Opt. 29, 2781-2792 (1990).
[CrossRef] [PubMed]

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Kuriki, K.

Kuriki, Y.

Lacroix, S.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, "Loss calculations for antiresonant waveguides," J. Lightwave Technol. 11, 416-423 (1993).
[CrossRef]

Lee, R.

Li, J.

Litchinitser, N. M.

Lu, C.

Lunt, E. J.

Matsuura, Y.

McPhedran, R. C.

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Miyagi, M.

Monro, T. M.

Mortensen, N.

Pearce, G. J.

Pfeiffer, L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Poli, F.

Ren, G.

Richardson, D. J.

Ripin, D. J.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 19, 2039-2041 (1999).
[CrossRef]

Rowland, K. J.

Schmidt, H.

Selleri, S.

Shapira, O.

Shum, P.

Simonsen, H.

Skorobogatiy, M.

Sørensen, T.

Steinvurzel, P. E.

Temelkuran, B.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Terrel, M.

Thomas, E. L.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 19, 2039-2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Tien, P. K.

Usner, B.

Vienne, G.

Viens, J. F.

Wang, G.

Weisberg, O.

White, T. P.

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Xu, Y.

Yariv, A.

Yeh, P.

Yin, D.

Yu, X.

Appl. Opt.

Appl. Phys. Lett.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

J. Lightwave Technol.

K. J. Rowland, S. Afshar V., and T. M. Monro, "Novel low-loss bandgaps in all-silica Bragg fibers," J. Lightwave Technol. 26, 43-51 (2008).
[CrossRef]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, "Guiding optical light in air using an all-dielectric structure," J. Lightwave Technol. 19, 2039-2041 (1999).
[CrossRef]

F. Poli, M. Foroni, A. Cucinotta, and S. Selleri, "Spectral behavior of integrated antiresonant reflecting hollowcore waveguides," J. Lightwave Technol. 25, 2599-2604 (2007).
[CrossRef]

T. Katagiri, Y. Matsuura, and M. Miyagi, "All-solid single-mode bragg fibers for compact fiber devices," J. Lightwave Technol. 24, 4314-4318 (2006).
[CrossRef]

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, "Loss calculations for antiresonant waveguides," J. Lightwave Technol. 11, 416-423 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Quantum Electron.

T. Baba and Y. Kokubun, "Dispersion and radiations loss characteristics of antiresonant reflecting optical waveguides - numerical results and analytical expressions," J. Quantum Electron. 28, 1689-1700 (1992).
[CrossRef]

Nanofluid.

H. Schmidt and A. R. Hawkins, "Optofluidic waveguides: I. Concepts and implementations," Microfluid. Nanofluid. 4, 3-16 (2008).
[CrossRef] [PubMed]

Nature

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Opt. Express

G. Vienne, Y. Xu, C. Jakobsen, H. Deyerl, J. Jensen, T. Sørensen, T. Hansen, Y. Huang, M. Terrel, R. Lee, N. Mortensen, J. Broeng, H. Simonsen, A. Bjarklev, and A. Yariv, "Ultra-large bandwidth hollow-core guiding in all-silica Bragg fibers with nano-supports," Opt. Express 12, 3500-3508 (2004).
[CrossRef] [PubMed]

K. Kuriki, O. Shapira, S. D. Hart, G. Benoit, Y. Kuriki, J. F. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, "Hollow multilayer photonic bandgap fibers for NIR applications," Opt. Express 12, 1510-1517 (2004).
[CrossRef] [PubMed]

D. Yin, J. P. Barber, A. R. Hawkins, and H. Schmidt, "Waveguide loss optimization in hollow-core ARROW waveguides," Opt. Express 13, 9331-9336 (2005).
[CrossRef] [PubMed]

D. Yin, H. Schmidt, J. P. Barber, E. J. Lunt, and A. R. Hawkins, "Optical characterisation of arch-shaped ARROW waveguides with liquid cores," Opt. Express 13, 10564-10570 (2005).
[CrossRef] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Solja¡ci’c, S. Jacobs, J. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Opt. Express 9, 748-779 (2001).
[CrossRef] [PubMed]

A. K. Abeeluck, N. M. Litchinitser, C. Headley, and B. J. Eggleton, "Analysis of spectral characteristics of photonic bandgap waveguides," Opt. Express 10, 1320-1333 (2002).
[PubMed]

I. M. Bassett and A. Argyros, "Elimination of polarization degeneracy in round waveguides," Opt. Express 10, 1342-1346 (2002).
[PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic representations of the fiber, stack and slab geometries discussed here. Left: An arbitrary Bragg fiber geometry. All parameters defined within. Refractive indices take any value such that n 1>n 0n core≥1. Right: The equivalent planar slab representation of the Bragg-cladding with the equivalent isolated constituent layers shown below. The vector diagram represents the decomposition of an incident ray’s wavevector.

Fig. 2.
Fig. 2.

Left: A bandgap map generated via the Bloch theorem (Section 2.1) for a Bragg fiber cladding like that considered in [4]: t 1=0.27µm, t 0=0.9µm, n 1=2.8 and n 0=1.55. Color scheme (for ñ<n 0): as described in text, Section 2.1; black for TE bands, black and grey for TM bands (⇒ white for TM bandgaps, white and grey for TE bandgaps). Solid blue line: the n 0-light-line. Dotted line: the Brewster line, ñ=n B. Right: A plot of all the SPARROW curves (dispersion curves of the equivalent isolated layers), via Eq. (6), for the same cladding and bandgap domain. Magenta: high-index (n 1) layer, n ˜ m 1 (k). Cyan: low-index (n 0) layer, ñ m0 (k).

Fig. 3.
Fig. 3.

Left: The bandgap map of Fig. 2 with the cladding layer dispersion (SPARROW) curves (Fig. 2) overlayed. Right: The same configuration but with the high-index layer’s thickness decreased: t 1=0.27µm→0.18µm. The bandgap topology dramatically changes between the two cases (new bandgaps are created). Using the nomenclature and analyses of Section 4.5: t 1=0.27µm produces N 1=2 and N 2=4 whereas t 1=0.18µm produces N 1=3 and N 2=6.

Fig. 4.
Fig. 4.

Top: A portion of the SPARROWcurves and bandgap map from Fig. 2. Green line: the TE01 mode’s Re{ñ} from the FEM calculation of the equivalent Bragg fiber, with a core of size t core=20µm. Red dashed line: the n core-light-line (ñ=1.45). Red circles: positions of the general antiresonance point kc (Section 4.2) on the n core-light-line. The gaps are labelled using the nomenclature of Section 4.1. The limit value Λ/λ=3 corresponds to λ=390nm in this case. Bottom: The associated CL spectrum. Cyan and magenta dashed lines: low- and high-index SPARROW resonances on the n core-light-line, respectively (corresponding to circles of the same color in the top plot). Red lines: positions of the general antiresonance points from the top plot (red circles).

Fig. 5.
Fig. 5.

SPARROW model curves overlayed upon a portion of the cladding Bandgap map of the Bragg fiber examined in [5] and [23]: t 1=0.37µm, t 0=4.1µm, n 1=1.45 and n 0=1. The color scheme is the same as for Figs. 2 and 3. The bandgaps are labelled according to the nomenclature introduced in Section 4.1. Red circles: intersection points (P, Section 4.1) of the SPARROWcurves. Magenta circles: ñ=n 0 resonances (Eqs. 3 and 7). Green dashed curves: a specific bandgap’s half-order curves, the intersection of which form P c (Section 4.4), the green circle. The chosen gap is of order 〈m 1,m 0〉=〈3,1〉 with P c=(k c,ñ c)≈(5.34898µm -1,0.976641).

Equations (15)

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Re { A TE , TM ( k , n ˜ ) } < 1 ,
λ m i = 2 t i m i n i 2 n core 2 + ( U λ 2 π t core ) 2 ,
λ m = 2 t 1 m n 1 2 n 0 2 .
Γ TE = k ax k bx k ax + k bx , Γ TM = n b 2 k ax n a 2 k bx n b 2 k ax n a 2 k bx ,
k ax t a = { m π for n a > n b and m ( m + 1 ) π for n a < n b and m +
n ˜ m i = [ n i 2 ( m i π t i k ) 2 ] 1 2 , m i
k m i = m i π t i [ n i 2 n ˜ 2 ] 1 2 ,
P ( m 1 , m 0 ) = ( k , n ˜ ) n ˜ m 1 = n ˜ m 0 = ( π 1 n 1 2 n 0 2 ( m 1 2 t 1 2 m 0 2 t 0 2 ) , n 1 2 n 0 2 η 2 1 η 2 ) ,
k c ( n ˜ ) = k m p ( n ˜ ) + k m q ( n ˜ ) 2 ,
λ m i = 2 n i t i m i
P c = ( k c , n ˜ c ) = P ( m 1 1 2 , m 0 + 1 2 ) = ( π 1 n 1 2 n 0 2 [ ( m 1 1 2 t 1 ) 2 ( m 0 + 1 2 t 0 ) 2 ] , n 1 2 n 0 2 η c 2 1 η c 2 ) ,
k c ( n ˜ c ) = k c .
m 0 < m 1 n 0 t 0 n 1 t 1 .
m 0 max = floor { m 1 n 0 t 0 n 1 t 1 } ,
N m 1 = { m 0 max + 1 when m 0 max < m 1 t 0 n 0 t 1 n 1 m 0 max when m 0 max = m 1 t 0 n 0 t 1 n 1

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