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Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 8 — Apr. 19, 2004
  • pp: 1540–1550
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Application of an ARROW model for designing tunable photonic devices

Natalia M. Litchinitser, Steven C. Dunn, Paul E. Steinvurzel, Benjamin J. Eggleton, Thomas P. White, Ross C. McPhedran, and C. Martijn de Sterke  »View Author Affiliations


Optics Express, Vol. 12, Issue 8, pp. 1540-1550 (2004)
http://dx.doi.org/10.1364/OPEX.12.001540


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Abstract

Microstructured optical fibers with the low refractive index core surrounded by high refractive index cylindrical inclusions reveal several intriguing properties. Firstly, there is a guiding regime in which the fibers’ confinement loss is strongly dependent of wavelength. In this regime, the positions of loss maxima are largely determined by the individual properties of high index inclusions rather than their position and number. Secondly, the spectra of these fibers can be tuned by changing the refractive index of the inclusions. In this paper we review transmission properties of these fibers and discuss their potential applications for designing tunable photonic devices.

© 2004 Optical Society of America

1. Introduction

Optical fibers, which are essentially dielectric structures transmitting electromagnetic waves at optical frequencies, exist in a large variety of forms. They can be natural such as the glass sponge [1

1. V. C. Sundar, A. D. Yablon, J. L. Grazul, M. Ilan, and J. Aizenberg, “Fibre-optical features of a glass sponge,” Nature 424, 899–900 (2003). [CrossRef] [PubMed]

] as well as artificially made [2

2. G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 1995).

]. Their applications range from long-haul telecommunications to medicine, spectroscopy and sensors. Recently, a new class of optical fibers, microstructured optical fibers (MOFs) or photonic crystal fibers, has been introduced [3

3. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998). [CrossRef] [PubMed]

12

12. J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003). [CrossRef] [PubMed]

]. These fibers are made of glass or polymer with a cross-section containing a structure on the scale of a micron. The presence of this structure (often in the form of circular air-holes or concentric cylinders) changes the transmission characteristics of the fiber. Many properties of MOFs are determined by the air-hole size and the spacing between them. Moreover, once the fiber has been made, its properties can be further modified by introducing various materials into the air-holes [13

13. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, “Tunable photonic band gap fiber,” in OSA Trends in Optics and Photonics (TOPS) Vol. 70, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington DC, 2002), pp. 466–468.

,14

14. T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]

]. Using materials with variable thermal or electro-optic properties allows the fibers to be reversibly tuned. Additional degrees of design freedom provided by MOFs are being utilized in various photonic devices including microfluidic fiber gratings [9

9. C. Kerbage and B. J. Eggleton, “Tunable microfluidic optical fiber gratings,” Appl. Phys. Lett. 82, 1338–1340 (2003). [CrossRef]

] or dynamically tunable MOFs [10

10. C. Kerbage, P. Steinvurzel, P. Reyes, P. S. Westbrook, R. S. Windeler, A. Hale, and B. J. Eggleton, “Highly tunable birefringent microstructured optical fiber,” Opt. Lett. 27, 842–844 (2002). [CrossRef]

].

MOFs with a solid core surrounded by air-holes guide light through a modified total internal reflection (TIR) mechanism. Filling the air-holes with high-index material rules out TIR-based guidance, since the refractive index of the core is lower than that of the cladding. Recently, the guiding properties of MOFs consisting of a low refractive index core and air-holes filled with high refractive index material [15

15. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594(2002). [CrossRef]

18

18. N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T.P. White, R.C. McPhedran, and C. Martijn de Sterke, “Resonances and modal cutoff in microstructured optical waveguides,” Opt. Express 11, 1243–1251 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1243 [CrossRef] [PubMed]

] were investigated. A spectral response of these fibers is approximately periodic in frequency. A new guiding regime was identified in which the positions of spectral minima are largely determined by the individual properties of high index inclusions rather than their position and number. The physical mechanism of guiding in this regime is similar to that in antiresonant reflecting optical waveguides (ARROW) [19

19. M. A. Duguay, Y. Kukubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multiplayer structures,” Appl. Phys. Lett. 49, 13–15 (1986). [CrossRef]

], widely used in the field of integrated optics. A simple analytical model was proposed to predict the locations of spectral minima based on the geometry and refractive indexes of the inclusions.

In a present paper we show how this simple model can be used for manipulating the properties of MOF with high-index inclusions and designing tunable fiber devices. A large variety of tunable photonic devices has been described in the literature including silica fiber-Bragg-grating-based (FBG) filters [20

20. A. Iocco, H. G. Limberger, R. P. Salathé, L. A. Everall, K. E. Chisholm, J. A. R. Williams, and I. Bennion, “Bragg grating fast tunable filter for wavelength division multiplexing,” J. Lightwave Technol. 17, 1217–1221 (1999). [CrossRef]

], polymer Bragg gratings [21

21. H. Y. Liu, G. D. Peng, and P. L. Chu, “Polymer fiber Bragg gratings with 28 dB transmission rejection,” IEEE Photon. Technol. Lett. 14, 935–937 (2002). [CrossRef]

], tunable filters based on FBG and long-period gratings (LPGs) written in an index-guiding MOF [9

9. C. Kerbage and B. J. Eggleton, “Tunable microfluidic optical fiber gratings,” Appl. Phys. Lett. 82, 1338–1340 (2003). [CrossRef]

,10

10. C. Kerbage, P. Steinvurzel, P. Reyes, P. S. Westbrook, R. S. Windeler, A. Hale, and B. J. Eggleton, “Highly tunable birefringent microstructured optical fiber,” Opt. Lett. 27, 842–844 (2002). [CrossRef]

]. A majority of the filtering applications requires introducing some kind of a resonant structure inside the core of the fiber such as FBGs or LPGs. Once such a resonant structure is introduced, its properties can be tuned only within a certain wavelength range that is determined by the properties of the fiber material (silica or polymer). ARROW-like MOFs with high index inclusions have several advantages for designing tunable devices. First, their spectral response consists of many narrow resonant features that are approximately periodically spaced in frequency. Therefore, no additional resonant structures are required to be introduced. The positions of these resonances are largely determined by the refractive indexes of the inclusions and the background material (silica or polymer), and by the size of the high-index inclusion. Second, ARROW-like MOFs offer a possibility of a more flexible tuning range compared to grating-based devices, which could be achieved by replacing the high-index material in the air-holes. A simple analytical model reviewed here takes into account advanced features of ARROW-like MOFs and thus could be utilized in designing of tunable photonic devices.

Fig. 1. (a) MOF with low-index core and high-index inclusions, (b) Corresponding cross-section of the refractive index profile along x axis, (c) Planar optical waveguide with low-index core and high-index layers.

In the following sections we review a theory that allows prediction of the transmission spectrum minima in MOF with high index inclusions (Section II) and discuss the possibility of designing novel photonic devices utilizing MOF with tunable refractive index of the cylindrical inclusions (Section III). Our findings are summarized in Section IV.

2. Theory

2.1 Planar waveguide: Antiresonant reflecting optical waveguide mode

The cross-section of a typical MOF consisting of a low-index solid core surrounded by ten hexagonal rings of circular air-holes filled with high-index liquid is shown in Fig. 1(a). The refractive index profile of this fiber along x direction is given in Fig. 1(b). Initially we simplify MOF by reducing it to a one-dimensional planar waveguide having a similar refractive index profile as shown in Fig. 1(c) [16

16. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1320 [CrossRef] [PubMed]

]. The propagation of a Gaussian beam in z direction has been investigated using the standard beam propagation method (BPM)[22

22. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Select. Topics Quantum Electron. 6, 150–162 (2000). [CrossRef]

]. The transmission spectrum is defined as the ratio of the integrated power within the core region at the end of the waveguide to that launched into the core. The main results of the simulations can be summarized as follows. First, the locations of the spectral minima are essentially unaffected by changes in lattice constant, provided that the refractive indexes (n1, n2) and the thickness of high-index layer d were kept constant. Second, the locations of the spectral minima remain unchanged when all layers except one on each side of the core were removed. Finally, the transmission minima shifted in either of the following cases: (i) d was changed while n1 and n2 were kept constant, or (ii) d was kept constant, while n1 or n2 were changed. These simulations identified a guiding regime in which the properties of high-index layer largely determine the spectral properties of the entire waveguide. In this regime the addition of new layers and changing their spacing results in a better confinement and an appearance of some fine structure near the transmission minima (that becomes increasingly more noticeable at longer wavelengths, see Ref. [16

16. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1320 [CrossRef] [PubMed]

]). These conclusions allow us to simplify the problem by replacing a 10-layer structure in Fig. 1(b) by 1-layer structure shown in Fig. 2(a). Figure 2(b) shows the calculated spectrum for n1=1.4, n2=1.8, d=3.437µm and a waveguide length of 5cm. Electric field profiles at wavelengths corresponding to (1) a high transmission at λ=0.676µm, and (2) a transmission minimum at λ=0.707µm are shown in Fig. 2(c). The electric field oscillations inside the high-index layer are enlarged in Fig. 2(d). It is noteworthy that at wavelengths corresponding to transmission minima, the electric field forms a standing wave pattern with an integer number of half-oscillations inside the high-index layer. This suggests that the guiding mechanism in this type of waveguides is very similar to an antiresonant reflecting optical waveguide (ARROW) principle [19

19. M. A. Duguay, Y. Kukubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multiplayer structures,” Appl. Phys. Lett. 49, 13–15 (1986). [CrossRef]

]. In ARROW light is confined in the core by antiresonant reflection from the high-index layers in the cladding. Each high-index layer can be considered as a Fabry-Perot-like (FP) resonator. Narrow-band resonances of this FP resonator correspond to transmission minima for the light propagating in the core. Therefore, at resonance the high-index layer becomes effectively transparent and light escapes completely from the entire structure. Wide antiresonances of the FP correspond to high transmission regions.

The resonant condition for a high-index layer is given by ktd=πm, where kt=2πλn22n12. We assume that light impinges the core/cladding interface at glancing angles (i.e. λ/a<<1). The wavelengths corresponding to transmission minima are given by:

λm=2dmn22n12,wherem=1,2,
(1)

Obviously, the simple model described here is valid only in a “short wavelength” regime defined by λd2n22n12.

Fig. 2. (a) A schematic of a waveguide, (b) Corresponding transmission spectrum at a distance of 5cm in z direction, (c) Electric field profile at a distance of 5cm at the wavelength corresponding to high transmission (1) and a transmission minimum (2), (d) Electric field oscillations inside the high-index layer.

2.2 Microstructured fiber: Scattering resonances

This notion was confirmed by studying the scattering of a plane wave at oblique incidence upon the surface of an infinite cylinder (shown in Fig. 3(a)) [25

25. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

,26

26. A. C. Lind and J. M. Greenberg, “Electromagnetic scattering by obliquely oriented cylinders,” J. Appl. Phys. 37, 3195–3203 (1966). [CrossRef]

]. The scattering properties can be characterized by a scattering cross section and a forward-to-backward scattering ratio which is a measure of the ratio of the energy flowing out of the cylinder to the energy reflected back. Figure 3(b) shows good qualitative agreement between MOF confinement loss and forward-to-backward scattering ratio for a plane wave scattered on a single high-index cylinder. The angle of incidence of the plane wave was varied according to the effective index of the MOF mode at each wavelength.

Fig. 3. Comparison of MOF loss properties with forward-to-backward scattering ratio for the plane wave scattering on a single cylinder.

2.3 Modal cutoff

vg=cn22βk112Δ(1η)
(2)

J0(ktd2)=0.
(3)

J1(ktd2)=0.
(4)

Resonance conditions for kt d/2 can be found analytically using the cosine approximation for the Bessel functions Jν when kt d/2>>ν.

From Eqs. (3) and (4) resonant wavelengths can be written as follows:

λm=2dn22n12m+12,m=1,2,
(5)

For HE2m the cutoff condition is given by

ktdJ0(ktd2)2J1(ktd2)=2Δ12Δ.
(6)

The solution of transcendental Eq. (6) is very close to the solution of Eq. (3) given by Eq. (5) as long as

4Δ112Δktd1.
(7)
Fig. 4. Upper plot shows the effective refractive index of the modes of the high-index layer as a function of the wavelength. Lower plot shows the effective refractive index of the mode propagating in the low-index core of the entire ARROW structure. Vertical dashed lines correspond to the modal cutoffs.

In our numerical example (shown in Fig. 3) 4Δ112Δktd=0.037÷0.055. Therefore the condition (5) can be used to predict the high-loss spectral wavelengths in wide range of parameters. The analytical predictions of equation (5) are compared to numerical results obtained using the multipole method [18

18. N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T.P. White, R.C. McPhedran, and C. Martijn de Sterke, “Resonances and modal cutoff in microstructured optical waveguides,” Opt. Express 11, 1243–1251 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1243 [CrossRef] [PubMed]

].

3. Potential applications

As shown in Fig. 2, the spectrum of an ARROW waveguide consists of several narrow transmission dips at wavelengths λm . These spectral dips can be utilized for making tunable optical filters. Since the resonant wavelengths in Eqs. (1) and (5) are functions of n2, the position of the spectral dips can be shifted by changing n2. Experimentally this can be realized by using materials with temperature dependent refractive index [13

13. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, “Tunable photonic band gap fiber,” in OSA Trends in Optics and Photonics (TOPS) Vol. 70, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington DC, 2002), pp. 466–468.

,14

14. T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]

]. Resonant wavelength shift in planar and cylindrical geometries is given by

Δλm=2d(n22(T2)n12n22(T1)n12){m1(m+12)1,
(8)

respectively.

In Eq. (8) we assume that the temperature sensitivity of a high-index material n2 is much higher than that of the background material n1. However, Eq. (8) can be easily modified to include the temperature dependence on n1.

Let’s consider designing a tunable filter based on ARROW-like planar waveguide or MOF. First we design a continuously tunable filter based on the planar waveguide shown in Fig. 2.

Fig. 5. (a) Transmission minimum (m=10) for different values of n2, for fixed values of n1=1.4, d=3.437µm. (b) Comparison of the analytical predictions and the numerical simulations for the location of the transmission minimum.
Fig. 6. (a) Schematic of MOF with a micro-heater. MOF air-holes are filled with a high-index material whose refractive index n2 changes with temperature T, (b) Longitudinal component of Poynting vector Sz for the lowest order MOF mode in transmission mode (n=1.8) and in filter mode (n=1.775) along with x cross section of Sz.

We choose a particular transmission dip at λ=0.777µm,corresponding to m=10 in Eq. (1). Figure 5(a) shows the evolution of this peak over the wavelength as n2 decreases. Comparison of the numerical results and analytical predictions for the location of the minimum versus n2 is shown in Fig. 5(b). Note, that even though ARROW-type of waveguide is inherently lossy, that should not preclude this waveguide from being used as a filter since only a short piece of fiber is required for this application. Alternatively, additional high-index layers can be used to reduce the confinement loss.

A type of filter described here can be realized in MOF geometry by placing a micro-heater on a surface of MOF filled with thermally tunable material such as a high index liquid (n589 nm =1.8,Cargille Laboratories series M with a temperature dependence of the refractive index given by dn/dT=-6.8*10-4/deg C). The schematic of the device is shown in Fig. 6(a). In this example we use Eq. (5) to find a value for the refractive index n2 at which the MOF with one ring of high-index inclusions switches from a transmission mode at initial (room) temperature to a filtering mode for λ=0.7525µm when the temperature increases.

Here we assume that the refractive index n2 decreases with temperature and equals 1.8 at room temperature. The refractive index required to tune the MOF was found to be 1.775. In this example other fiber parameters are n1=1.44, d=3.8µm, Λ=8µm. Figure 6(b) shows the longitudinal component of the Poynting vector Sz and its cross section along x axis for the lowest-order mode for n2(T1=1.8 and n2(T2)=1.775 calculated using the multipole method [23

23. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002). [CrossRef]

,24

24. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. Martijn de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002). [CrossRef]

]. However, multipole simulations only provide an information about a particular core mode and do not explicitly show where the power goes when it disappears from the core at a resonant wavelength. BPM provides more information about the light propagation and the results obtained from simulations using BPM can be directly compared with experiments.

We used a BPM to propagate a Gaussian beam in z direction in 1mm of ARROW-like MOF with two rings of inclusions shown in Fig. 7(a). A second ring of inclusions has been added to reduce the power leakage from the core. All other parameters are identical to those in Fig. 6. Figure 7(b) shows the transmission spectra for two cases: n2=1.8 (red line) and n2=1.775 (black line). Both spectra are taken after beam propagated along the fiber (in zdirection) at z=1mm. Simulations shown in Fig. 7(c) and 7(d) further illustrate the dynamic of light propagation in ARROW-like MOF at a design wavelength λ=0.7525µm for n2=1.8 (off-resonance) and n2=1.775 (on-resonance), respectively. At this wavelength light propagates in the low-index core when n2=1.8, since λ=0.7525µm corresponds to a high transmission part of the spectrum. Animation in Fig. 7(d) clearly shows that light escapes from the entire structure at the same wavelength when n2=1.775. These simulations confirm that the MOF switches from a high transmission mode to a filtering mode as the refractive index changes as predicted by Eq. (5).

Fig. 7. (a) MOF profile used in BPM simulations, (b) Transmission spectra at z=1 mm, (c) (1446 KB) Evolution of the beam profile in MOF with n2=1.8 (the frame shows output beam profile at z=1 mm), (d) (1446 KB) Evolution of the beam profile in MOF with n2=1.775 (the frame shows output beam profile at z=1 mm).

4. Summary

We reviewed some simple analytical approaches developed for understanding the spectral properties of MOFs with low refractive index core surrounded by high refractive index inclusions. Using the insight gained from a simple physical picture of light confinement and propagation in these MOFs, we demonstrated how the properties of these fibers can be adjusted in a controlled and predictable way providing a basis for novel photonic devices.

Acknowledgments

This work was produced with the assistance of the Australian Research Council (ARC) under the ARC Centres of Excellence Program. CUDOS (the Centre for Ultra-high bandwidth Devices for Optical Systems) is an ARC Centre of Excellence.

References and links

1.

V. C. Sundar, A. D. Yablon, J. L. Grazul, M. Ilan, and J. Aizenberg, “Fibre-optical features of a glass sponge,” Nature 424, 899–900 (2003). [CrossRef] [PubMed]

2.

G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 1995).

3.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998). [CrossRef] [PubMed]

4.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

5.

B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express 9, 698–713 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-698. [CrossRef] [PubMed]

6.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003). [CrossRef] [PubMed]

7.

P. St. J. Russell, “Photonic crystal fibres,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

8.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial wavguide,” Science 289, 415–419 (2000). [CrossRef] [PubMed]

9.

C. Kerbage and B. J. Eggleton, “Tunable microfluidic optical fiber gratings,” Appl. Phys. Lett. 82, 1338–1340 (2003). [CrossRef]

10.

C. Kerbage, P. Steinvurzel, P. Reyes, P. S. Westbrook, R. S. Windeler, A. Hale, and B. J. Eggleton, “Highly tunable birefringent microstructured optical fiber,” Opt. Lett. 27, 842–844 (2002). [CrossRef]

11.

M. van Eijkelenborg, M. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. M. Bassett, S. C. Fleming, R. C. McPhedran, C. M. de Sterke, and N. A. P. Nicorovici, “Microstructured polymer optical fibre,” Opt. Express 9, 319–327 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-7-319 [CrossRef] [PubMed]

12.

J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003). [CrossRef] [PubMed]

13.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, “Tunable photonic band gap fiber,” in OSA Trends in Optics and Photonics (TOPS) Vol. 70, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington DC, 2002), pp. 466–468.

14.

T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]

15.

N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594(2002). [CrossRef]

16.

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1320 [CrossRef] [PubMed]

17.

T. P. White, R. C. McPhedran, C. Martijn de Sterke, N. M. Litchinitser, and B. J. Eggleton, “Resonance and scattering in microstructured optical fibers,” Opt. Lett. 27, 1977–1979 (2002). [CrossRef]

18.

N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T.P. White, R.C. McPhedran, and C. Martijn de Sterke, “Resonances and modal cutoff in microstructured optical waveguides,” Opt. Express 11, 1243–1251 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1243 [CrossRef] [PubMed]

19.

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

20.

A. Iocco, H. G. Limberger, R. P. Salathé, L. A. Everall, K. E. Chisholm, J. A. R. Williams, and I. Bennion, “Bragg grating fast tunable filter for wavelength division multiplexing,” J. Lightwave Technol. 17, 1217–1221 (1999). [CrossRef]

21.

H. Y. Liu, G. D. Peng, and P. L. Chu, “Polymer fiber Bragg gratings with 28 dB transmission rejection,” IEEE Photon. Technol. Lett. 14, 935–937 (2002). [CrossRef]

22.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Select. Topics Quantum Electron. 6, 150–162 (2000). [CrossRef]

23.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002). [CrossRef]

24.

B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. Martijn de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002). [CrossRef]

25.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

26.

A. C. Lind and J. M. Greenberg, “Electromagnetic scattering by obliquely oriented cylinders,” J. Appl. Phys. 37, 3195–3203 (1966). [CrossRef]

27.

A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, New York, 1983)

OCIS Codes
(050.2230) Diffraction and gratings : Fabry-Perot
(230.3990) Optical devices : Micro-optical devices
(230.7370) Optical devices : Waveguides

ToC Category:
Focus Issue: Photonic crystals and holey fibers

History
Original Manuscript: March 9, 2004
Revised Manuscript: April 8, 2004
Published: April 19, 2004

Citation
Natalia Litchinitser, Steven Dunn, Paul Steinvurzel, Benjamin Eggleton, Thomas White, Ross McPhedran, and C. de Sterke, "Application of an ARROW model for designing tunable photonic devices," Opt. Express 12, 1540-1550 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-8-1540


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