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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 12 — Jun. 9, 2008
  • pp: 9112–9117
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Polarization control of defect modes in three-dimensional woodpile photonic crystals

Michael James Ventura and Min Gu  »View Author Affiliations


Optics Express, Vol. 16, Issue 12, pp. 9112-9117 (2008)
http://dx.doi.org/10.1364/OE.16.009112


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Abstract

The symmetry of a Fabry-Perot-like planar cavity embedded within a three-dimensional (3D) woodpile photonic crystal prevents the observation of polarization effects. In this letter we propose a geometry to break the degeneracy of the Fabry-Perot-like cavity modes by introducing asymmetry. The introduction of a one-dimensional (1D) lattice to the centre of a planar cavity allows for distinct modes parallel (TE) and perpendicular (TM) to the layer. This hybrid 3D-1D-3D lattice structure exhibits a pronounced increase in the quality-factor, and in particular shows an increase of up to 50% more than that of a planar cavity for TM modes.

© 2008 Optical Society of America

1. Introduction

2. Proposed hybrid 3D-1D-3D lattice

A sketch of the void-channel arrangement can be seen in Fig. 1(a) where the solid rods represent micro-void channels within a polymer host (black outline). Individual layers consist of a periodic arrangement of individual void-channels evenly spaced by and in-plane spacing (δx). Adjacent layers are perpendicular and spaced by a layer spacing (δz), while subsequent layers are offset by half and in-plane spacing. As in-plane layers are symmetrically stacked along the stacking direction of the crystal, this symmetry implies that the electromagnetic modes in this direction are degenerate for all polarizations. The band structures of woodpile photonic crystal lattices were calculated using an iterative eigensolver [8

8. M. Straub, M. Ventura, and M. Gu, “Multiple higher-order stop gaps in infrared polymer photonic crystals,” Phys. Rev. Lett. 91, 043901 (2003). [CrossRef] [PubMed]

]. For calculations lattice parameters were fixed to prior experimental conditions [7

7. M. J. Ventura, M. Straub, and M. Gu, “Planar cavity modes in void channel polymer photonic crystals,” Opt. Express 13, 2767–2773 (2005). [CrossRef] [PubMed]

] with a δx=1.4 µm, δz=1.5 µm and refractive index of 1.65. The band diagram in Fig. 1(a) is presented in normalized frequency units where a=δx. Although a complete photonic bandgap does not exist due to the low refractive index contrast [8

8. M. Straub, M. Ventura, and M. Gu, “Multiple higher-order stop gaps in infrared polymer photonic crystals,” Phys. Rev. Lett. 91, 043901 (2003). [CrossRef] [PubMed]

], a sizeable stop-gap is present between the forth and fifth band centered at normalized frequency 0.305 (4.6 µm). Frequencies that fall outside the gap are shaded. A Fabry-Perot style cavity as represented in Fig. 1(b) can be introduced as a planar cavity at the centre of the lattice [7

7. M. J. Ventura, M. Straub, and M. Gu, “Planar cavity modes in void channel polymer photonic crystals,” Opt. Express 13, 2767–2773 (2005). [CrossRef] [PubMed]

]. By displacing half of the crystal in the stacking direction by δd a localized dislocation breaks the periodicity of the surrounding lattice. Figure 1(b) show the band diagram as calculated for an appropriate super-cell [7

7. M. J. Ventura, M. Straub, and M. Gu, “Planar cavity modes in void channel polymer photonic crystals,” Opt. Express 13, 2767–2773 (2005). [CrossRef] [PubMed]

] where the single flat band at normalized frequency 0.306 (4.58 µm) within the bandgap represents a single localized defect mode. Like the woodpile lattice without a defect (Fig. 1(a)) no polarization effects in the stacking direction is noted due to the structural symmetry in this direction. The localized defect band, like all bands calculated consists of two degenerate bands. The corresponding mode distribution can be found elsewhere [7

7. M. J. Ventura, M. Straub, and M. Gu, “Planar cavity modes in void channel polymer photonic crystals,” Opt. Express 13, 2767–2773 (2005). [CrossRef] [PubMed]

].

Fig. 1. Band diagram calculations for woodpile lattices in the stacking direction (Γ-X’). (a) A simple woodpile lattice exhibits a stop-gap in the stacking direction between the forth and fifth band centered at normalized frequency 0.305. (b) A simple planar cavity introduced at the centre of a woodpile lattice reveals a single flat band within the stop-gap at normalized frequency 0.306. (c) The introduction of a 1D periodic lattice to the centre of the cavity in. (d) TE modes are defined perpendicular to the 1D lattice periodicity and TM modes are defined parallel to the 1D lattice periodicity.

To introduce polarization effects in the stacking direction of a woodpile lattice with a planar cavity requires the breaking of this symmetry. The introduction of a 1D lattice to the centre of the planar cavity is shown in Fig. 1(c). This periodic array introduces an asymmetric layer within the plane of the lattice and should lead to distinct effects on polarization of localized defect modes that occupy this region, which can be observed in the stacking direction as unique TE and TM modes. The band diagram for this hybrid 3D-1D-3D structure is shown in Fig. 1(c) where the periodicity of the 1D lattice (δa) is matched to the in-plane spacing of the 3D woodpile (δa=δx=1.4 µm). The stop-gap position and bandwidth is uneffected, however two localized defect modes are present with a separation of normalized frequency of 0.0023 (3.6 nm). The two modes are attributed to the breaking of the degeneracy of the planar cavity mode (Fig. 1(b)) into two distinct modes parallel to the 1D lattice (TE) and perpendicular to the 1D lattice (TM) (Fig. 1(d)). In Fig. 2 the electromagnetic energy density of TE and TM modes are calculated for a vertical plane. Overlaid on Figs. 2(a) and (b) is the lattice, while the scale bar indicates the energy density from the lowest density (black) to the highest density (white). Consistent with prior work [7

7. M. J. Ventura, M. Straub, and M. Gu, “Planar cavity modes in void channel polymer photonic crystals,” Opt. Express 13, 2767–2773 (2005). [CrossRef] [PubMed]

], the energy is confined to the planar defect. Figures 2(a) and 2(b) are the TE and TM modes, respectively, for a hybrid 3D-1D-3D PC, the main feature to note is that the TM mode is strongly confined to the 1D lattice.

Fig. 2. The energy density of TE and TM modes calculated for a vertical plane. Overlaid in black is a trace that outline of the lattice positions. (a) The TE and (b) TM modes of a hybrid 3D-1D-3D lattice. The scale bar indicates the energy density form low density (black) to high density (white).

3. Experimental verification

Fig. 3. TE (black) and TM (grey) infrared transmission spectra of the PC lattices measured in the stacking direction. (a) A woodpile lattice with a transmission dip centered at wavelength 4.65 µm denoting the main stop-gap for both TE and TM polarization. (b) A woodpile lattice with a planar defect of size Δd=2.2µm showing a peak within the stop gap centered at wavelength 4.7 µm from both TE and TM modes. (c) A planar cavity with a 1D lattice of period a=1.4 µm showing two distinct TE and TM polarized modes with a peak wavelength separation of 3.3 nm. (d) A schematic of the combined Parabola and Lorentzian fitting.

The introduction of a 1D lattice to the cavity (Fig. 3(c)) with a period of δa=1.4 µm reveals two independent peaks measured for both TE (black) and TM (grey) polarizations. This confirms the prediction that the splitting of the defect modes seen in the band diagram of Fig. 1(d) is indeed polarization-dependent. Furthermore the resonance position of both modes are separated by 3.3 nm which is in excellent agreement with the calculated wavelength splitting of 3.6 nm form the band diagram in Fig. 1(c). As a consequence of introducing a 1D lattice to the centre of the planar cavity, energy that would be otherwise lost to the open edges of the cavity can be confined. This physical effect in turn results in the enhancement of the cavity quality factor (Q-factor), which is measured as the sharpening of resonance modes. Q-factors of the defect peaks were obtained by fitting the defect resonance peak of TE and TM modes using a combined Lorentzian and parabola (see Fig. 3(d)). In Fig. 3(c) both TE and TM modes show the Q-factors of 54 and 72, respectively, which correspond to an increase of 34 % and 42 % in comparison with that in the case of a planar cavity.

Fig. 4. The quality factor of the TE (black diamonds) and TM (grey circles) defect modes as a function of the 1D cavity periodicity. The dashed lines are a guide for the eye.

4. Conclusion

In conclusion we have proposed a hybrid 3D-1D-3D lattice which exhibits strong polarization effects otherwise unavailable to simple woodpile lattices. The breaking of the degenerate mode associated with a planar cavity embedded within a woodpile lattice leads to an effect of polarization. This feature has been experimentally verified by the measurements of the TE and TM defect modes which exhibits an increase of the quality factor by more than 50% compared with that in the planar cavity.

Acknowledgments

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

References and links

1.

E. Yablonovitch, “Inhibited spontaneous emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef]

2.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]

3.

B. Gralak, M. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003). [CrossRef]

4.

A. Chutinan and S. Noda, “Highly confined waveguides and waveguide bends in three-dimensional photonic crystal,” Appl. Phys. Lett. 75, 3739–3741 (1999). [CrossRef]

5.

C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

6.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Özbay, and C. M. Soukoulis, “Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B. 64, 1951131–1951137 (2001). [CrossRef]

7.

M. J. Ventura, M. Straub, and M. Gu, “Planar cavity modes in void channel polymer photonic crystals,” Opt. Express 13, 2767–2773 (2005). [CrossRef] [PubMed]

8.

M. Straub, M. Ventura, and M. Gu, “Multiple higher-order stop gaps in infrared polymer photonic crystals,” Phys. Rev. Lett. 91, 043901 (2003). [CrossRef] [PubMed]

9.

M. J. Ventura, M. Straub, and M. Gu, “Void channel microstructures in resin solids as an efficient way to infrared photonic crystals,” Appl. Phys. Lett. 82, 1649–1651 (2003). [CrossRef]

10.

Y. A. Vlasov, V. N. Astratov, O. Z. Karimov, A. A. Kaplyanskii, V. N. Bogomolov, and A. V. Prokofiev, “Existence of a photonic pseudogap for visible light in synthetic opals,” Phys. Rev. B 55, R13357–R13360 (1997). [CrossRef]

11.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymanna, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: Fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003). [CrossRef]

12.

G. Zhou, M. J. Ventura, M. Straub, M. Gu, A. Ono, S. Kawata, X. H. Wang, and Y. Kivshar, “In-plane and out-of-plane band-gap properties of a two-dimensional triangular polymer-based void channel photonic crystal,” Appl. Phys. Lett. 84, 4415–4417 (2004). [CrossRef]

OCIS Codes
(050.2230) Diffraction and gratings : Fabry-Perot
(220.4000) Optical design and fabrication : Microstructure fabrication
(230.5440) Optical devices : Polarization-selective devices
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: April 29, 2008
Revised Manuscript: May 29, 2008
Manuscript Accepted: May 30, 2008
Published: June 4, 2008

Citation
Michael J. Ventura and Min Gu, "Polarization control of defect modes in three-dimensional woodpile photonic crystals," Opt. Express 16, 9112-9117 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-9112


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References

  1. E. Yablonovitch, "Inhibited spontaneous emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  3. B. Gralak, M. de Dood, G. Tayeb, S. Enoch, and D. Maystre, "Theoretical study of photonic band gaps in woodpile crystals," Phys. Rev. E 67, 066601 (2003). [CrossRef]
  4. A. Chutinan and S. Noda, "Highly confined waveguides and waveguide bends in three-dimensional photonic crystal," Appl. Phys. Lett. 75, 3739-3741 (1999). [CrossRef]
  5. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "High-density integrated optics," J. Lightwave Technol. 17, 1682-1692 (1999). [CrossRef]
  6. M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. ??zbay, and C. M. Soukoulis, "Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals," Phys. Rev. B. 64, 1951131-1951137 (2001). [CrossRef]
  7. M. J. Ventura, M. Straub, and M. Gu, "Planar cavity modes in void channel polymer photonic crystals," Opt. Express 13, 2767-2773 (2005). [CrossRef] [PubMed]
  8. M. Straub, M. Ventura, and M. Gu, "Multiple higher-order stop gaps in infrared polymer photonic crystals," Phys. Rev. Lett. 91, 043901 (2003). [CrossRef] [PubMed]
  9. M. J. Ventura, M. Straub, and M. Gu, "Void channel microstructures in resin solids as an efficient way to infrared photonic crystals," Appl. Phys. Lett. 82, 1649-1651 (2003). [CrossRef]
  10. Y. A. Vlasov, V. N. Astratov, O. Z. Karimov, A. A. Kaplyanskii, V. N. Bogomolov, and A. V. Prokofiev, "Existence of a photonic pseudogap for visible light in synthetic opals," Phys. Rev. B 55, R13357-R13360 (1997). [CrossRef]
  11. Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymanna, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystal templates by laser holography: Fabrication, optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003). [CrossRef]
  12. G. Zhou, M. J. Ventura, M. Straub, M. Gu, A. Ono, S. Kawata, X. H. Wang, and Y. Kivshar, "In-plane and out-of-plane band-gap properties of a two-dimensional triangular polymer-based void channel photonic crystal," Appl. Phys. Lett. 84, 4415-4417 (2004). [CrossRef]

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