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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 20 — Oct. 1, 2007
  • pp: 13049–13057
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Nano-lithographically fabricated titanium dioxide based visible frequency three dimensional gap photonic crystal

G. Subramania, Y-J. Lee, I. Brener, T.S. Luk, and P.G. Clem  »View Author Affiliations


Optics Express, Vol. 15, Issue 20, pp. 13049-13057 (2007)
http://dx.doi.org/10.1364/OE.15.013049


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Abstract

Photonic crystals (PC) have emerged as important types of structures for light manipulation. Ultimate control of light is possible by creating PCs with a complete three dimensional (3D) gap [1, 2]. This has proven to be a considerable challenge in the visible and ultraviolet frequencies mainly due to complications in integrating transparent, high refractive index (n) materials with fabrication techniques to create ~ 100nm features with long range translational order. In this letter, we demonstrate a nano-lithography approach based on a multilevel electron beam direct write and physical vapor deposition, to fabricate four-layer titania woodpile PCs that potentially exhibit complete 3D gap at visible wavelengths. We achieved a short wavelength bandedge of 525nm with a 300nm lattice constant PC. Due to the nanoscale precision and capability for defect control, the nanolithography approach represents an important step toward novel visible photonic devices for lighting, lasers, sensing and biophotonics.

© 2007 Optical Society of America

1. Introduction

Complete 3D gap PCs such as the “woodpile” lattice can alter light-matter interactions, many of which occur at optical frequencies, in interesting and fundamental ways. Large lattice constant structures (> 3μm) can be fabricated using contact photolithography [3

3. P. Yao, G. Schneider, D. Prather, E. Wetzel, and D. O’Brien, “Fabrication of three-dimensional photonic crystals with multilayer photolithogrpahy,” Opt. Exp. , 13, 2370–2376 (2005). [CrossRef]

] yielding bandgap in the mid-infrared. Structures with bandgap in the near-infrared require even smaller dimensions and have been fabricated from silicon [4

4. J.G. Fleming and S.Y. Lin, “Three-dimensional photonic crystal with a stop band from 1.35 to 1.95 μm,” Opt. Lett. 24(1), 49–51 (1999). [CrossRef]

] using high precision step and repeat aligners and gallium arsenide [5

5. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–607 (2000). [CrossRef] [PubMed]

] using wafer fusion, targeting the optical communication wavelengths (λ ~ 1.5μm). Both of these approaches, while yielding wafer scale 3D PCs, are generally quite complex and restrictive. Alternative nano-fabrication methods have also been explored [6

6. M. Deubel, G.V. Freyman, M. Wegener, S. Pereirra, K. Busch, and C.M. Soukoulis, “Direct laser writing of three dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004). [CrossRef] [PubMed]

, 7

7. Y. Lin, P.R. Herman, and K. Darmawikarta,“ Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86, 071117 (2005). [CrossRef]

, 8

8. A.F. Koenderink, P.M. Johnson, J.F.G. Lopez, and W.L. Vos, “Three-dimensional photonic crystals as cage for light,” C.R. Physique 3, 67–77 (2002). [CrossRef]

, 9

9. C. Lopez “Three dimensional photonic band gap materials: semiconductors for light”. J.Opt.A:Pure Appl. Opt. 8, R1–R14 (2006). [CrossRef]

] to fabricate 3D PCs, some of which show great promise. However, further progress still needs to be made from the standpoint of precision, defect control and engineering, and incorporation of high index materials.

A major advantage of 3DPCs with visible bandgaps is the availability of highly efficient nanoscale light sources such as semiconductor quantum dots (e.g. CdSe, CdSe) and dyes. By incorporating such light sources at specific locations within 3D PCs, their emission properties can be suitably manipulated by the photonic bandstructure to improve efficiency and to tune the emission profile, potentially enabling novel applications in lighting, displays, lasing and sensing. However, fabrication of complete gap 3D PCs in the visible, poses two significant challenges: choice of a suitable material with high refractive index and transparency, and patterning of structures with desired nanoscale periodicity (< 500nm) and symmetry. Titanium dioxide (TiO2) has a high refractive index (nanatase ~ 2.5;nrutile ~ 2.8) with negligible absorption at visible wavelengths [10

10. E.D. Palik,ed., Handbook of optical constants of solids (Academic Press, San Diego, CA, 1985).

]. This is an important advantage over metals which despite their high refractive index suffer large absorption at visible wavelengths. TiO2 has been used for infiltration of 3D PC templates [11

11. K. Awazu, X. Wang, M. Fujimaki, R. Kuriyama, A. Sai, and Y. Ohki, “Fabrication of two- and three-dimensional photonic crystals pf titania with submicrometer resolution by deep X-ray lithography,” J.V.S.T B 23, 934–939 (2005).

, 12

12. J.S. King, E. Graugnard, O.M. Roche, D.N. Sharp, J. Scrimgeour, R. Denning, A.J. Turberfield, and C.J. Summers, “Infiltration and inversion of holographically defined polymer photonic crystal templates by atomic layer deposition,” Adv. Mater. 18, 1561–1565 (2006). [CrossRef]

] including inverse opal PCs [13

13. P.V. Braun and P. Wiltzius, “Electrochemically grown photonic crystals,” Nature 402, 603–604 (1999). [CrossRef]

, 14

14. J.E.G.J. Wijnhoven and W.L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998). [CrossRef]

, 15

15. B.T. Holland, C.F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three dimensional arrays of spheroidal voids,” Science 281, 538–540 (1998). [CrossRef] [PubMed]

, 16

16. G. Subramania, K. Constant, R. Biswas, M.M. Sigalas, and k.M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999). [CrossRef]

]. However, the FCC symmetry of most inverse opals requires a refractive index contrast of n > 2.9 to create a complete 3D gap between higher order bands, which are more sensitive to disorder inherent in self-assembled opal templates [17

17. R. Biswas, M.M. Sigalas, G. Subramania, and K.M. Ho “Photonic band gaps in colloidal systems,” Phys. Rev. B. 57, 3701–3705 (1998). [CrossRef]

]. Nevertheless, higher refractive index material, like Sb 2 S 3 (n ~ 3.4) have been infiltrated into opal PCs for bandgap around 750nm wavelength [18

18. B. Juarez, M. Ibistate, J.M. Palacios, and C. Lopez, “High-energy photonic bandgap in Sb2S3 inverse opals by sulfidation processing,” Adv. Mater. 15, 319–322 (2003). [CrossRef]

]. In contrast, the woodpile lattice structure is shown to open a complete 3D gap for a refractive index contrast of just over 2.0 [19

19. K.M. Ho, C.T. Chan, C.M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gap in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994). [CrossRef]

]. We decided to use reactively sputter deposited amorphous TiO2 (n ~ 2.3 as measured by ellipsometry) as the high index material, because it has a well controlled anisotropic dry etch profile with good selectivity to the e-beam resist mask. This property allows for the definition of nanometer sized features in TiO2 films, thus enabling fabrication of visible PCs using woodpile lattices. The photonic band structure in Fig. 1(a) calculated for the corresponding woodpile lattice within the first Brillouin zone shown in Fig. 1(b) exhibits a complete 3D bandgap between reduced frequencies (ωred=aλ) of 0.4300 to 0.4462 with a gap/midgap ratio of 3.7%, where “a” is the lattice constant of the woodpile structure indicated in Fig. 1(c). This implies a wavelength gap of 15-25nm approaching the emission linewidths of green and red emitting monodisperse quantum dots and light emitting diodes. This will enable us to explore the effect of complete bandgap on phenomena such as band edge emission enhancement, emission lifetime increase in the gap as well as line narrowing effects of nanocavities. For instance, even with a moderate quality factors of a few hundreds achievable by 1-2 unit cell (9-17 layers) confinement [20

20. S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda,” Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004). [CrossRef] [PubMed]

], emission linewidths can be reduced to ~ 5 – 6nm which are well within the bandgap size.

Fig. 1. a) Band diagram for a woodpile PC where the rods are composed of reactively sputter deposited TiO2 with a refractive index of n =2.3. A complete 3D gap exists between the reduced frequencies of 0.4300 and 0.4462 indicated by the shaded region. The arrows at the X symmetry point indicates the lowest order stop bands along the stacking direction between reduced frequencies of 0.4137 and 0.4865 which is typically observed in near-normal incidence measurements. b) A schematic of the corresponding irreducible Brillouin zone indicating the various symmetry points. c) A schematic of the woodpile lattice with a lattice constant of “a” with each rod of width “d = 0.4a” and unit cell of height “c = √2a”.

2. Multilevel electron beam fabrication

Fig. 2. a)Scanning electron microscope(SEM) images of the PC structure shows a cross section of a 4 layer woodpile lattice of TiO2 rods. The lattice constant is 400 nm with each rod 160 nm wide and 110 nm high (magnified region inside the dotted square). The observed waviness in the rods results from a slight over-etching (~ 15%) of each layer to ensure the connectivity of TiO2 network after the low dielectric background material (SiO2) is etched away. b) Top view SEM image of a device with 300 nm lattice constant at 10KV accelerating voltage. The rods are 110 nm wide. The higher energy electrons used to obtain this image are able to penetrate deeper showing the underlying layers that appear in lighter shade (magnified region indicated by dotted square). The different layers are marked with a double arrow. The offset between layer 2 and layer 4 is very close to the ideal value of a/2.

3. Optical characterization using microspot spectroscopy

Figure 3(a) shows the devices exhibit bright coloration indicative of strong stop bands in the visible frequency. The 400nm device reflects orange light while the 300nm device reflects yellow light. The uniformity of the color across the device region for the 400nm device points to good structural uniformity. The 300nm device though mostly uniform in color displays some darker reddish regions in the middle and around the edges. Due to dose control limitations of our e-beam direct write system, the exposure is not simultaneously optimized for the different lattice constant devices on the same wafer. This can be solved by using separate exposures optimized for each lattice constant device. In order to characterize the bandgap, we performed microspot optical reflectance spectroscopy from 400 nm to 800 nm wavelengths on the devices by focusing the illumination with a microscope objective(NA = 0.25) with a spot size of ~ 25μm. Similar approach has been used previously to conduct single domain spectroscopy of self-assembled photonic crystals [28

28. Y.A. Vlasov, X-Z. Bo, J.C. Sturm, and D.J. Norris, “Single domain spectroscopy of self-assembled photonic crystals,” Appl. Phys. Lett. 76, 1627–1629 (2001). [CrossRef]

]. This also allows us to measure the more uniform region of the 300nm device. The relatively small NA corresponds to near normal incidence along the stacking direction thus probing the directional gap at the X symmetry point. Figure 3(b) shows a typical reflectance spectra from 300nm and 400nm devices. Each device shows a reflectance maximum at longer wavelengths corresponding to lowest order stop band and additional features at shorter wavelengths corresponding to higher order stop bands. For the 400nm device the lowest stop band maximum appears at 670nm with a short wavelength minimum (band edge) at 620nm. By reducing the lattice constant to 300nm the corresponding values are blue shifted to 620nm and 525nm which is well into the middle of the visible spectrum. Thus, we have demonstrated the fabrication of 3D PCs with sufficiently small lattice constants to potentially modify emission characteristics of embedded visible light sources.

Fig. 3. a) PCs with different lattice constants show characteristic colors which are reflected at the stop bands. Each device is a 80μm × 80μm square region. The colors appear quite uniform over the entire 400nm device and most of the 300nm device (see text for additional explanation). b) Optical reflectance spectrum from the devices obtained by micro-spectrometry with an objective lens with NA of 0.25 giving an incidence angle range of 0 →~ 15°. For the 400nm device we observe a long wavelength feature with a single peak at 670nm with several small peaks riding on a broad feature at shorter wavelengths. The long wavelength feature for the 300nm device is considerably broader with a shallower peak at 620nm which is blue shifted with respect to the 400nm device.

4. Comparison to computational models

In order to get a better insight into the observed optical response, we compared the experimental data with results from finite difference time domain(FDTD) and plane wave expansion(PWE) calculations.

Fig. 4. a) The experimental spectrum (solid line) for the a = 300nm device is plotted along with the spectrum from normal incidence FDTD calculations(dotted line). We find the reduced midgap frequency for the FDTD curve(ωred = 0.508) to be blue shifted by ~ 3% compared to the experimental curve(ωred = 0.492). To facilitate comparison, we define a width for the lower order stopband, as represented by the double arrows for the experi-mental(solid) and FDTD(dotted) spectra, and take the midpoint of the double arrows as the midgap position. The corresponding band diagram along the stacking direction (ΓX〈) is also plotted on the left side. The midgap frequency predicted for this case 0.432 which is ~ 13% red shifted from the measured value. b) Comparison of experimental spectrum with FDTD calculated spectrum for a = 400nm device. The reduced midgap frequency (ωred = 0.590) is within ~ 3%of that predicted by FDTD (ωred = 0.580). The peak reflectance value for the experimental curve is ~ 8% lower than that predicted by FDTD. The band diagram predicted midgap frequency (ωred = 0.546) is red-shifted by ~ 8% from the experimental value.

4.1. Finite difference time domain calculation (FDTD)

Simulated normal incidence reflectance spectra were calculated using a commercial FDTD software(OptiFDTD). To approximate our spectroscopy geometry of focused light source on a small sample, we utilized a supercell of five unit cells in the plane of the fabricated structure with perfectly matched layer boundary conditions. We discretized the structure on a15nm mesh and illuminated it with Gaussian source of width ~ 2a to maintain a tractable computational load. The experimental features typically agreed with the normal incidence FDTD prediction to within 5 – 10%. Figure 4(a) shows that for the 300nm device the reduced midgap frequency (ωred) from experiment was 0.492 compared to FDTD value of 0.508. The reflectance peak intensity was ~ 40% for both cases. Higher frequency features of the experimental spectra also exhibited a similar trend as the FDTD predictions. For the 400 nm device the midgap frequency of ωred = 0.590 matched closely with the corresponding FDTD value of 0.580 as seen in Fig. 4(b), while the peak intensity of 40% was lower than the calculated value of 48%. A similar trend in the higher frequency response for the experimental and FDTD data is again observed. Since the experimental data of the 400nm device spans a greater range of reduced frequency we are able to observe a greater number of higher frequency features. We attribute the observed discrepancy between the experimental and FDTD features to a combination of following factors. First, the experimental data contains reflectance from off-normal incidence angles which is not accounted for in the normal incidence FDTD model. Second, woodpile parameters (e.g. rod width, height, overlap) used as inputs for the FDTD model contain measurement uncertainties. Third, discretization of the structure in the FDTD domain space introduces additional approximations that may shift the calculated spectra. Nevertheless, the good match between experimental and simulated reflectance for a four layer TiO2 woodpile PC suggests that fabrication of additional unit cells by the multistep lithography technique will result in a stronger photonic response consistent with 3D bandgap.

4.2. Plane wave expansion (PWE)

We also compared the experimental response to bandstructure calculations along the stacking direction (ΓX〈). The bandstructure was calculated using PWE method [29

29. K.M. Ho, C.T. Chan, and C.M. Soukoulis, “Existence of a photonic band gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990). [CrossRef] [PubMed]

, 30

30. T. Suzuki and P.K.L. Yu, “Emission power of an electrical dipole in the photonic band structure of the fcc lattice,” J. Opt. Soc. Am. B 12, 570–581 (1995). [CrossRef]

] with 240-480 plane waves. We found the theoretical midgap position for 300 nm device to be 0.432 and for 400nm device to be 0.546. The observed blue shift of the peak position by ~ 10 – 15% from the midgap can be attributed to having only 4 layers (i.e. one unit cell) of PC along the stacking direction, as adding more layers is shown to shift the peak towards longer wavelengths by that amount [5

5. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–607 (2000). [CrossRef] [PubMed]

]. Thus the PWE method, which is computationally less intensive than FDTD, gives a reasonably good estimate of the frequencies of the optical features. Finally, we note that the ratio of c to a is different for the 300nm device (ca = 1.46) and the 400nm device (ca = 1.1). PWE calculations indicates that the 300nm device is more likely to show a full 3D gap as the ca ratio is closer to the ideal value of √2. In this case, this could not be directly verified experimentally as there is only one unit cell along the vertical. However, our current spectroscopy setup which only probes the ΓX〈 pseudogap shows that the 300nm device does exhibit a significantly wider reflectance feature than the 400nm device, consistent with our expectations.

5. Conclusion

The individual devices that were fabricated here are only 80μm × 80μm in size. However, one can make larger areas if required by field stitching these individual patterns. The process developed here can also be easily transfered to a large volume lithographic fabrication such as nanoimprint lithography. In conclusion, we have demonstrated that by using a nano-lithographic approach we can fabricate an omni-directional gap 3D PC in the visible frequency, in particular a TiO2 based woodpile lattice with precise structural control to produce predictable optical response. By patterning mechanically robust multilayers of TiO2 rods with dimensions of ~ 100nm and periodicities < 500nm and with excellent alignment between layers, we have shown that multistep e-beam direct write process is suitable for fabrication of visible 3D PCs with large number of layers if necessary for 3D gap PC devices. In combination with the availability of strong visible light emitters such as quantum dots, dyes and LEDs, a systematic study of light emission in 3D PC environment is possible leading to novel photonic devices in the future.

Acknowledgements

We thank Aaron Gin for reviewing the manuscript and providing valuable suggestions. San-dia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

References and links

1.

E. Yablanovitch, “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.

P. Yao, G. Schneider, D. Prather, E. Wetzel, and D. O’Brien, “Fabrication of three-dimensional photonic crystals with multilayer photolithogrpahy,” Opt. Exp. , 13, 2370–2376 (2005). [CrossRef]

4.

J.G. Fleming and S.Y. Lin, “Three-dimensional photonic crystal with a stop band from 1.35 to 1.95 μm,” Opt. Lett. 24(1), 49–51 (1999). [CrossRef]

5.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–607 (2000). [CrossRef] [PubMed]

6.

M. Deubel, G.V. Freyman, M. Wegener, S. Pereirra, K. Busch, and C.M. Soukoulis, “Direct laser writing of three dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004). [CrossRef] [PubMed]

7.

Y. Lin, P.R. Herman, and K. Darmawikarta,“ Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86, 071117 (2005). [CrossRef]

8.

A.F. Koenderink, P.M. Johnson, J.F.G. Lopez, and W.L. Vos, “Three-dimensional photonic crystals as cage for light,” C.R. Physique 3, 67–77 (2002). [CrossRef]

9.

C. Lopez “Three dimensional photonic band gap materials: semiconductors for light”. J.Opt.A:Pure Appl. Opt. 8, R1–R14 (2006). [CrossRef]

10.

E.D. Palik,ed., Handbook of optical constants of solids (Academic Press, San Diego, CA, 1985).

11.

K. Awazu, X. Wang, M. Fujimaki, R. Kuriyama, A. Sai, and Y. Ohki, “Fabrication of two- and three-dimensional photonic crystals pf titania with submicrometer resolution by deep X-ray lithography,” J.V.S.T B 23, 934–939 (2005).

12.

J.S. King, E. Graugnard, O.M. Roche, D.N. Sharp, J. Scrimgeour, R. Denning, A.J. Turberfield, and C.J. Summers, “Infiltration and inversion of holographically defined polymer photonic crystal templates by atomic layer deposition,” Adv. Mater. 18, 1561–1565 (2006). [CrossRef]

13.

P.V. Braun and P. Wiltzius, “Electrochemically grown photonic crystals,” Nature 402, 603–604 (1999). [CrossRef]

14.

J.E.G.J. Wijnhoven and W.L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998). [CrossRef]

15.

B.T. Holland, C.F. Blanford, and A. Stein, “Synthesis of macroporous minerals with highly ordered three dimensional arrays of spheroidal voids,” Science 281, 538–540 (1998). [CrossRef] [PubMed]

16.

G. Subramania, K. Constant, R. Biswas, M.M. Sigalas, and k.M. Ho, “Optical photonic crystals fabricated from colloidal systems,” Appl. Phys. Lett. 74, 3933–3935 (1999). [CrossRef]

17.

R. Biswas, M.M. Sigalas, G. Subramania, and K.M. Ho “Photonic band gaps in colloidal systems,” Phys. Rev. B. 57, 3701–3705 (1998). [CrossRef]

18.

B. Juarez, M. Ibistate, J.M. Palacios, and C. Lopez, “High-energy photonic bandgap in Sb2S3 inverse opals by sulfidation processing,” Adv. Mater. 15, 319–322 (2003). [CrossRef]

19.

K.M. Ho, C.T. Chan, C.M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gap in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994). [CrossRef]

20.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda,” Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004). [CrossRef] [PubMed]

21.

G. Subramania and S.Y. Lin. “Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography,” Appl. Phys. Lett. 74, 5037–5039 (2004). [CrossRef]

22.

M. Qi, E. Lidorikis, P.T. Rakich, S.G. Johnson, J.D. Joannopoulos, E.P. Ippen, and H. Smith, “A three dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004). [CrossRef] [PubMed]

23.

A.S.P. Chang, Y.S. Kim, M. Chen, Z.P. Yang, J.A. Bur, S.Y. Lin, and K.M. Ho, “Visible three-dimensional metallic photonic crystals with non-localized propagation modes beyond waveguide cutoff,” Opt. Express 15, 8248–8437 (2007). [CrossRef]

24.

A. Fiegel and B. Sfez, “Overlapped woodpile photonic crystals,” Appl. Opt. 43, 793–795 (2004). . [CrossRef]

25.

R. Rabady and I. Avrutsky, “Titania, silicon dioxide, and tantalum pentaoxide waveguides and optical resonant filters prepared with radio-frequency magnetron sputtering and annealing,” Appl. Opt. 44(3), 378–383 (2005). [CrossRef] [PubMed]

26.

M.M. Sigalas, C.M. Soukoulis, C.T. Chan, R. Biswas, and K.M. Ho, “ Effect of disorder on photonic band gaps,” Phys. Rev. B 59, 12767–12770 (1999). [CrossRef]

27.

G. Subramania, “Planarization of three-dimensional photonic crystals and other multi-level nanoscale structures,” Nanotechnology 18, 035303(7pp) (2007). [CrossRef] [PubMed]

28.

Y.A. Vlasov, X-Z. Bo, J.C. Sturm, and D.J. Norris, “Single domain spectroscopy of self-assembled photonic crystals,” Appl. Phys. Lett. 76, 1627–1629 (2001). [CrossRef]

29.

K.M. Ho, C.T. Chan, and C.M. Soukoulis, “Existence of a photonic band gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990). [CrossRef] [PubMed]

30.

T. Suzuki and P.K.L. Yu, “Emission power of an electrical dipole in the photonic band structure of the fcc lattice,” J. Opt. Soc. Am. B 12, 570–581 (1995). [CrossRef]

OCIS Codes
(050.7330) Diffraction and gratings : Volume gratings
(160.4670) Materials : Optical materials
(220.3740) Optical design and fabrication : Lithography
(220.4241) Optical design and fabrication : Nanostructure fabrication
(050.6875) Diffraction and gratings : Three-dimensional fabrication

ToC Category:
Photonic Crystals

History
Original Manuscript: July 27, 2007
Revised Manuscript: September 20, 2007
Manuscript Accepted: September 21, 2007
Published: September 25, 2007

Virtual Issues
Vol. 2, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Ganapathi Subramania, Yun-Ju Lee, Igal Brener, Ting-Shan Luk, and Paul G. Clem, "Nano-lithographically fabricated titanium dioxide based visible frequency three dimensional gap photonic crystal," Opt. Express 15, 13049-13057 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-20-13049


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References

  1. E. Yablanovitch, "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. P. Yao, G. Schneider, D. Prather, E. Wetzel and D. O’Brien, "Fabrication of three-dimensional photonic crystals with multilayer photolithogrpahy," Opt. Express 13, 2370-2376 (2005). [CrossRef]
  4. J. G. Fleming and S. Y. Lin, "Three-dimensional photonic crystal with a stop band from 1.35 to 1.95 µm," Opt. Lett. 24, 49-51 (1999). [CrossRef]
  5. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three dimensional photonic bandgap crystals at nearinfrared wavelengths," Science 289, 604-607 (2000). [CrossRef] [PubMed]
  6. M. Deubel, G. V. Freyman, M. Wegener, S. Pereirra, K. Busch and C. M. Soukoulis, "Direct laser writing of three dimensional photonic crystal templates for telecommunications," Nat. Mater. 3, 444-447 (2004). [CrossRef] [PubMed]
  7. Y. Lin, P. R. Herman, and K. Darmawikarta, "Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals," Appl. Phys. Lett. 86, 071117 (2005). [CrossRef]
  8. A. F. Koenderink, P. M. Johnson, J. F. G. Lopez, and W. L. Vos, "Three-dimensional photonic crystals as cage for light," C. R. Phys. 3, 67-77 (2002). [CrossRef]
  9. C. Lopez "Three dimensional photonic band gap materials: semiconductors for light," J. Opt. A: Pure Appl. Opt. 8, R1-R14 (2006). [CrossRef]
  10. E. D. Palik, ed., Handbook of optical constants of solids (Academic Press, San Diego, CA, 1985).
  11. K. Awazu, X. Wang, M. Fujimaki, R. Kuriyama, A. Sai and Y. Ohki, "Fabrication of two- and three-dimensional photonic crystals pf titania with submicrometer resolution by deep X-ray lithography," J. Vac. Sci. Technol. B 23, 934-939 (2005).
  12. J. S. King, E. Graugnard, O. M. Roche, D. N. Sharp, J. Scrimgeour, R. Denning, A. J. Turberfield, and C. J. Summers, "Infiltration and inversion of holographically defined polymer photonic crystal templates by atomic layer deposition," Adv. Mater. 18, 1561-1565 (2006). [CrossRef]
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