OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 20 — Oct. 1, 2007
  • pp: 13236–13243
« Show journal navigation

Investigation of optical properties of circular spiral photonic crystals

Nir Grossman, Aleksandr Ovsianikov, Alexander Petrov, Manfred Eich, and Boris Chichkov  »View Author Affiliations


Optics Express, Vol. 15, Issue 20, pp. 13236-13243 (2007)
http://dx.doi.org/10.1364/OE.15.013236


View Full Text Article

Acrobat PDF (1678 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The photonic bandgap of three-dimensional photonic crystals, formed by arranging circular spirals in face-centre-cubic lattice, was theoretically investigated. The structure was found to have a relative photonic bandgap of up to 25% in both direct and inversed configurations. The conditions under which the structure has a bandgap larger than 10% are described. Some considerations for optimizing such photonic crystal fabrication by two-photon polymerization are given. The theoretical results are implemented to fabricate polymeric structures that can be used as templates for photonic crystals with full photonic bandgap larger than 10% centered in the near-infrared region.

© 2007 Optical Society of America

1. Introduction

Photonic crystals are artificial periodic dielectric microstructures [1

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]

,2

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

]. Due to this periodicity they can diffract electromagnetic waves in a way that prevents their propagation. The range of wavelengths in which no propagating states exist can be interpreted as a gap in the dispersion function, it is also known as a photonic bandgap. By tailoring parameters such as the structure dimensions and dielectric contrast, the position of the central frequency of the photonic bandgap can be precisely adjusted. Defects introduced in the periodic structure can be used as lossless waveguides or to “store light” with resolution down to the wavelength size. Many exciting applications were proposed, but maybe the most important ones are in the optical communication field, where the information is carried by a light wave with a wavelength of about 1.5 μm. Ability to mold the information flow in three-dimensions with a resolution on the order of the wavelength has the potential to revolutionize the information technology [3

3. Busch Kurt, Lölkes Stefan, Wehrspohn Ralf, and B. Föll Helmut, Photonic Crystals (Wiley-VCH, Berlin, 2004)

, 4

4. Jean-Michel Lourtioz, Henri Benisty, Vincent Berger, Jean-Michel Gerard, Daniel Maystre, and Alexei Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer-Verlag Berlin and Heidelberg2005)

].

In order to realize the discussed applications, an omni-directional suppression of the propagating states is required. This feature can be achieved only with three-dimension photonic crystals, which exhibit complete photonic bandgaps, i.e. the bandgaps overlapping in all possible propagation directions. Currently the largest theoretically predicted complete photonic bandgap appears in the ‘rod-connected diamond structure’ proposed in 1991 by Chan et al. [5

5. C.T. Chan, K.M. Ho, and C.M. Soukoulis, “Photonic bandgaps in experimentally realizable periodic dielectric structures,” Europhys. Lett. 16, 563 (1991) [CrossRef]

, 6

6. C.T. Chan, S. Datta, K.M. Ho, and C.M. Soukoulis, “A-7 structure: A family of photonic crystals,” Phys. Rev. B 50, 1988 (1994) [CrossRef]

]. Silicon realization of this structure (refractive index of n=3.6) might have up to 30% relative complete gap (the ratio between the gap size and the mid gap frequency). Since the central wavelength (the wavelength in the center of the photonic bandgap) is approximately equal half of the crystal period, the structure must be fabricated with submicron resolution in order to shift the bandgap to the optical communication wavelengths. Despite some progress in the last years, realization of this particular structure with a submicron resolution is beyond present technological capabilities. Fortunately, the design can be simplified at the expense of the bandgap size. The <100> diamond like structure, also known as the woodpile structure, is a good example of a simplified architecture [7

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

]. In this case, some of the short rods that were connecting the lattice points in the rod-connected diamond structure were replaced by longer rods. The result is a simple four-layer version of the diamond structure that can be manufactured by the semiconductor technology via a layer-by-layer approach [8

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

]. Although this structure is noticeably different from the original diamond structure, it would still exhibit a relative complete gap of 18%. However, in order to increase the size of the bandgap for a given material more complicated three-dimensional structures are generally required [9

9. K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata,“Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication,” Appl. Phys. Lett. 83, 2091 (2003). [CrossRef]

].

The circular spirals based face-centre-cubic (fcc) lattice photonic crystals (Fig. 1) were proposed by Chutinan and Noda [10

10. A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev B 57, R2006 (1998) [CrossRef]

] in 1998 is an example of superior structure. Each spiral has a pitch C, a diameter D and is made of rods with a cross section width w and length l. The fcc configuration is achieved by shifting adjacent spirals in by half a period as they wind in the vertical <001> direction. The lateral lattice constant a is twice the distance between adjacent spirals and the vertical lattice constant is the pitch length C.

In their pioneering work Chutinan and Noda predicted that this structure would exhibit maximal relative complete gap of the 28% when fabricated in silicon (n=3.5) [10

10. A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev B 57, R2006 (1998) [CrossRef]

], which is the second largest bandgap predicted to-date. They reported that the structural configuration that would yield the largest gap is obtained when the rods have a diameter of 0.22a (here “a” is the lateral lattice constant), and the spirals have a diameter of 0.32a and a pitch of a. The realization of this structure, is quite complex- mainly due to the half a period shift between the adjacent objects. As a result, despite its attractiveness, the structure received minor attention since its proposal.

Fig. 1. Sketch of a spiral and its parameters together with an array of 4 × 4 spirals that are arranged in fcc lattice. The lattice constant a is equal twice the distance between adjacent spirals. Each spiral has a pitch C, a diameter D and is made of rods with a width w and a length l.

In 2005 Seet et al. showed for the first time that the fcc spiral structure can be manufactured using two-photon polymerization (2PP) technique [11

11. K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, “Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing,” Adv. Mater. 17, No.5, 541 (2005) [CrossRef]

]. They fabricated circular spirals in fcc lattice arrangement, with the distance between adjacent spirals of 1.8 μm (i.e. a = 3.6 μm), the spiral diameter of 2.7 μm (0.75a) and a pitch of 3.6 μm (a). The rods had elliptical cross section, which is an inherent feature of the fabrication technique (typically with an aspect ratio between 2 and 3). The structure did not have complete bandgap since its normalized parameters were significantly different from the ones suggested in ref [10

10. A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev B 57, R2006 (1998) [CrossRef]

]. Later, the structure was also fabricated with spirals that wind in the <100> direction in order to reduce the structure dimensions [12

12. K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, “Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 μm,” Appl. Phys. Lett. 88, 221101 (2006) [CrossRef]

]. In this case, the distances between adjacent spirals was reduced to 1 μm and 1.4 μm in the <010> and in the <001> directions, respectively and the pitch length was reduced to 0.8 μm (0.4a -0.3a). Here, the structure had a local pseudo gap in the Γ-Z direction. According to our calculations, no complete band gap could have been obtained with these structure proportions even if it would have been realized in silicon.

In order to provide guidelines for fabrication of the fcc spiral structure with a complete photonic bandgap, we investigated how the structural proportions can be altered without destroying the complete bandgap. Later, we used the results to fabricate fcc spiral structure in the SU8 material.

2. Band structure calculations

2.1. Methods

The fcc spiral structure has five variable parameters: the spiral’s diameter, the spiral’s pitch, the rod’s width, the rod’s length and the distance between adjacent spirals (see Fig. 1). Here, the parameters were normalized in respect to the lattice constant a, which is twice the distance between adjacent spirals. The band structures were calculated using the MIT’s Photonic Bands (MPB) tool that was developed by Johnson et al. [13

13. S. G. Johnson “MIT Photonic-Bands,” (Massachusetts Institute of Technology2002) http://ab-initio.mit.edu/wiki/index.php/MIT_Photonic_Bands

, 14

14. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173 (2001) [CrossRef] [PubMed]

]. The photonic crystal structure used in the simulations was constructed by overlapping dielectric ellipsoids (‘geometric-object’) with material refractive index n=3.5. The ellipsoids, closely packed along the spiral track, produced a smooth structure. This way the realistic fabrication approach of 2PP process was imitated. Each structure was represented by its unit-cell in which a computational grid with resolution between 16 and 32 pixels/unit-cell-direction was defined. The effective dielectric tensor in each grid point was found by averaging over a mesh of 3 points. We used a convergence tolerance of 1.0e-7.

2.2 Results and discussion

In the case of direct configuration, i.e. dielectric structure and air background the structure with the maximal relative complete bandgap was obtained when the spirals were made of rods with the width of 0.2a, length of 0.25a and had a diameter of 0.4a and a pitch length of a, Fig. 2(a). In the parametric space the structure is represented by the 4 element vector [w, l, D, C] = [0.2a 0.25a, 0.4a, a]. The structure has a fill factor of 20%, i.e. the dielectric material constitutes 20% of the total volume. It has a complete photonic bandgap between the second and the third bands with the relative width of 24.6%. The gap is centered at 0.58 normalized frequency (see Fig. 2(b)). The lower gap edge is located near the X direction, at (0.4, 0, 0) and the upper edge at R (0.5, 0.5, 0.5). In the inverted configuration, i.e. dielectric background, the maximal relative complete bandgap was found when [w, l, D, C] = [0.5a, 0.55a, 0.35a, a], corresponding to a dielectric fill factor of 22%. The relative complete photonic bandgap was 25.1%. The gap in this case is centered at 0.56 normalized frequency. Despite the differences between the optimal structure parameters reported here and the ones that were previously reported by ref [10

10. A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev B 57, R2006 (1998) [CrossRef]

], the resulted fill factors in both cases are the same, while the sizes of the maximal relative bandgaps differ by about 3%. The differences might be due to difference in the specifications that were used in calculation however, since we did not have an access to the method that was used in ref [10

10. A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev B 57, R2006 (1998) [CrossRef]

] we could not make an evidential conclusion.

The size of the bandgap was found to be more sensitive to changes in the relative spiral diameter and less sensitive to changes in the relative rod dimensions, Fig. 2(c). In fact, the complete gap is dropped by half when the spiral diameter is decreased by only 25% (in these cases a single parameter was changed each time while the others were kept in their optimal value). Changes in the rods width have in general stronger impact on the bandgap size than changes in the rods length. In order to center the gap at the 1.5μm wavelength the lattice constant should be 0.9μm. The structure dimensions would be then [w, l, D, C] = [0.17μm, 0.22μm, 0.35μm, 0.9μm].

Extensive efforts in the recent years led to significant improvements in the spatial resolution of the 2PP technique. Suspended rods with lateral size smaller than 50nm have been demonstrated [20

20. S. Juodkazis1, V. Mizeikis1, K. Seet1, M. Miwa, and H. Misawa, “Two-photon lithography of nanorods in SU-8 photoresist,” Nanotechnology 16, 846–849 (2005) [CrossRef]

, 21

21. D. Tan et al., “Reduction in feature size of two-photon polymerization using SCR500,” Appl Phys Lett 90, 071106 (2007) [CrossRef]

]. However, despite these remarkable achievements, the implementation of such resolution in large scale photonic crystal structures is still a major technological challenge. In particular, the realization of rod with symmetrical cross-section is hindered by the elongated shape of the voxel. The elongation characteristic is due to the intensity distribution in the focal point, and is an intrinsic property of the 2PP technique. The optimal configurations presented above are highly sensitive to changes in the elongation factors, i.e. the ratio between the rod’s length and width (see Fig. 3(a)). In case of the inversed configuration, the bandgaps are closed at elongation factors larger than 2 (see Fig. 3(a) left). In order to overcome this constrain, the width of the rods could be increased (by overlapping two parallel rods, for example) to match the length. The disadvantage of this approach is obviously the fact that it will shift the photonic bandgap to longer wavelengths. We therefore investigated how the structure configuration can be changed to perhaps more feasible for fabrication, while still maintaining large photonic bandgaps. The width and length of the rods as well as the spiral diameter were independently changed in the range of ±33% from their optimal values by increments of 0.05 and the photonic bandgaps at all possible combinations were calculated.

Fig. 2. (a) Two unit cells of the optimal fcc spiral structure in the direct configuration. (b) Photonic band structure of the fcc spiral structure made of n=3.5 material. (c) Sensitivity of the bandgap to the changes in the rod’s length (triangular), rod’s width (circular) and spiral’s diameter (rectangular). (left) direct configuration, (right) inverse configuration. (d) The distributions of the electric energy in the electromagnetic wave that propagates in the ΓZ direction. (top) ‘dielectric mode’ bellow the bandgap, (bottom) ‘air mode’ above the bandgap.

We have observed, that the range of configurations, revealing photonic bandgaps larger than 10%, can be confined by an isosurface in the parametric space, which can be expressed by equations Eq. (1) and Eq. (2), corresponding to the direct and the invert cases, respectively (a is the lattice constant). According to our calculations, each parametric combination in this range will reveal a photonic bandgap larger than 10%. Fig. 3(b) depicts the photonic bandgap map of the inverse spiral architecture. Fig. 3(c) presents the dependence of the photonic bandgap on the elongation factor. In order to minimize the elongation effect, the optimal configurations for each elongation factor were searched and presented in Fig. 3(d). In the case of the direct architecture, the optimal values of the rod’s width and spiral’s diameter (0.25a and 0.4a, respectively) are preserved for wide range of elongation factors. For refractive indexes of about 3 the photonic band gap center frequency can be approximated for the direct and inverse cases by Eq. (3) and Eq. (4), respectively.

[wd,ld,Dd,Cd]=[(0.15a:0.35a),(0.15a:0.4a),(0.3a:0.5a),~a]
(1)
[wi,li,Di,Ci]=[(0.3a:0.55a),(0.15a:0.75a),(0.3a:0.45a),~a]
(2)
fd=0.17ln(wl)+0.005
(3)
fi=1.22wl+0.225
(4)
Fig. 3. (a) The effect of the axial elongation on the maximal photonic bandgap for the inverse (left) and direct (right) architectures. (b) Bandgap map, i.e. bandgap as a function of spiral diameter and rod’s width of the inverse spiral structure. (c) The dependence of the photonic bandgap of the inverse architecture on the elongation factor for all structure configurations in the simulated range. (d) Parameters that optimize the photonic bandgap as a function of the elongation factor. Spiral diameter (black, rectangular), rod’s width (red, triangle), Relative size of the photonic bandgap (blue, circle).

3. Structure realization

3.1. Methods

We used a femtosecond laser (MTS Mini Ti:Sapphire laser kit from KM-Labs) to realize the structure. The laser system provided pulses with duration of 100 fs at 80 MHz repetition rate. The emission spectrum was centered at 770 nm wavelength. Since the resins have relatively low single-photon absorption at these wavelengths the laser radiation can be focused within the volume of the material. The beam was focused with a high NA objective lens (1.4) into the commercial SU-8 10 photoresist (Micro Resist Technology). The samples were set on a piezo stage with 3nm resolution and 100μm travel distance (Piezo Jena). The experimental setup is described in detail elsewhere [16

16. J. Serbin, A. Ovsianikov, and B. Chichkov, “Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties,” Opt. Express 12, 5221 (2004) [CrossRef] [PubMed]

]. The SU-8 was spin-coated at 5000 rpm for 30 seconds and soft-baked on a hotplate at 95°C for 50 minutes. After the exposure, the samples were post-baked at 95°C for 12 minutes. In order to realize stable spirals structure with fine resolution we used a ‘pinpoint’ writing technique in which single voxels (volume pixels) are superimposed along the required trace. The distance between adjacent voxels was set to 40 nm, resulting structures exhibit smooth surface. In comparison with the standard line writing this approach enables superior resolution since it allows optimization of each single voxel [17

17. H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, and S. Kawata, “Shape precompensation in two-photon nanowriting of photonic lattices,” Appl Phys Lett 85, 3708 (2004) [CrossRef]

].

Fig. 4. (a) Side view of SEM image of 40μm × 40μm fcc spiral structure that was realized in SU8 resin. (b) Top view. (c) ΓZU band structure for n=3.5 refractive index (left) and polymeric n=1.6 refractive index (right). (d) Sketch describes the formation of sinusoidal lines by the overlapping spirals. The arrows indicate the winding direction of the spirals which are segmented in such a way that the colors represent ¼ pitch length sequential layers.

3.2 Results and discussion

The structure presented in Fig. 4(a) and Fig 4(b) is an example of a 40 μm × 40 μm fcc spiral structure that was fabricated using the method described above. The distance between adjacent spirals here is 1.5 μm (a= 3μm), and each spiral has 1.2 μm diameter (0.4a) and 3 μm pitch (a) and they complete 6 vertical revolutions. The rods have width of 0.45 μm (0.15a) and length of 0.9 μm (0.3a). The polymeric structure satisfies the 10% complete gap boundary conditions that were presented above and can be used as a template for high refractive index material (a replication approach is described for example in ref [19

19. N. Tétreault, et al., “New Route to Three-Dimensional Photonic Bandgap Materials: Silicon Double Inversion of Polymer Templates,” Adv. Mater. 18, 457–460 (2006) [CrossRef]

]). The structure presented above is a polymeric template for 15% relative complete bandgap at 5.6 μm wavelength (for silicon replica). A Γ-Z pseudo bandgap is not expected in this case as can be seen in Fig. 4(c).

An interesting layered like pattern formed by the overlapping spirals is clearly seen in Fig. 4(b). It has parallel narrow sinusoidal rods with amplitude of approximately half the spirals pitch and is extending along the <110> or <-110> directions. Like in the woodpile structure case, the rods in adjacent layers are rotated by 90° relative to each other and every other layer is shifted by half the rods spacing in the direction that is orthogonal to the rods-see inset of Fig. 4(b). In subsequent simulations it was verified that this feature appeared in all the structures that exhibit complete bandgaps and disappeared when the gap was closed. These results imply that the overlapping of the spirals in a manner that forms such secondary structure is a necessary condition for obtaining the complete bandgap. If this is the case, the fcc circular spiral structure is in fact an indirect way to form layered like structure. In comparison with the regular woodpile structure a much larger bandgap can be achieved in this configuration, which imply that by modifying the shape of the rods to non-straight or sinusoidal one the bandgap of lined photonic crystal could be enhanced.

4. Conclusion

Reference and Links

1.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]

2.

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

3.

Busch Kurt, Lölkes Stefan, Wehrspohn Ralf, and B. Föll Helmut, Photonic Crystals (Wiley-VCH, Berlin, 2004)

4.

Jean-Michel Lourtioz, Henri Benisty, Vincent Berger, Jean-Michel Gerard, Daniel Maystre, and Alexei Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer-Verlag Berlin and Heidelberg2005)

5.

C.T. Chan, K.M. Ho, and C.M. Soukoulis, “Photonic bandgaps in experimentally realizable periodic dielectric structures,” Europhys. Lett. 16, 563 (1991) [CrossRef]

6.

C.T. Chan, S. Datta, K.M. Ho, and C.M. Soukoulis, “A-7 structure: A family of photonic crystals,” Phys. Rev. B 50, 1988 (1994) [CrossRef]

7.

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

8.

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

9.

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata,“Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication,” Appl. Phys. Lett. 83, 2091 (2003). [CrossRef]

10.

A. Chutinan and S. Noda, “Spiral three-dimensional photonic-band-gap structure,” Phys. Rev B 57, R2006 (1998) [CrossRef]

11.

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, “Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing,” Adv. Mater. 17, No.5, 541 (2005) [CrossRef]

12.

K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, “Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 μm,” Appl. Phys. Lett. 88, 221101 (2006) [CrossRef]

13.

S. G. Johnson “MIT Photonic-Bands,” (Massachusetts Institute of Technology2002) http://ab-initio.mit.edu/wiki/index.php/MIT_Photonic_Bands

14.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173 (2001) [CrossRef] [PubMed]

15.

H. B. Sun, S. Matsuo, and H. Misawa, “Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin,” Appl. Phys. Lett. 74, 786 (1999) [CrossRef]

16.

J. Serbin, A. Ovsianikov, and B. Chichkov, “Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties,” Opt. Express 12, 5221 (2004) [CrossRef] [PubMed]

17.

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, and S. Kawata, “Shape precompensation in two-photon nanowriting of photonic lattices,” Appl Phys Lett 85, 3708 (2004) [CrossRef]

18.

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

19.

N. Tétreault, et al., “New Route to Three-Dimensional Photonic Bandgap Materials: Silicon Double Inversion of Polymer Templates,” Adv. Mater. 18, 457–460 (2006) [CrossRef]

20.

S. Juodkazis1, V. Mizeikis1, K. Seet1, M. Miwa, and H. Misawa, “Two-photon lithography of nanorods in SU-8 photoresist,” Nanotechnology 16, 846–849 (2005) [CrossRef]

21.

D. Tan et al., “Reduction in feature size of two-photon polymerization using SCR500,” Appl Phys Lett 90, 071106 (2007) [CrossRef]

OCIS Codes
(140.3390) Lasers and laser optics : Laser materials processing
(220.4000) Optical design and fabrication : Microstructure fabrication
(230.5298) Optical devices : Photonic crystals
(160.5335) Materials : Photosensitive materials

ToC Category:
Photonic Crystals

History
Original Manuscript: August 15, 2007
Revised Manuscript: September 21, 2007
Manuscript Accepted: September 24, 2007
Published: September 27, 2007

Citation
Nir Grossman, Aleksandr Ovsianikov, Alexander Petrov, Manfred Eich, and Boris Chichkov, "Investigation of optical properties of circular spiral photonic crystals," Opt. Express 15, 13236-13243 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-20-13236


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486 (1987). [CrossRef] [PubMed]
  3. B. Kurt, L. Stefan, W. Ralf, and B. Föll Helmut, Photonic Crystals (Wiley-VCH, Berlin, 2004).
  4. J.-M. Lourtioz, H.i Benisty, V. Berger, J.-M. Gerard, D. Maystre, A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer-Verlag Berlin and Heidelberg 2005).
  5. C. T. Chan, K. M. Ho and C. M. Soukoulis, "Photonic bandgaps in experimentally realizable periodic dielectric structures," Europhys. Lett. 16, 563 (1991). [CrossRef]
  6. C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, "A-7 structure: A family of photonic crystals," Phys. Rev. B 50, 1988 (1994). [CrossRef]
  7. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413 (1994). [CrossRef]
  8. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604 (2000). [CrossRef] [PubMed]
  9. K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata," Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication," Appl. Phys. Lett. 83, 2091 (2003). [CrossRef]
  10. A. Chutinan, and S. Noda, "Spiral three-dimensional photonic-band-gap structure," Phys. Rev B 57, R2006 (1998). [CrossRef]
  11. K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing," Adv. Mater. 17, 541 (2005). [CrossRef]
  12. K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, "Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 µm," Appl. Phys. Lett. 88, 221101 (2006). [CrossRef]
  13. S. G. Johnson "MIT Photonic-Bands," (Massachusetts Institute of Technology 2002), http://ab-initio.mit.edu/wiki/index.php/MIT_Photonic_Bands>
  14. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173 (2001). [CrossRef] [PubMed]
  15. H. B.  Sun, S.  Matsuo, and H.  Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett.  74, 786 (1999). [CrossRef]
  16. J. Serbin, A. Ovsianikov, and B. Chichkov, "Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties," Opt. Express 12, 5221 (2004). [CrossRef] [PubMed]
  17. H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004). [CrossRef]
  18. M. Deubel, G. V. Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, "Direct laser writing of three-dimensional photonic-crystal templates for telecommunications," Nat. Mater. 3, 444 (2004). [CrossRef] [PubMed]
  19. N. Tétreault,  et al., "New Route to Three-Dimensional Photonic Bandgap Materials: Silicon Double Inversion of Polymer Templates," Adv. Mater. 18, 457-460 (2006). [CrossRef]
  20. S. Juodkazis1, V. Mizeikis1, K. Seet1, M. Miwa, and H. Misawa, "Two-photon lithography of nanorods in SU-8 photoresist," Nanotechnology 16, 846-849 (2005). [CrossRef]
  21. D. Tan,  et al., "Reduction in feature size of two-photon polymerization using SCR500," Appl Phys Lett 90, 071106 (2007). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited