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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 10590–10596
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Nanocavities at the surface of three-dimensional photonic crystals

Kenji Ishizaki, Kou Gondaira, Yuji Ota, Katsuyoshi Suzuki, and Susumu Noda  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 10590-10596 (2013)
http://dx.doi.org/10.1364/OE.21.010590


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Abstract

We investigate nanocavities at the surface of three-dimensional (3D) photonic crystals, where the polarization-independent surface-mode gap can be utilized. We consider the formation of various nanocavities by introducing artificial defects utilizing the 3D structures around the surface and discuss the possibilities for increasing the Q-factors of the surface nanocavities with TE-like polarization based on the advanced designs of donor-type defects. We also introduce the design of acceptor-type defects and show that TM-like nanocavities are obtained. We then fabricate the designed nanocavities and examine their resonant characteristics; we successfully demonstrate TE-like nanocavities with Q-factors of ~40,000, which is four-times higher than previous surface cavities and as high as that of the cavities embedded inside 3D photonic crystals. TM-like nanocavities with Q-factors of ~22,000 are also demonstrated for the first time.

© 2013 OSA

1. Introduction

In this work, we study the creation of surface nanocavities by addressing the advantages of a high degree of design freedom and the polarization-independent surface-mode gap. We discuss the possibility of increasing the Q-factor of surface nanocavities with TE-like polarization by introducing two design concepts. We also discuss the creation of cavities with desired polarization, focusing on the formation of TM-like nanocavities where the electric field is polarized in the surface-normal direction. We then experimentally fabricate the designed nanocavities and demonstrate their resonant characteristics. We believe that these results will become important foundations for the manipulation of photons at the surface of 3D photonic crystals.

2. Nanocavity designs

Figure 1
Fig. 1 Schematic illustration of a nanocavity at the surface of 3D photonic crystal with stacked-stripe structures, whose surface possess the cross-geometric pattern.
shows a schematic image of a nanocavity at the surface of a 3D photonic crystal. We used a 3D photonic crystal with a stacked-stripe (or woodpile) structure [1

1. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000). [CrossRef] [PubMed]

], which has successfully demonstrated a variety of photon manipulations. At the surface of such a 3D photonic crystal, the formation of a surface-mode gap has been experimentally proven [7

7. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef] [PubMed]

], within which the existence of photons with any polarizations (including TE/TM polarizations) is inhibited. Figure 2(a)
Fig. 2 Characteristics of surface-mode gap. (a) Calculated band diagram. The insets show the representative directions in real and reciprocal spaces. (b), (c) Calculated electric-field distributions of higher- and lower-edge modes of surface-mode gap, respectively.
shows the calculated photonic band diagram of the surface modes by a 3D finite-difference time-domain (FDTD) method, showing the formation of the surface-mode gap. We set the width and the height of the rods as 0.4a and 0.4a. Here, a is the center-to-center separation of parallel rods. Figures 2(b) and 2(c) illustrate representative electric-field distributions of the upper- and lower-edge modes of the surface-mode gap at the X point in the reciprocal space [(kx,ky) = (π/a,0)]. It can be seen in Figs. 2(b) and 2(c) that the dominant component of the higher- and lower-edge modes are Ey and Ez, respectively, thus the polarization of those modes are classified as TE-like and TM-like. Those results suggest that the cavity modes with TE-like or TM-like polarizations can be obtained by introducing adequate defect structures around the surface, utilizing the polarization characteristics of those band-edge modes of the surface-mode gap.

In our second design consideration, we expanded the design area by moving artificial defects from the very surface to slightly inside the photonic crystals, such as the second or third layer. In this case, the center of the electric-field distribution is also expected to move to slightly inside the photonic crystal, and the amount of the electric field just at the interface between the photonic-crystal surface and air is reduced. As a result, the loss into air from the cavity might be reduced. This consideration is unique at the surface of 3D photonic crystals, differing from the low-dimensional structures. Figure 4(a)
Fig. 4 Design of TE-like nanocavities composed of the defects formed in the second layer. (a) Schematic images of the structure. (b) Calculated electric-field distribution (Ey component). (c) Calculated Q-factors for the cases with the defects in the second layer and the surface layer.
shows the considered structure, where we increased the rod width in the second layer within a particular range instead of increasing the rod width in just the surface layer. As shown in Fig. 4(b), the dominant component of the electric field was also Ey, as is the case of introducing the cavity in the surface layer [Fig. 3 (c)]. Figure 4(c) shows the calculated Q-factors by varying the defect length Ld, where the width of the defect rod was 0.60a. The Q-factors of the cavities just at the surface layer are also shown for comparison, where the width of the defect rod was 0.52a. In both cases the number of stacked layers was sixteen. Figure 4(c) shows that the Q-factors increase about twofold when cavities are introduced in the second layer. These results suggest that the reduction of the optical loss into air is possible by changing the positions of the artificial defects, which is unique consideration in the use of 3D structures. Here, it is noteworthy that these two advanced design considerations for increasing the Q-factor of surface nanocavities are expected to be similarly applicable when using the surfaces of the other types of 3D photonic crystals.

We also investigated whether the creation of TM-like nanocavities is possible. We focused on the fact that the lower-edge mode of the surface-mode gap possesses TM-like polarization [Fig. 2(c)]. Based on this, it is expected that TM-like cavities can be obtained by introducing defects where the volume of the rods around the surface is partially decreased; such defects can be called as acceptor-type defects due to the similarity with the acceptor ions in semiconductors [14

14. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67(24), 3380–3383 (1991). [CrossRef] [PubMed]

]. Figure 5(a)
Fig. 5 Design of TM-like nanocavities. (a) Schematic images of the structure. (b) Calculated electric field distribution (Ez component). (c) Calculated Q-factors.
shows a schematic of the designed structure for TM-like nanocavity. As an example, we narrowed the rod in the second layer within a particular range. Of course, we can also introduce such acceptor-type defects into the other layers, such as the surface layer. We set the width 0.21a and calculated the electric field distributions. As shown in Fig. 5(b), we confirmed that the dominant component at the surface is Ez as the lower-edge mode of the surface-mode gap [Fig. 2(c)], and TM-like nanocavity is obtained. Figure 5(c) shows the calculated Q-factors, and we expect that the Q-factors of such TM-like nanocavities could increase by incorporating the method about the gradual modification of the rod widths as discussed in Fig. 3.

3. Fabrication and experiments

Next, we fabricated the designed nanocavities at the surface of the 3D photonic crystals with sixteen stacked layers and examined their resonant characteristics. For the fabrication, we employed highly-precise alignment and wafer-bonding techniques [1

1. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000). [CrossRef] [PubMed]

,12

12. K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013). [CrossRef]

,18

18. S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst. 16(5), 1140–1144 (2007). [CrossRef]

]. We used GaAs or Si for the constituent materials. The period of stripe pattern was a = 500 nm, and the width and the height of the rods were set at 200 nm ( = 0.4a). Figure 6
Fig. 6 Experimental demonstrations of TE-like nanocavities. (a), (b) Top-view SEM image of a cavity constructed by gradually modifying the rod widths and its resonant spectrum, respectively. The constituent material of the photonic crystal was Si. (c), (d) Top-view SEM image of a cavity constructed by introducing defect in the second layer and its resonant spectrum, respectively. The constituent material of the photonic crystal was GaAs.
shows the experimental results of the TE-like nanocavities with two designs. Figure 6(a) shows the SEM image of the fabricated nanocavity composed by gradually increasing the rod width in the surface layer as designed in Fig. 3. For this nanocavity, we measured a resonant spectrum with a measurement technique in which we irradiated light in an oblique direction (45° with respect to the surface normal) and collected the radiated light from the cavity in the same direction [7

7. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef] [PubMed]

]. We used a wavelength-tunable continuous laser as the light source. Figure 6(b) shows the obtained result. We successfully obtained a Q-factor of ~40,000. In addition to such a nanocavity in the surface layer, we also fabricated the nanocavities formed in the second layer. Figure 6(c) shows representative SEM image, showing that we successfully realized the designed structure in the second layer. Figure 6(d) shows the observed resonant spectrum for the case with Ld = 3a. From Fig. 6(d), we estimated the maximum experimental Q-factor as ~40,000.

In addition to TE-like nanocavities, we fabricated TM-like nanocavities and examined their characteristics. Figures 7(a)
Fig. 7 Experimental demonstration of TM-like nanocavities. (a), (b) Top-view SEM image of a cavity constructed by decreasing the rod width in the second layer and its resonant spectrum, respectively. The constituent material of the photonic crystal was GaAs.
and 7(b) show a SEM image of the fabricated nanocavity and the measured resonant spectrum, respectively. An acceptor-type defect was well fabricated by decreasing the rod width in the second layer [Fig. 7(a)]. In Fig. 7(b), which shows the resonant spectrum where Ld = 6a, we obtained a Q-factor up to 22,000 in the TM-like nanocavity. Although the obtained Q-factor is slightly high compared with the calculation result [Fig. 5(c)], this is thought to be due to the difference between the calculated and fabricated structures. To the best of our knowledge, this experimental Q-factor is the highest among the TM-like nanocavities in photonic crystals, including 1D or 2D systems, suggesting that the surfaces of 3D photonic crystals are essentially useful fields for manipulating photons with any polarizations. Furthermore, note that our TM-like cavity possesses a high Q-factor from the viewpoint of acceptor-type nanocavities; for example, Q-factors of ~1,000 were reported in an acceptor-type nanocavity in 2D photonic crystals [19

19. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000). [CrossRef] [PubMed]

]. Since the electromagnetic fields of surface modes tend to penetrate into air, surface modes are expected to be applicable as a field for efficient sensing applications [13

13. T. Yoshie, L. Tang, and S.-Y. Su, “Optical microcavity: Sensing down to single molecules and atoms,” Sensors (Basel) 11(12), 1972–1991 (2011). [CrossRef] [PubMed]

]. Advancements in acceptor-type nanocavities, where we can obtain electromagnetic fields penetrating into air only at a certain location, would be advantageous for new sensing applications.

4. Conclusions

Acknowledgments

This work was partly supported by the Global Center of Excellence program for Education and Research on Photonics and Electronics Science and Engineering of Kyoto University, by Core Research for Evolutional Science and Technology program of Japan Science and Technology agency, and by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science.

References and links

1.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000). [CrossRef] [PubMed]

2.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305(5681), 227–229 (2004). [CrossRef] [PubMed]

3.

P. Lodahl, A. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430(7000), 654–657 (2004). [CrossRef] [PubMed]

4.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004). [CrossRef] [PubMed]

5.

M. Imada, L.-H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88(17), 171107 (2006). [CrossRef]

6.

S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2(1), 52–56 (2008). [CrossRef]

7.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef] [PubMed]

8.

S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8(9), 721–725 (2009). [CrossRef] [PubMed]

9.

S. Kawashima, K. Ishizaki, and S. Noda, “Light propagation in three-dimensional photonic crystals,” Opt. Express 18(1), 386–392 (2010). [CrossRef] [PubMed]

10.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011). [CrossRef]

11.

K. Suzuki, K. Ishizaki, Y. Ota, and S. Noda, “Surface modes of three-dimensional photonic crystals constructed using a top-down approach,” Opt. Express 19(25), 25651–25656 (2011). [CrossRef] [PubMed]

12.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013). [CrossRef]

13.

T. Yoshie, L. Tang, and S.-Y. Su, “Optical microcavity: Sensing down to single molecules and atoms,” Sensors (Basel) 11(12), 1972–1991 (2011). [CrossRef] [PubMed]

14.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67(24), 3380–3383 (1991). [CrossRef] [PubMed]

15.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed]

16.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]

17.

Y. Tanaka, T. Asano, and S. Noda, “Design of photonic crystal nanocavity with Q-factor of ~109,” J. Lightwave Technol. 26(11), 1532–1539 (2008). [CrossRef]

18.

S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst. 16(5), 1140–1144 (2007). [CrossRef]

19.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000). [CrossRef] [PubMed]

OCIS Codes
(240.6690) Optics at surfaces : Surface waves
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(160.5298) Materials : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: February 5, 2013
Revised Manuscript: March 21, 2013
Manuscript Accepted: April 16, 2013
Published: April 23, 2013

Citation
Kenji Ishizaki, Kou Gondaira, Yuji Ota, Katsuyoshi Suzuki, and Susumu Noda, "Nanocavities at the surface of three-dimensional photonic crystals," Opt. Express 21, 10590-10596 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10590


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References

  1. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science289(5479), 604–606 (2000). [CrossRef] [PubMed]
  2. S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science305(5681), 227–229 (2004). [CrossRef] [PubMed]
  3. P. Lodahl, A. Floris Van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature430(7000), 654–657 (2004). [CrossRef] [PubMed]
  4. M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature429(6991), 538–542 (2004). [CrossRef] [PubMed]
  5. M. Imada, L.-H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett.88(17), 171107 (2006). [CrossRef]
  6. S. A. Rinne, F. García-Santamaría, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics2(1), 52–56 (2008). [CrossRef]
  7. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature460(7253), 367–370 (2009). [CrossRef] [PubMed]
  8. S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater.8(9), 721–725 (2009). [CrossRef] [PubMed]
  9. S. Kawashima, K. Ishizaki, and S. Noda, “Light propagation in three-dimensional photonic crystals,” Opt. Express18(1), 386–392 (2010). [CrossRef] [PubMed]
  10. A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics5(2), 91–94 (2011). [CrossRef]
  11. K. Suzuki, K. Ishizaki, Y. Ota, and S. Noda, “Surface modes of three-dimensional photonic crystals constructed using a top-down approach,” Opt. Express19(25), 25651–25656 (2011). [CrossRef] [PubMed]
  12. K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics7(2), 133–137 (2013). [CrossRef]
  13. T. Yoshie, L. Tang, and S.-Y. Su, “Optical microcavity: Sensing down to single molecules and atoms,” Sensors (Basel)11(12), 1972–1991 (2011). [CrossRef] [PubMed]
  14. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett.67(24), 3380–3383 (1991). [CrossRef] [PubMed]
  15. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003). [CrossRef] [PubMed]
  16. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater.4(3), 207–210 (2005). [CrossRef]
  17. Y. Tanaka, T. Asano, and S. Noda, “Design of photonic crystal nanocavity with Q-factor of ~109,” J. Lightwave Technol.26(11), 1532–1539 (2008). [CrossRef]
  18. S. Kawashima, M. Imada, K. Ishizaki, and S. Noda, “High-precision alignment and bonding system for the fabrication of 3-D nanostructures,” J. Microelectromech. Syst.16(5), 1140–1144 (2007). [CrossRef]
  19. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature407(6804), 608–610 (2000). [CrossRef] [PubMed]

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