Abstract

Topological photonics has emerged as a novel approach to engineering the flow of light and provides unprecedented means for developing diverse photonic elements, including robust optical waveguides immune to structural imperfections. However, the development of nanoscale standing-wave cavities in topological photonics is rather slow, despite its importance when building densely integrated photonic integrated circuits. In this Letter, we report a photonic crystal nanocavity based on a topological corner state, supported at a 90-deg-angled rim of a two-dimensional photonic crystal. A combination of the bulk-edge and edge-corner correspondences guarantees the presence of the higher-order topological state in a hierarchical manner. We experimentally observe a corner mode that is tightly localized in space while supporting a high Q factor over 2,000, verifying its promise as a nanocavity. These results cast new light on the way to introduce nanocavities in topological photonics platforms.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (5)

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Rev. Mod. Phys. 91, 015006 (2019).
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[Crossref]

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[Crossref]

2018 (14)

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, Nat. Photonics 12, 408 (2018).
[Crossref]

C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, Nature 555, 346 (2018).
[Crossref]

M. Serra-Garcia, V. Peri, R. Süsstrunk, O. R. Bilal, T. Larsen, L. G. Villanueva, and S. D. Huber, Nature 555, 342 (2018).
[Crossref]

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[Crossref]

S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, F. Schindler, C. H. Lee, M. Greiter, T. Neupert, and R. Thomale, Nat. Phys. 14, 925 (2018).
[Crossref]

F. Liu, H. Deng, and K. Wakabayashi, Phys. Rev. B 97, 035442 (2018).
[Crossref]

B.-Y. Xie, H.-F. Wang, H.-X. Wang, X.-Y. Zhu, J.-H. Jiang, M.-H. Lu, and Y.-F. Chen, Phys. Rev. B 98, 205147 (2018).
[Crossref]

X. Chen, F. Shi, H. Liu, J. Lu, W. Deng, J. Dai, Q. Cheng, and J.-W. Dong, Phys. Rev. Appl. 10, 044002 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Science 359, eaar4005 (2018).
[Crossref]

H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, Nat. Commun. 9, 981 (2018).
[Crossref]

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[Crossref]

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[Crossref]

T. Asano and S. Noda, Proc. IEEE 106, 2183 (2018).
[Crossref]

2017 (5)

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Science 357, 61 (2017).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Phys. Rev. B 96, 245115 (2017).
[Crossref]

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, Science 358, 636 (2017).
[Crossref]

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Nat. Photonics 11, 651 (2017).
[Crossref]

F. Liu and K. Wakabayashi, Phys. Rev. Lett. 118, 076803 (2017).
[Crossref]

2015 (1)

T. Ma, A. B. Khanikaev, S. H. Mousavi, and G. Shvets, Phys. Rev. Lett. 114, 127401 (2015).
[Crossref]

2014 (3)

L. Lu, J. D. Joannopoulos, and M. Soljačić, Nat. Photonics 8, 821 (2014).
[Crossref]

M. Xiao, Z. Q. Zhang, and C. T. Chan, Phys. Rev. X 4, 021017 (2014).
[Crossref]

X. Huang, M. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. B 90, 075423 (2014).
[Crossref]

2013 (1)

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, Nat. Photonics 7, 1001 (2013).
[Crossref]

2009 (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[Crossref]

2008 (1)

T. Baba, Nat. Photonics 2, 465 (2008).
[Crossref]

2006 (1)

R. Soref, IEEE J. Sel. Top. Quantum Electron. 12, 1678 (2006).
[Crossref]

1993 (1)

Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
[Crossref]

1989 (1)

J. Zak, Phys. Rev. Lett. 62, 2747 (1989).
[Crossref]

1985 (1)

J. Zak, Phys. Rev. B 32, 2218 (1985).
[Crossref]

1979 (1)

W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979).
[Crossref]

Alù, A.

X. Ni, M. Weiner, A. Alù, and A. B. Khanikaev, Nat. Mater. 18, 113 (2019).
[Crossref]

Amo, A.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Rev. Mod. Phys. 91, 015006 (2019).
[Crossref]

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Nat. Photonics 11, 651 (2017).
[Crossref]

Andler, G.

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” arXiv:1812.08185 (2018).

Arakawa, Y.

Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, Commun. Phys. 1, 86 (2018).
[Crossref]

T. Yamaguchi, Y. Ota, R. Katsumi, K. Watanabe, S. Ishida, A. Osada, Y. Arakawa, and S. Iwamoto, “GaAs valley photonic crystal waveguide with light-emitting InAs quantum dots,” arXiv:1904.02847 (2019).

Asano, T.

T. Asano and S. Noda, Proc. IEEE 106, 2183 (2018).
[Crossref]

Baba, T.

T. Baba, Nat. Photonics 2, 465 (2008).
[Crossref]

Bahari, B.

B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, Science 358, 636 (2017).
[Crossref]

Bahl, G.

C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, Nature 555, 346 (2018).
[Crossref]

Bandres, M. A.

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Science 359, eaar4005 (2018).
[Crossref]

Barik, S.

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, Science 359, 666 (2018).
[Crossref]

Bayer, F.

S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, F. Schindler, C. H. Lee, M. Greiter, T. Neupert, and R. Thomale, Nat. Phys. 14, 925 (2018).
[Crossref]

Benalcazar, W. A.

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, Nat. Photonics 12, 408 (2018).
[Crossref]

C. W. Peterson, W. A. Benalcazar, T. L. Hughes, and G. Bahl, Nature 555, 346 (2018).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Phys. Rev. B 96, 245115 (2017).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Science 357, 61 (2017).
[Crossref]

Berger, C.

S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, F. Schindler, C. H. Lee, M. Greiter, T. Neupert, and R. Thomale, Nat. Phys. 14, 925 (2018).
[Crossref]

Bergholtz, E. J.

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” arXiv:1812.08185 (2018).

Bernevig, B. A.

F. Schindler, Z. Wang, M. G. Vergniory, A. M. Cook, A. Murani, S. Sengupta, A. Y. Kasumov, R. Deblock, S. Jeon, I. Drozdov, H. Bouchiat, S. Guéron, A. Yazdani, B. A. Bernevig, and T. Neupert, Nat. Phys. 14, 918 (2018).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Science 357, 61 (2017).
[Crossref]

W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Phys. Rev. B 96, 245115 (2017).
[Crossref]

Bilal, O. R.

M. Serra-Garcia, V. Peri, R. Süsstrunk, O. R. Bilal, T. Larsen, L. G. Villanueva, and S. D. Huber, Nature 555, 342 (2018).
[Crossref]

Bloch, J.

P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Nat. Photonics 11, 651 (2017).
[Crossref]

Bouchiat, H.

F. Schindler, Z. Wang, M. G. Vergniory, A. M. Cook, A. Murani, S. Sengupta, A. Y. Kasumov, R. Deblock, S. Jeon, I. Drozdov, H. Bouchiat, S. Guéron, A. Yazdani, B. A. Bernevig, and T. Neupert, Nat. Phys. 14, 918 (2018).
[Crossref]

Bourennane, M.

A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, “Corner states of light in photonic waveguides,” arXiv:1812.08185 (2018).

Brehm, J.

S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, F. Schindler, C. H. Lee, M. Greiter, T. Neupert, and R. Thomale, Nat. Phys. 14, 925 (2018).
[Crossref]

Cai, T.

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, Science 359, 666 (2018).
[Crossref]

Carusotto, I.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Rev. Mod. Phys. 91, 015006 (2019).
[Crossref]

Chan, C. T.

M. Xiao, Z. Q. Zhang, and C. T. Chan, Phys. Rev. X 4, 021017 (2014).
[Crossref]

X. Huang, M. Xiao, Z.-Q. Zhang, and C. T. Chan, Phys. Rev. B 90, 075423 (2014).
[Crossref]

Chen, K. P.

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, Nat. Photonics 12, 408 (2018).
[Crossref]

Chen, M.

X.-D. Chen, W. Deng, F. Shi, F. Zhao, M. Chen, and J. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” arXiv:1812.08326 (2018).

Chen, X.

X. He, E. Liang, J. Yuan, H. Qiu, X. Chen, F. Zhao, and J. Dong, Nat. Commun. 10, 872 (2019).
[Crossref]

X. Chen, F. Shi, H. Liu, J. Lu, W. Deng, J. Dai, Q. Cheng, and J.-W. Dong, Phys. Rev. Appl. 10, 044002 (2018).
[Crossref]

Chen, X.-D.

X.-D. Chen, W. Deng, F. Shi, F. Zhao, M. Chen, and J. Dong, “Direct observation of corner states in second-order topological photonic crystal slabs,” arXiv:1812.08326 (2018).

Chen, Y.-F.

B.-Y. Xie, H.-F. Wang, H.-X. Wang, X.-Y. Zhu, J.-H. Jiang, M.-H. Lu, and Y.-F. Chen, Phys. Rev. B 98, 205147 (2018).
[Crossref]

X. Zhang, H.-X. Wang, Z.-K. Lin, Y. Tian, B. Xie, M.-H. Lu, Y.-F. Chen, and J.-H. Jiang, Nat. Phys. (2019).
[Crossref]

B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, and Y.-F. Chen, “Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals,” arXiv:1812.06263 (2018).

Cheng, Q.

X. Chen, F. Shi, H. Liu, J. Lu, W. Deng, J. Dai, Q. Cheng, and J.-W. Dong, Phys. Rev. Appl. 10, 044002 (2018).
[Crossref]

Chong, Y.

H. Xue, Y. Yang, F. Gao, Y. Chong, and B. Zhang, Nat. Mater. 18, 108 (2019).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Nature 461, 772 (2009).
[Crossref]

Christodoulides, D. N.

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Science 359, eaar4005 (2018).
[Crossref]

Collins, M. J.

J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, and M. C. Rechtsman, Nat. Photonics 12, 408 (2018).
[Crossref]

Cook, A. M.

F. Schindler, Z. Wang, M. G. Vergniory, A. M. Cook, A. Murani, S. Sengupta, A. Y. Kasumov, R. Deblock, S. Jeon, I. Drozdov, H. Bouchiat, S. Guéron, A. Yazdani, B. A. Bernevig, and T. Neupert, Nat. Phys. 14, 918 (2018).
[Crossref]

Dai, J.

X. Chen, F. Shi, H. Liu, J. Lu, W. Deng, J. Dai, Q. Cheng, and J.-W. Dong, Phys. Rev. Appl. 10, 044002 (2018).
[Crossref]

Deblock, R.

F. Schindler, Z. Wang, M. G. Vergniory, A. M. Cook, A. Murani, S. Sengupta, A. Y. Kasumov, R. Deblock, S. Jeon, I. Drozdov, H. Bouchiat, S. Guéron, A. Yazdani, B. A. Bernevig, and T. Neupert, Nat. Phys. 14, 918 (2018).
[Crossref]

DeGottardi, W.

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, Science 359, 666 (2018).
[Crossref]

Deng, H.

F. Liu, H. Deng, and K. Wakabayashi, Phys. Rev. B 97, 035442 (2018).
[Crossref]

Deng, W.

X. Chen, F. Shi, H. Liu, J. Lu, W. Deng, J. Dai, Q. Cheng, and J.-W. Dong, Phys. Rev. Appl. 10, 044002 (2018).
[Crossref]

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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. (a) Conceptual schematic of a 2D system supporting both the 1D edge and 0D corner states. (b) Schematic illustration of the investigated 2D PhC. (c) Top view of the PhC, showing how to define the unit cell for the topological (red) and trivial (blue) PhC. Unit cells for the (d) trivial and (e) topological PhC. The insets show magnetic (Hz) field profiles simulated at the X point for the lowest and second-lowest energy bands. (f) Photonic band structure simulated for the PhC with d1=0.7a and d2=0.1a using the 2D plane wave expansion method. (g) Same as in (f) but with d1=d2=0.4a, showing Dirac points at the X point and quadratic band touching at the M point.
Fig. 2.
Fig. 2. (a) Schematic of the investigated 1D interface. (b) Projected band structure simulated along with the interface. The red and light gray lines are of the localized 1D edge mode and of the light line, respectively. The blue curves correspond to those of bulk modes. (c) Field profile for the topological 1D mode localized at the edge, simulated at the Γ point. All simulation in these plots is performed with the 2D plane wave expansion method.
Fig. 3.
Fig. 3. (a) Excitation spectra simulated for the corner (red), edge (blue), and bulk (green) constituted from a PhC with d1=0.7a and d2=0.1a. These spectra were calculated using the 2D finite difference time domain method. (b) Magnetic field profile for the mode of the resonance peak at 0.342a/λ, exhibiting localization at the corner. (c) Evolutions of Q factors (red points) and mode volumes (blue) as a function of d1, while modifying d2 according to d2=0.8ad1. The slab thickness is assumed to be 0.5a. The calculations were done with a 3D finite difference time domain simulator.
Fig. 4.
Fig. 4. (a) Scanning electron microscope image of a fabricated sample with d1=0.6a and d2=0a. The inset shows a close-up picture around the corner. (b) Spectrum of the PL emission around the corner. The broad emission peaks widely spanning from 1000 nm to over 1125 nm originate from the QD ensemble. (c) Close-up PL spectrum of the resonance peak at 1078 nm. The black solid line is of fitting using a Lorentzian function with a linearly increasing background. (d) Summary of position-dependent PL measurements around the corner. The green (orange) points show the normalized intensities of the target resonance peak taken along with the x(y) direction. The tip of the corner of the topological PhC is taken as the origin of the measurements. The solid lines are of numerical simulations convolved with Gaussian functions expressing the spatial resolution of the PL setup. The spatial resolution for the x direction (1μm) is better than that of the y direction (1.8μm), owing to a mechanical slit placed in front of the spectrometer and transmitting signal from a limited range of the x axis.