Abstract

In a planar optical cavity, the resonance frequencies increase as a function of in-plane wavevector according to a standard textbook formula. This has well-known consequences in many different areas of optics, from the shifts of etalon peaks at non-normal angles, to the properties of transverse modes in laser diodes, to the effective mass of microcavity photons, and so on. However, this standard formula is valid only when the reflection phase of each cavity mirror is approximately independent of angle. There is a certain type of mirror—a subwavelength dielectric grating near a guided mode resonance—with not only a strongly angle-dependent reflection phase, but also very high reflectance and low losses. Simulations show that by using such mirrors, high-quality-factor planar cavities can be designed that break all these textbook rules, leading to resonant modes that are slow, stopped or even backward-propagating in the in-plane direction. In particular, we demonstrate experimentally high-Q planar cavities whose resonance frequency is independent of in-plane wavevector—i.e., the resonant modes have zero in-plane group velocity, for one polarization but both in-plane directions. We discuss potential applications in various fields including lasers, quantum optics, and exciton-polariton condensation.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (1)

F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, “Bosonic condensation and disorder-induced localization in a flat band,” Phys. Rev. Lett. 116(6), 066402 (2016).
[Crossref] [PubMed]

2015 (3)

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114(7), 073601 (2015).
[Crossref] [PubMed]

R. Yang, W. Zhu, and J. Li, “Realization of “trapped rainbow” in 1D slab waveguide with surface dispersion engineering,” Opt. Express 23(5), 6326–6335 (2015).
[Crossref] [PubMed]

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114(24), 245504 (2015).
[Crossref] [PubMed]

2014 (6)

S. Flach, D. Leykam, J. D. Bodyfelt, P. Matthies, and A. S. Desyatnikov, “Detangling flat bands into Fano lattices,” Europhys. Lett. 105(3), 30001 (2014).
[Crossref]

J.-H. Jiang and S. John, “Photonic crystal architecture for room-temperature equilibrium Bose-Einstein condensation of exciton polaritons,” Phys. Rev. X 4(3), 031025 (2014).
[Crossref]

Y.-C. Cheng and K. Staliunas, “Negative Goos-Hänchen shift in reflection from subwavelength gratings,” J. Nanophotonics 8(1), 084093 (2014).
[Crossref]

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(11), 803–813 (2014).
[Crossref]

R. Yang, W. Zhu, and J. Li, “Giant positive and negative Goos-Hänchen shift on dielectric gratings caused by guided mode resonance,” Opt. Express 22(2), 2043–2050 (2014).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

2013 (1)

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. de Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Loncar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13(12), 5791–5796 (2013).
[Crossref] [PubMed]

2012 (5)

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4(3), 379–440 (2012).
[Crossref]

V. Liu and S. Fan, “S4: a free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183(10), 2233–2244 (2012).
[Crossref]

M. Khorasaninejad, N. Abedzadeh, J. Walia, S. Patchett, and S. S. Saini, “Color matrix refractive index sensors using coupled vertical silicon nanowire arrays,” Nano Lett. 12(8), 4228–4234 (2012).
[Crossref] [PubMed]

2011 (2)

M. A. Kats, D. Woolf, R. Blanchard, N. Yu, and F. Capasso, “Spoof plasmon analogue of metal-insulator-metal waveguides,” Opt. Express 19(16), 14860–14870 (2011).
[Crossref] [PubMed]

R. Magnusson, M. Shokooh-Saremi, K. J. Lee, J. Curzan, D. Wawro, S. Zimmerman, W. Wu, J. Yoon, H. G. Svavarsson, and S. H. Song, “Leaky-mode resonance photonics: an applications platform,” Proc. SPIE 8102, 810202 (2011).
[Crossref]

2010 (2)

P. Viktorovitch, B. Ben Bakir, S. Boutami, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, C. Seassal, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “3D harnessing of light with 2.5D photonic crystals,” Laser Photonics Rev. 4(3), 401–413 (2010).
[Crossref]

M. Shokooh-Saremi and R. Magnusson, “Leaky-mode resonant reflectors with extreme bandwidths,” Opt. Lett. 35(8), 1121–1123 (2010).
[Crossref] [PubMed]

2009 (1)

M. Peckus, R. Rogalskis, M. Andrulevicius, T. Tamulevicius, A. Guobiene, V. Jarutis, V. Sirutkaitis, and K. Staliunas, “Resonators with manipulated diffraction due to two- and three-dimensional intracavity photonic crystals,” Phys. Rev. A 79(3), 033806 (2009).
[Crossref]

2008 (5)

R. Iliew, C. Etrich, T. Pertsch, F. Lederer, and K. Staliunas, “Subdiffractive all-photonic crystal Fabry-Perot resonators,” Opt. Lett. 33(22), 2695–2697 (2008).
[Crossref] [PubMed]

J.-W. Dong, K.-S. Wu, C. Mu, and H.-Z. Wang, “Multiple omnidirectional resonances in a metamaterial sandwich,” Phys. Lett. A 372(24), 4532–4535 (2008).
[Crossref]

S. Boutami, B. Ben Bakir, X. Letartre, J. L. Leclercq, and P. Viktorovitch, “Photonic crystal slab mirrors for an ultimate vertical and lateral confinement of light in vertical Fabry Perot cavities,” Proc. SPIE 6989, 69890V (2008).
[Crossref]

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, “Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals,” Phys. Rev. Lett. 101(15), 153903 (2008).
[Crossref] [PubMed]

J. L. Zhang, W. D. Shen, P. Gu, Y. G. Zhang, H. T. Jiang, and X. Liu, “Omnidirectional narrow bandpass filter based on metal-dielectric thin films,” Appl. Opt. 47(33), 6285–6290 (2008).
[Crossref] [PubMed]

2007 (4)

J. S. Q. Liu and M. L. Brongersma, “Omnidirectional light emission via surface plasmon polaritons,” Appl. Phys. Lett. 90(9), 091116 (2007).
[Crossref]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

K. Staliunas, M. Peckus, and V. Sirutkaitis, “Sub- and superdiffractive resonators with intracavity photonic crystals,” Phys. Rev. A 76(5), 051803 (2007).
[Crossref]

A. Hosseini and Y. Massoud, “Optical range microcavities and filters using multiple dielectric layers in metal-insulator-metal structures,” J. Opt. Soc. Am. A 24(1), 221–224 (2007).
[Crossref] [PubMed]

2006 (5)

2004 (2)

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys. Condens. Matter 16(34), 6317–6324 (2004).
[Crossref]

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, “Omnidirectional resonance in a metal–dielectric–metal geometry,” Appl. Phys. Lett. 84(22), 4421–4423 (2004).
[Crossref]

1997 (1)

1986 (1)

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta Int. J. Opt. 33(5), 607–619 (1986).
[Crossref]

1979 (1)

P. Vincent and M. Nevière, “Corrugated dielectric waveguides: A numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[Crossref]

1971 (1)

1964 (1)

Abedzadeh, N.

M. Khorasaninejad, N. Abedzadeh, J. Walia, S. Patchett, and S. S. Saini, “Color matrix refractive index sensors using coupled vertical silicon nanowire arrays,” Nano Lett. 12(8), 4228–4234 (2012).
[Crossref] [PubMed]

Aieta, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

Amo, A.

F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, “Bosonic condensation and disorder-induced localization in a flat band,” Phys. Rev. Lett. 116(6), 066402 (2016).
[Crossref] [PubMed]

Andersson, E.

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114(24), 245504 (2015).
[Crossref] [PubMed]

Andrulevicius, M.

M. Peckus, R. Rogalskis, M. Andrulevicius, T. Tamulevicius, A. Guobiene, V. Jarutis, V. Sirutkaitis, and K. Staliunas, “Resonators with manipulated diffraction due to two- and three-dimensional intracavity photonic crystals,” Phys. Rev. A 79(3), 033806 (2009).
[Crossref]

Baboux, F.

F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, “Bosonic condensation and disorder-induced localization in a flat band,” Phys. Rev. Lett. 116(6), 066402 (2016).
[Crossref] [PubMed]

Ben Bakir, B.

P. Viktorovitch, B. Ben Bakir, S. Boutami, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, C. Seassal, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “3D harnessing of light with 2.5D photonic crystals,” Laser Photonics Rev. 4(3), 401–413 (2010).
[Crossref]

S. Boutami, B. Ben Bakir, X. Letartre, J. L. Leclercq, and P. Viktorovitch, “Photonic crystal slab mirrors for an ultimate vertical and lateral confinement of light in vertical Fabry Perot cavities,” Proc. SPIE 6989, 69890V (2008).
[Crossref]

Bertoni, H. L.

Biondi, M.

F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, “Bosonic condensation and disorder-induced localization in a flat band,” Phys. Rev. Lett. 116(6), 066402 (2016).
[Crossref] [PubMed]

Blanchard, R.

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

M. A. Kats, D. Woolf, R. Blanchard, N. Yu, and F. Capasso, “Spoof plasmon analogue of metal-insulator-metal waveguides,” Opt. Express 19(16), 14860–14870 (2011).
[Crossref] [PubMed]

Bloch, J.

F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, “Bosonic condensation and disorder-induced localization in a flat band,” Phys. Rev. Lett. 116(6), 066402 (2016).
[Crossref] [PubMed]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

Bodyfelt, J. D.

S. Flach, D. Leykam, J. D. Bodyfelt, P. Matthies, and A. S. Desyatnikov, “Detangling flat bands into Fano lattices,” Europhys. Lett. 105(3), 30001 (2014).
[Crossref]

Boutami, S.

P. Viktorovitch, B. Ben Bakir, S. Boutami, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, C. Seassal, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “3D harnessing of light with 2.5D photonic crystals,” Laser Photonics Rev. 4(3), 401–413 (2010).
[Crossref]

S. Boutami, B. Ben Bakir, X. Letartre, J. L. Leclercq, and P. Viktorovitch, “Photonic crystal slab mirrors for an ultimate vertical and lateral confinement of light in vertical Fabry Perot cavities,” Proc. SPIE 6989, 69890V (2008).
[Crossref]

Brongersma, M. L.

J. S. Q. Liu and M. L. Brongersma, “Omnidirectional light emission via surface plasmon polaritons,” Appl. Phys. Lett. 90(9), 091116 (2007).
[Crossref]

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, “Omnidirectional resonance in a metal–dielectric–metal geometry,” Appl. Phys. Lett. 84(22), 4421–4423 (2004).
[Crossref]

Burek, M. J.

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R. Magnusson, M. Shokooh-Saremi, K. J. Lee, J. Curzan, D. Wawro, S. Zimmerman, W. Wu, J. Yoon, H. G. Svavarsson, and S. H. Song, “Leaky-mode resonance photonics: an applications platform,” Proc. SPIE 8102, 810202 (2011).
[Crossref]

M. Shokooh-Saremi and R. Magnusson, “Leaky-mode resonant reflectors with extreme bandwidths,” Opt. Lett. 35(8), 1121–1123 (2010).
[Crossref] [PubMed]

Sirutkaitis, V.

M. Peckus, R. Rogalskis, M. Andrulevicius, T. Tamulevicius, A. Guobiene, V. Jarutis, V. Sirutkaitis, and K. Staliunas, “Resonators with manipulated diffraction due to two- and three-dimensional intracavity photonic crystals,” Phys. Rev. A 79(3), 033806 (2009).
[Crossref]

K. Staliunas, M. Peckus, and V. Sirutkaitis, “Sub- and superdiffractive resonators with intracavity photonic crystals,” Phys. Rev. A 76(5), 051803 (2007).
[Crossref]

Soljacic, M.

M. Ibanescu, M. Soljacic, S. G. Johnson, and J. D. Joannopoulos, “Ultra-flat bands in two-dimensional photonic crystals,” Proc. SPIE 6128, 612808 (2006).
[Crossref]

Song, S. H.

R. Magnusson, M. Shokooh-Saremi, K. J. Lee, J. Curzan, D. Wawro, S. Zimmerman, W. Wu, J. Yoon, H. G. Svavarsson, and S. H. Song, “Leaky-mode resonance photonics: an applications platform,” Proc. SPIE 8102, 810202 (2011).
[Crossref]

Spracklen, A.

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114(24), 245504 (2015).
[Crossref] [PubMed]

Staliunas, K.

Y.-C. Cheng and K. Staliunas, “Negative Goos-Hänchen shift in reflection from subwavelength gratings,” J. Nanophotonics 8(1), 084093 (2014).
[Crossref]

M. Peckus, R. Rogalskis, M. Andrulevicius, T. Tamulevicius, A. Guobiene, V. Jarutis, V. Sirutkaitis, and K. Staliunas, “Resonators with manipulated diffraction due to two- and three-dimensional intracavity photonic crystals,” Phys. Rev. A 79(3), 033806 (2009).
[Crossref]

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, “Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals,” Phys. Rev. Lett. 101(15), 153903 (2008).
[Crossref] [PubMed]

R. Iliew, C. Etrich, T. Pertsch, F. Lederer, and K. Staliunas, “Subdiffractive all-photonic crystal Fabry-Perot resonators,” Opt. Lett. 33(22), 2695–2697 (2008).
[Crossref] [PubMed]

K. Staliunas, M. Peckus, and V. Sirutkaitis, “Sub- and superdiffractive resonators with intracavity photonic crystals,” Phys. Rev. A 76(5), 051803 (2007).
[Crossref]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(1), 016601 (2006).
[Crossref] [PubMed]

Svavarsson, H. G.

R. Magnusson, M. Shokooh-Saremi, K. J. Lee, J. Curzan, D. Wawro, S. Zimmerman, W. Wu, J. Yoon, H. G. Svavarsson, and S. H. Song, “Leaky-mode resonance photonics: an applications platform,” Proc. SPIE 8102, 810202 (2011).
[Crossref]

Takashima, T.

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys. Condens. Matter 16(34), 6317–6324 (2004).
[Crossref]

Takeda, H.

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys. Condens. Matter 16(34), 6317–6324 (2004).
[Crossref]

Tamir, T.

Tamulevicius, T.

M. Peckus, R. Rogalskis, M. Andrulevicius, T. Tamulevicius, A. Guobiene, V. Jarutis, V. Sirutkaitis, and K. Staliunas, “Resonators with manipulated diffraction due to two- and three-dimensional intracavity photonic crystals,” Phys. Rev. A 79(3), 033806 (2009).
[Crossref]

Thomson, R. R.

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114(24), 245504 (2015).
[Crossref] [PubMed]

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

Türeci, H. E.

F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, “Bosonic condensation and disorder-induced localization in a flat band,” Phys. Rev. Lett. 116(6), 066402 (2016).
[Crossref] [PubMed]

Twitchen, D. J.

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. de Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Loncar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13(12), 5791–5796 (2013).
[Crossref] [PubMed]

Viktorovitch, P.

P. Viktorovitch, B. Ben Bakir, S. Boutami, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, C. Seassal, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “3D harnessing of light with 2.5D photonic crystals,” Laser Photonics Rev. 4(3), 401–413 (2010).
[Crossref]

S. Boutami, B. Ben Bakir, X. Letartre, J. L. Leclercq, and P. Viktorovitch, “Photonic crystal slab mirrors for an ultimate vertical and lateral confinement of light in vertical Fabry Perot cavities,” Proc. SPIE 6989, 69890V (2008).
[Crossref]

Vincent, P.

P. Vincent and M. Nevière, “Corrugated dielectric waveguides: A numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[Crossref]

Walia, J.

M. Khorasaninejad, N. Abedzadeh, J. Walia, S. Patchett, and S. S. Saini, “Color matrix refractive index sensors using coupled vertical silicon nanowire arrays,” Nano Lett. 12(8), 4228–4234 (2012).
[Crossref] [PubMed]

Wang, H. Z.

Wang, H.-Z.

J.-W. Dong, K.-S. Wu, C. Mu, and H.-Z. Wang, “Multiple omnidirectional resonances in a metamaterial sandwich,” Phys. Lett. A 372(24), 4532–4535 (2008).
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Y.-H. Chen, J.-W. Dong, and H.-Z. Wang, “Conditions of near-zero dispersion of defect modes in one-dimensional photonic crystals containing negative-index materials,” J. Opt. Soc. Am. B 23(4), 776–781 (2006).
[Crossref]

Wang, Z.

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114(7), 073601 (2015).
[Crossref] [PubMed]

Wawro, D.

R. Magnusson, M. Shokooh-Saremi, K. J. Lee, J. Curzan, D. Wawro, S. Zimmerman, W. Wu, J. Yoon, H. G. Svavarsson, and S. H. Song, “Leaky-mode resonance photonics: an applications platform,” Proc. SPIE 8102, 810202 (2011).
[Crossref]

Woolf, D.

Wu, K.-S.

J.-W. Dong, K.-S. Wu, C. Mu, and H.-Z. Wang, “Multiple omnidirectional resonances in a metamaterial sandwich,” Phys. Lett. A 372(24), 4532–4535 (2008).
[Crossref]

Wu, W.

R. Magnusson, M. Shokooh-Saremi, K. J. Lee, J. Curzan, D. Wawro, S. Zimmerman, W. Wu, J. Yoon, H. G. Svavarsson, and S. H. Song, “Leaky-mode resonance photonics: an applications platform,” Proc. SPIE 8102, 810202 (2011).
[Crossref]

Yamamoto, Y.

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(11), 803–813 (2014).
[Crossref]

Yang, R.

Yang, W.

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4(3), 379–440 (2012).
[Crossref]

Yanik, M. F.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, “Omnidirectional resonance in a metal–dielectric–metal geometry,” Appl. Phys. Lett. 84(22), 4421–4423 (2004).
[Crossref]

Yi, J.

Yoon, J.

R. Magnusson, M. Shokooh-Saremi, K. J. Lee, J. Curzan, D. Wawro, S. Zimmerman, W. Wu, J. Yoon, H. G. Svavarsson, and S. H. Song, “Leaky-mode resonance photonics: an applications platform,” Proc. SPIE 8102, 810202 (2011).
[Crossref]

Yoshino, K.

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys. Condens. Matter 16(34), 6317–6324 (2004).
[Crossref]

Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
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M. A. Kats, D. Woolf, R. Blanchard, N. Yu, and F. Capasso, “Spoof plasmon analogue of metal-insulator-metal waveguides,” Opt. Express 19(16), 14860–14870 (2011).
[Crossref] [PubMed]

Zhang, B.

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114(7), 073601 (2015).
[Crossref] [PubMed]

Zhang, J. L.

Zhang, Y. G.

Zhu, W.

Zia, R.

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, “Omnidirectional resonance in a metal–dielectric–metal geometry,” Appl. Phys. Lett. 84(22), 4421–4423 (2004).
[Crossref]

Zibrov, A. S.

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. de Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Loncar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13(12), 5791–5796 (2013).
[Crossref] [PubMed]

Zimmerman, S.

R. Magnusson, M. Shokooh-Saremi, K. J. Lee, J. Curzan, D. Wawro, S. Zimmerman, W. Wu, J. Yoon, H. G. Svavarsson, and S. H. Song, “Leaky-mode resonance photonics: an applications platform,” Proc. SPIE 8102, 810202 (2011).
[Crossref]

Zussy, M.

P. Viktorovitch, B. Ben Bakir, S. Boutami, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, C. Seassal, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “3D harnessing of light with 2.5D photonic crystals,” Laser Photonics Rev. 4(3), 401–413 (2010).
[Crossref]

Adv. Opt. Photonics (1)

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4(3), 379–440 (2012).
[Crossref]

Appl. Opt. (1)

Appl. Phys. (Berl.) (1)

P. Vincent and M. Nevière, “Corrugated dielectric waveguides: A numerical study of the second-order stop bands,” Appl. Phys. (Berl.) 20(4), 345–351 (1979).
[Crossref]

Appl. Phys. Lett. (2)

H. Shin, M. F. Yanik, S. Fan, R. Zia, and M. L. Brongersma, “Omnidirectional resonance in a metal–dielectric–metal geometry,” Appl. Phys. Lett. 84(22), 4421–4423 (2004).
[Crossref]

J. S. Q. Liu and M. L. Brongersma, “Omnidirectional light emission via surface plasmon polaritons,” Appl. Phys. Lett. 90(9), 091116 (2007).
[Crossref]

Comput. Phys. Commun. (1)

V. Liu and S. Fan, “S4: a free electromagnetic solver for layered periodic structures,” Comput. Phys. Commun. 183(10), 2233–2244 (2012).
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Europhys. Lett. (1)

S. Flach, D. Leykam, J. D. Bodyfelt, P. Matthies, and A. S. Desyatnikov, “Detangling flat bands into Fano lattices,” Europhys. Lett. 105(3), 30001 (2014).
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J. Nanophotonics (1)

Y.-C. Cheng and K. Staliunas, “Negative Goos-Hänchen shift in reflection from subwavelength gratings,” J. Nanophotonics 8(1), 084093 (2014).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

J. Phys. Condens. Matter (1)

H. Takeda, T. Takashima, and K. Yoshino, “Flat photonic bands in two-dimensional photonic crystals with kagome lattices,” J. Phys. Condens. Matter 16(34), 6317–6324 (2004).
[Crossref]

Laser Photonics Rev. (1)

P. Viktorovitch, B. Ben Bakir, S. Boutami, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, C. Seassal, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “3D harnessing of light with 2.5D photonic crystals,” Laser Photonics Rev. 4(3), 401–413 (2010).
[Crossref]

Nano Lett. (3)

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. de Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Loncar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13(12), 5791–5796 (2013).
[Crossref] [PubMed]

M. Khorasaninejad, N. Abedzadeh, J. Walia, S. Patchett, and S. S. Saini, “Color matrix refractive index sensors using coupled vertical silicon nanowire arrays,” Nano Lett. 12(8), 4228–4234 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

Nat. Mater. (2)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nat. Mater. 12(1), 20–24 (2012).
[Crossref] [PubMed]

Nat. Phys. (1)

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(11), 803–813 (2014).
[Crossref]

Nature (1)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

Opt. Acta Int. J. Opt. (1)

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Opt. Lett. (2)

Phys. Lett. A (1)

J.-W. Dong, K.-S. Wu, C. Mu, and H.-Z. Wang, “Multiple omnidirectional resonances in a metamaterial sandwich,” Phys. Lett. A 372(24), 4532–4535 (2008).
[Crossref]

Phys. Rev. A (2)

K. Staliunas, M. Peckus, and V. Sirutkaitis, “Sub- and superdiffractive resonators with intracavity photonic crystals,” Phys. Rev. A 76(5), 051803 (2007).
[Crossref]

M. Peckus, R. Rogalskis, M. Andrulevicius, T. Tamulevicius, A. Guobiene, V. Jarutis, V. Sirutkaitis, and K. Staliunas, “Resonators with manipulated diffraction due to two- and three-dimensional intracavity photonic crystals,” Phys. Rev. A 79(3), 033806 (2009).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(1), 016601 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, “Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals,” Phys. Rev. Lett. 101(15), 153903 (2008).
[Crossref] [PubMed]

Z. Wang, B. Zhang, and H. Deng, “Dispersion engineering for vertical microcavities using subwavelength gratings,” Phys. Rev. Lett. 114(7), 073601 (2015).
[Crossref] [PubMed]

S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, and R. R. Thomson, “Observation of a localized flat-band state in a photonic Lieb lattice,” Phys. Rev. Lett. 114(24), 245504 (2015).
[Crossref] [PubMed]

F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, “Bosonic condensation and disorder-induced localization in a flat band,” Phys. Rev. Lett. 116(6), 066402 (2016).
[Crossref] [PubMed]

Phys. Rev. X (1)

J.-H. Jiang and S. John, “Photonic crystal architecture for room-temperature equilibrium Bose-Einstein condensation of exciton polaritons,” Phys. Rev. X 4(3), 031025 (2014).
[Crossref]

Proc. SPIE (3)

M. Ibanescu, M. Soljacic, S. G. Johnson, and J. D. Joannopoulos, “Ultra-flat bands in two-dimensional photonic crystals,” Proc. SPIE 6128, 612808 (2006).
[Crossref]

S. Boutami, B. Ben Bakir, X. Letartre, J. L. Leclercq, and P. Viktorovitch, “Photonic crystal slab mirrors for an ultimate vertical and lateral confinement of light in vertical Fabry Perot cavities,” Proc. SPIE 6989, 69890V (2008).
[Crossref]

R. Magnusson, M. Shokooh-Saremi, K. J. Lee, J. Curzan, D. Wawro, S. Zimmerman, W. Wu, J. Yoon, H. G. Svavarsson, and S. H. Song, “Leaky-mode resonance photonics: an applications platform,” Proc. SPIE 8102, 810202 (2011).
[Crossref]

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Supplementary Material (1)

NameDescription
» Visualization 1: MPG (4872 KB)      In this finite-difference time-domain simulation (Lumerical Inc.), a dipole emits light into "Structure A" (cf. Table 1 and Fig. 3(a)), then turns off. Much of the emitted light enters a mode which remains localized in the in-plane direction.

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Figures (5)

Fig. 1
Fig. 1

(a) In a laser cavity with a laterally-stopped-light resonance (ωres independent of kxy, so the in-plane group velocity ∂ωres/∂kx = ∂ωres/∂ky = 0), there are a large number of degenerate modes, including localized modes. These localized modes do not spread out, despite the absence of curvature or any other in-plane light guiding. For example, with a localized pump, the system will lase on a localized mode that best overlaps the pump [4]. Visualization 1 shows a simulated movie of this effect. (b) An alternative way to understand the stable localized modes is as a result of negative Goos–Hänchen shifts. (c) Such a cavity also acts as a Fabry-Pérot etalon that works for any incident wavefront. (d) If a quantum emitter such as a quantum dot is placed on such a cavity, it will have Purcell-enhanced light-matter coupling to a mode localized in its vicinity. (e) Microcavity theory parametrizes ωres(θ) via “photon effective mass”; we can make cavities where this parameter is positive, negative, or infinite.

Fig. 2
Fig. 2

(a) Our planar cavity has two mirrors. The bottom is a normal metal mirror. The top mirror is a resonant grating filter, i.e. a high-index grating that both supports in-plane guided modes and enables them to couple out. (b) At the guided mode resonance feature, the grating reflectance approaches 100%. (c) The two mirrors together form a cavity with a narrow cavity resonance, which sits within the broader guided mode resonance [4,27].

Fig. 3
Fig. 3

(a)-(c) For three different cavities we designed (see Table 1 for parameters), we send in a CW plane-wave from the substrate (through the thin gold) at a given wavelength and angle. The plot shows the energy stored in the cavity, so a bright band occurs at the cavity resonance. These three cavities (a-c) show some of the possibilities, where the light in the cavity is (a) stopped, (b) reversed, or (c) slowed in the plane of the cavity. The white dashed curve is the curve we would expect from ordinary planar cavities, Eq. (1). See Fig. 5 for other polarizations and directions. (d) Schematic of our cavities, which use a conventional gold mirror on one side, and a hexagonal array of dielectric cylinders on the other side. For cavity (a), with 1.5µm light incident 5° from normal, we show (e) the Poynting vector, and (f) the electric field amplitude profile (both averaged over the y-coordinate pointing into the page). Although the incident light tilts rightward, the energy flows leftward in the cylinder array, giving an overall average energy flow of zero, as we expect. (g) Reflection phase and amplitude of just the cylinder array (i.e., leaving out the gold) for the structure (a).

Fig. 4
Fig. 4

(a) Scanning electron micrograph of the cavity, showing the array of amorphous silicon pillars. The experiments (b) and corresponding simulations (c) show a transmission peak which is almost angle-independent, but slightly decreases in frequency away from normal (opposite of conventional cavities). The indicated angle is the angle of light in air, relative to the wafer normal. The simulation parameters were based on SEM measurements of the structure, see Table 1. The inset of (b) shows the wavelength at the maximum of each curve, compared to the textbook relation (Eq. (1), dashed curve). Transmission is in arbitrary units in (b), and fraction transmitted in (c).

Fig. 5
Fig. 5

(a-c) represent the cavities of Fig. 3(a-c) respectively. For each of these, (i) and (ii) are s-polarization light, and (iii) an (iv) are p-polarization, tilted in the two non-equivalent planes of mirror symmetry of the hexagonal lattice.

Tables (1)

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Table 1 Geometric Parameters for Simulations Hereina

Equations (1)

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ω res,m ( k xy ) = [ ω res,m (0) 2 + ( c| k xy |/n ) 2 ] 1/2 = ω res,m ( 0 ) / cosθ,

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