Abstract

Highly directional radiation from photonic structures is important for many applications, including high-power photonic crystal surface-emitting lasers, grating couplers, and light detection and ranging devices. However, previous dielectric, few-layer designs only achieved moderate asymmetry ratios, and a fundamental understanding of bounds on asymmetric radiation from arbitrary structures is still lacking. Here, we show that breaking the 180° rotational symmetry of the structure is crucial for achieving highly asymmetric radiation. We develop a general temporal coupled-mode theory formalism to derive bounds on the asymmetric decay rates to the top and bottom of a photonic crystal slab for a resonance with arbitrary in-plane wavevector. Guided by this formalism, we show that infinite asymmetry is still achievable even without the need for back-reflection mirrors, and we provide numerical examples of designs that achieve asymmetry ratios exceeding 104. The emission direction can also be rapidly switched from top to bottom by tuning the wavevector or frequency. Furthermore, we show that with the addition of weak material absorption loss, such structures can be used to achieve perfect absorption with single-sided illumination, even for single-pass material absorption rates less than 0.5% and without back-reflection mirrors. Our work provides new design principles for achieving highly directional radiation and perfect absorption in photonics.

© 2016 Optical Society of America

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References

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2016 (3)

J. R. Piper and S. Fan, “Broadband absorption enhancement in solar cells with an atomically thin active layer,” ACS Photon. 3, 571–577 (2016).
[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

B. C. P. Sturmberg, T. K. Chong, D.-Y. Choi, T. P. White, L. C. Botten, K. B. Dossou, C. G. Poulton, K. R. Catchpole, R. C. McPhedran, and C. Martijn de Sterke, “Total absorption of visible light in ultrathin weakly absorbing semiconductor gratings,” Optica 3, 556–562 (2016).

2015 (4)

H. Subbaraman, X. Xu, A. Hosseini, X. Zhang, Y. Zhang, D. Kwong, and R. T. Chen, “Recent advances in silicon-based passive and active optical interconnects,” Opt. Express 23, 2487–2511 (2015).
[Crossref]

Y. Ota, S. Iwamoto, and Y. Arakawa, “Asymmetric out-of-plane power distribution in a two-dimensional photonic crystal nanocavity,” Opt. Lett. 40, 3372–3375 (2015).
[Crossref]

L. Zhu, F. Liu, H. Lin, J. Hu, Z. Yu, X. Wang, and S. Fan, “Angle-selective perfect absorption with two-dimensional materials,” Light Sci. Appl. 5, e16052 (2015).
[Crossref]

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a vander Waals crystal,” Phys. Rev. B 92, 201405 (2015).
[Crossref]

2014 (11)

A. Pospischil, M. M. Furchi, and T. Mueller, “Solar-energy conversion and light emission in an atomic monolayer p-n diode,” Nat. Nanotechnol. 9, 257–261 (2014).
[Crossref]

Y. Sun, W. Tan, H.-Q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with PT phase transition,” Phys. Rev. Lett. 112, 143903 (2014).
[Crossref]

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1, 347–353 (2014).
[Crossref]

Y. Liu, A. Chadha, D. Zhao, J. R. Piper, Y. Jia, Y. Shuai, L. Menon, H. Yang, Z. Ma, S. Fan, F. Xia, and W. Zhou, “Approaching total absorption at near infrared in a large area monolayer graphene by critical coupling,” Appl. Phys. Lett. 105, 181105 (2014).
[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).
[Crossref]

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8, 406–411 (2014).
[Crossref]

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light trapping textures designed by electromagnetic optimization for subwavelength thick solar cells,” IEEE J. Photovoltaics 4, 175–182 (2014).
[Crossref]

A. Oskooi, Y. Tanaka, and S. Noda, “Tandem photonic-crystal thin films surpassing Lambertian light-trapping limit over broad bandwidth and angular range,” Appl. Phys. Lett. 104, 091121 (2014).
[Crossref]

J. R. Piper, V. Liu, and S. Fan, “Total absorption by degenerate critical coupling,” Appl. Phys. Lett. 104, 251110 (2014).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

A. Yaacobi, J. Sun, M. Moresco, G. Leake, D. Coolbaugh, and M. R. Watts, “Integrated phased array for wide-angle beam steering,” Opt. Lett. 39, 4575–4578 (2014).
[Crossref]

2013 (4)

K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38, 100–102 (2013).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2, e84 (2013).
[Crossref]

Y. Ra’di, V. S. Asadchy, and S. A. Tretyakov, “Total absorption of electromagnetic waves in ultimately thin layers,” IEEE Trans. Antennas Propag. 61, 4606–4614 (2013).
[Crossref]

2012 (5)

C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24, OP98–OP120 (2012).

J. Lee, B. Zhen, S.-L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[Crossref]

Z. Ruan and S. Fan, “Temporal coupled-mode theory for light scattering by an arbitrarily shaped object supporting a single resonance,” Phys. Rev. A 85, 043828 (2012).
[Crossref]

M. J. Burek, N. P. de Leon, B. J. Shields, B. J. M. Hausmann, Y. Chu, Q. Quan, A. S. Zibrov, H. Park, M. D. Lukin, and M. Lončar, “Free-standing mechanical and photonic nanostructures in single-crystal diamond,” Nano Lett. 12, 6084–6089 (2012).
[Crossref]

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

2011 (3)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref]

C.-H. Lin, R.-L. Chern, and H.-Y. Lin, “Polarization-independent broad-band nearly perfect absorbers in the visible regime,” Opt. Express 19, 415–424 (2011).
[Crossref]

2010 (5)

D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express 18, 18278–18283 (2010).
[Crossref]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref]

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. USA 107, 17491–17496 (2010).
[Crossref]

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

2009 (1)

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[Crossref]

2008 (2)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[Crossref]

A. del Campo and E. Arzt, “Fabrication approaches for generating complex micro- and nanopatterns on polymeric surfaces,” Chem. Rev. 108, 911–945 (2008).
[Crossref]

2007 (1)

J. Schrauwen, F. V. Laere, D. V. Thourhout, and R. Baets, “Focused-ion-beam fabrication of slanted grating couplers in silicon-on-insulator waveguides,” IEEE Photon. Technol. Lett. 19, 816–818 (2007).
[Crossref]

2006 (1)

2005 (1)

Z. Wang and S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl. Phys. B 81, 369–375 (2005).
[Crossref]

2004 (4)

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
[Crossref]

W. Suh and S. Fan, “All-pass transmission or flattop reflection filters using a single photonic crystal slab,” Appl. Phys. Lett. 84, 4905 (2004).
[Crossref]

E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, “Ultracompact biochemical sensor built with two-dimensional photonic crystal microcavity,” Opt. Lett. 29, 1093–1095 (2004).
[Crossref]

D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29, 2749–2751 (2004).
[Crossref]

2003 (1)

2002 (1)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[Crossref]

1999 (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

1993 (1)

1982 (1)

1947 (1)

Absil, P.

Arakawa, Y.

Arzt, E.

A. del Campo and E. Arzt, “Fabrication approaches for generating complex micro- and nanopatterns on polymeric surfaces,” Chem. Rev. 108, 911–945 (2008).
[Crossref]

Asadchy, V. S.

Y. Ra’di, V. S. Asadchy, and S. A. Tretyakov, “Total absorption of electromagnetic waves in ultimately thin layers,” IEEE Trans. Antennas Propag. 61, 4606–4614 (2013).
[Crossref]

Atabaki, A.

M. T. Wade, F. Pavanello, R. Kumar, C. M. Gentry, A. Atabaki, R. Ram, V. Stojanovic, and M. A. Popovic, “75% efficient wide bandwidth grating couplers in a 45  nm microelectronics CMOS process,” in IEEE Optical Interconnects Conference (OI) (IEEE, 2015), pp. 46–47.

Avouris, P.

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[Crossref]

Baets, R.

J. Schrauwen, F. V. Laere, D. V. Thourhout, and R. Baets, “Focused-ion-beam fabrication of slanted grating couplers in silicon-on-insulator waveguides,” IEEE Photon. Technol. Lett. 19, 816–818 (2007).
[Crossref]

D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29, 2749–2751 (2004).
[Crossref]

Baranov, D. G.

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a vander Waals crystal,” Phys. Rev. B 92, 201405 (2015).
[Crossref]

Bassim, N.

D. G. Baranov, J. H. Edgar, T. Hoffman, N. Bassim, and J. D. Caldwell, “Perfect interferenceless absorption at infrared frequencies by a vander Waals crystal,” Phys. Rev. B 92, 201405 (2015).
[Crossref]

Bates, K. A.

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Bienstman, P.

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ACS Photon. (2)

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1, 347–353 (2014).
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Appl. Opt. (1)

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IEEE J. Photovoltaics (1)

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IEEE J. Quantum Electron. (1)

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IEEE Photon. Technol. Lett. (1)

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IEEE Trans. Antennas Propag. (1)

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J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Light Sci. Appl. (2)

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Supplementary Material (1)

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» Supplement 1: PDF (2087 KB)      This document provides supplementary information to the main text.

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Figures (4)

Fig. 1.
Fig. 1.

Temporal coupled-mode theory setup and transmission spectrum. (a) Schematic of our TCMT setup with four ports and two resonances related by the time-reversal operation. This general setup is valid for structures with arbitrary shapes and incident angles as long as the assumption of four ports and two resonances is correct. (b) Typical transmission spectrum of an inversion-symmetric, C 2 z -symmetry-broken structure, with the Fano resonances exhibiting full transmission at certain frequencies as predicted by our TCMT formalism. Strong asymmetry is achieved when the Fano resonance is aligned with the frequencies where the background reaches full transmission (red circles).

Fig. 2.
Fig. 2.

Simulated structures and verification of TCMT bounds. (a) The P -symmetric structure we use in our numerical examples and its structural parameters. a : periodicity of photonic crystal, h : height of central slab, w : width of central slab, n 0 : refractive index of central slab, d : height of additional pieces on the sides (the width of the additional pieces is ( a w ) / 2 ), n d : refractive index of additional pieces on the sides; (b) numerical verification of TCMT bounds on asymmetric radiation for P -symmetric structures. Red lines indicate the bound from Eq. (11). Each blue cross indicates simulation results of the asymmetry for a given structure, optimized over in-plane momentum. The transmissivity t is fitted from the Fabry–Perot background, and the asymmetric coupling ratio is calculated from the Poynting flux in the top and bottom directions.

Fig. 3.
Fig. 3.

Examples of highly asymmetric radiation. (a) Plot of the asymmetry ratio and quality factor as a function of k x , along the k y = 0 axis in momentum space. Strong asymmetric radiation occurs over a range of momenta, including the point of highest quality factor. Inset: log scale plot of the z -component of the electric field amplitude at the highest asymmetry point. (b) Similar plot for a different set of parameters, showing rapid switching of asymmetric direction by tuning the frequency or in-plane momentum.

Fig. 4.
Fig. 4.

Perfect absorption with single-sided illumination and no backing mirror for single-pass absorption less than 0.5%. (a) Schematic for perfect absorption at one incident angle and perfect transmission at the opposite incident angle. (b) Transmission, reflection, and absorption spectra for no loss ( Q n r = ) and critical loss ( Q n r = Q r ), consistent with the theoretical results in (a). (c) Loss dependence of absorption, showing near-perfect absorption for critical coupling.

Equations (13)

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d A d t = ( j ω 1 τ 1 τ n r ) A + K T | s + , | s = C | s + + D A ,
C = e j φ ( 0 r 0 j t r 0 j t 0 0 j t 0 r j t 0 r 0 ) , D = K σ x = ( 0 d 1 d 2 0 0 d 3 d 4 0 ) ,
| d 2 | 2 + | d 4 | 2 = | d 1 | 2 + | d 3 | 2 = 2 τ ,
e j φ ( r d 2 * + j t d 4 * ) + d 1 = 0 ,
e j φ ( j t d 2 * + r d 4 * ) + d 3 = 0 .
R = | S 12 | 2 = | e j φ r + d 1 d 2 j ( ω ω 0 ) + 1 τ + 1 τ n r | 2 ,
T = | S 14 | 2 = | e j φ j t + d 1 d 4 j ( ω ω 0 ) + 1 τ + 1 τ n r | 2
R = [ r ( ω ω 0 ) ± 4 τ 1 τ 2 r 2 τ 2 2 τ σ 1 σ 2 r 2 ] 2 + ( 1 σ r ) 2 ( ω ω 0 ) 2 + 1 τ 2 ,
a 2 = | j t + r a r e j θ r + j t a r e j θ | 2 = t 2 + r 2 a r 2 + 2 t r a r sin θ r 2 + t 2 a r 2 2 t r a r sin θ ,
| t r a r r + t a r | a | t + r a r r t a r | .
1 t 1 + t a 2 = 1 a r 2 1 + t 1 t .
R 14 = R 23 = r 2 4 , T 14 = ( 1 + t 2 ) 2 , T 23 = ( 1 t 2 ) 2 ,
A 14 = 1 R 14 T 14 = 1 t 2 , A 23 = 1 + t 2 .

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