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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 13 — Jun. 18, 2012
  • pp: 14705–14713
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Fiber-to-chip coupler designed using an optical transformation

Petr Markov, Jason G. Valentine, and Sharon M. Weiss  »View Author Affiliations


Optics Express, Vol. 20, Issue 13, pp. 14705-14713 (2012)
http://dx.doi.org/10.1364/OE.20.014705


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Abstract

An integrated silicon photonics coupler for fiber to waveguide conversion was designed employing a transformation optics approach. Quasi-conformal mapping was used to obtain achievable material properties, which were realized by a distorted hexagonal lattice of air holes in silicon. The coupler, measuring only 10 μm in length and fabricated with a single-step lithography process, exhibits a peak simulated transmission efficiency of nearly 100% for in-plane mode conversion and a factor of 5 improvement over butt coupling for fiber to waveguide mode conversion in experimental testing.

© 2012 OSA

1. Introduction

Integrated silicon photonics has a great potential for providing significantly improved computing performance. For instance, faster and lower loss interconnects for multi-core processors are envisioned by utilizing silicon-compatible on-chip optical waveguides and modulators [1

1. M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006). [CrossRef]

,2

2. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

]. While on-chip light sources have been developed in recent years [3

3. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005). [CrossRef] [PubMed]

,4

4. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14(20), 9203–9210 (2006). [CrossRef] [PubMed]

], the most common excitation method for photonic platforms are off-chip lasers. However, there is a substantial mode mismatch between off-chip light sources and on-chip waveguides, preventing efficient coupling. For example, the smallest spot size achievable from commercially available off-chip lasers (using lensed fiber-coupled lasers) is typically ≈3 µm while silicon-compatible single-mode waveguides typically have dimensions of ≈500 × 250 nm [5

5. OZ Optics lensed fiber spec sheet, “Tapered and lensed fibers,” (OZ Optics Limited 2011)http://www.ozoptics.com/ALLNEW_PDF/DTS0080.pdf

].

In this work, we demonstrate an approach employing transformation optics that allows reduction in the coupler size and complexity of fabrication, while also maintaining a relatively high coupling efficiency. Transformation optics provides a means to control light propagation through spatial transformations in the permittivity and permeability tensors [17

17. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

].The theory has led to the development of several complex optical devices, including invisibility cloaks [18

18. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

22

22. J. H. Lee, J. Blair, V. A. Tamma, Q. Wu, S. J. Rhee, C. J. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17(15), 12922–12928 (2009). [CrossRef] [PubMed]

], multifunctional optical devices [23

23. T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical ‘Janus’ device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.) 22(23), 2561–2564 (2010). [CrossRef]

], and photonic black holes [24

24. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]

,25

25. Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An electromagnetic black hole made of Metamaterials,” http://arxiv.org/abs/0910.2159v2.

]. Based on this methodology, we present simulated and experimental results of a transformation-optical (TO) fiber-to-chip coupler. The coupler is fabricated using a single-step lithography process and exhibits low coupling losses while maintaining a significantly smaller footprint compared to other coupler designs [7

7. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [CrossRef] [PubMed]

15

15. M. Fan, M. Popović, and F. X. Kärtner, “High directivity, vertical fiber-to-Chip Coupler with anisotropically radiating grating teeth,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, Technical Digest (CD) (Optical Society of America, 2007), paper CTuDD3.

].

2. Transformation design

In order to realize the isotropic permittivity profile, a hexagonal lattice of fixed diameter sub-wavelength air holes with varying filling fraction was employed [20

20. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009). [CrossRef] [PubMed]

]. The hole array is placed in the device layer of an SOI wafer and the spatially varying filling fraction was computed in order to most closely match the effective waveguide mode index to the permittivity profile dictated by the transformation. We chose to implement uniform-size holes with variable spacing owing to the more forgiving fabrication tolerances that this approach offers compared to fixed-spacing and arbitrary hole size [22

22. J. H. Lee, J. Blair, V. A. Tamma, Q. Wu, S. J. Rhee, C. J. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17(15), 12922–12928 (2009). [CrossRef] [PubMed]

]. Other methods of obtaining variable permittivity that use random hole placement either based on a probability function or a grayscale image have a lower resolution and therefore require a much smaller hole size in order to be effective [21

21. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009). [CrossRef]

,30

30. D. H. Spadoti, L. H. Gabrielli, C. B. Poitras, and M. Lipson, “Focusing light in a curved-space,” Opt. Express 18(3), 3181–3186 (2010). [CrossRef] [PubMed]

].

The Maxwell-Garnett effective medium approximation was used to determine the desired filling fraction profile. An algorithm was developed to determine the proper hole placement in the distorted lattice. The performance of the algorithm was evaluated by extracting the effective permittivity of the distorted lattice. The hexagonal lattice arrangement allows for maximum packing density and therefore can achieve a greater range of permittivity values. For our design, the hole diameter was chosen to be 110 nm to ensure consistent hole-to-hole uniformity using standard electron-beam lithography processing. Reducing the hole diameter would lead to a more accurate permittivity profile, resulting in improved coupler performance.

3. Fabrication

The coupler design was fabricated on an SOI wafer with a 220 nm p-type, 14–22 Ω-cm resistivity, Si(100) device layer and 1 μm buried oxide layer (SOITEC). Electron-beam lithography (JEOL JBX-9300–100kV) was performed using poly(methyl methacrylate) (PMMA) resist. After pattern exposure and development in methyl isobutyl ketone (MIBK) and isopropyl alcohol in a ratio of 1:3 (v/v), anisotropic reactive ion etching was performed (Oxford PlasmaLab 100) using C4F8/SF6/Ar process gases to etch the exposed portion of the 220 nm Si layer. The 110 nm diameter holes with variable spacing were fabricated with relatively low size deviation due to proximity effects. In addition to the TO coupler (Fig. 2(a)
Fig. 2 (a) Scanning-electron microscope image of TO coupler, (b) Electric field (Ey) snapshot of the transformation-optical coupler with 110 nm holes demonstrating efficient in-plane mode conversion (top view), (c) Mode profiles at various points along the transformation-optical coupler with continuously-varying permittivity in 3D mode conversion, (d) Field (Ey)snapshot of the transformation-optical coupler with continuously-varying permittivity in 3D mode conversion (side view).
), several other geometries were fabricated for performance comparison: waveguides without a coupler, TO coupler outline without holes, and a TO coupler with holes only in the wider (x = 0-5 µm) region (“Restricted placement”). After etching, the chips were masked with a thick PMMA protective layer and then cleaved and polished down to the couplers on one side and cleaved through the waveguides on the other. The PMMA protective layer was removed with ultrasonication in acetone before measurements were performed. We note that the 3 μm wide end of the coupler could be extended to eliminate the need for polishing, although additional transmission losses through that section may be incurred. Experimental data was obtained using a lensed polarization-preserving fiber to couple light into and out of the waveguides. Measurements were performed using a broadband TE-polarized LED source (Agilent 83437A, 1500-1700 nm) and an optical spectrum analyzer (Agilent 86140B). For higher resolution measurements, a tunable TE-polarized laser source (Velocity 6328, 1520-1570 nm) and a broadband photodiode (Newport 1835-C) were utilized.

4. Simulation and experiment

To analyze the efficiency of the TO coupler for fiber-to-waveguide mode conversion (3D mode conversion), the input mode was approximated by a rectangular 3000 nm × 3000 nm plane wave centered in the middle of the coupler. Instead of the Gaussian-like field profile of a real fiber, the plane wave has a uniform field profile contributing to additional loss (illustrated in Fig. 2(d)) in the simulation which is not present in experimental measurements. Despite this additional loss, the simulation results (Fig. 4(a)
Fig. 4 Plot of the (a) simulated power transmission and (b) experimental transmission through the couplers: TO coupler, TO coupler with holes present only in wider half of coupler (Restricted placement), and TO coupler outline without holes. For comparison, a coupler with a perfect refractive index gradient transformation was simulated and a butt-coupled waveguide without a coupler was simulated and experimentally investigated.
) provide a good comparison between different coupler designs and match reasonably well with the experimental measurements (Fig. 4(b)). The slight differences between simulations and experiments are likely caused by fabrication errors, namely non-uniformity in the hole size and distortion in the hole shape. For the butt-coupled waveguide without any included transition region between the fiber and waveguide, an average transmission of 1% was simulated and very low power was measured at the output of the waveguide. The fabricated TO coupler showed a peak 5-fold improvement over butt coupling in experiment for the design with 110 nm holes. A maximum transmission of 17% was simulated. In comparison, the TO coupler outline without holes showed an average simulated transmission of 10% and a 3-fold improvement over butt-coupling in measurement. Due to the out-of-plane losses and inaccuracies in approximating the fiber mode in simulation, the maximum achievable transmission for our in-plane mode conversion TO coupler was found to be approximately 21% by simulating a continuously varying index profile (“Perfect index”) for the TO coupler.

Besides the lack of an out-of-plane transformation, the TO coupler efficiency is also affected by inaccuracies in replicating the designed permittivity profile. As shown in Fig. 4,the TO coupler efficiency varies with wavelength and does not match the efficiency of the continuously-varying index obtained directly from the transformation (perfect index). This inconsistency is due to the discretization in the refractive index profile caused by use of110 nm diameter air holes. The discretization becomes more drastic in the narrow end of the coupler where the spacing between air holes is large enough to cause interference effects. Namely, the two holes at the end of the coupler, separated by about 1 µm, form a Fabry-Perot type structure, which exhibits similar oscillations to the ones seen in the TO coupler transmission. Furthermore, due to the strong field confinement in the narrow end of the coupler, small deviations in the lateral positioning of the holes in this section lead to large differences in the effective index of the mode, making it challenging to match the perfect index profile.

In order to demonstrate that the transmission curve for the TO coupler can be flattened to increase the wavelength tolerance of the coupler performance, two approaches could be taken: (1)eliminating the transformation in the narrow end of the coupler at the expense of peak coupling efficiency, and (2)reducing the size of the holes. The second approach will minimize the transformation errors due to the permittivity discretization but, because of the fabrication difficulties, it was not investigated. The first approach was simulated and fabricated by removing all holes in the narrow half of the coupler (x = 5-10µm, “Restricted placement”), thus truncating the transformation. As shown in Fig. 4(b), this approach indeed demonstrated flattening of the transmission spectrum. The experimental transmission curve shows an increase with wavelength, which does not appear in simulation. One possible reason for this small discrepancy between experiment and simulation is the slight inhomogeneity in the hole profile, which causes stronger scattering from holes at shorter wavelengths.

5. Conclusion

An ultra-compact fiber-to-chip coupler was designed and fabricated employing the transformation optics approach. The coupler showed a 5fold improvement over butt coupling while being only 10 µm in length, representing a major improvement compared with conventional coupler designs. Due to the compact design, ease of alignment, and CMOS compatible fabrication techniques, the TO coupler is a promising candidate for future use in the development of integrated silicon photonic components.

Acknowledgments

References and links

1.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006). [CrossRef]

2.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

3.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005). [CrossRef] [PubMed]

4.

A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14(20), 9203–9210 (2006). [CrossRef] [PubMed]

5.

OZ Optics lensed fiber spec sheet, “Tapered and lensed fibers,” (OZ Optics Limited 2011)http://www.ozoptics.com/ALLNEW_PDF/DTS0080.pdf

6.

A. Khilo, M. A. Popović, M. Araghchini, and F. X. Kärtner, “Efficient planar fiber-to-chip coupler based on two-stage adiabatic evolution,” Opt. Express 18(15), 15790–15806 (2010). [CrossRef] [PubMed]

7.

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [CrossRef] [PubMed]

8.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3μms quare Si wire waveguides to single-mode fibers,” Electron. Lett. 38(25), 1669–1670 (2002). [CrossRef]

9.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17(12), 2613–2615 (2005). [CrossRef]

10.

K. K. Lee, D. R. Lim, D. Pan, C. Hoepfner, W.-Y. Oh, K. Wada, L. C. Kimerling, K. P. Yap, and M. T. Doan, “Mode transformer for miniaturized optical circuits,” Opt. Lett. 30(5), 498–500 (2005). [CrossRef] [PubMed]

11.

L. H. Gabrielli and M. Lipson, “Integrated Luneburg lens via ultra-strong index gradient on silicon,” Opt. Express 19(21), 20122–20127 (2011). [CrossRef] [PubMed]

12.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002). [CrossRef]

13.

D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). [CrossRef] [PubMed]

14.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic naveguides,” J. Lightwave Technol. 25(1), 151–156 (2007). [CrossRef]

15.

M. Fan, M. Popović, and F. X. Kärtner, “High directivity, vertical fiber-to-Chip Coupler with anisotropically radiating grating teeth,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, Technical Digest (CD) (Optical Society of America, 2007), paper CTuDD3.

16.

B. Moslehi, J. Ng, I. Kasimoff, and T. Jannson, “Fiber-optic coupling based on nonimaging expanded-beam optics,” Opt. Lett. 14(23), 1327–1329 (1989). [CrossRef] [PubMed]

17.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

18.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

19.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008). [CrossRef] [PubMed]

20.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009). [CrossRef] [PubMed]

21.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009). [CrossRef]

22.

J. H. Lee, J. Blair, V. A. Tamma, Q. Wu, S. J. Rhee, C. J. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17(15), 12922–12928 (2009). [CrossRef] [PubMed]

23.

T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical ‘Janus’ device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.) 22(23), 2561–2564 (2010). [CrossRef]

24.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]

25.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An electromagnetic black hole made of Metamaterials,” http://arxiv.org/abs/0910.2159v2.

26.

C. García-Meca, M. M. Tung, J. V. Galán, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Squeezing and expanding light without reflections via transformation optics,” Opt. Express 19(4), 3562–3575 (2011). [CrossRef] [PubMed]

27.

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010). [CrossRef] [PubMed]

28.

X. Zang and C. Jiang, “Manipulating the field distribution via optical transformation,” Opt. Express 18(10), 10168–10176 (2010). [CrossRef] [PubMed]

29.

Z. Chang, X. Zhou, J. Hu, and G. Hu, “Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries,” Opt. Express 18(6), 6089–6096 (2010). [CrossRef] [PubMed]

30.

D. H. Spadoti, L. H. Gabrielli, C. B. Poitras, and M. Lipson, “Focusing light in a curved-space,” Opt. Express 18(3), 3181–3186 (2010). [CrossRef] [PubMed]

31.

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(3), 687–702 (2010). [CrossRef]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(220.1770) Optical design and fabrication : Concentrators
(160.3918) Materials : Metamaterials

ToC Category:
Integrated Optics

History
Original Manuscript: March 8, 2012
Revised Manuscript: May 31, 2012
Manuscript Accepted: June 4, 2012
Published: June 15, 2012

Citation
Petr Markov, Jason G. Valentine, and Sharon M. Weiss, "Fiber-to-chip coupler designed using an optical transformation," Opt. Express 20, 14705-14713 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-14705


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References

  1. M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron.12(6), 1699–1705 (2006). [CrossRef]
  2. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005). [CrossRef] [PubMed]
  3. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005). [CrossRef] [PubMed]
  4. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express14(20), 9203–9210 (2006). [CrossRef] [PubMed]
  5. OZ Optics lensed fiber spec sheet, “Tapered and lensed fibers,” (OZ Optics Limited 2011) http://www.ozoptics.com/ALLNEW_PDF/DTS0080.pdf
  6. A. Khilo, M. A. Popović, M. Araghchini, and F. X. Kärtner, “Efficient planar fiber-to-chip coupler based on two-stage adiabatic evolution,” Opt. Express18(15), 15790–15806 (2010). [CrossRef] [PubMed]
  7. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett.28(15), 1302–1304 (2003). [CrossRef] [PubMed]
  8. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3μms quare Si wire waveguides to single-mode fibers,” Electron. Lett.38(25), 1669–1670 (2002). [CrossRef]
  9. G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett.17(12), 2613–2615 (2005). [CrossRef]
  10. K. K. Lee, D. R. Lim, D. Pan, C. Hoepfner, W.-Y. Oh, K. Wada, L. C. Kimerling, K. P. Yap, and M. T. Doan, “Mode transformer for miniaturized optical circuits,” Opt. Lett.30(5), 498–500 (2005). [CrossRef] [PubMed]
  11. L. H. Gabrielli and M. Lipson, “Integrated Luneburg lens via ultra-strong index gradient on silicon,” Opt. Express19(21), 20122–20127 (2011). [CrossRef] [PubMed]
  12. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron.38(7), 949–955 (2002). [CrossRef]
  13. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett.29(23), 2749–2751 (2004). [CrossRef] [PubMed]
  14. F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic naveguides,” J. Lightwave Technol.25(1), 151–156 (2007). [CrossRef]
  15. M. Fan, M. Popović, and F. X. Kärtner, “High directivity, vertical fiber-to-Chip Coupler with anisotropically radiating grating teeth,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science, Technical Digest (CD) (Optical Society of America, 2007), paper CTuDD3.
  16. B. Moslehi, J. Ng, I. Kasimoff, and T. Jannson, “Fiber-optic coupling based on nonimaging expanded-beam optics,” Opt. Lett.14(23), 1327–1329 (1989). [CrossRef] [PubMed]
  17. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  18. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
  19. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett.101(20), 203901 (2008). [CrossRef] [PubMed]
  20. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009). [CrossRef] [PubMed]
  21. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009). [CrossRef]
  22. J. H. Lee, J. Blair, V. A. Tamma, Q. Wu, S. J. Rhee, C. J. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express17(15), 12922–12928 (2009). [CrossRef] [PubMed]
  23. T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical ‘Janus’ device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.)22(23), 2561–2564 (2010). [CrossRef]
  24. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009). [CrossRef]
  25. Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An electromagnetic black hole made of Metamaterials,” http://arxiv.org/abs/0910.2159v2 .
  26. C. García-Meca, M. M. Tung, J. V. Galán, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Squeezing and expanding light without reflections via transformation optics,” Opt. Express19(4), 3562–3575 (2011). [CrossRef] [PubMed]
  27. P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express18(2), 767–772 (2010). [CrossRef] [PubMed]
  28. X. Zang and C. Jiang, “Manipulating the field distribution via optical transformation,” Opt. Express18(10), 10168–10176 (2010). [CrossRef] [PubMed]
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