On-chip transformation optics for multimode waveguide bends

Nature Communications

Volumn 3, Issue , 2012, Pages

  Gabrielli, Lucas H ^a   Liu, David ^b   Johnson, Steven G ^b   Lipson, Michal ^a  

^a School of Chemical and Molecular Engineering   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PERFORMANCE ASSESSMENT; THEORETICAL STUDY;

ANISOTROPY; ARTICLE; DEVICES; FINITE ELEMENT ANALYSIS; MICROSCOPY; OPTICS; TELECOMMUNICATION;

EID: 84870803383     PISSN: None     EISSN: 20411723     Source Type: Journal    
DOI: 10.1038/ncomms2232     Document Type: Article

References (38)

1. Agrawal, G. P. Fiber-Optic Communication Systems 2nd edn (Wiley, 1997).
2. Leonhardt, U. Optical conformal mapping. Science 312, 1777-1780 (2006).
3. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780-1782 (2006).
4. Logg, Anders, Mardal, Kent-Andre & Wells, Garth (eds) Automated Solution of Differential Equations by the Finite Element Method, Volume 84 of Lecture Notes in Computational Science and Engineering. (Springer, 2012).
5. Roberts, D. A., Rahm, M., Pendry, J. B. & Smith, D. R. Transformation-optical design of sharp waveguide bends and corners. Appl. Phys. Lett. 93, 251111 (2008).
6. Mei, Z. L. & Cui, T. J. Arbitrary bending of electromagnetic waves using isotropic materials. J. Appl. Phys. 105, 104913 (2009).
7. Ma, Y. G., Wang, N. & Ong, C. K. Application of inverse, strict conformal transformation to design waveguide devices. J. Opt. Soc. Am. A 27, 968-972 (2010).
8. Schmiele, M., Varma, V. S., Rockstuhl, C. & Lederer, F. Designing optical elements from isotropic materials by using transformation optics. Phys. Rev. A 81, 033837 (2010).
9. Smith, D., Mock, J., Starr, A. & Schurig, D. Gradient index metamaterials. Phys. Rev. E 71, 036609 (2005).
10. Kurt, H. & Citrin, D. S. Graded index photonic crystals. Opt. Express 15, 1240-1253 (2007).
11. Vasić, B., Gajić, R. & Hingerl, K. Graded photonic crystals for implementation of gradient refractive index media. J. Nanophotonics 5, 051806 (2011).
12. Gao, H., Zhang, B., Johnson, S. G. & Barbastathis, G. Design of thin-film photonic metamaterial Lüneburg lens using analytical approach. Opt. Express 20, 1617-1628 (2012).
13. Xu, F., Tyan, R.-C., Sun, P.-C., Fainman, Y., Cheng, C.-C. & Scherer, A. Fabrication, modeling, and characterization of form-birefringent nanostructures. Opt. Lett. 20, 2457-2459 (1995).
14. Levy, U. et al. Inhomogenous dielectric metamaterials with space-variant polarizability. Phys. Rev. Lett. 98, 243901 (2007).
15. Li, J. & Pendry, J. B. Hiding under the carpet: a new strategy for cloaking. Phys. Rev. Lett. 101, 203901-203904 (2008).
16. Ulrich, R. & Martin, R. J. Geometrical optics in thin film light guides. Appl. Opt. 10, 2077-2085 (1971).
17. Zernike, F. Luneburg lens for optical waveguide use. Opt. Commun. 12, 379-381 (1974).
18. Chen, B.-U., Marom, E. & Lee, A. Geodesic lenses in single-mode LiNbO3 waveguides. Appl. Phys. Lett. 31, 263-265 (1977).
19. Yao, S. K., Anderson, D. B., August, R. R., Youmans, B. R. & Oania, C. M. Guided-wave optical thin-film Luneburg lenses: fabrication technique and properties. Appl. Opt. 18, 4067-4079 (1979).
20. Brazas, J., Kohnke, G. & McMullen, J. Mode-index waveguide lens with novel gradient boundaries developed for application to optical recording. Appl. Opt. 31, 3420-3428 (1992).
21. Murali, R., Brown, D. K., Martin, K. P. & Meindl, J. D. Process optimization and proximity effect correction for gray scale e-beam lithography. J. Vacuum Sci. Technol. B 24, 2936-2939 (2006).
22. Kim, J., Joy, D. C. & Lee, S.-Y. Controlling resist thickness and etch depth for fabrication of 3D structures in electron-beam grayscale lithography. Microelectron. Eng. 84, 2859-2864 (2007).
23. Mosher, L., Waits, C. M., Morgan, B. & Ghodssi, R. Double-exposure grayscale photolithography. J. Microelectromechanical Syst. 18, 308-315 (2009).
24. Di Falco, A., Kehr, S. C. & Leonhardt, U. Luneburg lens in silicon photonics. Opt. Express 19, 5156-5162 (2011).
25. Gabrielli, L. H. & Lipson, M. Integrated Luneburg lens via ultra-strong index gradient on silicon. Opt. Express 19, 20122-20127 (2011).
26. Randel, S. et al. 6 x 56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6 x 6 MIMO equalization. Opt. Express 19, 16697-16707 (2011).
27. Bai, N. et al. Mode-division multiplexed transmission with inline few-mode fiber amplifier. Opt. Express 20, 2668-2680 (2012).
28. Riesen, N., Love, J. D. & Arkwright, J. W. Few-mode elliptical-core fiber data transmission. IEEE Photonic. Technol. Lett. 24, 344-346 (2012).
29. Ryf, R. et al. in National Fiber Optic Engineers Conference, OSA Technical Digest PDP5C.2 (Optical Society of America, 2012).
30. Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics 6, 488-496 (2012).
31. Ward, A. J. & Pendry, J. B. Refraction and geometry in maxwell's equations. J. Mod. Opt. 43, 773-793 (1996).
32. Knupp, P. & Steinberg, S. Fundamentals of Grid Generation (CRC Press, 1999).
33. Thompson, J. F., Soni, B. K. & Weatherill., N. P. Handbook of Grid Generation (CRC Press, 1999).
34. Boyd, J. P. Chebyshev and Fourier Spectral Methods 2nd edn (Dover, 2001).
35. Boyd, S. & Vandenberghe., L. Convex Optimization (Cambridge Univ. Press, 2004).
36. Powell, M. J. D. in Proceedings of the Sixth workshop on Optimization and Numerical Analysis, (eds) Gomez, S. & Hennart, J. P., 51-67 (Kluwer Academic Publishers, 1994).
37. Powell, M. J. D. Direct search algorithms for optimization calculations. Acta Numerica 7, 287-336 (1998).
38. Johnson, S. G. The nlopt nonlinear-optimization package. (http://ab-initio.mit.edu/nlopt).