Integrated nonreciprocal optical components are necessary for on-chip optical isolation and circulation. Different methods were proposed recently to substitute conventional magneto-optical bulk components . One of the approaches is to exploit the Faraday effect for a nonreciprocal phase shift in the waveguides combined with a Mach–Zehnder interferometer . Further miniaturization was proposed based on nonreciprocal disk resonators  and photonic crystal resonators . The proposed integrated concepts use epitaxially grown iron garnets. Up to 5500°/cm Faraday rotation was demonstrated in Ce and Bi comodified iron garnet (CeBiIG) epitaxial films . The magneto-optical garnets are used as a core material of the slab or as a cladding material. These approaches involve structuring of the garnet or high-precision bonding. On the other hand, for non-garnet magneto-optical materials based on polymers, Verdet constants in the order of −106 °/(Tm) at 1.55μm wavelength were demonstrated recently [6-9]. These polymeric materials may allow a new class of nonreciprocal devices with magneto-optical cladding and can be combined with high-index waveguides in silicon (n=3.5). Apart from a simplified deposition, the cladding will also cover the sidewalls of the waveguides and will allow the use of TE-modes in ring resonators and photonic crystals. Another novel approach is to coat silicon structures with iron garnets with pulsed laser deposition . Unfortunately the crystal structure of silicon and the silica is not compatible with the cerium and bismuth doped iron garnets (Ce:YIG, BIG) which exhibit a strong Faraday rotation. Therefore, yttrium iron garnet buffer layer is needed to successfully coat Ce:YIG and BIG layers onto silicon chips .
Fig. 1: Ring resonator build from silicon placed on a SiO2 substrate. The ring is covered with a magneto-optical polymer and static magnetic field is applied orthogonal to the ring plane.
- Characterization of magneto-optical polymers on silicon waveguides
- Optical isolators and circulators at 1.55 µm wavelength in the micrometer scale
- Finite Integration Technique (MWS CST) 
- Finite Difference Mode Solver (wgms3D) 
- Electron beam lithography of SOI wafers
- DUV lithography of SOI wafers
- Polymer deposition with drop casting and spin coating
- Pulsed laser deposition of iron garnets
- Transmission characterization with butt coupling scheme
- External Mach-Zehnder interferometer to measure nonreciprocal phase shift
A ring resonator can be used as an optical isolator. For this purpose it is covered with a magneto-optical cladding and a static magnetic field is applied orthogonal to the plane in which the ring lies. For such an arrangement a TE-polarized wave that is clockwise traveling will experience slightly different effective index compared to a counter-clockwise traveling wave. This also means that both modes are separated in resonance frequency as shown in Fig. 2a. For the example given in Fig. 2 this means that a wave at 193.715 THz traveling from Port 2 to Port 1 can excite the counter-clockwise traveling mode and will be scattered in the ring. A wave traveling from Port 1 o Port 2on the other hand can only excite the clockwise traveling wave which is not at resonance at 193.715 THz. Therefore its energy will be transmitted to Port 2.
Fig. 2a: Spectrum of a ring resonator with gyrotropic cladding.
Fig. 2b: H-field pattern for a wave of 193.715 THz frequency entering at Port 1.
Fig. 2c H-field pattern for a wave of 193.715 THz frequency entering at Port 2.
We have estimated the resonance separation of the modes with the help of perturbation theory. The results can be found in Ref  and . We have also demonstrated in simulation the effect of backscattering suppression in non-reciprocal ring resonators with corrugation 16; 17.
List of publications
Fan, S. et al. Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”, Science 335, 38, (2012).
Jalas, D., Stepan, A., Petrov, A. Y. & Eich, M.; Experimental demonstration of magneto optical phase shift in silicon on insulator waveguides; 2011 8th IEEE International Conference on : Group IV Photonics (GFP), 160–162 (2011).
Jalas, D., Petrov, A., Stepan, A. & Eich, M.; Nonreciprocal nanophotonic structures. 2nd International Workshop on Tunable and Active Silicon Photonics. Berlin, Germany. September 2011.
Eich, M. et al.; Magnetooptical effects in silicon-organic nanophotonic structures. ICONO 12. Dublin, Ireland. September 2011.
Jalas, D., Petrov, A. Y. & Eich, M. Theory of gyrotropic ring resonators with counterpropagating modes coupling, Photonics Nanostruct. Fundam. Appl. 9, 351–357, (2011).
Jalas, D., Petrov, A., Krause, M., Hampe, J. & Eich, M. Integrated Non Reciprocal Ring Resonators, AMR 216, 533–538, (2011).
Jalas, D., Petrov, A., Krause, M., Hampe, J. & Eich, M. Resonance splitting in gyrotropic ring resonators, Opt. Lett. 35, 3438–3440, (2010).
Petrov, A. Y., Jalas, D., Krause, M., Hampe, J. & Eich, M. Nonreciprocal silicon waveguides and ring resonators with gyrotropic cladding, 7th IEEE International Conference on Group IV Photonics (GFP), 234–236, (2010).
Petrov, A. Y., Jalas, D., Krause, M. & Eich, M. Backscattering suppression in nonreciprocal ring resonators, AIP Conf. Proc. 1291, 82–84, (2010).
Prof. Dr. Thierry Verbiest
KU Leuven, Molecular Imaging and Photonics
Prof. Dr. Guy Koeckelberghs
KU Leuven, Polymer Chemistry and Materials
Priv.-Doz. Dr. Helmut Karl
University of Augsburg, AG Nanostructures
Dr. Palash Gangopadhyay
University of Arizona, College of Optical Sciences
1. Dötsch, H. et al. Applications of magneto-optical waveguides in integrated optics: review, J. Opt. Soc. Am. B 22, 240–253, (2005).
2. Fujita, J., Levy, M., Osgood, R. M., JR., Wilkens, L. & Dotsch, H. Waveguide optical isolator based on Mach--Zehnder interferometer, Appl. Phys. Lett. 76, 2158–2160, (2000).
3. Kono, N., Kakihara, K., Saitoh, K. & Koshiba, M. Nonreciprocal microresonators for the miniaturization of optical waveguide isolators, Opt. Express 15, 7737–7751, (2007).
4. Wang, Z. & Fan, S. Optical circulators in two-dimensional magneto-optical photonic crystals, Opt. Lett. 30, 1989–1991, (2005).
5. Sekhar, M. C. et al. Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films, Appl. Phys. Lett. 94, 181916-3, (2009).
6. Gangopadhyay, P. et al. Efficient Faraday rotation in conjugated polymers, Proc. SPIE 6331, 63310Z-5, (2006).
7. Koeckelberghs, G. et al. Regioregularity in poly(3-alkoxythiophene)s: effects on the Faraday rotation and polymerization mechanism, Macromol. Rapid Comm. 27, 1920–1925, (2006).
8. Gangopadhyay, P. et al. Faraday Rotation Measurements on Thin Films of Regioregular Alkyl-Substituted Polythiophene Derivatives, J. Phys. Chem. C 112, 8032–8037, (2008).
9. Araoka, F., Abe, M., Yamamoto, T. & Takezoe, H. Large faraday rotation in a π-conjugated poly(arylene ethynylene) thin film, Appl. Phys. Express 2, 11501, (2009).
10. Bi, L. et al. On-chip optical isolation in monolithically integrated non-reciprocal optical resonators, Nat Photon 5, 758–762, (2011).
11. Wehlus, T., Körner, T., Leitenmeier, S., Heinrich, A. & Stritzker, B. Magneto-optical garnets for integrated optoelectronic devices, phys. stat. sol. (a) 208, 252–263, (2011).
12. Available at www.cst.com ,
13. Krause, M.; Available at www.om.tu-harburg.de/wgms3d/ ,
14. Jalas, D., Petrov, A., Krause, M., Hampe, J. & Eich, M. Resonance splitting in gyrotropic ring resonators, Opt. Lett. 35, 3438–3440, (2010).
15. Petrov, A. Y., Jalas, D., Krause, M., Hampe, J. & Eich, M. Nonreciprocal silicon waveguides and ring resonators with gyrotropic cladding, 7th IEEE International Conference on Group IV Photonics (GFP), 234–236, (2010).
16. Petrov, A. Y., Jalas, D., Krause, M. & Eich, M. Backscattering suppression in nonreciprocal ring resonators, AIP Conf. Proc. 1291, 82–84, (2010).
17. Jalas, D., Petrov, A. Y. & Eich, M. Theory of gyrotropic ring resonators with counterpropagating modes coupling. TaCoNa-Photonics 2010, Photonics Nanostruct. Fundam. Appl. 9, 351–357, (2011).