Label-free optical biosensors are important tools to study the kinetics, interaction and presence of (bio)chemical compounds in various fields such as biotechnology, pharma, diagnostics as well as environmental and food quality monitoring. Systems based on planar optical waveguides with input/output grating couplers are of interest as they offer multiple tuning parameters for the chip design and their high sensitivity. In the present paper, an algorithm based on the Finite-Elements Method (FEM) is proposed for finding the chip response and optimizing the sensitivity of the sensor system. Total field and scattered field coupled with the Transmission Line Transfer Matrix Method (TLTMM) are compared for the FEM. Unlike some widely used approximations, the impact of the grating depth, shape, duty cycle as well as losses and surface roughness are taken into account. Another advantage of the presented method is the possibility to implement a large part of the algorithm with commercially available FEM solver. Several practical situations are treated proving the validity of the approach against the Local Interference Method (LIME). The waveguide losses appear to be a decisive parameter for the chip design.
2. Schmitt, K. and C. Hoffmann, "High-refractive-index waveguide platforms for chemical and biosensing," Optical Guided-wave Chemical and Biosensors I, Vol. 7, 21-54, 2009.
3. Cottier, K., "Advanced label-free biochemical sensors based on integrated optical waveguide gratings,", Ph.D. Thesis, Universite de Neuchatel, May 2004.
4. Cottier, K., M. Wiki, G. Voirin, H. Gao, and R. Kunz, "Labelfree highly sensitive detection of (small) molecules by wavelength interrogation of integrated optical chips," Sensors and Actuators B: Chemical, Vol. 91, No. 1-3, 241-251, 2003.
5. Kunz, R. and K. Cottier, "Optimizing integrated optical chips for label-free (bio-) chemical sensing," Analytical and Bioanalytical Chemistry, Vol. 384, 180-190, Dec. 2005.
6. Kunz, R., J. Dubendorfer, and R. Morf, "Finite grating depth effects for integrated optical sensors with high sensitivity," Biosensors and Bioelectronics, Vol. 11, No. 6-7, 653-667, 1996.
7. Tiefenthaler, K. and W. Lukosz, "Sensitivity of grating couplers as integrated-optical chemical sensors," JOSA B, Vol. 6, 209-220, Oct. 1989.
8. Cottier, K., R. Kunz, and H. Herzig, "Efficient and practical modeling of finite waveguide grating couplers," Japanese Journal of Applied Physics, Vol. 43, 5742-5746, Aug. 2004.
9. Moreno, E., D. Erni, C. Hafner, R. Kunz, and R. Vahldieck, "Modeling and optimization of non-periodic grating couplers," Optical and Quantum Electronics, Vol. 34, No. 11, 1051-1069, 2002.
10. Chen, C. L., Foundations for Guided-Wave Optics, Wiley, 2006.
11. Palmer, C. and T. Rgl, "Diffraction Gratings and Applications," Marcel Dekker, 1997.
12., COMSOL, Plasmonic Wire Grating, Apr. 2011, http://www. comsol.com/showroom/gallery/10032.
13. Fernandez, F. and Y. Lu, Microwave and Optical Waveguide Analysis by the Finite Element Method, John Wiley & Sons, 1996.
14. COMSOL, "RF Module User's Guide," Oct. 2011, http://comsol. com.
15. Oraizi, H. and M. Afsahi, "Analysis of planar dielectric multilayers as FSS by transmission line transfer matrix method (TLTMM)," Progress In Electromagnetics Research, Vol. 74, 217-240, 2007.
16. Oraizi, H. and M. Afsahi, "Transmission line modeling and numerical simulation for the analysis and optimum design of metamaterial multilayer structures," Progress In Electromagnetics Research B, Vol. 14, 263-283, 2009.
17. Brazas, J. and L. Li, "Analysis of input-grating couplers having finite lengths," Appl. Opt., Vol. 34, 3786-3792, Jul. 1995.
18. Maron, M., Numerical Analysis: A Practical Approach, Collier Macmillan, 1982.
19. Horvath, R., L. Wilcox, H. Pedersen, N. Skivesen, J. Hesthaven, and P. Johansen, "Analytical and numerical study on grating depth effects in grating coupled waveguide sensors," Applied Physics B: Lasers and Optics, Vol. 81, No. 1, 65-73, 2005.
20. Esboubas, L., S. Tisserand, and A. Gatto, "Le bilan des pertes dans les couches minces optiques par mesures d'absorption et d'attenuation a la propagation guidee," Journal of Optics, Vol. 29, No. 1, 40, 1998.
21. Coves, A., B. Gimeno, M. Andres, A. Blas, V. Boria, and J. Morro, "Analysis and applications of dielectric frequency-selective surfaces under plane-wave excitation," IEEE Antennas and Propagation Society International Symposium, Vol. 2, 825-828, June 2003.