Computational Methods for Nano-scale Optics

1. Computational Methods for Nano-scale Optics Amit Hochman Advisor: Prof. Yehuda Leviatan Dept. of Electrical Engineering, Technion – Israel Institute of Technology.

2. Light intensity in a bent photonic-crystal waveguide Introduction • Nano-scale optical devices have features smaller than the wavelength of visible light (350nm – 700nm, in air). • Manipulation of light at this scale opens up a very broad range of new devices and functionalities. • Analysis requires rigorous electromagnetic treatment by efficient computational methods. Ray-optics and similar approximations are inadequate. Samjic et al., Opt. Express., 11, 1378 (2003).

3. Photonic Crystal Waveguide splitter Charlton et al., Mat. Sci. Eng., B74, 17 (2000). Introduction • Nano-optical devices: • Waveguides and optical circuitry. • Near-field ScanningOptical Microscopes.

4. Kelemen et al., Appl. Opt., 45, 2777 (2006). Pendry et al., Science, 23, 1780 (2006). Introduction Integrated Optical Motor • Optically driven nano-machines. • Cloaking devices.

5. Russell, Science 299 (2003). W. Barnes et al., Nature 424, 824 (2003). Introduction • Photonic-crystal fibers. • Plasmonic devices.

6. Outline • Aspects of computational methods. • Examples from our research: • Photonic-Crystal Fibers (PCFs). • The Source-Model Technique Package. • Plasmonic devices. • Summary.

7. Designing a waveguide bend Devices require careful modeling(and fabrication)… Aspects of computational methods • The analysis of nano-scale optical devices usually requires solving Maxwell’s equations in complex geometries. • This tends to be computationally intensive. • Therefore, highly-efficient solution methods are in high demand. • Fast analysis tools are essential for synthesis (i.e. design), which usually requires repeated analyses of similar structures.

8. Aspects of computational methods • General purpose, commercial software packages can solve a wide range of problems, and are adequate in some cases. • However, there is a trade-off between generality and efficiency/accuracy.

9. Russell, Science 299 (2003). Photonic Crystal Fibers (PCFs) • Photonic Crystal Fibers or Holey Fibers are a new class of fibers, characterized by microscopic holes (or veins) running parallel to the fiber axis. • They are manufactured by heating a macroscopic structured–preform (typically a few centimeters in diameter), and drawing it down to the required dimensions (typically 125 µm).

10. PCFs – some features • Hollow core PCFs • Light is guided in air. This is good for: • Sensing applications. • Particle acceleration applications. • High-power delivery (medical applications). • Solid core PCFs • High nonlinearities with small input power. • Single mode guidance. • Tunable group velocity dispersion. • Broadband light sources for various applications (Optical Coherence Tomography, spectroscopy).

11. The Source-Model Technique Package • The SMTP is freely available for download. • In a comparison made with other methods (as part of an EU scientific collaboration exercise) the SMTP yielded the best accuracy per computation resources. • Written in MATLAB. Includes a graphicaluser interface.

12. The Source-Model Technique • A generalization of image theory. • In contrast to more general methods, like Finite Difference\Element methods, a piecewise homogeneous cross-section is assumed. • This allows an economic representation of the electromagnetic field. • In contrast to more restrictive methods, like the multipole method, boundaries can be arbitrarily shaped. Piecewise homogeneous PCF cross-section.

13. Sample results – leaky modes Longitudinal component of the electric field. Slightly less leaky Very leaky

14. A gas sensor Cross-section of fiber • Gas is allowed to infiltrate the holes. • Light guided by the fiber is absorbed at wavelengths characteristic to the gas. • The fraction of light in the holes is an important factor. Absorption spectrum (acetylene) Computed light intensity

15. Other structures analyzed

16. Light intensity around a silver nano-cylinder. Ditlbacher et al., Phys. Rev. Lett. 95, 257403 (2005). Plasmonic Waveguides • Plasmonics deals with the interaction of light and metals, which under certain conditions resembles the interaction of light with an electron plasma. • Plasmonic Waveguides are long cylinders of arbitrary cross-section, made from noble metals that have a plasma-like permittivity function. Silver nanowire

17. W. Barnes et al., Nature 424, 824 (2003) V. Podolsky et al., Opt. Express. 11, 735 (2003). What are PWs good for? • Optical waveguides and interconnects of small cross-section. • Arrays of PWs may have a negative index of refraction.

18. Basic modeling scenarios 1. Scattering in free-space 3. Scattering near layered media 2. Modal analysis in free-space 4. Modal analysis near layered media

19. C. Rockstuhl, et al., J. Opt. Soc. Am. A 20, 1969 (2003). A few results (validation) • Magnitude of |Hz|, near a silver PW. • Results obtained by Rockstuhl et al. • Results obtained with the SMT:

20. Coupling results for PWs • Coupling of a beam of light to a silver PW under a prism. • Value shown is the magnitude of Hx(t) at some instant in time. Permittivity of silver taken from Johnson and Christy [6].

21. Summary • Nano-optical structures open up a broad range of new devices and functionalities. • Their analysis and design requires the development of efficient computational tools. • A few examples of our work on photonic-crystal fibers and plasmonic waveguides have been shown.

22. Thank you