Computational Methods for Computational Methods for Nano-scale OpticsNano-scale Optics

Advisor:

Prof. Yehuda Leviatan

Amit Hochman

Dept. of Electrical Engineering, Technion – Israel Institute of Technology.

IntroductionIntroduction

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).Samjic et al., Opt. Express., 11, 1378 (2003).

Light intensity in a bent photonic-crystal waveguide

1 m

IntroductionIntroduction

Nano-optical devices:

Waveguides and optical circuitry.

Photonic Crystal Waveguide splitter

Charlton et al., Mat. Sci. Eng., B74, 17 (2000).

Charlton et al., Mat. Sci. Eng., B74, 17 (2000).

1 m Near-field ScanningOptical Microscopes.

IntroductionIntroduction

Optically driven nano-machines.

Cloaking devices.

Integrated Optical Motor

Kelemen et al., Appl. Opt., 45, 2777 (2006).Kelemen et al., Appl. Opt., 45, 2777 (2006).

Pendry et al., Science, 23, 1780 (2006).Pendry et al., Science, 23, 1780 (2006).

IntroductionIntroduction

Photonic-crystal fibers.

Russell, Science 299 (2003).Russell, Science 299 (2003).

W. Barnes et al., Nature 424, 824 (2003).W. Barnes et al., Nature 424, 824 (2003).

Plasmonic devices.

OutlineOutline

Aspects of computational methods.

Examples from our research:

Photonic-Crystal Fibers (PCFs). The Source-Model Technique Package.

Plasmonic devices. Summary.

Aspects of computational methodsAspects 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.

Designing a waveguide bend

Devices require careful modeling(and fabrication)…

Aspects of Aspects of computational methodscomputational 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.

Photonic Crystal Fibers (PCFs)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).

Russell, Science 299 (2003).Russell, Science 299 (2003).

PCFs – some featuresPCFs – 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).

The Source-Model Technique PackageThe 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.

The Source-Model TechniqueThe 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.

Sample results – leaky modesSample results – leaky modes

Very leaky Slightly less leaky

Longitudinal component of the electric field.

A gas sensorA gas sensor 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

Cross-section of fiber

Other structures analyzedOther structures analyzed

x/

y/

-2 -1 0 1 2

-2

-1

0

1

2

0

0.2

0.4

0.6

0.8

1

x/

y/

-5 0 5

-5

0

5

-0.5

0

0.5

x/

y/

0

0

Plasmonic WaveguidesPlasmonic 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.

Ditlbacher et al., Phys. Rev. Lett. 95, 257403 (2005).Ditlbacher et al., Phys. Rev. Lett. 95, 257403 (2005).

Silver nanowire

Light intensity around a silver nano-cylinder.

Optical waveguides and interconnects of small cross-section.

Arrays of PWs may have a negative index of refraction.

W. Barnes et al., Nature 424, 824 (2003)W. Barnes et al., Nature 424, 824 (2003)

What are PWs good for?What are PWs good for?

V. Podolsky et al., Opt. Express. 11, 735 (2003).V. Podolsky et al., Opt. Express. 11, 735 (2003).

2. Modal analysis in free-space2. Modal analysis in free-space

Basic modeling scenariosBasic modeling scenarios

,i iE H

,s sE H

,i iE H

,s sE H

( , )exp( )

( , )

x yj z

x y

E

H

1. Scattering in free-space1. Scattering in free-space

4. Modal analysis near layered 4. Modal analysis near layered mediamedia

3. Scattering near layered media3. Scattering near layered media

( , )exp( )

( , )

x yj z

x y

E

H

A few results (validation)A few results (validation)

x[m]

y[m

]

=250nm

-5 0 5

x 10-8

-5

0

5x 10

-8

2

4

6

x 10-3

x[m]

y[m

]

=214nm

-5 0 5

x 10-8

-5

0

5x 10

-8

2

4

6

8

10

12

x 10-3

x[m]

y[m

]

=266nm

-2 0 2

x 10-8

-2

0

2

x 10-8

2

4

6

8

10

12x 10

-3

x[m]

y[m

]

=195nm

-2 0 2

x 10-8

-2

0

2

x 10-8

0.005

0.01

0.015

0.02

x[m]

y[m

]

=250nm

-5 0 5

x 10-8

-5

0

5x 10

-8

2

4

6

x 10-3

x[m]

y[m

]

=214nm

-5 0 5

x 10-8

-5

0

5x 10

-8

2

4

6

8

10

12

x 10-3

x[m]

y[m

]

=266nm

-2 0 2

x 10-8

-2

0

2

x 10-8

2

4

6

8

10

12x 10

-3

x[m]

y[m

]

=195nm

-2 0 2

x 10-8

-2

0

2

x 10-8

0.005

0.01

0.015

0.02

x[m]

y[m

]

=250nm

-5 0 5

x 10-8

-5

0

5x 10

-8

2

4

6

x 10-3

x[m]

y[m

]

=214nm

-5 0 5

x 10-8

-5

0

5x 10

-8

2

4

6

8

10

12

x 10-3

x[m]

y[m

]

=266nm

-2 0 2

x 10-8

-2

0

2

x 10-8

2

4

6

8

10

12x 10

-3

x[m]

y[m

]

=195nm

-2 0 2

x 10-8

-2

0

2

x 10-8

0.005

0.01

0.015

0.02

x[m]

y[m

]

=250nm

-5 0 5

x 10-8

-5

0

5x 10

-8

2

4

6

x 10-3

x[m]y[

m]

=214nm

-5 0 5

x 10-8

-5

0

5x 10

-8

2

4

6

8

10

12

x 10-3

x[m]

y[m

]

=266nm

-2 0 2

x 10-8

-2

0

2

x 10-8

2

4

6

8

10

12x 10

-3

x[m]

y[m

]

=195nm

-2 0 2

x 10-8

-2

0

2

x 10-8

0.005

0.01

0.015

0.02

x[m]

y[m]

=250nm

-50

5x 10

-8

-5 0 5x 10

-8

2 4 6 x 10-3

x[m]

y[m]

=214nm

-50

5x 10

-8

-5 0 5x 10

-8

2 4 6 8 10 12

x 10-3

x[m]

y[m]

=266nm

-20

2x 10-8

-2 0 2

x 10-8

2 4 6 8 10 12x 10

-3

x[m]

y[m]

=195nm

-20

2x 10-8

-2 0 2

x 10-8

0.005

0.01

0.015

0.02

Magnitude of |Hz|, near a silver PW.

Results obtained by Rockstuhl et al.

Results obtained with the SMT:C. Rockstuhl, et al., J. Opt. Soc. Am. A 20, 1969 (2003).C. Rockstuhl, et al., J. Opt. Soc. Am. A 20, 1969 (2003).

Coupling results for PWsCoupling 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.

633nm

50nmR

Permittivity of silver taken from Johnson and Christy [6].

SummarySummary

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.

Thank youThank you