computational methods for nano-scale optics advisor: prof. yehuda leviatan amit hochman dept. of...
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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
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