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Nanophotonics-An Overview NSF-RISE Workshop July 9-14, 2007 Anup Sharma Department of Physics Alabama A&M University [email protected] What is Nanophotonics? Science of Light-Matter Interaction at Nanometer scale (< 1 micron to ≥ 1 nm). Examples of Nanophotonics.

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Nanophotonics-An Overview NSF-RISE Workshop July 9-14, 2007 Anup Sharma Department of Physics

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Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

Nanophotonics-An Overview

NSF-RISE Workshop

July 9-14, 2007

Anup Sharma

Department of Physics

Alabama A&M University

[email protected]


What is nanophotonics science of light matter interaction at nanometer scale 1 micron to 1 nm

What is Nanophotonics?Science of Light-Matter Interaction at Nanometer scale (< 1 micron to ≥ 1 nm)


Examples of nanophotonics

Examples of Nanophotonics

  • Iridescent colors on butterfly wings are due to Photonic-Crystals. i.e. Stacks of Nanoscale Gratings


Emission of semiconductor cds inas inp cdse nanospheres depends on the size

Emission of Semiconductor (CdS, InAs, InP, CdSe) Nanospheres depends on the size

Used for Bioimaging and Fabrication of Quantum-Well Lasers


Metal nanoparticles enhance raman scattering signals by several orders of magnitude

Metal Nanoparticles Enhance Raman Scattering Signals by several orders of magnitude

This Effect is called Surface Enhanced Raman Scattering (SERS)


Nanophotonics can be divided into three parts

Nanophotonics can be divided into three parts

Example: Near-Field confinement of radiation by squeezing light through nanoscale apertures

1. Nanoscale confinement of Radiation

Used for Near-Field Microscopy to resolve below the Far-Field Diffraction Limit. Also used for Near-Field Optical/UV Lithography.


2 nanoscale confinement of matter

2. Nanoscale confinement of Matter

Nanoscale Cyrstals are used for:

  • (i) Optical Upconversion of radiation in Rare-Earth Nanocrystals.

  • (ii) Size-dependent Emission properties of nanoscale semiconductor crystals (Quantum dots or Q-dots)

    Metal nanoparticles and nanotips used in Surface Enhanced Raman Spectroscopy

    Photonic Bandgap Crystals and Photonic Bandgap Fibers (Photonic Fibers) involve periodic variation of dielectric constant over wavelength-scale.

    Applications: Fabrication of MOEMS (Micro Opto Electro Mechanical Systems), Micro-Optics, i.e. Microlasers, Directional Couplers between waveguides, Biophotonic Chips etc.


3 nanoscale photoprocesses

3. Nanoscale Photoprocesses

Examples: Nanoscale Lithography, Fabrication of Nanoscale Structures, Nanoscale Optical Memories

Foundations for Nanophotonics

Basic Equations describing propagation of photons in dielectrics has some similarities to propagation of electrons in crystals

Similarities between Photons and Electrons

Wavelength of Light,

Wavelength of Electrons,


Maxwell s equations for light

Maxwell’s Equations for Light

Eigenvalue Wave Equation:

Describes the allowed frequencies of light

Schrodinger’s Eigenvalue Equation for Electrons:

Describes allowed Energies of Electrons


Free space solutions

Free Space Solutions:

Photon Plane Wave:

Electron Plane Wave:

Interaction Potential in a Medium:

Propagation of Light affected by the Dielectric Medium (refractive index)

Propagation of Electrons affected by Coulomb Potential


Propagation through classically forbidden zones

Propagation through Classically Forbidden Zones:

Photon tunneling through classically forbidden zones. E and B fields decay exponentially. k-vector imaginary.

Electron Wavefunction decays exponentially in forbidden zones


Confinement of light and electrons

Confinement of Light and Electrons

Confinement of Light results in field variations similar to the confinement of Electron in a Potential Well. For Light, the analogue of a Potential Well is a region of high refractive-index bounded by a region of lower refractive-index.

Microscale Confinement of Light Nanoscale Confinement of Electrons


Differences between light and electron waves

Differences between Light and Electron Waves:

Electron Momentum generally bigger than photon momentum and so wavelength of light generally < 1 micron while wavelength of electrons generally < 1 nm.

Light wave is described by a vector field described by E and B while electron wavefunction is scalar

Photons satisfy Bose-Einstein statistics while Electrons are Fermions


Free space propagation

Free-Space Propagation:

  • Free space propagation of both electrons and photons can be described by Plane Waves.

  • Momentum for both electrons and photons, p = (h/2π)k

  • For Photons, k = (2π/λ) while for Electrons, k = (2π/h)mv

  • For Photons, Energy E = pc =(h/2π)kc while for Electrons,


Electronic and photonic crystals

Electronic and Photonic Crystals

Similar to the periodic electron-crystal lattice, one can fabricate photonic-crystal lattice. The refractive index varies with a much larger period of around 200 nm.


Nanoscale optical interactions

Nanoscale Optical Interactions

Light propagating in a medium of high refractive index can be totally internally reflected at the interface with a lower refractive index.

This involves interaction of light with matter over nanoscale distances. Some examples:

Applications:

Existence of an evanescent wave was first demonstrated by Newton. Light is transmitted not only at the point of contact but also

through the neighboring regions due to penetration evanescent field through thin air film


Excitation of surface plasmon resonance by evanescent tail

Excitation of Surface Plasmon Resonance by Evanescent-Tail

Surface plasmon is a wave at the interface of a metal and a dielectric film. This is a widely used technique for Biosensing and instruments using this technique are available commercially. To generate a Surface Plasma Wave, the diagram shown below is used.

For Surface Plasma Wave traveling in z-direction, the condition to excite it optically is,

reflected light intensity is seen. Thickness of metal film is 40-50 nm. By coating the dielectric film with biological antibodies, this is a widely used technique for sensing antigens, proteins etc.

When the resonance condition is met, a sharp decrease of the internally


Nanoscale confinement of light near field microscopy for sub wavelength resolution

Nanoscale Confinement of Light: Near-Field Microscopy for Sub-Wavelength Resolution

In Far-Field Microscopy,

This can be overcome with Near-Field Techniques by having nanoscale apertures or by using aperture-less techniques which enhance light interaction over nanoscale dimensions with the use of nanoscale tips, nanospheres etc. The idea of using sub-wavelength aperture to improve optical resolution was first proposed by Synge in a letter to Einstein in 1928. These ideas were implemented into optics much later in 1972 [Ash and Nicholls]

Schematic set-ups for Near-Field Scanning Optical Microscope (NSOM)

Aperture-less Technique: Near-Field around Nano-Tip

Near-field light decays over a distance of 50 nm from aperture.

Tapered Optical-Fiber


Theoretical results for near field nanoscopic interactions

Theoretical Results for Near-Field Nanoscopic Interactions

Light Diffraction by Sub-Wavelength [(a / λ) < 1] Circular Aperture

Only the terms with (1/r) contribute to net average radiation intensity when flux over a spherical surface is evaluated. Other terms give evanescent near-field radiation over distances less than (λ/2π).


Aperture less near field microscopy

Aperture-less Near-Field Microscopy

Effect of Evanescent Coupling on radiative life-time of a dipole is shown below:

In the aperture-less technique of microscopy, a metal tip of diameter < 50 nm is used to enhance inelastic scattering like Raman, fluorescence, nonlinear phenomena. For small distances between the tip and sample substrate (<50 nm), this enhancement is due to the near-field component of light diffracted by the tip.

The radiative decay rate for the dipole is calculated as the dipole is translated along the x-axis for a fixed distance (D) between the two substrates. This is shown below.

Limitation of small throughput of apertures can be overcome. Enhances inelastic light scattering from sample by generating surface plasma in the metals

Above calculations clearly show that sub-wavelength resolution is due to coupling of the evanescent field to the environment. A. Rahmani et. al., Phys. Rev. A 56, 3245 (1997)


Nanoscale confinement of matter or quantum confined materials

Nanoscale Confinement of Matter or Quantum-Confined Materials

Quantum-confined materials refer to structures which are constrained to nanoscale lengths in one, two or all three dimensions. The length along which there is Quantum confinement must be small than de Broglie wavelength of electrons for thermal energies in the medium.

Thermal Energy, E =

de Broglie Wavelength,

For T = 10 K, the calculated λ in GaAs is 162 nm for Electrons and 62 nm for Holes

For effective Quantum-confinement, one or more dimensions must be less than 10 nm. Structures which are Quantum-confined show strong effect on their Optical Properties. Artificially created structures with Quantum-confinement on one, two or three dimensions are called, Quantum Wells, Quantum Wires and Quantum Dots respectively.


Quantum confined materials

Z

Quantum-Confined Materials

Nanoscale Confinement in 1-Dimension results in a “Quantum Well”

Quantization of energy into discrete levels has applications for fabrication of new solid-state lasers. Two or more Quantum wells side-by-side give rise to Multiple Quantum Wells (MQM) structure.

Motion is confined only in the Z-direction. For electrons and holes moving in the Z-direction in low bandgap material, their motion can be described by Particle in a Box. If the depth of Potential Well is V, for energies E<V, we can write,

At 300 K, The band gap of GaAs is 1.43 eV while it is 1.79 eV for AlxGa1-xAs (x=0.3). Thus the electrons and holes in GaAs are confined in a 1-D potential well of length L in the Z-direction.

n = 1, 2, 3,…..


1 d confinement quantum well

R

1-D Confinement: Quantum-Well

Energy-levels

Wave-functions in a Semi-conductor Quantum-Well

Efficiency of a Quantum-Well Laser depends on the density of states First let us find the density of states in a bulk semiconductor: no confinement

For electrons in conduction-band

dN is proportional to

This represents a sphere in momentum-space of radius R =

(2mE)1/2

The number of states dN between energy E and E+dE is proportional to the volume of shell between R and R+dR

Density, D(E)=dN / dE


Density of states for quantum confinement

Density of States for Quantum-Confinement

Density of States

Quantum Well: 1D Confinement

Due to 1-D confinement, the number of continuous energy states in the 2-D phase space satisfy

Quantum Wire: 2D Confinement

2D confinement in X and Z directions. For wires (e.g. of InP, CdSe). with rectangular cross-section, we can write:

Quantum Dot: 3D Confinement

For a cubical box with the discrete energy levels are given by:


Manifestations of new optical effects due to quantum confinement

Manifestations of new optical effects due to Quantum Confinement

Size Dependence of Optical Properties

In general, confinement produces a blue shift of the band-gap. Location of discrete energy levels depends on the size and nature of confinement.

Increase of Oscillator Strengths

This implies increase of optical transition probability. This happens anytime the energy levels are squeezed into a narrow range, resulting in an increase of energy density. The oscillator strengths increase as the confinement increases from Bulk to Quantum Well to Quantum Wire to Quantum Dot.

New Intraband Transitions

Confinement produces sub-bands within the conduction and valence bands, enabling intraband optical transitions which are not allowed in bulk. These IR transitions have applications to making new Quantum Cascade Lasers and also detectors. Oscillator strengths increase as the width of Quantum Well decreases.


Quantum dots

Quantum Dots

The most important optical feature of these structures is that absorption/emission spectra shifts to shorter wavelengths as the size becomes smaller. The luminescence spectra for InAs, InP and CdSe Quantum Dots is shown below.

Likewise, Quantum-Dot Quantum Well refers to alternate layers of high and low bandgap semiconductors. Covering the surface of a Quantum Dot reduces non-radiative decay of electrons close to the surface and thus enhances luminescence intensity.

Core-Shell Quantum Dot refers to a Quantum-Dot surrounded by a shell of higher band-gap semiconductor.


Quantum confined lasing structures

Quantum Confined Lasing Structures

Semiconductor Laser is the best known application of quantum confined structures. Size of laser is around 100μm x 100μm x100μm and lasing wavelength can be tailored by the choice of the gain medium between 400 to 1600 nm.

Single Quantum Well (SQW) lasers employ a much thinner (<10 nm) gain medium. Due to discrete energy levels, the threshold current for lasing is smaller, 0.5 mA as compared to 20 mA for double heterostructure laser (DHL). Line Widths are narrower, each mode can be < 10 MHz. It can be modulated at higher frequencies.

First continuous wave semiconductor diode laser was a Double Heterostructure Laser. It was demonstrated by Alferov in USSR and by Panish and Hayashi in US.

Thickness of GaAs was greater than 100 micron. So this is not a Quantum-Confined Laser

Edge-Emitting Diode Laser


Quantum cascade qc laser

Quantum Cascade (QC) Laser

Operates within the sub-bands of the Conduction band. It is different from other designs where emission is due to electron-hole recombination. Often called Unipolar Laser. In conventional semiconductor lasers one electron can emit only one photon as it combines with a hole. QC laser is a Multiple Quantum Well (MQW). Discovered in 1996 (Appl. Phy. Lett. 68, 3680).

There could be ~50 Quantum Wells in MQW geometry. The barrier layer is very thin (1-3 nm)An excited electron emits 25-75 photons as it cascades down the ladder of sub-bands in the Conduction Band. QC lasers have been demonstrated for wavelengths between 3-20 micron. Useful for sensing atmospheric pollution


From semi conductor quantum dots to metal nano particles

From Semi-Conductor Quantum-Dots to Metal Nano-Particles

Under some conditions, one can resonantly excite a surface plasma-wave on the interface of metal and dielectric: Surface Plasmon Resonance (SPR). Applications of SPR has resulted in the field of Plasmonics

Propagating SPR at Optical Frequency on a metal nano-wire: ‘Light on a Wire’

Science Daily(March 2005)Engineers Study Whether Plasmonics, 'Light On A Wire,' Is Circuitry Wave Of Future— If data drove itself around in cars, photonics would be a roomy minivan and electronics would be a nimble coupe. Photonic components such as fiber optic cables can carry a lot of data but are bulky compared to electronic circuits. Electronic components such as wires and transistors carry less data but can be incredibly small…..a single technology that has the capacity of photonics and the smallness of electronics would be the best bridge of all. A new research group in Stanford's School of Engineering is pioneering just such a technology: plasmonics……..

A new Journal called “plasmonics” published by Springer, beginning March 2006


Plasmonics

Plasmonics

Some Interesting Phenomena

● Interaction of light wave with metal nanoparticles

● Generation of surface plasma waves and dependence of plasmon resonance on metal particle size and geometry

● Dependence of plasmon resonance condition on the dielectric adjacent to the metal film and its application for sensing

● Enhancement of electromagnetic field close to metal nanoparticles and its application to spectroscopy like Surface Enhanced Raman and Fluorescence

● Application of metal nanotips for apertureless imaging

● Effects of metal nanoshells on plasmon resonance

● Propagation of high-frequency electromagnetic waves along sub-wavelength-wide metal waveguides

● Effect of metal surface on radiative decay of molecules


Excitation of surface plasmon wave

Generation of Surface Plasmons in a Bulk Metal Film

Excitation of Surface Plasmon Wave

Surface plasma waves can be generated optically on bulk surface at the interface of metal and dielectric. These are referred as Surface Plasmons. The traveling wave is associated with a wavevector k(sp). Special excitation geometry is required to produce such a wave.

In nanoparticles, the surface plasmon wave is localized (not traveling) and so no special excitation geometry is required.

For Surface Plasma Wave traveling in z-direction, the condition to excite it optically is,

Wavelengths which are absorbed by metal nanoparticles and produce such a wave are called Surface Plasmon Bands or Plasmon Bands.

Where, k(sp) is the wavevector of the surface plasma wave and k=(2π/λ) that of the light wave.


Surface plasmon resonance spr on metal nano particles

Surface Plasmon Resonance (SPR) on Metal Nano-Particles

Most of the applications of such localized plasmon waves is due to electromagnetic field enhancement in the viscinity of the metal nanoparticle surface. Light absorption by nanoparticles takes place within a narrow range of wavelengths. This resonance (SPR) depends on size, shape and the nature of metal nanoparticle. This is shown in the graph below for gold nanoparticles.

SPR can be understood from dielectric properties of metal nano-particles. This can be understood in a simple way from Drude’s Model for Dielectric Constant in Metals.

Where m is electron mass and –e is its charge. Г is a damping constant and

electric field Solution are of form,


Spr on metal nano particles

SPR on Metal Nano-Particles

This gives

Where plasma frequency,

Real part of Dielectric Constant

Substituting in equation above, we get

As can be seen from above, real part of ε(ω) can be negative for

Polarization vector, P is

Calculated Plasma Wavelength for Silver is 137 nm and for Copper 114 nm. Thus in the visible region, Re{ε(ω)} is negative.

N is number density of electrons and χ is susceptibility.


Spr on metal nano particles1

SPR on Metal Nano-Particles

Surface Plasmon Resonance takes place for frequency which satisfies:

Constant Г (ε2) describes damping of electron motion. In bulk metals, this is largely due to electron-electron and electron-phonon scattering. However in metal nanoparticles, surface effects dominate since electron motion is constrained by the size of nanospheres. This damping is inversely proportional to the size of sphere. Thus the effect of size on plasmon resonance in metal nanospheres is contained in Г.

Absorption of incident light by Metal Nanospheres embedded in a Dielectric is given the Extinction Coefficient:

Where, λ is the wavelength of light, εh is the dielectric constant of surrounding medium, N is the number density of metal spheres and V its volume, ε1 and ε2 are the real and imaginary parts of the metal dielectric constant


Spr on metal nano shells

SPR on Metal Nano-Shells

Dielectric Core surrounded by Gold Shell

Another type of nanosphere is dielectric sphere coated with a nanoshell of metals like gold. Core materials like AuS and silica of radius between 30-250 nm and shell thickness of 10-30 nm. Thinness of the shell results in a substantial red-shift of plasmon resonance. Effective dielectric constant of the dielectric medium with embedded nanoparticles is given by

Here f is the volume fraction of nanoparticles, δ is the ratio of core volume to the volume of particle and εh, εs, εc are respectively the dielectric constants of the surrounding medium, the shell and the core. In general, as the thickness decreases, the resonance shifts to longer wavelength. This is due to increased electron scattering and an increase in the damping constant in metal dielectric constant. As seen from equations above, the condition for resonance is

Re(εs) + 2εh = 0


Spr on metal nano shells1

SPR on Metal Nano-Shells

In general, as the shell thickness decreases, the resonance shifts to longer wavelengths.

Vial on the left has solid gold colloids. Others have colloids with metal nano-shells with decreasing thickness. Vial on left absorbs IR

Fabrication of Metal Nanoshells

For fabrication, the dielectric sphere is coated with a layer of amines which binds 1-2 nm gold colloids from suspension. This is followed by a chemical treatment with HAuCl4 in the presence of formaldehyde. This results in an additional layer of gold.


Applications of plasmonics

Applications of Plasmonics

Metal nanoshells have several potential uses. It has been shown that a coating of these prevents photo-oxidation of polymer semiconducting devices if the resonance condition for nanoshells is at the wavelength of maximum photo-oxidation. Nanoshells thus act an an extinction filter

Nanoshells have also been used for whole blood immunoassay. Nanoshells can be attached to antibodies as shown below.

They form nanoshell dimers when they attach to the antigen resulting in a change of plasmon resonance condition. This can be monitored optically.


Applications of plasmonics1

Applications of Plasmonics

Plasmonic Wave Guiding

Light on a Wire

Waveguiding in traditional optical waveguides involves structures which cannot be smaller than λ/2. Further, waveguiding along bent guides is very lossy. The latter problem is overcome in photonic bandgap structures. But the dimensions of the structures are still limited by the wavelength of light.

These surface excitations can be at any frequency between UV and IR and so these waveguides combine the less bulky nature of metal waveguides with the high bandwidth of optical waveguides. Typical size of metal nanosphere is 50 nm. Plasmon excitations can travel over bent plasmonic waveguides. A weakness of this technique is high loss (6 dB/μm) and transmission has been demonstrated over short (~ 1 μm) distances. It is an active area of research for future applications.

The latter restriction can be overcome by waveguiding of plasmonic excitation in closely placed metal nanoparticles.


Applications of plasmonics2

Applications of Plasmonics

Electromagnetic field is enhanced locally on the surface of metal particles. This enhancement is especially strong at plasmon resonance.

Surface Enhanced Raman Scattering (SERS)

Aperture-Less Near-Field Microscopy

Local field enhancement due to surface plasmons has been developed as a technique for aperture-less near-field microscopy.

A nano-tip metal needle is used within the focal volume of an excitation laser.


Applications of plasmonics3

Applications of Plasmonics

Surface Plasmon-Wave Bio-Sensor

Excitation of a plasmon wave at the interface between a metal and dielectric films has been used for sensing by evanescent wave spectroscopy.

The evanescent wave associated with plasmon wave, penetrates the dielectric film to sense in the medium around. Evanescent wave can be absorbed by molecules being sensed. The technique shown above is for biosensing by antibodies. As they conjugate with specific antigens, the dielectric constant of the film changes and this is sensitively observed as an increase of internally reflected light since the condition for plasmon resonance is no longer met. This technique is widely used in several commercially available sensors.


Photonic crystals

1D Photonic Crystal: Stack of alternating refractive index material in Z direction

Photonic Crystals

In common “Electronic Crystals” like NaCl, the periodicity is ~ 1 nm. Photonic Crystals are produced by periodically varying refractive index in one, two or three dimensions. The period is comparable to the wavelength of light. Thus the field of Photonic Crystals can be looked upon as Microphotonics. However, in order to fabricate Photonic Crystals with micron-scale period, the fabrication technique must have nano-scale resolution. Thus it is appropriate to include Photonic Crystals in our study of Nanophotonics. Figures below show schematic representations of 1D, 2D and 3D Photonic Crystals.

2D Photonic Crystal: Periodic variation of refractive index in X and Y directions

3D Photonic Crystal: Periodic variation of refractive index in X, Y and Z directions


Photonic crystals1

Photonic Crystals

In Nature, parts of several living organisms have Photonic Crystals in them. Iridescent colors of butterfly wings and peacock feathers are due to Photonic Crystals.

Photonic Band Gap crystals have several photonics-related applications, including microlasers, and waveguides/ waveguide-couplers, photonic band-gap optical fibers with novel dispersion characteristics etc.


Similarities between electronic and photonic crystals

Similarities between Electronic and Photonic Crystals

The most striking similarity is the Band-Gap within the spectra of Electron and Photon Energies

Likewise, diffraction of light within a Photonic Crystal is forbidden for a range of frequencies which gives the concept of Photonic Band-Gap.The forbidden range of frequencies depends on the direction of light with respect to the photonic crystal lattice. However, for a sufficiently refractive-index contrast (ratio n1/n2), there exists a Band-Gap which is omni-directional.

Solution of Schroedinger’s equation in a 3D periodic coulomb potential for electron crystal forbids propagation of free electrons with energies within the Energy Band-Gap.


Band gap in photonic crystals

Band-Gap in Photonic Crystals

Band-Gap frequencies when incident on the photonic crystal will be not be transmitted but be reflected/diffracted

Optical characteristics of Photonic Crystals can best be understood by plotting the Dispersion Curve, i.e. variation of frequency (ω) of light with components of its wave-vector (k). Similar dispersion curves in Electronic Crystals, i.e. variation of energy E with k of electrons reveal the Electronic Band Gap.

Period of refractive index variation in Photonic Crystals is taken as a. Figure shows dispersion character of light in a bulk medium with a uniform refractive index, n


Theoretical modeling of photonic crystals

Theoretical Modeling of Photonic Crystals

Thus the incident and diffracted z-components of wave-vector are shifted with respect to each other by integral multiple of (2π/a). A special case of diffraction is Bragg Diffraction, when incident light is reflected by the photonic crystal

1D Photonic Crystal

It is simplest to plot the dispersion curves for 1D Photonic Crystals. Incident light with a wave-vector (k) is diffracted by the 1D photonic crystal (period, a).

Incident light can be diffracted into many possible directions as shown in the figure above. Wave-vectors are related by (show as Home-Work):

Thus, whenever kz is a multiple of (π/a), the incident wave is reflected back. It cannot propagate in the photonic crystal and the group-velocity of such a wave is zero.


Dispersion in 1d photonic crystals

Dispersion in 1D Photonic Crystals

Deviation from the straight-line dispersion curve of a uniform bulk medium is seen in the diagram. To ensure Bragg reflection for kz = ±N(π/a), the curve becomes horizontal.

It is necessary to plot the above dispersion curve only for values of kz between –π/a and π/a. All other values of kz can be got by diffraction of waves with kz between –π/a and π/a. The region of kz between –π/a and π/a is called the First Brillouin Zone. There is a band of frequencies that are forbidden for all possible values of kz. This is the Band-Gap for the 1D Photonic Crystal.


2d photonic crystals

2D Photonic Crystals

Compared to 1D Photonic Crystal, it is relatively more difficult to deduce the Dispersion Curves for 2D and 3D Photonic Crystal. The software for doing this is publicly available at: http://www.elec.gla.ac.uk/groups/opto/photoniccrystal/Software/SoftwareMain.htm

Dispersion curves for k for the boundary of the shaded region are plotted in three parts: In the first part (Г to M), k increases from 0 to ГM along the same direction. In the second part, the tip of k vector moves from M to K. In the third part (Г to K), k increases from 0 to ГK along the same direction. For sufficiently high ratio of refractive index (n1/n2), there exists a Band-Gap.

Just like for 1D case, it is necessary only to investigate dispersion curves for values of k within the First Brillouin Zone.


Properties of photonic crystals

Properties of Photonic Crystals

Super Refraction or Super Prism Effect

Prism effect is related to the derivative (dn/dλ) of refractive index with wavelength. This derivative can be made unusually large in photonic crystals. This can be understood with dispersion curves for 2D photonic crystals mentioned earlier.

Prism effect refers to separation of colors by refraction through a prism. This is related to dispersion or variation of refractive index with wavelength.

In a normal bulk medium like glass, dispersion is small.

Photonic crystals can also exhibit an effective negative refractive index as explained below.

This effect is seen in photonic crystals in the microwave and visible regions of spectrum.


Fabrication techniques for photonic crystals

Fabrication Techniques for Photonic Crystals

Fabrication of 1D and 2D Photonic Crystals

These are relatively easy to fabricate using UV and Electron-Beam Lithography. Bragg Grating in an optical fiber is a simple 1D Photonic Crystal. It is fabricated by UV Lithography

Fabrication of 3D Photonic Crystals

1. Sedimentation of monodisperse colloidal nanospheres of polystyrene or silica.

Fiber Bragg-Grating

2. Two-photon Lithography

Since two-photon absorption takes place only close to the focal point of a laser, one can

Holographic UV Lithography with 244 nm UV light

fabricate structures deep within the volume of the polymer matrix.

US Patent 6,873,762, awarded 2005


Applications of photonic crystals

Applications of Photonic Crystals

Photonic Components using 2D Photonic Crystals

2D Photonic crystals have a potential for fabricating waveguides and related components for integrated optics.

Unlike the conventional refractive planar waveguides, these work by diffraction. Modes that cannot propagate through the 2D photonic crystal lattice (i.e. those within the band-gap) can propagate easily within the waveguides, including those waveguides which have a sharp bend at right angle.

Microcavity Effect in 3D Photonic Crystals

Defects in a Photonic Crystal Lattice produce microcavities which have size-dependent radiation modes. Just like electronic crystal these produce defect-states in the Band-Gap. Microcavity is resonant for wavelength λ, satisfying,

D = N(λ/2), where N is an integer and D, the characteristic size of the cavity.Microcavity lasers have been fabricated by this technique.


Photonic crystal optical fibers

Photonic Crystal Optical Fibers

This is a special class of 2D photonic crystal where the dimension of the medium perpendicular to the crystal plane could be 100s of meters long. These are known by several names: Photonic Crystal Fiber (Phillip Russell), Photonic Bandgap Fiber, Holey Fiber, Microstructured Fiber and Bragg Fiber.

Frequencies in the Band-gap propagate within the fiber-core, which is like a defect in 2D photonic crystal. Hollow-core fibers have several advantages as compared to the conventional solid-core fiber. While hollow-core photonic band-gap fibers work by diffraction, solid-core photonic band-gap fibers work by both internal refraction as well as diffraction.

• Since light travels in air, group velocity dispersion can be zero for all wavelengths.

• By filling the hollow-core with gas, the fiber can be used as a very sensitive gas sensor.

• In hollow-core, even those wavelengths can propagate which have high loss in conventional fibers. Propagation for ~1000 m has been shown for wavelengths like 1.5 micron and 10 micron with an attenuation of around ~ 1dB/km.


Nanophotonics for biotechnology and nanomedicine

Nanophotonics for Biotechnology and Nanomedicine

Bioimaging with fluorophore embedded Nanoparticles

Specific molecules like proteins are difficult to image directly in a biological tissue. Nanoparticles are used for enhancing the contrast. To be able to use fluorophores like dyes or rare-earth-ions for biological imaging or as tracers they must be biologically benign. In principle this can be accomplished by embedding the fluorophores inside transparent shells of glass etc. Being small, the nanoparticles can flow with the bloodstream without interrupting any process. The example below illustrates how such nanoparticles can be used for bioimaging tissues or cells with a specific protein (here A).

The technique involves immobilizing antibodies for protein A on the nanoparticle surface. These nanoparticles will attach only to protein A. Illumination with a light source of suitable wavelength will reveal the site of protein A with a characteristic fluorescence.


Bioimaging with nanoparticles

Bioimaging with Nanoparticles

Nanoparticles are also used for bioimaging by non-optical techniques like Magnetic Resonance Imaging (MRI), Radioactive Nanoparticles as tracers to detect drug pathways or imaging by Positron Emission Tomography (PET), and Ultrasonic Imaging. For MRI, the magnetic nanoparticles could be made of

oxide particles which are coated with some biocompatible polymer.

Newer Nanoparticle Heterostructures have been investigated which offer the possibility of imaging by several techniques simultaneously. An example is Magnetic Quantum Dot.


Targeted therapy with nanocapsules

Targeted Therapy with Nanocapsules

This technique of therapy uses the same specific antibody-antigen binding that is used for bioimaging. Nanocapsules of drugs conjugated with specific antibodies get attached to diseased portions of tissues which express signature proteins. Release of drug at the required site minimizes side effects to healthy tissues.

The drug is encapsulated in a lipid layer on nanoparticle which also has an antibody to specifically target the site of interest. Since lipids are natural constituents of cell membranes, the drug is absorbed by cell by lipid-exchange.

In one study, Nanoparticles were made of Human Serum Albumin (HSA), which is the most abundant blood protein. Drug Herceptin was attached to nanoparticle. This drug binds to protein HER2 found in breast cancer tumors. HER2 multiplies abnormally in cancerous cells. Herceptin thus specifically targets HER2 with minimal side effects on normal tissues. Radioactive nanoparticles could be used for local exposure to radiation.


Biomedical applications of nanoparticles

Biomedical Applications of Nanoparticles

Elastic Properties of DNA

Biosensing with Nanoparticles

Strands of DNA can be attached to 500 nm beads at the ends and held by laser-tweezers as shown below.

Surface of nanoparticles are conjugated with antibodies for biosensing.

Attachment of antibodies to antigens can lead to aggregation. This changes the Plasmon Resonance properties of the nanoparticle which can be observed by Extinction Spectrum. Alternately, sensing can lead to detection of antigens by SERS spectrum.

DNA is in an aqueous medium. Refractive index of beads is greater than that of the liquid medium. The beads get trapped at the beam-waists of focused laser beams. By moving the laser tweezers, the DNA can be stretched. Forces involved in stretching DNA can be measured to an accuracy of few pico-Newtons.


Micro nano uv lithography of biological substrates

Micro/Nano UV Lithography of Biological Substrates

Outline of Presentation:

  • History of Lithography

  • Examples of Biological Substrates

  • What can Lithography Accomplish?

    IV. Case Studies: Four Specific Examples from our Research


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

I. HISTORY OF LITHOGRAPHY:

Invented by Alois Senefelder in Germany in 1798 Based originally on the chemical repellence of oil and water.

Designs were drawn with greasy (Hydrophobic) crayon on specially prepared limestone (Hydrophilic).

The stone was moistened with water, which the stone accepts in areas not covered by the crayon. An oily ink, applied with a roller, adheres only to the drawing and is repelled by the wet parts of the stone.

The print is then made by pressing paper against the inked drawing.


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

I. LITHOGRAPHY: Drawing patterns on substrates

Examples of UV Lithography

  • Development of Microchips

    on Silicon Wafers

    2. Fabrication of MEMS Devices

    Role of UV

  • UV induces chemical changes in

    the substrate/photoresist

  • UV Wavelength limits the minimum size of patterns

    UV Wavelengths for Lithography

    near UV (380–200 nm)

    far or vacuum UV (200–10 nm;

    FUV or VUV)

    extreme UV (1–31 nm; EUV or XUV).


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

II. Biological Substrates

  • Examples of Substrates used to immobilize biological molecules:

  • Biomembranes for Protein immobilization

Model biomembrane

Example:Phosphatidylcholine (Egg PC)

  • C. K. Yee et. al., Adv. Mater. 2004, 16, 1184

  • Sharma et. al., Optics Letters2005, 30, 501

  • Cooper et. al. Anal Biochem.2000,277, 196-205. – Sensor for Cholera Toxin

  • Swanson et. al., United States Patent 6893814 – Influenza Sensor


Ii biological substrates

II. Biological Substrates

2. Biocompatible Polymers for immobilizing DNA, tissue fragments. Example: Poly-Amino acids (Poly-L-Lysine) film coated on glass substrate

It attaches ionically to the phosphate group of the DNA backbone. Subsequent UV-light exposure is used to cross-link oligonucleotides to the Polymer surface.

Erie Scientific Poly-L-Lysine slides

Used in fabrication of DNA Microarrays

G. C. Vivian et. al., Nature Geneticssupplement, 1999, 21, 15-19.


Ii biological substrates1

II. Biological Substrates

3. Micro/Nanoporous polymer films for encapsulation of biomolecules

Example: • Nanoporous poly(methylsilsesquioxane) (PMSSQ) thin films on Silicon substrate

•Porous Sol-Gel Silica glasses

Matrix

Antibody

Proteins, enzymes, antibodies, whole cells have been embedded within sol-gel glasses. They retain their bioactivity and remain accessible to external reagents. Sol-gel glasses are optically transparent, so it is possible to couple optics and bioactivity to make biosensors.

D. Jiang et. Al; Anal Chem. 2003, 75, 4578-84. – sensor for hyaluronan and laminin (liver fibrosis markers)

Livage et al; J. Phys.: Condens. Matter 2001, 13, R673-R691 - Sol-Gel glass

H. C. Kim et. al., Nanoletters 2004, 7, 1169-1174 – Photopatterned Nanoporous Media


Iii uv lithography of biological substrates

III. UV Lithography of Biological Substrates

  • Why Lithography of Biological Substrates?

  • Development of High Density Microarrays for DNA and Protein Sensors

High throughput, Multianalyte Microarray Biochip Sensor

Current technology limits the size of each spot to 10-100 micron

UV lithography promises spot size of ~ 100 nm, i.e. 10,000 higher density

  • P. Blanchard, Genetic Engineering1998, 20, 111-123

  • L. Demers, Genetic Engineering News2003, 23,

  • Spotting accomplished by ultrasharp pen tips as in AFM

  • R. D. Piner et. al; Science 1999, 283, 661-663


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

  • UV Patterning on Biosubstrates

    Examples:

    Development of monolithic biochips.

    Fabrication of Photonic Components

    like Waveguides and Gratings

    S. Huang et al; J. Micromech. Microeng. 2005,15, 2235-2242

    A. Sharma et. al., Optics Letters2005, 30, 501

    UV-activated Hydrophobic Hydrophilic

    Conversion: Fabrication of Micro/Nanowells

    A. Hozumi et al; Langmuir. 2002,18, 9022-9027


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

  • Fabrication of Bioelectronics & BioMEMS

    Examples:

    Fabrication of Microfluidic

    Channels

    Fabrication of nano-gap electrodes:

    conduction properties of DNA

    J. Lee et. al., MRS, 2002, pg. 185


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

UV

Hydrophobic

Substrate

Mask: Opaque Grid

Lithography on Polybutadiene thin-films

Microarray of Hydrophilic Wells on Polybutadiene thin-films using lithographic masks

Effect of UV: Makes Substrate Hydrophilic

Hydrophilic Dye (Rhodamine 6G) sticks to areas exposed to UV

Spot Size: 100 μm x 100 μm

DNA sensor chips involve immobilizing oligonucleotides on an array of hydrophilic wells separated by hydrophobic barriers

Prevents cross-contamination


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

UV

Sputtered Gold

Hydrophobic

Substrate

Mask: Opaque Squares

Lithography on Polybutadiene thin-films

Sputtered Gold attaches only to areas not exposed to UV

Spot Size: 100 μm x 100 μm

Gold-coated surfaces are widely used to immobilize biomolecules for sensing-related applications. A common technique involves an intermediate thiol self-assembled monolayer (SAM) on gold substrate. Gold provides a bio-inert shield against a substrate that could denature proteins.


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

Polystyrene/Gold Spheres

Lithography on Poly-L-Lysine thin-films

UV

Hydrophilic

Substrate

Mask: Opaque Grid

Polystyrene and Gold Micro/Nano spheres stick to surface not exposed to UV

Gold

Polystyrene

300 nm10 micron 300 nm

Nanoporous substrates with controlled porosity


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

Lithography on Poly-L-Lysine thin-films

UV

Polystyrene Wall

Hydrophilic Well

Polystyrene Microspheres stick to surface not exposed to UV

300 nm

10 micron

Ridged Hydrophilic Wells


Interferometric maskless uv lithography

UV

UV

Interferometric (Maskless) UV Lithography

Spacing between Interference Fringes

λUV = 244 nm θ = 45 deg Λ = 170 nm


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

Interferometric (Maskless) UV Lithography

Fabrication of Microarrays

Done by Sequential Fabrication of Two Perpendicular Gratings

Minimum Spot-Size in Array with 244 nm UV: 200nm X 200 nm


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

INTERFEROMETRIC UV LITHOGRAPHY OF POLYMER SUBSTRATES

Lithography on Polybutadiene thin-films

Grating Period: 900 nm

Array of Nanowells

Dimension of wells: 500 nm x 500 nm x 30 nm


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

UV Lithography of Model Biomembrane (Phospholipid Bilayer) in Aqueous Phase

Example: Bilayer of Phosphatidylcholine (NBD-Egg PC)

Stack of Phospholipid Bilayers


Uv lithography of membrane in aqueous phase

UV (184-257 nm)

Mask

Backfilled voids

Lipid void-array

UV Lithography of Membrane in Aqueous Phase

C. K. Yee et. al., Adv. Mater. 2004, 16, 1184


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

INTERFEROMETRIC LITHOGRAPHY

OF MODEL MEMBRANE


Mechanism for lithographic membrane grating formation

Mechanism for Lithographic Membrane Grating Formation

  • Gradient Force

  • 2. UV Induced Photodissociation

Grating Formation


Detection of membrane grating growth

Detection of Membrane-Grating Growth

Solid supported membrane bilayer floats on a layer of hydration

UV intermittently on for 0.5 seconds and off for 40 seconds

A. Sharma et. al., Optics Letters2005, 30, 501


Mechanism for lithographic grating formation

Mechanism for Lithographic Grating Formation

The Membrane shows elastic behavior

As the UV is blocked, it relaxes


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

Elastic Relaxation of Biomembrane

Solid supported membrane bilayer floats on a layer of hydration

Effect of humidity on grating relaxation


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

BIOSENSING WITH MEMBRANE GRATING


Nanophotonics an overview nsf rise workshop july 9 14 2007 anup sharma department of physics

BIOSENSING WITH MEMBRANE

MICRO-ARRAY

Transduction Mechanism: Fluorescence


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