photonics metamaterials

Photonics Metamaterials

Praveen Sharma

2010B1A3526G

Fundamentals of Crystals

Material properties are determined by the properties of their sub-units with their spatial distribution.

Electromagnetic properties as a function of the ratio a the “lattice constant” of the material/structure and λ the wavelength of the incoming light (a/) can be organized in three large groups:

Natural crystals and metamaterials have lattice constants much smaller than the light wavelengths: a << λ. These materials are treated as homogeneous media with parameters ε and μ.

Fundamentals of Crystals

When a is in the same range of the wavelength of the incoming light one defines a photonic crystal; a material with subunits bigger than atoms but smaller than the EM wavelength.

In photonic crystals a is the distance between repeat units with a different dielectric constant.

Effective medium description with

Maxwell equations with , µ, n.

Structure dominates. Properties

determined by diffraction and

interference.

Properties described using

geometrical optics

Example: Optical crystals,

metamaterials

Examples: Photonics crystals. X-

ray diffraction optics

Examples: Lens system

Shadows

Photonics Crystals

Photonic crystals are periodic optical nanostructures that affect the motion of photons in much the same way that semiconductors affect electrons.

Photonic crystals have properties governed by the diffraction of the periodic structures and may exhibit a band gap for photons.

Photons (behaving as waves) propagate through this structure – or not – depending on their wavelength.

Wavelengths that are allowed to travel are known as modes; groups of allowed modes form bands.

Disallowed bands of wavelengths are called photonic band gaps

Photonics Crystals

They typically are not described well using effective parameters ε and μ and may be artificial or natural.

In 1987 Sajeev John and Eli Yablonovitch proposed of photonics crystals with periodicity of n in 2D and 3D.

1D crystals (example Braggs Mirror or Distributed Bragg Reflector) were known since 1887 .

Distributed Bragg Reflector

formed from multiple layers of alternating materials with varying refractive index with each layer boundary causes a partial reflection of an optical wave.

for waves whose wavelength is close to four times the optical thickness of the layers, the many reflections combine with constructive interference, and the layers act as a high-quality reflector.

The range of wavelengths that are reflected is called the photonic stop band . Within this range of wavelengths, light is "forbidden" to propagate in the structure.

Distributed Bragg Reflector

Bloch’s Waves

modified slide from Rob Engelen

Origin of Photonic Band Gap

Bragg’s Scattering

Bragg’s Scattering

Regardless of how small the reflectivity r form an individual scatter, the total reflectivity R for a semi-infinite structure is given by :

Photonic Band Gap

So light cannot propagate in a crystal when frequency of incident light satisfies Bragg’s Condition :

Photonic Band Gap (PBG)

Photonic Band Gap

In a periodic system, when half the wavelength corresponds to the periodicity i.e., λ/2 = a then Bragg’s Condition K= π/a prohibits photon propagation

Band Structure of 1D Photonics Crystal

The dispersion curve of a 1D “photonic crystal” deviates from the straight-line dispersion curve of a uniform bulk medium.

Band Structure of 1D Photonics Crystal

This is because at k=π/a formation of standing waves occur which have zero group velocity discontinuity at that point

The energy of Standing waves being either in the high or the low index regions therefore we have dielectric band & air band

Band Structure of 2D Photonics

For a 2D crystal

Band Structure of 2D Photonics

Photonics in Nature

In Parides sesostris, the Emerald-patched Cattleheart butterfly, photonic crystals are formed of arrays of Nano - sized holes in the chitin of the wing scales.

The holes have a diameter of about 150 nanometers and are about the same distance apart.

The holes are arranged regularly in small patches; neighboring patches contain arrays with differing orientations.

The result is that these Emerald-patched Cattleheart scales reflect green light evenly at different angles instead of being iridescent.

Iridescence is generally known as the property of certain surfaces that appear to change color as the angle of view or the angle of illumination changes

Photonics in Nature

Photonics Crystal Application

Most proposals for devices that make use of photonic crystals do not use the properties of the crystal directly but make use of defect modes.

Such a defect is made when the lattice is changed locally. As a result, light with a frequency inside the bandgap can now propagate locally in the crystal, i.e. at the position of the defect.

Optical Fiber

An optical fiber is a cylindrical dielectric waveguide (non conducting waveguide) that transmits light along its axis, by the process of total internal reflection.

The fiber consists of a core surrounded by a cladding layer, both of which are made of dielectric materials.

To confine the optical signal in the core, the refractive index of the core must be greater than that of the cladding.

Light travels through the fiber core, bouncing back and forth off the boundary between the core and cladding.

Photonic Crystal Fiber

Photonic crystal optic fibers are a special class of 2D photonic crystals

obtains its waveguide properties not from a spatially varying glass composition but from an arrangement of very tiny and closely spaced air holes which go through the whole length of fiber.

the simplest type of photonic crystal fiber has a triangular pattern of air holes, with one hole missing i.e. with a solid core surrounded by an array of air holes.

Photonic Crystal Fiber

The guiding properties of this type of PCF can be roughly understood with an effective index model: the region with the missing hole has a higher effective refractive index, similar to the core in a conventional fiber.

The gray area indicates glass, and the white circles air holes with typical dimensions of a few micrometers.

Photonic Band Gap Fibers

based on a photonic bandgap of the cladding region

The refractive index of the core itself can be lower than that of the cladding structure.

Essentially, a kind of two-dimensional Bragg mirror is employed.

Metamaterial Photonics

In photonic crystals, the size and periodicity of the scattering elements are on the order of the wavelength rather than subwavelength.

subwavelength is used to describe an object having one or more dimensions smaller than the length of the wave with which the object interacts.

At optical frequencies(of GHz order) electromagnetic waves interact with an ordinary optical material (e.g., glass) via the electronic polarizability of the material.

This creates a state where the effective permeability of the material is unity, μeff = 1


Hence, the magnetic component of a radiated electromagnetic field has virtually no effect on natural occurring materials at optical frequencies.

However, the proper design of the elementary building blocks of the photonic metamaterial allows for a non-vanishing magnetic response and even for μ<0 at optical frequencies.

Photonic metamaterials, are a type of electromagnetic metamaterial, which are designed to interact with optical frequencies which are terahertz (THz), infrared (IR), and eventually, visible wavelengths.

Structures Containing Nano-Resonators

Photonic metamaterials typically contain some kind of metallic nanoscopic electromagnetic resonators.

An early approach, which has been taken over from previous work in the microwave domain, is based on split-ring resonators.

The resonances of such a resonator can be in the mid-infrared domain (with wavelengths of a few microns) when its width is reduced to the order of a few hundred nanometers.

A magnetic field, oriented perpendicular to the plane of the rings, induces an opposing magnetic field due to the Lenz’s law, which leads to a diamagnetic response resulting in a negative permittivity in a certain range of frequencies

Nano-Resonators


When light impinges such nano-resonators, it can excite electromagnetic oscillations.

These are particularly strong for frequencies near the resonance frequency.

As the period of the structure is well below half the optical wavelength, there are no photonic bandgap effects, and the effect on light propagation can be described with a (frequency-dependent) effective relative permittivity ε and relative permeability μ of the metamaterial


The electric resonances of individual nanorods originate from the excitation of the surface waves on the metal air interface.

In a paired nanorod configuration two types of plasmon polariton waves can be supported: symmetric and anti-symmetric.

Problems Encountered

Constructing Photonics Materials in near-infrared and visible frequencies turned out not to be straightforward for at least two reasons:

1. technical challenges related to the fabrication of resonant structures on the nanoscale .

2. resonance frequency saturates as the size of the SRR reduces, and the amplitude of the resonant permeability decreases

Modern nanofabrication techniques such as Scanning Electron Beam Lithography enable the fabrication of optical components on the scale of the optical wavelength with a relative precision in the few nanometer range

References

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).

R. A. Depine and A. Lakhtakia (2004). "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity". Microwave and Optical Technology Letters 41.

Veselago, V. G. (1968). "The electrodynamics of substances with simultaneously negative values of [permittivity] and [permeability]". Soviet Physics Uspekhi 10 (4): 509–514.

http://en.wikipedia.org/wiki/Veselago

References

S. John, Phys. Rev. Lett. 58, 2486 (1987).

Advances in Complex Artificial Electromagnetic Media by Nathan Kundtz Department of Physics , Duke University.

K. Ohtaka, Phys. Rev. B 19, 5857 (1979)

Schurig,, D. et al. (2006). "Metamaterial Electromagnetic Cloak at Microwave Frequencies".

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