Photonic crystal

A photonic crystal is an

There are two strategies for opening up the complete photonic band gap. The first one is to increase the refractive index contrast for the band gap in each direction becomes wider and the second one is to make the Brillouin zone more similar to sphere.^[5] However, the former is limited by the available technologies and materials and the latter is restricted by the crystallographic restriction theorem. For this reason, the photonic crystals with a complete band gap demonstrated to date have face-centered cubic lattice with the most spherical Brillouin zone and made of high-refractive-index semiconductor materials. Another approach is to exploit quasicrystalline structures with no crystallography limits. A complete photonic bandgap was reported for low-index polymer quasicrystalline samples manufactured by 3D printing.^[6]

The periodicity of the photonic crystal structure must be around or greater than half the wavelength (in the medium) of the light waves in order for interference effects to be exhibited.

History

Photonic crystals have been studied in one form or another since 1887, but no one used the term photonic crystal until over 100 years later—after Eli Yablonovitch and Sajeev John published two milestone papers on photonic crystals in 1987.^[4][7] The early history is well-documented in the form of a story when it was identified as one of the landmark developments in physics by the American Physical Society.^[8]

Before 1987, one-dimensional photonic crystals in the form of periodic multi-layer dielectric stacks (such as the

By 1991, Yablonovitch had demonstrated the first three-dimensional photonic band-gap in the microwave regime.[5] The structure that Yablonovitch was able to produce involved drilling an array of holes in a transparent material, where the holes of each layer form an inverse diamond structure – today it is known as Yablonovite.

In 1996, Thomas Krauss demonstrated a two-dimensional photonic crystal at optical wavelengths.^[15] This opened the way to fabricate photonic crystals in semiconductor materials by borrowing methods from the semiconductor industry.

Pavel Cheben demonstrated a new type of photonic crystal waveguide – subwavelength grating (SWG) waveguide.^[16][17] The SWG waveguide operates in subwavelength region, away from the bandgap. It allows the waveguide properties to be controlled directly by the nanoscale engineering of the resulting metamaterial while mitigating wave interference effects. This provided “a missing degree of freedom in photonics”^[18] and resolved an important limitation in silicon photonics which was its restricted set of available materials insufficient to achieve complex optical on-chip functions.^[19][20]

Today, such techniques use photonic crystal slabs, which are two dimensional photonic crystals "etched" into slabs of semiconductor. Total internal reflection confines light to the slab, and allows photonic crystal effects, such as engineering photonic dispersion in the slab. Researchers around the world are looking for ways to use photonic crystal slabs in integrated computer chips, to improve optical processing of communications—both on-chip and between chips.^{[citation needed]}

Autocloning fabrication technique, proposed for infrared and visible range photonic crystals by Sato et al. in 2002, uses electron-beam lithography and dry etching: lithographically formed layers of periodic grooves are stacked by regulated sputter deposition and etching, resulting in "stationary corrugations" and periodicity. Titanium dioxide/silica and tantalum pentoxide/silica devices were produced, exploiting their dispersion characteristics and suitability to sputter deposition.^[21]

Such techniques have yet to mature into commercial applications, but two-dimensional photonic crystals are commercially used in

Study has proceeded more slowly in three-dimensional than in two-dimensional photonic crystals. This is because of more difficult fabrication.

• Examples of possible photonic crystal structures in 1, 2 and 3 dimensions
• 
  Comparison of 1D, 2D and 3D photonic crystal structures (from left to right, respectively).
• 
  Schematic of a 1D photonic crystal structure, made of alternating layers of a high-dielectric constant material and a low-dielectric constant material. These layers are typically quarter wavelength in thickness.
• 
  2D photonic crystal structure in a square array.
• 
  Schematic of a 2D photonic crystal made of circular holes.
• 
  A woodpile structured 3D photonic crystal. These structures have a three-dimensional bandgap for all polarizations

One-dimensional photonic crystals

To produce a one-dimensional photonic crystal,

${\displaystyle N^{2}}$

${\displaystyle N^{4}}$

A one-dimensional photonic crystal can be implemented using repeated alternating layers of a metamaterial and vacuum.^[37] If the metamaterial is such that the relative permittivity and permeability follow the same wavelength dependence, then the photonic crystal behaves identically for TE and TM modes, that is, for both s and p polarizations of light incident at an angle.

Recently, researchers fabricated a graphene-based Bragg grating (one-dimensional photonic crystal) and demonstrated that it supports excitation of surface electromagnetic waves in the periodic structure by using 633 nm He-Ne laser as the light source.^[38] Besides, a novel type of one-dimensional graphene-dielectric photonic crystal has also been proposed. This structure can act as a far-IR filter and can support low-loss surface plasmons for waveguide and sensing applications.^[39] 1D photonic crystals doped with bio-active metals (i.e. silver) have been also proposed as sensing devices for bacterial contaminants.^[40] Similar planar 1D photonic crystals made of polymers have been used to detect volatile organic compounds vapors in atmosphere.^[41][42] In addition to solid-phase photonic crystals, some liquid crystals with defined ordering can demonstrate photonic color.^[43] For example, studies have shown several liquid crystals with short- or long-range one-dimensional positional ordering can form photonic structures.^[43]

Two-dimensional photonic crystals

In two dimensions, holes may be drilled in a substrate that is transparent to the wavelength of radiation that the bandgap is designed to block. Triangular and square lattices of holes have been successfully employed.

The Holey fiber or

Three-dimensional photonic crystals

There are several structure types that have been constructed:^[44]

• Spheres in a diamond lattice
• Yablonovite
• The woodpile structure – "rods" are repeatedly etched with beam lithography, filled in, and covered with a layer of new material. As the process repeats, the channels etched in each layer are perpendicular to the layer below, and parallel to and out of phase with the channels two layers below. The process repeats until the structure is of the desired height. The fill-in material is then dissolved using an agent that dissolves the fill-in material but not the deposition material. It is generally hard to introduce defects into this structure.
• Inverse opals or Inverse Colloidal Crystals-Spheres (such as
  cubic close packed lattice suspended in a solvent. Then a hardener is introduced that makes a transparent solid out of the volume occupied by the solvent. The spheres are then dissolved with an acid such as Hydrochloric acid. The colloids can be either spherical^[25] or nonspherical.^{[45][46][47][48]} contains in excess of 750,000 polymer nanorods.^{[clarification needed]} Light focused on this beam splitter penetrates or is reflected, depending on polarization.^[49][50]

Photonic crystal cavities

Not only band gap, photonic crystals may have another effect if we partially remove the symmetry through the creation a nanosize

Fabrication challenges

Higher-dimensional photonic crystal fabrication faces two major challenges:

• Making them with enough precision to prevent scattering losses blurring the crystal properties
• Designing processes that can robustly mass-produce the crystals

One promising fabrication method for two-dimensionally periodic photonic crystals is a photonic-crystal fiber, such as a holey fiber. Using fiber draw techniques developed for communications fiber it meets these two requirements, and photonic crystal fibres are commercially available. Another promising method for developing two-dimensional photonic crystals is the so-called photonic crystal slab. These structures consist of a slab of material—such as silicon—that can be patterned using techniques from the semiconductor industry. Such chips offer the potential to combine photonic processing with electronic processing on a single chip.

For three dimensional photonic crystals, various techniques have been used—including

• Plane wave expansion method
• Inverse dispersion method^[63]
• Finite element method
• Finite difference time domain
  method
• Order-n spectral method^[64][65]
• KKR method
• Bloch wave – MoM method

Essentially, these methods solve for the frequencies (normal modes) of the photonic crystal for each value of the propagation direction given by the wave vector, or vice versa. The various lines in the band structure, correspond to the different cases of n, the band index. For an introduction to photonic band structure, see K. Sakoda's ^[66] and Joannopoulos ^[51] books.

The plane wave expansion method can be used to calculate the band structure using an eigen formulation of the Maxwell's equations, and thus solving for the eigen frequencies for each of the propagation directions, of the wave vectors. It directly solves for the dispersion diagram. Electric field strength values can also be calculated over the spatial domain of the problem using the eigen vectors of the same problem. For the picture shown to the right, corresponds to the band-structure of a 1D distributed Bragg reflector (DBR) with air-core interleaved with a dielectric material of relative permittivity 12.25, and a lattice period to air-core thickness ratio (d/a) of 0.8, is solved using 101 planewaves over the first irreducible Brillouin zone. The Inverse dispersion method also exploited plane wave expansion but formulates Maxwell's equation as an eigenproblem for the wave vector k while the frequency ${\displaystyle \omega }$ is considered as a parameter.^[63] Thus, it solves the dispersion relation ${\displaystyle k(\omega )}$ instead of ${\displaystyle \omega (k)}$, which plane wave method does. The inverse dispersion method makes it possible to find complex value of the wave vector e.g. in the bandgap, which allows one to distinguish photonic crystals from metamaterial. Besides, the method is ready for the frequency dispersion of the permittivity to be taken into account.

To speed calculation of the frequency band structure, the Reduced Bloch Mode Expansion (RBME) method can be used.^[67] The RBME method applies "on top" of any of the primary expansion methods mentioned above. For large unit cell models, the RBME method can reduce time for computing the band structure by up to two orders of magnitude.

Applications

Photonic crystals are attractive optical materials for controlling and manipulating light flow. One dimensional photonic crystals are already in widespread use, in the form of thin-film optics, with applications from low and high reflection coatings on lenses and mirrors to colour changing paints and inks.^[68][69][48] Higher-dimensional photonic crystals are of great interest for both fundamental and applied research, and the two dimensional ones are beginning to find commercial applications.

The first commercial products involving two-dimensionally periodic photonic crystals are already available in the form of photonic-crystal fibers, which use a microscale structure to confine light with radically different characteristics compared to conventional

SWG photonic crystal waveguides have facilitated new integrated photonic devices for controlling transmission of light signals in photonic integrated circuits, including fibre-chip couplers, waveguide crossovers, wavelength and mode multiplexers, ultra-fast optical switches, athermal waveguides, biochemical sensors, polarization management circuits, broadband interference couplers, planar waveguide lenses, anisotropic waveguides, nanoantennas and optical phased arrays.[19]^[71][72] SWG nanophotonic couplers permit highly-efficient and polarization-independent coupling between photonic chips and external devices.^[17] They have been adopted for fibre-chip coupling in volume optoelectronic chip manufacturing.^[73][74][75] These coupling interfaces are particularly important because every photonic chip needs to be optically connected with the external world and the chips themselves appear in many established and emerging applications, such as 5G networks, data center interconnects, chip-to-chip interconnects, metro- and long-haul telecommunication systems, and automotive navigation.

In addition to the foregoing, photonic crystals have been proposed as platforms for the development of solar cells ^[76] and optical sensors,^[77] including chemical sensors and biosensors.^[78][79]

See also

Wikimedia Commons has media related to Photonic crystals.

References

External links

Wikimedia Commons has media related to Photonic crystals.

• Business report on Photonic Crystals in Metamaterials – see also Scope and Analyst
• Photonic crystals tutorials by Prof S. Johnson at MIT
• Photonic crystals an introduction
• Invisibility cloak created in 3-D; Photonic crystals(BBC)