Distributed Bragg Reflector
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A distributed Bragg reflector (DBR) is a
reflector Reflector may refer to: Science * Reflector, a device that causes reflection (for example, a mirror or a retroreflector) * Reflector (photography), used to control lighting contrast * Reflecting telescope * Reflector (antenna), the part of an ant ...
used in
waveguides A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities de ...
, such as
optical fiber An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparency and translucency, transparent fiber made by Drawing (manufacturing), drawing glass (silica) or plastic to a diameter slightly thicker than that of a Hair ...
s. It is a structure formed from multiple layers of alternating materials with varying
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, o ...
, or by periodic variation of some characteristic (such as height) of a dielectric waveguide, resulting in periodic variation in the effective refractive index in the guide. Each layer boundary causes a partial reflection of an optical wave. For waves whose vacuum
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
is close to four times the
optical thickness In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to ''transmitted'' radiant power through a material. Thus, the larger the optical depth, the smaller the amount of transmitted radiant power through ...
of the layers, the many reflections combine with
constructive interference In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
, and the layers act as a high-quality reflector. The range of wavelengths that are reflected is called the photonic
stopband A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level. Depending on applic ...
. Within this range of wavelengths, light is "forbidden" to propagate in the structure.


Reflectivity

The DBR's
reflectivity The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electroni ...
, R, for
intensity Intensity may refer to: In colloquial use * Strength (disambiguation) *Amplitude *Level (disambiguation) *Magnitude (disambiguation) In physical sciences Physics *Intensity (physics), power per unit area (W/m2) * Field strength of electric, ma ...
is approximately given by :R = \left frac\right2, where n_o,\ n_1,\ n_2 and n_s\, are the respective refractive indices of the originating medium, the two alternating materials, and the terminating medium (i.e. backing or substrate); and N is the number of repeated pairs of low/high refractive index material. This formula assumes the repeated pairs all have a quarter-wave thickness (that is n d = \lambda / 4, where n is the refractive index of the layer, d is the thickness of the layer, and \lambda is the wavelength of the light). The frequency bandwidth \Delta f_0 of the photonic stopband can be calculated by :\frac = \frac\arcsin\left(\frac\right), where f_o is the central frequency of the band. This configuration gives the largest possible ratio \frac that can be achieved with these two values of the refractive index. Increasing the number of pairs in a DBR increases the mirror reflectivity and increasing the refractive index contrast between the materials in the Bragg pairs increases both the reflectivity and the bandwidth. A common choice of materials for the stack is
titanium dioxide Titanium dioxide, also known as titanium(IV) oxide or titania , is the inorganic compound with the chemical formula . When used as a pigment, it is called titanium white, Pigment White 6 (PW6), or CI 77891. It is a white solid that is insoluble ...
(''n'' ≈ 2.5) and
silica Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is o ...
(''n'' ≈ 1.5). Substituting into the formula above gives a bandwidth of about 200 nm for 630 nm light. Distributed Bragg reflectors are critical components in
vertical cavity surface emitting laser The vertical-cavity surface-emitting laser, or VCSEL , is a type of semiconductor laser diode with laser beam emission perpendicular from the top surface, contrary to conventional edge-emitting semiconductor lasers (also ''in-plane'' lasers) which ...
s and other types of narrow-linewidth
laser diode The laser diode chip removed and placed on the eye of a needle for scale A laser diode (LD, also injection laser diode or ILD, or diode laser) is a semiconductor device similar to a light-emitting diode in which a diode pumped directly with e ...
s such as distributed feedback (DFB) lasers and distributed bragg reflector (DBR) lasers. They are also used to form the cavity resonator (or
optical cavity An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that forms a cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and pro ...
) in
fiber laser A fiber laser (or fibre laser in British English) is a laser in which the active gain medium is an optical fiber doped with rare-earth elements such as erbium, ytterbium, neodymium, dysprosium, praseodymium, thulium and holmium. They are re ...
s and free electron lasers.


TE and TM mode reflectivity

This section discusses the interaction of transverse electric (TE) and
transverse magnetic A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and microwav ...
(TM) polarized light with the DBR structure, over several wavelengths and incidence angles. This reflectivity of the DBR structure (described below) was calculated using the
transfer-matrix method In statistical mechanics, the transfer-matrix method is a mathematical technique which is used to write the partition function into a simpler form. It was introduced in 1941 by Hans Kramers and Gregory Wannier. In many one dimensional latti ...
(TMM), where the TE mode alone is highly reflected by this stack, while the TM modes are passed through. This also shows the DBR acting as a
polarizer A polarizer or polariser is an optical filter that lets light waves of a specific polarization pass through while blocking light waves of other polarizations. It can filter a beam of light of undefined or mixed polarization into a beam of well ...
. For TE and TM incidence we have the reflection spectra of a DBR stack, corresponding to a 6 layer stack of dielectric contrast of 11.5, between an air and dielectric layers. The thicknesses of the air and dielectric layers are 0.8 and 0.2 of the period, respectively. The wavelength in the figures below, corresponds to multiples of the cell period. This DBR is also a simple example of a 1D
photonic crystal A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of natural crystals gives rise to X-ray diffraction and that the ato ...
. It has a complete TE band gap, but only a pseudo TM band gap.


Bio-inspired Bragg Reflectors

Bio-inspired Bragg Reflectors are 1D photonic crystals inspired by nature. Reflection of light from such a nanostructured matter results in structural colouration. When designed from mesoporous metal-oxides or polymers, these devices can be used as low-cost vapor/solvents sensors. For example, colour of this porous multi-layered structures will change when the matter filling up the pores is substituted by another, e.g. substituting air with water.


See also

* * * ** * * * * *


References

{{Reflist Optical devices Fiber optics