A distributed Bragg reflector (DBR) is a
reflector 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, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means t ...
s. It is a structure formed from multiple layers of alternating materials with varying
refractive index, 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 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 throug ...
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 destructiv ...
, and the layers act as a high-quality reflector. The range of wavelengths that are reflected is called the photonic
stopband. 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 Reflection (physics), reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the respon ...
,
, 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
:
where
and
are the respective refractive indices of the originating medium, the two alternating materials, and the terminating medium (i.e. backing or substrate); and
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
, where
is the refractive index of the layer,
is the thickness of the layer, and
is the wavelength of the light).
The frequency
bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...
of the photonic stopband can be calculated by
:
where
is the central frequency of the band. This configuration gives the largest possible ratio
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 (''n'' ≈ 2.5) and
silica (''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 diodes such as
distributed feedback (DFB) lasers and
distributed bragg reflector (DBR) lasers. They are also used to form the
cavity resonator
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonat ...
(or
optical cavity) 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 related ...
s and
free electron lasers.
TE and TM mode reflectivity
This section discusses the interaction of
transverse electric (TE)
and
transverse magnetic (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 (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.
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. 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
Structural coloration in animals, and a few plants, is the production of colour by microscopically structured surfaces fine enough to interfere with visible light instead of pigments, although some structural coloration occurs in combination wit ...
. 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