Distributed Bragg reflector
Encyclopedia
A distributed Bragg reflector (DBR) is a reflector
used in waveguides
, such as optical fiber
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 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 stopband
. Within this range of wavelengths, light is "forbidden" to propagate in the structure.
,
, for intensity
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.
The bandwidth
of the photonic stopband can be calculated by
where
is the central wavelength of the band.
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 lasers and other types of narrow-linewidth laser diode
s such as distributed feedback laser
s. They are also used to form the cavity resonator (or optical cavity
) in fiber laser
s and free electron laser
s.
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.
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
used in waveguides
Waveguide (optics)
An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber and rectangular waveguides....
, such as optical fiber
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...
s. It is a structure formed from multiple layers of alternating materials with varying refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
, 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 wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
is close to four times the optical thickness
Optical path length
In optics, optical path length or optical distance is the product of the geometric length of the path light follows through the system, and the index of refraction of the medium through which it propagates. A difference in optical path length between two paths is often called the optical path...
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 stopband
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...
. Within this range of wavelengths, light is "forbidden" to propagate in the structure.
Reflectivity
The DBR's reflectivityReflectivity
In optics and photometry, reflectivity is the fraction of incident radiation reflected by a surface. In general it must be treated as a directional property that is a function of the reflected direction, the incident direction, and the incident wavelength...
,
, for intensityIntensity (physics)
In physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...
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.The bandwidth
of the photonic stopband can be calculated bywhere
is the central wavelength of the band.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
Titanium dioxide, also known as titanium oxide or titania, is the naturally occurring oxide of titanium, chemical formula . When used as a pigment, it is called titanium white, Pigment White 6, or CI 77891. Generally it comes in two different forms, rutile and anatase. It has a wide range of...
(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 lasers and other types of narrow-linewidth laser diode
Laser diode
The laser diode is a laser where the active medium is a semiconductor similar to that found in a light-emitting diode. The most common type of laser diode is formed from a p-n junction and powered by injected electric current...
s such as distributed feedback laser
Distributed feedback laser
A distributed feedback laser is a type of laser diode, quantum cascade laser or optical fibre laser where the active region of the device is periodically structured as a diffraction grating...
s. They are also used to form the cavity resonator (or optical cavity
Optical cavity
An optical cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric...
) in fiber laser
Fiber laser
A fiber laser or fibre laser 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, and thulium. They are related to doped fiber amplifiers, which provide light amplification without lasing...
s and free electron laser
Free electron laser
A free-electron laser, or FEL, is a laser that shares the same optical properties as conventional lasers such as emitting a beam consisting of coherent electromagnetic radiation which can reach high power, but which uses some very different operating principles to form the beam...
s.
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
Transfer-matrix method (optics)
The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium. This is for example relevant for the design of anti-reflective coatings and dielectric mirrors.The reflection of light from a single...
(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
Polarizer
A polarizer is an optical filter that passes light of a specific polarization and blocks waves of other polarizations. It can convert a beam of light of undefined or mixed polarization into a beam with well-defined polarization. The common types of polarizers are linear polarizers and circular...
.
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
Photonic crystal
Photonic crystals are periodic optical nanostructures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons...
. It has a complete TE band gap, but only a pseudo TM band gap.
See also
- Bragg's lawBragg's lawIn physics, Bragg's law gives the angles for coherent and incoherent scattering from a crystal lattice. When X-rays are incident on an atom, they make the electronic cloud move as does any electromagnetic wave...
- Bragg diffraction
- DiffractionDiffractionDiffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
- Diffraction gratingDiffraction gratingIn optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as...
- Diffraction grating
- Dielectric mirrorDielectric mirrorA dielectric mirror is a type of a mirror composed of multiple thin layers of dielectric material, typically deposited on a substrate of glass or some other optical material. By careful choice of the type and thickness of the dielectric layers, one can design an optical coating with specified...
- Fabry–Pérot interferometer
- Fiber Bragg gratingFiber Bragg gratingA fiber Bragg grating is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by adding a periodic variation to the refractive index of the fiber core, which generates a...
- Photonic crystal fiber
- VCSELVCSELThe 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 which emit from surfaces formed by cleaving the individual chip out of a...