Encyclopedia … combined with a great Buyer's Guide!

Bragg Mirrors

Acronym: DBR = distributed Bragg reflector

Definition: mirror structures based on Bragg reflection at a period structure

More general term: distributed mirrors

German: Bragg-Spiegel

Category: photonic devicesphotonic devices


Cite the article using its DOI: https://doi.org/10.61835/hac

Get citation code: Endnote (RIS) BibTex plain textHTML

A Bragg mirror (also called distributed Bragg reflector) is a mirror structure which consists of an alternating sequence of layers of two different optical materials. The most frequently used design is that of a quarter-wave mirror, where each optical layer thickness corresponding to one quarter of the wavelength for which the mirror is designed. The latter condition holds for normal incidence; if the mirror is designed for larger angles of incidence, accordingly thicker layers are needed.

The principle of operation of such a reflector can be understood as follows. Each interface between the two materials contributes a Fresnel reflection. For the design wavelength, the optical path length difference between reflections from subsequent interfaces is half the wavelength; in addition, the amplitude reflection coefficients for the interfaces have alternating signs. Therefore, all reflected components from the interfaces interfere constructively, which results in a strong reflection. The reflectance (reflectivity) achieved is determined by the number of layer pairs and by the refractive index contrast between the layer materials. The reflection bandwidth is determined mainly by the refractive index contrast; if that is too small, even using a very large number of coating layers will not work.

field penetration in a Bragg mirror
Figure 1: Field penetration into a Bragg mirror, calculated with the software RP Coating.

Figure 1 shows the field penetration into a Bragg mirror made of eight layer pairs of TiO2 and SiO2. The blue curve shows the intensity distribution of a wave with the design wavelength of 1000 nm, incident from the right-hand side. Note that the intensity is oscillating outside the mirror due to the interference of the counterpropagating waves. The gray curve shows the intensity distribution for 800 nm, where a significant part of the light can get through the mirror coating.

reflectance and dispersion of a Bragg mirror
Figure 2: Reflectance (black curve) and chromatic dispersion (blue curve) of the same mirror as above.

Figure 2 shows the reflectance and the group delay dispersion as functions of the wavelength. The reflectance is high over some optical bandwidth, which depends on the refractive index contrast of the materials used and on the number of layer pairs. The dispersion is calculated from the second derivative of the reflection phase with respect to the optical frequency. It is small near the center of the reflection band, but grows rapidly near the edges.

field penetration in a Bragg mirror
Figure 3: Field penetration into the Bragg mirror as a function of wavelength. The colors indicate the optical intensity inside the mirror.

Figure 3 shows with a color scale how the optical field penetrates into the mirror. It can be seen that there is little field penetration well within the reflection band.

Bragg mirror reflectance vs. incidence angle
Figure 4: The reflectance spectrum of a Bragg mirror for different incidence angles from normal incidence (red) up to 60° (blue) in steps of 10°.

Figure 4 shows reflectance spectra of a Bragg mirror for different angles of incidence. The larger that angle, the more the reflection spectrum is shifted towards shorter wavelengths.

Types of Bragg Mirrors

Bragg mirrors for applications in optics can be fabricated with different technologies:

There are other multilayer mirror designs which deviate from the simple quarter-wave design. They generally have a lower reflectance for the same number of layers, but can be optimized e.g. as dichroic mirrors or as dispersive chirped mirrors for dispersion compensation.

More to Learn

Encyclopedia articles:


Questions and Comments from Users


For a Bragg mirror, why are there smaller reflectivity peaks outside the main one?

The author's answer:

That's not easy, but best understood in cases with few layer pairs and a low reflectivity per layer pair, where we can neglect effects of multiple reflections. The reflected light amplitude is then the superposition of one amplitude contribution per layer pair. The wavelength offset from the wavelength of peak reflectivity determines the phase change between two such contributions. If you had only two of those, you would get a purely oscillatory behavior of reflectivity vs. wavelength. With more of them, it gets more complicated, but certainly you shouldn't expect the reflectivity to monotonously decay for increasing phase changes.

Mathematically, you can approach that with a Fourier transform, e.g. applied to a rectangular function resembling amplitude contributions from some finite length in which you have the refractive index oscillations.


Does the reflectance spectrum of a Bragg mirror depend on whether the light is incident from the air side or from the glass substrate side? For example, could a 'hot mirror' be laminated between two sheets of glass and still have the same reflectance spectrum as one where the light is incident from air? Or would the alternating sequence of layers need to be changed to obtain the same reflectance spectrum?

The author's answer:

The reflectance of such a device cannot depend on the direction of light propagation. So if you take the same device both times and only come with light from different sides, you get the same reflectance.

However, the reflectance can change if you modify the setup, for example by putting a layer of glass on top of a mirror.


Why do the spectral features shift to shorter wavelengths when the mirror is tilted? Shouldn't the wavelength grow since the optical distance between the films also grows?

The author's answer:

It is surprising indeed, but I have explained that in a blog article.


What is the origin of the reflection bandwidth of a Bragg mirror?

The author's answer:

The Bragg condition is still approximately fulfilled for wavelengths which are close enough to the Bragg wavelength. More precisely, the optical phase changes caused by the wavelength deviation are small enough not to cause substantial changes of the reflectance. If the refractive index contrast is strong, a relatively small number of layers is relevant, so that the involved phase changes are relatively small for a given wavelength deviation.


Why does the thickness need to be 1/4 of the wavelength, not 1/2 the wavelength?

The author's answer:

The λ/4 thickness implies λ/2 for the way back and forth through one layer, or a <$\pi$> phase shift. That looks like the wrong condition at a first glance. However, in addition there is a <$\pi$> phase difference between subsequent reflections because it makes a difference whether you go from higher refractive index to a lower one or vice versa. As a result, the phases of reflected contributions from different interfaces are the same, so that they can add up constructively.

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.

Spam check:

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.


Share this with your network:

Follow our specific LinkedIn pages for more insights and updates: