What is the thickness of distributed Bragg reflector?

Thickness of a Distributed Bragg Reflector (DBR)

A Distributed Bragg Reflector (DBR) is a structure composed of multiple layers of alternating materials with different refractive indices. The primary function of a DBR is to reflect specific wavelengths of light while allowing others to pass through.

Basic Structure:
The basic DBR structure consists of a periodic arrangement of two materials, A and B, that are stacked to form a one-dimensional photonic crystal. Each layer has an optical thickness of one quarter of the targeted wavelength of light, leading to constructive interference for that wavelength and its harmonics.

Formula for Thickness:
The optical thickness of each layer (n*d) is given by the equation:

n*d = λ0 / 4n

where n is the refractive index of the layer, d is the physical thickness of the layer, and λ0 is the targeted center wavelength of the DBR reflector band.

Calculating Total Thickness of DBR

To calculate the total thickness of a DBR, sum the thicknesses of all individual layers:

Total Thickness (T) = ∑ (ni * di)

where i ranges over all layers in the DBR.

Example Design:
A typical DBR might alternate between layers of high-index material like gallium arsenide (GaAs) with a refractive index around 3.5 and low-index material like aluminum oxide (AlAs) with a refractive index of about 2.9. For a targeted wavelength of 850 nm:

The quarter-wavelength optical thickness for GaAs is:
d(GaAs) = 850 nm / (4 * 3.5) ≈ 60.7 nm

The quarter-wavelength optical thickness for AlAs is:
d(AlAs) = 850 nm / (4 * 2.9) ≈ 73.3 nm

Number of Periods:
The number of periods (pairs of layers A and B) in a DBR can vary depending on the desired reflectivity. Higher reflectivity requires more periods. A typical DBR may have anywhere from 10 to 30 periods. The reflectivity increases as the number of periods increases.

Applications of Distributed Bragg Reflectors

DBRs are widely used in optoelectronics for devices such as:

  • Laser diodes to form the resonant cavity
  • Optical filters
  • Wavelength specific mirrors
  • Sensors

The thickness of the layers within a DBR is critical as it determines the wavelength of light that is reflected. Precision in fabrication is essential to achieve the desired optical properties of the DBR.

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