models.roptics.distributed_bragg_reflector
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2 n H 2 N n H 1 – ----------------- nL na nb - R = ------------------------------------------2 2N n n H H 1 + ------- ------------ n L n a n b 2
Figure 2: Geometry used to model a distributed Bragg reflector. Dielectric layers are added to the surface shown in blue, which is between an air domain and a substrate. The layers of greater refractive index are made of ZnS with nH=2.32, and the layers of lower refractive index contain MgF2 with nL=1.38. The refractive index of the air and substrate domains are 1.0 and 1.5 respectively. The optical thicknesses of the layers are calculated such that nHtH = nLtL = λ0/4.
GEOMETRY 1
Add some parameters for the refractive index of the materials and the central wavelength.
3 |
DISTRIBUTED BRAGG REFLECTOR
Solved with COMSOL Multiphysics 5.0
Figure 3: Response of the distributed Bragg grating for two configurations, N=2 and N=5.
Results and Discussion
Figure 3 shows the response of the dielectric mirror across a range of wavelengths from 400 nm to 800 nm. The vacuum wavelength λ0 used in the specification of the layers is 550 nm. At this wavelength, the N=2 configuration gives roughly an 87% reflectance whereas the N=5 configuration gives roughly 99.5% reflectance. The computed values of R agree with Equation 1. The calculated stop-band is 180 nm using Equation 2. As shown in Figure 3 this is roughly correct for the N=5 case. The agreement can be expected to improve as the number of layers is increased, with the reflectance approaching 100% throughout the stop-band.
ห้องสมุดไป่ตู้
Model Library path: Ray_Optics_Module/Tutorial_Models/
distributed_bragg_reflector
Modeling Instructions
From the File menu, choose New.
NEW
1 In the New window, click Model Wizard.
Solved with COMSOL Multiphysics 5.0
Distributed Bragg Reflector
Introduction
A distributed Bragg reflector, or dielectric mirror, is a reflector used in waveguides, such as optical fibers. A distributed Bragg reflector has extremely low losses at optical and infrared frequencies compared to ordinary metallic mirrors. Its structure is formed from layers of alternating materials with high and low refractive indices. Typically the stack would be made up of an odd number of layers where the first and last layers are chosen to have high refractive index. Each layer boundary causes a partial reflection of an optical wave. When the wavelength is close to four times the optical thickness of the layers, the many reflected waves tend to interfere constructively, causing the layers to act as a high-quality reflector. The range of wavelengths in which most of the incident intensity is reflected is called the photonic stopband. In the limit in which the reflector contains a very large number of layers, radiation in this range of wavelengths cannot propagate into the structure. Distributed Bragg reflectors are critical components in vertical cavity surface emitting lasers and other types of narrow-linewidth laser diodes such as distributed feedback lasers.
(1)
where na and nS are the refractive indices of the ambient medium and substrate, respectively. N is the number of pairs of dielectric layers; for example, N=5 implies that the reflector consists of 11 layers (5 pairs plus an additional layer of high refractive index on top). The bandwidth Δλ of the photonic stop-band is given by: 4 λ0 n H – n L Δλ 0 = --------- asin ------------------- n H + n L π where λ0 is the central wavelength of the band. (2)
Figure 1: Bragg reflector with 9 layers (N=4).
1 |
DISTRIBUTED BRAGG REFLECTOR
Solved with COMSOL Multiphysics 5.0
Model Definition
The model consists of two domains with differing material properties, with a number of Thin Dielectric Film features added to the Material Discontinuity feature separating them. Figure 1 shows the geometry used to model a distributed Bragg reflector. The blue surface represents the boundary to which dielectric layers are added, with the top domain containing air and the bottom domain containing a substrate. The red arrow (activated in the Material Discontinuity feature) shows the sense in which the thin dielectric layers are stacked. The last Thin Dielectric Film in the model tree represents the topmost thin film in the model.
2 |
DISTRIBUTED BRAGG REFLECTOR
Solved with COMSOL Multiphysics 5.0
To show the response of the mirror across a span of wavelengths, a range of wavelengths (or frequencies) can be specified using the Release from Grid feature. This functionality is activated if the Frequency-dependent refractive indices is chosen in the interface properties. Of particular interest in this devices, is the reflectance R of the device and what range of wavelengths it is effective over, Δλ. The reflectance for the distributed Bragg reflector is given by:
MODEL WIZARD
1 In the Model Wizard window, click 3D.
4 |
DISTRIBUTED BRAGG REFLECTOR
Solved with COMSOL Multiphysics 5.0
2 In the Select physics tree, select Optics>Ray Optics>Geometrical Optics (gop). 3 Click Add. 4 Click Study. 5 In the Select study tree, select Preset Studies>Ray Tracing. 6 Click Done.
Figure 2: Geometry used to model a distributed Bragg reflector. Dielectric layers are added to the surface shown in blue, which is between an air domain and a substrate. The layers of greater refractive index are made of ZnS with nH=2.32, and the layers of lower refractive index contain MgF2 with nL=1.38. The refractive index of the air and substrate domains are 1.0 and 1.5 respectively. The optical thicknesses of the layers are calculated such that nHtH = nLtL = λ0/4.
GEOMETRY 1
Add some parameters for the refractive index of the materials and the central wavelength.
3 |
DISTRIBUTED BRAGG REFLECTOR
Solved with COMSOL Multiphysics 5.0
Figure 3: Response of the distributed Bragg grating for two configurations, N=2 and N=5.
Results and Discussion
Figure 3 shows the response of the dielectric mirror across a range of wavelengths from 400 nm to 800 nm. The vacuum wavelength λ0 used in the specification of the layers is 550 nm. At this wavelength, the N=2 configuration gives roughly an 87% reflectance whereas the N=5 configuration gives roughly 99.5% reflectance. The computed values of R agree with Equation 1. The calculated stop-band is 180 nm using Equation 2. As shown in Figure 3 this is roughly correct for the N=5 case. The agreement can be expected to improve as the number of layers is increased, with the reflectance approaching 100% throughout the stop-band.
ห้องสมุดไป่ตู้
Model Library path: Ray_Optics_Module/Tutorial_Models/
distributed_bragg_reflector
Modeling Instructions
From the File menu, choose New.
NEW
1 In the New window, click Model Wizard.
Solved with COMSOL Multiphysics 5.0
Distributed Bragg Reflector
Introduction
A distributed Bragg reflector, or dielectric mirror, is a reflector used in waveguides, such as optical fibers. A distributed Bragg reflector has extremely low losses at optical and infrared frequencies compared to ordinary metallic mirrors. Its structure is formed from layers of alternating materials with high and low refractive indices. Typically the stack would be made up of an odd number of layers where the first and last layers are chosen to have high refractive index. Each layer boundary causes a partial reflection of an optical wave. When the wavelength is close to four times the optical thickness of the layers, the many reflected waves tend to interfere constructively, causing the layers to act as a high-quality reflector. The range of wavelengths in which most of the incident intensity is reflected is called the photonic stopband. In the limit in which the reflector contains a very large number of layers, radiation in this range of wavelengths cannot propagate into the structure. Distributed Bragg reflectors are critical components in vertical cavity surface emitting lasers and other types of narrow-linewidth laser diodes such as distributed feedback lasers.
(1)
where na and nS are the refractive indices of the ambient medium and substrate, respectively. N is the number of pairs of dielectric layers; for example, N=5 implies that the reflector consists of 11 layers (5 pairs plus an additional layer of high refractive index on top). The bandwidth Δλ of the photonic stop-band is given by: 4 λ0 n H – n L Δλ 0 = --------- asin ------------------- n H + n L π where λ0 is the central wavelength of the band. (2)
Figure 1: Bragg reflector with 9 layers (N=4).
1 |
DISTRIBUTED BRAGG REFLECTOR
Solved with COMSOL Multiphysics 5.0
Model Definition
The model consists of two domains with differing material properties, with a number of Thin Dielectric Film features added to the Material Discontinuity feature separating them. Figure 1 shows the geometry used to model a distributed Bragg reflector. The blue surface represents the boundary to which dielectric layers are added, with the top domain containing air and the bottom domain containing a substrate. The red arrow (activated in the Material Discontinuity feature) shows the sense in which the thin dielectric layers are stacked. The last Thin Dielectric Film in the model tree represents the topmost thin film in the model.
2 |
DISTRIBUTED BRAGG REFLECTOR
Solved with COMSOL Multiphysics 5.0
To show the response of the mirror across a span of wavelengths, a range of wavelengths (or frequencies) can be specified using the Release from Grid feature. This functionality is activated if the Frequency-dependent refractive indices is chosen in the interface properties. Of particular interest in this devices, is the reflectance R of the device and what range of wavelengths it is effective over, Δλ. The reflectance for the distributed Bragg reflector is given by:
MODEL WIZARD
1 In the Model Wizard window, click 3D.
4 |
DISTRIBUTED BRAGG REFLECTOR
Solved with COMSOL Multiphysics 5.0
2 In the Select physics tree, select Optics>Ray Optics>Geometrical Optics (gop). 3 Click Add. 4 Click Study. 5 In the Select study tree, select Preset Studies>Ray Tracing. 6 Click Done.