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mode analysis in ring waveguides
Posted Dec 14, 2011, 7:51 a.m. EST RF & Microwave Engineering, Wave Optics, Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.2, Version 4.2a, Version 5.1, Version 5.2 3 Replies
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Hello,
using the 2D-axisymmetric space dimension and the RF-module, I'm doing a mode analysis of a ring waveguide, where the diameter d of the ring (not the waveguide itself!) is in the order of 100e-6 m, i.e. the radius r_ring approx. 50e-6 m.
Since the problem can be represented in cylindrical coordinates (r, phi, z), and the structure does not depend on phi, it is sufficient to define the cross section of the waveguide and tell Comsol to use the appropriate space dimension; this is exactly what the mentioned 2D-axisymmetric simulation does.
The waveguide is made of a core with refractive index n_core, and some cladding with n_clad, with n_clad < n_core to allow light to propagate. As an example, n_clad = 1.5 and n_core = 2.0.
The mode analysis works fine, but I've got an issue with the exact definition of the effective refractive index n_eff, which, in usual linear waveguides, usually is some value between n_clad and n_core. As an initial guess for the mode solver, it is helpful to provide some value in the vicinity of the expected n_eff.
However, in this ring structure, things are different.
I only get results when I provide a value much smaller than n_core: It turned out that a value in the order of (n_core * r_ring) is expected. Note that r_ring is something like 50e-6 m, i.e. very small.
Similarly, the calculated effective mode indices belonging to the modes are also much smaller than n_core.
They all are approximately r_ring * n_core.
So the problem is that I expect n_eff to be in the order of n_core, but the n_eff calculated by Comsol (or n_eff's if there is more than one mode) are way too small.
Is there something special about the definition of n_eff in bent waveguides?
Since n_eff actually is the real part of the propagation constant (divided by k0, (k0=2 pi / lambda)), maybe the cylindrical coordinates somehow affect the definition of the propagation constant. Likewise, also the imaginary part which relates to damping of the electric field along propagation direction, may be altered.
I would greatly appreciate your answers.
regards,
H. Hartwig
using the 2D-axisymmetric space dimension and the RF-module, I'm doing a mode analysis of a ring waveguide, where the diameter d of the ring (not the waveguide itself!) is in the order of 100e-6 m, i.e. the radius r_ring approx. 50e-6 m.
Since the problem can be represented in cylindrical coordinates (r, phi, z), and the structure does not depend on phi, it is sufficient to define the cross section of the waveguide and tell Comsol to use the appropriate space dimension; this is exactly what the mentioned 2D-axisymmetric simulation does.
The waveguide is made of a core with refractive index n_core, and some cladding with n_clad, with n_clad < n_core to allow light to propagate. As an example, n_clad = 1.5 and n_core = 2.0.
The mode analysis works fine, but I've got an issue with the exact definition of the effective refractive index n_eff, which, in usual linear waveguides, usually is some value between n_clad and n_core. As an initial guess for the mode solver, it is helpful to provide some value in the vicinity of the expected n_eff.
However, in this ring structure, things are different.
I only get results when I provide a value much smaller than n_core: It turned out that a value in the order of (n_core * r_ring) is expected. Note that r_ring is something like 50e-6 m, i.e. very small.
Similarly, the calculated effective mode indices belonging to the modes are also much smaller than n_core.
They all are approximately r_ring * n_core.
So the problem is that I expect n_eff to be in the order of n_core, but the n_eff calculated by Comsol (or n_eff's if there is more than one mode) are way too small.
Is there something special about the definition of n_eff in bent waveguides?
Since n_eff actually is the real part of the propagation constant (divided by k0, (k0=2 pi / lambda)), maybe the cylindrical coordinates somehow affect the definition of the propagation constant. Likewise, also the imaginary part which relates to damping of the electric field along propagation direction, may be altered.
I would greatly appreciate your answers.
regards,
H. Hartwig
3 Replies Last Post Dec 2, 2015, 7:58 p.m. EST
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Posted:
1 decade ago
I just want to share the answer that I got from the support in case someone is interested.
The numerical values refer to an example geometry that I sent to the support.
Still, the dependence on radius r does not allow to exactly determine the effective refractive index since there is some ambiguity in the value for r (center of waevguide, center of light distribution, peak, etc...).
here the answer:
In the Mode Analysis study, it is assumed a known (exponential)
out-of-plane behavior of the fields, i.e. a dependency of the type
exp(alpha*X), where X is the out of plane coordinate. The Mode Analysis is
intended to be used in 2D, where X is the z coordinate (a length), and
alpha (the eigenvalue) expresses the variation of phase for a unit length.
In axisymmetry, X is phi (an angle). I checked the implementation and the
problem is handled correctly, but in this case alpha must be intended as
the variation of phase per unit angle, and so to retrieve the
corresponding
"per unit length" parameters it should be scaled with the radius (for
example, dividing the effective mode indices by the mean radius of 30e-6 m
the result is around 1.8). We are currently addressing this problem and
improvements will be added in future releases.
The numerical values refer to an example geometry that I sent to the support.
Still, the dependence on radius r does not allow to exactly determine the effective refractive index since there is some ambiguity in the value for r (center of waevguide, center of light distribution, peak, etc...).
here the answer:
In the Mode Analysis study, it is assumed a known (exponential)
out-of-plane behavior of the fields, i.e. a dependency of the type
exp(alpha*X), where X is the out of plane coordinate. The Mode Analysis is
intended to be used in 2D, where X is the z coordinate (a length), and
alpha (the eigenvalue) expresses the variation of phase for a unit length.
In axisymmetry, X is phi (an angle). I checked the implementation and the
problem is handled correctly, but in this case alpha must be intended as
the variation of phase per unit angle, and so to retrieve the
corresponding
"per unit length" parameters it should be scaled with the radius (for
example, dividing the effective mode indices by the mean radius of 30e-6 m
the result is around 1.8). We are currently addressing this problem and
improvements will be added in future releases.
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Posted:
1 decade ago
Dear H Hartwig
I have same confusions about this problem.
The values must have some meaning.
I also agree that this value is related to the effective radius and effective index somehow.
Maybe we can discuss more on it?
My email: flou@kth.se
best regards,
Fei
I have same confusions about this problem.
The values must have some meaning.
I also agree that this value is related to the effective radius and effective index somehow.
Maybe we can discuss more on it?
My email: flou@kth.se
best regards,
Fei
Hello,
using the 2D-axisymmetric space dimension and the RF-module, I'm doing a mode analysis of a ring waveguide, where the diameter d of the ring (not the waveguide itself!) is in the order of 100e-6 m, i.e. the radius r_ring approx. 50e-6 m.
Since the problem can be represented in cylindrical coordinates (r, phi, z), and the structure does not depend on phi, it is sufficient to define the cross section of the waveguide and tell Comsol to use the appropriate space dimension; this is exactly what the mentioned 2D-axisymmetric simulation does.
The waveguide is made of a core with refractive index n_core, and some cladding with n_clad, with n_clad < n_core to allow light to propagate. As an example, n_clad = 1.5 and n_core = 2.0.
The mode analysis works fine, but I've got an issue with the exact definition of the effective refractive index n_eff, which, in usual linear waveguides, usually is some value between n_clad and n_core. As an initial guess for the mode solver, it is helpful to provide some value in the vicinity of the expected n_eff.
However, in this ring structure, things are different.
I only get results when I provide a value much smaller than n_core: It turned out that a value in the order of (n_core * r_ring) is expected. Note that r_ring is something like 50e-6 m, i.e. very small.
Similarly, the calculated effective mode indices belonging to the modes are also much smaller than n_core.
They all are approximately r_ring * n_core.
So the problem is that I expect n_eff to be in the order of n_core, but the n_eff calculated by Comsol (or n_eff's if there is more than one mode) are way too small.
Is there something special about the definition of n_eff in bent waveguides?
Since n_eff actually is the real part of the propagation constant (divided by k0, (k0=2 pi / lambda)), maybe the cylindrical coordinates somehow affect the definition of the propagation constant. Likewise, also the imaginary part which relates to damping of the electric field along propagation direction, may be altered.
I would greatly appreciate your answers.
regards,
H. Hartwig
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Posted:
9 years ago
I am also working on ring waveguide, particularly ring resonator. I am trying to simulate the ring resonator in 2D domain to minimize the computational time and memory usage (I am running the simulation on a Core 2 Quad with only 4 GB of memory). In such a case, I am utilizing the Effective Index Method. More details, my methodology is to design the cross-section of the waveguide core surrounding by the cladding and then run the boundary mode analysis to find out the modal index. However, the modal index found out by this method is just for straight waveguide instead of in a bending case. Could anyone suggest method for how to find the modal index of bent waveguide? Many thanks.