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Effective area calculation for PCF design

Posted Jan 27, 2010, 10:36 p.m. EST Version 4.2 15 Replies

Jais John
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I am designing a PCF. for that I want to calculate the effective area.
The equation for effective area is attached.
In that equation how can I calculate the electric field 'E' value?
I have an idea about it, we can calculate it from the option postprocessing-subdomain integration.
I want to know the expressions for 2nd and 4th order integration of that E value...

Thanks.....

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15 Replies Last Post Nov 9, 2016, 7:09 a.m. EST
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Jan 28, 2010, 1:27 a.m. EST
Hi

Well you double integration over dxdy is the "Integration Coupling Variables" - "Boundary Integration Variables" for 3D or a "Subdomain Integration Variable" for 2D.
You need to identify the name of your "E" and integrate abs(E)^2 or E*conj(E) I would expect, if E is complex. Respectively to the forth power.

These integrations are in facts sum over the nodes/elements, so just be careful that the sum of a product is not necesarily the product of the sums, etc.

It is as when you want to know the surface of the side of a cube: you select the side and type "1" in the Boundary Integrand and you get the boundary area, respectively "1" in the sub-domain integrand and you get your cube=subdomain in 3D total volume.

Hope this helps
Ivar
Hi Well you double integration over dxdy is the "Integration Coupling Variables" - "Boundary Integration Variables" for 3D or a "Subdomain Integration Variable" for 2D. You need to identify the name of your "E" and integrate abs(E)^2 or E*conj(E) I would expect, if E is complex. Respectively to the forth power. These integrations are in facts sum over the nodes/elements, so just be careful that the sum of a product is not necesarily the product of the sums, etc. It is as when you want to know the surface of the side of a cube: you select the side and type "1" in the Boundary Integrand and you get the boundary area, respectively "1" in the sub-domain integrand and you get your cube=subdomain in 3D total volume. Hope this helps Ivar
Md. Anwar Hossain
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Posted: 1 decade ago Aug 26, 2011, 10:21 a.m. EDT
Hello Ivar

Thank you for your guidline. I am also designing PCF using comsol 4.2. As per your instruction i have defined effective area as follows:
intop1(abs(Ez)^2)^2/intop1(abs(Ez)^4)

Geometry entity level: entire model

i have done this intregation over entire model and got some results but my found results are about 1 um^2 higher with compare to finite diffirence method (FDM). Using same parameters, I am getting always 1 um^2 higher effective area with compare to FDM. Would please clarify me?

Thank in advanced

Anwar

Hello Ivar Thank you for your guidline. I am also designing PCF using comsol 4.2. As per your instruction i have defined effective area as follows: intop1(abs(Ez)^2)^2/intop1(abs(Ez)^4) Geometry entity level: entire model i have done this intregation over entire model and got some results but my found results are about 1 um^2 higher with compare to finite diffirence method (FDM). Using same parameters, I am getting always 1 um^2 higher effective area with compare to FDM. Would please clarify me? Thank in advanced Anwar
Christos Markos
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Posted: 1 decade ago Sep 23, 2011, 4:36 a.m. EDT
Hello guys,

Well I cannot unfortunately calculate the effective modal area of a PCF. I am using COMSOL 3.5 and the equation I used to calculate the area was the one Md. Anwar Hossain mentioned in his previous reply i.e. intop1(abs(Ez)^2)^2/intop1(abs(Ez)^4).

The error is:

Error :6099
Evaluation of post processing expression failed
Unknown function
- function: intop1
Failed to evaluate expression
- Expression: into1(abs(Ez)^2)^2/intop1(abs(Ez)^4)

Could you please help me to find the effective area of the fundamental mode? I am new in COMSOL

Thanks guys,
Take care
Hello guys, Well I cannot unfortunately calculate the effective modal area of a PCF. I am using COMSOL 3.5 and the equation I used to calculate the area was the one Md. Anwar Hossain mentioned in his previous reply i.e. intop1(abs(Ez)^2)^2/intop1(abs(Ez)^4). The error is: Error :6099 Evaluation of post processing expression failed Unknown function - function: intop1 Failed to evaluate expression - Expression: into1(abs(Ez)^2)^2/intop1(abs(Ez)^4) Could you please help me to find the effective area of the fundamental mode? I am new in COMSOL Thanks guys, Take care
Md. Anwar Hossain
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Posted: 1 decade ago Sep 23, 2011, 8:49 a.m. EDT
Define that expression in a variable under model--definition
then define integration (intop1) by right clicking on definition. This integration (intop1) you will get under model couplings.
Finally, run the program after defining the domain on which you want to perform integration for having Aeff.

Hope you will have good results.

Anwar




Hello guys,


Well I cannot unfortunately calculate the effective modal area of a PCF. I am using COMSOL 3.5 and the equation I used to calculate the area was the one Md. Anwar Hossain mentioned in his previous reply i.e. intop1(abs(Ez)^2)^2/intop1(abs(Ez)^4).

The error is:

Error :6099
Evaluation of post processing expression failed
Unknown function
- function: intop1
Failed to evaluate expression
- Expression: into1(abs(Ez)^2)^2/intop1(abs(Ez)^4)

Could you please help me to find the effective area of the fundamental mode? I am new in COMSOL

Thanks guys,
Take care


Define that expression in a variable under model--definition then define integration (intop1) by right clicking on definition. This integration (intop1) you will get under model couplings. Finally, run the program after defining the domain on which you want to perform integration for having Aeff. Hope you will have good results. Anwar [QUOTE] Hello guys, Well I cannot unfortunately calculate the effective modal area of a PCF. I am using COMSOL 3.5 and the equation I used to calculate the area was the one Md. Anwar Hossain mentioned in his previous reply i.e. intop1(abs(Ez)^2)^2/intop1(abs(Ez)^4). The error is: Error :6099 Evaluation of post processing expression failed Unknown function - function: intop1 Failed to evaluate expression - Expression: into1(abs(Ez)^2)^2/intop1(abs(Ez)^4) Could you please help me to find the effective area of the fundamental mode? I am new in COMSOL Thanks guys, Take care [/QUOTE]
Christos Markos
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Posted: 1 decade ago Sep 23, 2011, 9:26 a.m. EDT
Dear Anwar,

Thanks a lot for your reply and your time. I tried to define the equation but unfortunately I couldn't. The reason is i am really dummy with COMSOL and even the simplest thing it is really hard for me to find. Could you please be more specific with the steps I have to follow? My apologies and thanks again

Take care,
Chris
Dear Anwar, Thanks a lot for your reply and your time. I tried to define the equation but unfortunately I couldn't. The reason is i am really dummy with COMSOL and even the simplest thing it is really hard for me to find. Could you please be more specific with the steps I have to follow? My apologies and thanks again Take care, Chris
Md. Anwar Hossain
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Posted: 1 decade ago Sep 23, 2011, 9:44 a.m. EDT
Plz check the operator name. You have written wrongly in your posted expression. However, you have to mention the same name of the operator in integration. Please check slowly. Hope you will have good results.

Anwar


Dear Anwar,

Thanks a lot for your reply and your time. I tried to define the equation but unfortunately I couldn't. The reason is i am really dummy with COMSOL and even the simplest thing it is really hard for me to find. Could you please be more specific with the steps I have to follow? My apologies and thanks again

Take care,
Chris


Plz check the operator name. You have written wrongly in your posted expression. However, you have to mention the same name of the operator in integration. Please check slowly. Hope you will have good results. Anwar [QUOTE] Dear Anwar, Thanks a lot for your reply and your time. I tried to define the equation but unfortunately I couldn't. The reason is i am really dummy with COMSOL and even the simplest thing it is really hard for me to find. Could you please be more specific with the steps I have to follow? My apologies and thanks again Take care, Chris [/QUOTE]
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Sep 23, 2011, 10:16 a.m. EDT
Hi

intop() is the V4 operator default name, its different in 3.5, chceck our doc for model coupling integration variables

--
Good luck
Ivar
Hi intop() is the V4 operator default name, its different in 3.5, chceck our doc for model coupling integration variables -- Good luck Ivar
Christos Markos
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Posted: 1 decade ago Sep 26, 2011, 4:33 a.m. EDT
Hi again,

I checked out the integration operator in 3.5 (postint) and I still cant get any result. Could you please verify that this is the correct operator that I am using?

Thanks a lot
Hi again, I checked out the integration operator in 3.5 (postint) and I still cant get any result. Could you please verify that this is the correct operator that I am using? Thanks a lot
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Sep 26, 2011, 7:07 a.m. EDT
Hi

Sorry but I do not have access to 3.5 any longer, I have jumped fully into the v4 waters ;)
(and I'm not from COMSOL neither so I have no insentives to keep older versions)

--
Good luck
Ivar
Hi Sorry but I do not have access to 3.5 any longer, I have jumped fully into the v4 waters ;) (and I'm not from COMSOL neither so I have no insentives to keep older versions) -- Good luck Ivar
Deepak Jain
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Posted: 1 decade ago Mar 29, 2012, 4:44 a.m. EDT
Hi Anwar,

one things that i want to make clear that in domain for integration you should not chose entire domain. Select only core that might give more result. Please check and let us know also.

regards
deepak


Sorry Guys I was wrong. You need to chose whole domain.
Hi Anwar, one things that i want to make clear that in domain for integration you should not chose entire domain. Select only core that might give more result. Please check and let us know also. regards deepak Sorry Guys I was wrong. You need to chose whole domain.
Md. Anwar Hossain
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Posted: 1 decade ago Mar 29, 2012, 4:49 a.m. EDT
Dear Deepak

Thank you so much for your kind cooperation. You are right as I have got a very good results using the domain of core only.

Best Regards
Anwar
Dear Deepak Thank you so much for your kind cooperation. You are right as I have got a very good results using the domain of core only. Best Regards Anwar
Selim Habib
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Posted: 1 decade ago Aug 12, 2012, 10:37 a.m. EDT
Hi,
How do I set domain of the core?
Hi, How do I set domain of the core?
Enrico Coscelli
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Posted: 1 decade ago Oct 5, 2012, 9:50 a.m. EDT
I don't think you can use the core domain only.

The easiest way to calculate effective area is to use the z-component of the power flow. If you integrate Pozav_rfwv over the cross-section and divide it by the integral of Pozav_rfwv^2 you'll get the right Aeff value, provided that the z-component of the electric field is small enough (which is true in most cases).

I don't think you can use the core domain only. The easiest way to calculate effective area is to use the z-component of the power flow. If you integrate Pozav_rfwv over the cross-section and divide it by the integral of Pozav_rfwv^2 you'll get the right Aeff value, provided that the z-component of the electric field is small enough (which is true in most cases).
Md. Anwar Hossain
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Posted: 1 decade ago Oct 5, 2012, 10:10 a.m. EDT
Thank you very much for your suggestions. Would you please help me for calculating mode field diameter using Petermann II definition?

Thanks in advance



I don't think you can use the core domain only.

The easiest way to calculate effective area is to use the z-component of the power flow. If you integrate Pozav_rfwv over the cross-section and divide it by the integral of Pozav_rfwv^2 you'll get the right Aeff value, provided that the z-component of the electric field is small enough (which is true in most cases).


Thank you very much for your suggestions. Would you please help me for calculating mode field diameter using Petermann II definition? Thanks in advance [QUOTE] I don't think you can use the core domain only. The easiest way to calculate effective area is to use the z-component of the power flow. If you integrate Pozav_rfwv over the cross-section and divide it by the integral of Pozav_rfwv^2 you'll get the right Aeff value, provided that the z-component of the electric field is small enough (which is true in most cases). [/QUOTE]
Jincy Johny
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Posted: 7 years ago Nov 9, 2016, 7:09 a.m. EST
Hi,

I would like to know more details about the ''Aeff'' equation of a PCF. What is actually the meaning of the numerator and denominator part in the ''Aeff'' equation :
- why the numerator is square of double integral of abs(E)^2 over dx dy.
- why the denominator is double integral of abs(E)^4 over dx dy.

Thanks in advance.
Jincy
Hi, I would like to know more details about the ''Aeff'' equation of a PCF. What is actually the meaning of the numerator and denominator part in the ''Aeff'' equation : - why the numerator is square of double integral of abs(E)^2 over dx dy. - why the denominator is double integral of abs(E)^4 over dx dy. Thanks in advance. Jincy

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