Imaginary value of current dipole moment
Posted 2024年2月13日 GMT-5 08:48 4 Replies
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I'm confused to put value for dipole point source with current dipole moment in ewfd wavelength module.
In a textbook, E-field is proportional to Gd, where G is total green function and d is dipole moment. Since comsol only allows us to set 'current dipole moment(p)' instead of dipole moment, we can think p of time derivative of dipole moment. so assuming dipole moment oscillates with exp(-iwt), p=-iwd can be obtained. so E-field is proportional to Gp/(-i*w). Therefore, if I set the value of p as real number, the E-field should be seen with imaginary part of E. and p as imaginary number, E-field should be seen with real part of E-field.
However, always reasonable E-field distribution is seen with real part of E-field, whatever real number or imaginary number I put in the current dipole moment(p). why is that?
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Physical, measurable, fields have real values. The purpose of introducing a term like exp(-iwt) is for the mathematical convenience it provides in managing/identifying phase and in taking derivatives and computing integrals. There are many discussions explaining more about "complex representation of waves" on the internet, so I suggest you search for that phrase. Frequency-domain Comsol Models will typically represent field quantities as complex. They may be complex scalars or complex vectors. If you plot such a quantity using Comsol Multiphysics, it usually displays only the real part. Note that you need to be especially careful when multiplying such quantities together, since the multiplication operation will include the imaginary parts. Often, certain useful quantities expressed in electromagnetic work require the multiplication of a complex number by the complex conjugate of either that same number or by another number, rather than simply multiplying two numbers directly. The risk of confusion increases when vectors are involved. In addition, these quantities may be functions of space and time (x,y,z,t). So be careful. If you are going to work with waves in frequency domain, you need to become familiar with, and comfortable with, complex representations of scalars and vectors, and the notions of fields (e.g., scalars and/or vectors that are functions of position and time).
-------------------Scientific Applications & Research Associates (SARA) Inc.
www.comsol.com/partners-consultants/certified-consultants/sara
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Physical, measurable, fields have real values. The purpose of introducing a term like exp(-iwt) is for the mathematical convenience it provides in managing/identifying phase and in taking derivatives and computing integrals. There are many discussions explaining more about "complex representation of waves" on the internet, so I suggest you search for that phrase. Frequency-domain Comsol Models will typically represent field quantities as complex. They may be complex scalars or complex vectors. If you plot such a quantity using Comsol Multiphysics, it usually displays only the real part. Note that you need to be especially careful when multiplying such quantities together, since the multiplication operation will include the imaginary parts. Often, certain useful quantities expressed in electromagnetic work require the multiplication of a complex number by the complex conjugate of either that same number or by another number, rather than simply multiplying two numbers directly. The risk of confusion increases when vectors are involved. In addition, these quantities may be functions of space and time (x,y,z,t). So be careful. If you are going to work with waves in frequency domain, you need to become familiar with, and comfortable with, complex representations of scalars and vectors, and the notions of fields (e.g., scalars and/or vectors that are functions of position and time).
Thank you for your reply Robert. I agree that measurable physical quantity should be real value. I think I should clarify my question again.
For example, whether I put value of current dipole moment of electric dipole point source as 1 or 1j, the result of e-field is same. However, this should be different because e-field is expressed as a product of dyadic green function and dipole moment. If I express the equation,
E(r)=G(r,r')p(r')/(-1jw), where E(r) is e-field, G(r,r') is dyadic green function, p(r') is current dipole moment, w is angular frequency.
Then if we think about real part of E-field in both cases,
i) when p=1,
real(E(r))= real(G(r,r')/(-1j*w))
ii)when p=1j,
real(E(r))= real(G(r,r')/(-w)).
They should be different. But if I calculate the comsol, they seems to be identical. why is that?
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Hmm. May I assume you are not plotting the norm (that is, the magnitude) of the field quantities of interest to you? If you are, that would have no dependence on the phase of your input. Anyway, if not that, then I suggest you post your .mph file to the forum, so we can all see what you are doing within the actual model and post-processing. Note: If your .mph file is > 5 MB, then select "Clear All Built Meshes" from the Mesh menu and "Clear All Solutions" from the Study menu, and then save it (or by another name) and post that.
-------------------Scientific Applications & Research Associates (SARA) Inc.
www.comsol.com/partners-consultants/certified-consultants/sara
Please login with a confirmed email address before reporting spam
Hmm. May I assume you are not plotting the norm (that is, the magnitude) of the field quantities of interest to you? If you are, that would have no dependence on the phase of your input. Anyway, if not that, then I suggest you post your .mph file to the forum, so we can all see what you are doing within the actual model and post-processing. Note: If your .mph file is > 5 MB, then select "Clear All Built Meshes" from the Mesh menu and "Clear All Solutions" from the Study menu, and then save it (or by another name) and post that.
Plotting ewfd.normE was the problem. As I plotting ewfd.Ez instead of normE, everything worked as I anticipated. Thank you so much for your help.
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