Discussion Forum

Constantinos,

Set up of excitation of the oblique plane wave is described in the following examples from Comsol model library:

www.comsol.com/showroom/gallery/8610/
www.comsol.com/showroom/gallery/12407/

Regards,
Sergei

Hello sir,

Because I am new to the software I would like to understand some things and am sure you can help me.

I tried the www.comsol.com/showroom/gallery/8610/ example.

In order to be sure that I have understood things correctly:

a) Periodic Condition (Floquet periodicity): is used in order to assume that the block is infinite in the x-direction ??

b) Scattering Boundary Condition: is used to propagate light polarised in the y-axis with the direction being tilted ??


If this is correct, then I assume I can use almost the same basic theory to make a stripe of graphene being infinite in x-direction using the a) condition and propagating light onto it using the b) condition.

Sorry if I look too beginner to you.

Thank you.

a) Periodic Condition (Floquet periodicity): is used in order to assume that the block is infinite in the x-direction ??

b) Scattering Boundary Condition: is used to propagate light polarised in the y-axis with the direction being tilted ??

Checking the other example you have given me, the more complicated I found out these two phrases:

Floquet period: The E-field polarization has Ey only and the boundaries are always either parallel or perpendicular to the E-field polarization. Apply periodic boundary conditions on the boundaries parallel to the E-field except those you already assigned to the ports.

Perfect electric Boundary: Apply a perfect electric conductor condition on the boundaries perpendicular to the E-field. This condition creates a virtually infinite modeling space.

Hence, the floquet has another role and not for assuming that the block look infinite in x-direction.
According to the above prases I should use Perfect E Bound. for infinite grahene stripe.
So, in what does floquet periodicity helps?

Constantinos,

a) Floquet periodicity means that structure is repeated in the direction normal to the Floquet boundaries. ”Floquet periodicity” states that field magnitude is the same but there is phase shift due to wave propagation in the direction normal to the boundary. Suppose that at boundary 1 field is E1. Then, field at the boundary 2 is equal E2=E1*exp(-j*kn*delta), where “kn” is wavector component NORMAL to the boundary, and “delta” is the distance between boundaries. Typically, this BC is used in case of oblique incident wave and repeating unit cell in the normal direction.

b) In that particular case, Scattering Boundary Condition is used to excite oblique incident wave.

Regards,
Sergei

Hello sir again,

I spend the whole day ending up probably with wrong values.

By checking the example with the ports, the person in that example uses light which is polarised in the y-direction.
Maybe I am wrong.

What I want to do is to emit light from above port, being polarised in the x-direction and at the same time being able to tilt it along the plane of XY.

Can you give me some help with this?

Because what I see in the example, the person uses an Ey=exp(-i*kax*x) component which I guess gives polarisation in y-axis.

Constantinos,

For x-polarized wave, incident wavector is

k={0, k0*sin(theta), k0*cos(theta)}

and incident electric field is

E={E0*exp(-j*(ky*y+kz*z)), 0, 0},

as shown in the attached picture.

Regards,
Sergei

k={0, k0*sin(theta), k0*cos(theta)}

E={E0*exp(-j*(ky*y+kz*z)), 0, 0},

Hello mr. Sergei,

You are the most helpful man in this forum and thank you very much sir.

I will be needing your help for the next few days if it is possible and you can spend some time of yours too.

In the example above, the wave is tilted with an angle with respect to YZ plane.
However in my case I want to shine light with angle with respect to XZ plane.

I am sending you the results of what you told me to put in the model, in order to check if I did things right.
And also am sending you the model's picture with the light I want to shine in my way.

The model is meant to be a graphene stripe which is infinite along x direction but having a finite width along y direction.
I want to produce plasmons and in order to produce them I must have a kx component that matches plasmons' k-vector that is parallel to x-axis.

Constantinos,

1. I don’t think that the way you placed PMLs will perform as non-reflectinf boundary for various reasons.

2. Port setting is not correct. Since the wave vector is in the x-z plane, you have two options for EM field:
(a) E={Ex, 0,Ez}, H={0,Hy,0} which corresponds to TM polarization for ports at planes z=const
(b) E={0,Ey,0}, H={Hx,0,Hz} which corresponds to TE polarization for ports at planes z=const
Accordingly, you can set up port by specifying magnetic field for TM polarization, or electric field for TE polarization.

Your expression abs(kaz+kay) for propagation constant has no physical meaning. Propagation constant should be specified as the component of the wavevector which is normal to the port boundary.

I would suggest take close look at the “Fresnel Equations” model from Comsol RF library and make sure you have clear physical understanding of port set up for TM and TE polarization cases. Also, this model illustrates how to use PEC or PMC boundary conditions to model infinite extension of the modeling domain in one direction depending on the wave polarization. After that, you can use this model to introduce Transition Boundary condition at the interface between to domains to represent your grapheme layer. After that, search Comsol conference papers about modeling surface plasmon propagation. I suspect, that what you are trying to model resembles classical Kretchmann-Raether configuration of plasmon excitation.

Regards,
Sergei

Thank you very much sir,

I have finally built my model and is working. At least I can excite correctly the frequencies and angles I want.

The only thing I am afraid I have written wrong is the Relative permittivity of my material.
I have Relative Permittivity(real) and Relative permittivity(imaginary).

For example, my dielectric function gives me this: 1 + i*(4.5e-8)

The latter one is thus the rel.perm.imaginary.

Should I type it in the materia properties as i*(4.5e-8) or should I neglect the i value and just type (4.5e-8) ?

Thank you again!

Constantinos,

You should type epsr=1-j*4.5e-8.

Imaginary part is related to dielectric losses. In Comsol convention, negative imaginary part means losses, and positive imaginary part means material gain. So, your material air (real part of relative permittivity is equal to one) with small losses.

Regards,
Sergei

Thank you again sir,

If I have in my parameter list parameters that depend on frequency, how I am going to define frequency in those parameters?

For example: omega=2*pi* frequency

By setting a range of frequencies in the study: range( 4[THz], 0.5[THz], 6[THz])

What should frequency be defined in the above example?

(should it be 2*pi*freq? or is it something else that the comsol defines frequency?)

Thank you again.

Constantinos,

Comsol uses variable “emw.freq” for frequency. By setting a range of frequencies in the study: range( 4[THz], 0.5[THz], 6[THz]) means that variable emw.freq changes according to the specified range.


If, for example, you have frequency dependent relative permittivity, then you could use Model Definitions>Functions>Interpolation options to define two functions “eps_real” and “eps_imag” for real and imaginary parts of relative permittivity. Then, in the Materials node, complex valued frequency-dependent relative permittivity will be specified as:

epsr=eps_real(emw.freq)-j*eps_imag(emw.freq)


Regards,
Sergei