Have a look at the V parameter defining your waveguide. Apart from this, to have TIR guidance, the effective refractive index has to be properly defined. If all confinement loss and dispersive nature are accounted for, it is possible to have this mode.

@Rajib Biswas,

Thank you so much, In fact, it is difficult to define the V parameter for this since this is glass tube.

That is why we just observed the homogeneous electric field pattern by COMSOL to identify HE11-like mode.

We could get homogeneous-like (HE11-like) pattern for small inner-radius, but that distort when the inner-radius increases.

We need to see the HE11 mode of the glass tube by COMSOL. Please suggest if someone has done this simulation.

Is it possible to restrict the COMSOL solver to a defined range of effective indices?

For a mode to be bound by total internal reflection, the effective index must be lower than the index of the glass, and higher than the air cladding surrounding the tube. It follows that the field inside the hollow bore of the tube will be evanescent, with an imaginary transverse propagation constant.

A reasonable first estimate of the effective index can be made by solving the scalar wave equation for the tube. For the lowest order mode in this approximation, the field inside the tube is described by a modified Bessel function of the first kind

ψ(r) = c0 I0(ζr) (r

@ Alan Robinson ,

Thank you so much for the complete answer. That is very useful to enhance my knowledge.

To be honest we do not know how to restrict the neff with COMSOL and we also seeking a way to do that. Because, we have to increase the “desired number of modes” until the desired mode is shown.

I am sending some of the the simulated results herewith. Please help us to find the correct neff to FSM of PCF cladding.

Thank you so much again.

@ Udaya Rahubadde

I don't have experience of photonic crystal fibres. My work has largely been with conventional cylindrically symmetrical silica-based fibres.

Regarding your glass tube simulations, what is the horizontal scale of the images in your document?

Does the inner circle on the second row show the 0.36 μm tube bore? If so, it seems that you are showing only the central 3 μm diameter of the 6 μm tube. Is the first row (0.30 μm bore) shown to the same radial scale? There seems to be a sharp singularity at the centre of the waveguide, which seems physically unrealistic. Do you get the same solutions with a finer mesh size?

Do the colours indicate field strength, and what is the scale? Does the field change sign between red and blue, or are the colours adjusted to whatever minimum and maximum values fall within the region displayed?

Have you simulated a glass tube of 3 μm radius with an air cladding, as shown in your first post, or did you impose some other boundary condition such as zero radial field gradient at the outer radius, to emulate propagation in an extended photonic crystal cladding more closely?

For an air-clad silica tube of radius a = 3 μm, the normalised frequency at 700 nm, V = 28.5

To a first approximation we can ignore the central bore, and estimate

U = 2.405 exp(-1/V) = 2.32

Hence W = 28.4 and ζ=W/a = 9.46

The evanescent decay constant ζ is relatively insensitive to the exact value of effective index. The scalar field solution within the central bore is proportional to I0(ζr), so we expect the field to increase from the centre by a factor 1.57 at radius 0.15 μm, and by 1.86 at 0.18 μm.

Within the glass tube wall, the field amplitude will rise to an annular maximum, then fall almost to zero at the outer glass-air boundary.

If instead, you impose an outer boundary condiition of zero normal gradient, the field will be more uniform within the glass, but the modes will have different effective indices.

I am not convinced that this approach will give the answer you are looking for.

Do you have a plausible looking solution for the solid core photonic crystal case? If so, can you calculate the Lorentzian of the field within the core and substitute into the wave equation to estimate the effective index?

Hope this helps.

@ Alan Robinson,

Thank you so much again for the brilliant opinion to learn EM propagation through the glass tube.

Sorry the simulated results are different with the first post.

In the 1st raw, the outer diameter (2a) of the tube 6 μm and the inner diameter (2b) is 0.03 μm.

In the 2nd raw, the outer diameter (2a) of the tube 6 μm and the inner diameter (2b) is 0.36 μm.

Yes, we get the same solutions for 1730 and 28694 (extremely fine) mesh elements.

The mode 1 has another orthogonal mode. But mode 2 and 3 are having circular symmetry with the single radial maximum in the glass region.

Yes the colour indicate the field strength (surface plot/ density plot). Red is maximum and blue is minimum the scale is attached herewith. The 3D plot for the 1st structure is attached here fore your consideration.

@ Udaya Rahubadde

Your figures are colourful, but very difficult to extract quantitative information from. Apart from the intrinsic difficulty, I personally do not have perfect colour vision, so cannot easily distinguish between yellow/green shades.

Are you plotting field amplitude, or a component of the field in a particular direction?

You do not show how the field varies at the outer edge of the 6 μm tube, so I still cannot judge what your boundary conditions are.

Are you able to generate a simple 2-dimensional plot of field strength against radius along a diameter through the tube, including the outer boundary?

For the first mode, it would be useful to do this in two orthogonal directions, aligned with the symmetry axes.

Are the three new Structure?.jpeg images all for 0.03 μm bore tubes? An expanded plot showing the field within the 0.1 μm radius central region would be helpful in this case.

Do the arrows in Structure2.jpeg indicate electric field direction? If so, it looks like a TM0n mode. Probably TM01, though it could be TM02 or higher order, depending on the behaviour at larger radii.

Structure1.jpeg shows two very narrow peaks near the centre. I can't tell whether they are within the bore or just outside, but their presence suggests a strong azimuthal field dependence. I would not expect to see this in the HE11 mode.

@ Alan Robinson,

Dear Professor,

We didn't concern about the colour vision, extremely sorry for that and we are sending the field variation with horizontal distance here with.

Yes, the arrow means electric field.

the colour indicates the amplitude of electric field field= (Ex^2+Ey^2+Ez^2)^0.5

I am sending the amplitude of electric field variation through the horizontal distance.

structure 1,2,3 corresponds to the mode1, mode2, mode 3 of raw 1 (0.03 μm bore tube)

structure 4,5,6 corresponds to the mode1, mode2, mode 3 of raw 2(0.36 μm bore tube)

Thank you

Kind Regards

Udaya

@ Udaya Rahubadde

The colour contour plots are very useful in combination with other information, especially when the direction of the electric field vector is provided. There are traces of the arrows in the 1.pdf document from your second reply, but they were only partially resolved. The field directions were clearer in Structure1.jpeg and Structure2.jpg from your third reply, but were without information as to which modes they described, or sufficient detail at either large radii (>1 μm) or small radii (

@ Added an answer

Thank you so much for the advice to identify the HE11 mode and the other modes.