TE and TM modes in an optical fibre do not have a uniform linear polarisation direction, so cannot be described as horizontal or vertical.

In TE modes, the electric field vector is everywhere transverse and perpendicular to the waveguide axis.  In TM modes, the magnetic field is transverse.

In a circular dielectric waveguide such as an optical fibre, the electric field of the TM modes is largely radial with a small axial component, and the transverse magnetic field is circumferential.  For TE modes, the magnetic field is radial, and the electric field direction circular.  In both TE and TM modes, the transverse field components are zero at the centre of the fibre.

See slides 19 and 25 here: https://www.slideshare.net/byomakesh_22/mode-pptbmk

Most of the modes supported by a circular optical fibre, including the fundamental, are hybrid modes.  The commonly used LP modes are solutions of the scalar wave equation, and not true eigenmodes, except in the limit where the core-cladding index difference tends to zero.  In practice, they are a good approximation for the small index differences used in practice.

The fundamental LP01 mode corresponds to the hybrid HE11 solution to the vector wave equation.

The first order LP11 mode is a superposition of the TE01, TM01 and HE21 modes.

Thank you so much. it is very useful answer for me.  Could you please tell me how to find the mesh size for FEM simulations. I know the mesh size must be smaller than the working wavelength. but COMSOL takes more longer time to simulate such problem. Please help me to solve this problem. Thank you again.

TE and TM is used to describe polarization relative to a device (modes in a waveguide, waves incidence onto a surface, etc.), while vertical and horizontal describe polarization relative to the ground.

Thanks Alan, so does a TE or a TM mode have a vertical and a horizontal polarization component, as in does one TE mode contain two orthogonal polarizations which can be used to transmit two different signals?

I just want to know how using TE and TM modes for mode division multiplexing differs from using orthogonal polarization multiplexing? can they be used at the same time?

Also is the case similar for rectangular silicon photonic waveguides?

TE and TM modes only truly exist inside metal waveguides with a homogeneous fill.  Otherwise, they do not.  They are, however, very good approximations and are called quasi-TE and quasi-TM modes.  In optical fibers we have LP modes.

@Raymond Rumpf - can you explain or provide a reference for why TE and TM modes do not exist in a metal-free optical fibre?

As stated in my previous response, LP modes of a cylindrical dielectric waveguide are solutions of the scalar wave equation and are approximations.  Strictly speaking, they are only valid in the weakly guiding limit where the core-clad index difference tends to zero, although they are sufficiently accurate for many practical applications.

In circular core fibres there are exact TE and TM solutions, but most modes are hybrid HE and EH modes.

See for example slides 3.63 - 3.65 here: http://people.ee.ethz.ch/~fyuriy/oe/oe_optcom_chapters/Optoelectronics_2010_Ch03.pdf

There is a more detailed explanation in Chapter 11 of A. W. Snyder & J. D. Love's "Optical Waveguide Theory" (1983).  The analytic solutions for each family of modes in step index fibres are listed in table 12.3.  TE, TM and hybrid modes of a graded profile fibre are discussed in sections 12.16, 12.17 and 12.18.  Chapter 31 describes the derivation from Maxwell's equations, with a discussion of the weak guidance approximation in chapter 32.  http://www.springer.com/gb/book/9780412099502

@Sahil Sakpal

A TE mode is not easily split into horizontal or vertically polarised components. It is a single unique eigenmode, not a degenerate pair of modes with identical propagation constants and orthogonal polarisation states, such as the fundamental HE11 mode.

As I explained, the electric field vector in TM modes is radial, while E field lines are approximately circular in TM modes.  When you launch a linearly polarised signal, you will, in general, excite a combination of TE, TM, HE and EH modes.  These propagate at different speeds, so during propagation the mode field distribution and the polarisation state will evolve.

To launch a TE or TM mode you would need to match both the mode field distribution and the spatial variation in polarisation orientation over the fibre cross-section.  I have not considered how to achieve this.

Fortunately, the velocity differences between the true modes comprising an LP approximation are small in typical low NA fibres, and the linearly polarised approximation works pretty well.  In practice, there will be coupling between polarisation states and between modes - arising both from fibre and cable imperfections and from induced bends and stresses in a deployed cable.  It may be difficult to separate such extrinsic coupling mechanisms from mode crosstalk due to intrinsic velocity differences between TE, TM and hybrid components.

What type of fibre do you intend to use for your mode and polarisation multiplexing?  Have you decided which modes would you excite?

@ Udaya Rahubadde 

I have not used Comsol for waveguide simulations, so I can't offer much help.  The usual suggestion is to start with a moderately coarse mesh and refine it until changes in the solution become sufficiently small for your purposes.

For scalar wave solutions in circular waveguides, it is often possible to take account of cylindrical symmetry and reduce the wave equation from 2D to 1 dimension by first selecting an azimulthal mode order and imposing a (sin / cos (m theta)) azimuthal variation.  With a uniform cladding refractive index, the field of a bound mode is described by a modified Bessel function of the the second kind and integer order m, so the radial wave equation need only be solved explicitly within the core.  Less straightforward if you need a vector solution, unfortunately.

@ Sahil Sakpal  "Also is the case similar for rectangular silicon photonic waveguides?"

Not something I have thought about in detail, but my guess is that you may not get true TE and TM modes, but I would expect the modes to be predominantly linearly polarized, with E-field largely aligned with the sides of the rectangular cross-section.

Asymmetry between horizontal and vertical polarizations will break the degeneracy between polarisation states found in circular or square core fibres, and will help to reduce polarisation coupling - as in the case of polarisation-maintaining fibre.

Hello to All, i got some results of optical ring resonator from Lumerical FDTD Soln software. My question is how can one distinguish between TM and TE mode by simply visualizing its intensity graph

Usually the TE mode is visually well rounded and TM mode is vertically squeezed, which is mostly seen in plasmonic modes.

TE and TM modes only exist in certain waveguides with mostly homogeneous dielectrics.  Otherwise they are hybrid modes and contain all six field components.  In dielectric waveguides the modes are mostly linearly polarized and analysis can be approximated this way, although it is not strictly true.  These are usually called LP modes.  Your optical source is probably linearly polarized.  If you excite a waveguide with this linear polarization aligned at 45 degrees with respect to the waveguide, half of your power will go into one LP mode and half into the other.  The important thing to consider is whether the waveguide actually supports both LP modes.  If not, half your source power will go into one guided mode and the other half of your power will escape.  There is also the losses associated with butt coupling.  If the mode from your source does not look similar to the mode in the waveguide or it is not well aligned, you will get some scattering losses as well.

What are the advantages of the TE mode of propagation of light over the TM mode in a slot waveguide?