# Polarization of elliptical fiber modes

• Sciencestd
In summary, the three modes in an elliptical fiber with a core of that type will have linear polarization in either the x or y plane, depending on the V-number value.
Sciencestd

If I have three modes in an optical fiber with elliptical facet as shown in the figure, what would be the polarization direction of the modes... what I know that it is linear polarization and could have several configuration.. but what I want really to know that if could be a situation where the oscillation of the modes are in the same time in the same direction.. or if the polarization in middle mode points up then the sides modes point down and vice versa..?!

You say you have three modes as shown in the figure as if the figure shows three modes. You understand that that picture would only be one of the three modes, right? Also, that picture doesn’t seem right in that the higher order modes should show lobes along the long axis shouldn’t they?

Look at figure 6 in this reference:
https://www.ijert.org/research/fem-study-of-elliptical-coreoptical-fibres-IJERTV2IS70065.pdf
That’s what the modes usually look like in a three mode elliptical fiber.

Given a large enough core compared to the wavelength you can certainly have a mode like you show but then there would be many more allowed modes because you would have more than three transverse modes in the other dimension and all combinations of those orthogonal indices.

In a three mode fiber generally all of the modes can have linear polarization on either axis. The reason you don’t get a combination of those polarizations such as 45 degree linear polarization or circular polarization or some arbitrary elliptical polarization is because the manufacturing process of making the core elliptical results in nonuniform stress which in turn causes stress birefringence. The two linear modes travel at such different speeds that the phase between them changes so fast energy can’t couple between them.

For the three lobed mode like you show the direction of polarization will be in the same direction throughout the mode, for example, vertical.

Your question of whether the instantaneous field can be up in one lobe when it down in another is different. With linear polarization the field is oscillating up and down in a plane. It is switching between pointing up and down at terahertz frequencies. Your picture of up and can only be a instantaneous snapshot of the field direction. In that case those aren’t different polarization’s. All lobes are oscillating with the same vertical polarization but the lobes are out of phase.

That also is something that cannot happen in a propagating mode. By definition a transverse mode is a mode that propagates down the fiber without the mode shape changing. If there is a phase variation across the mode, energy will flow in the transverse direction (perpendicular to the phase front, you see) and the transverse shape will change. By definition that is not a mode.

Sciencestd and berkeman
Thank you so much for your detailed answer and the article you shared thank you :)
About the three modes alignment, I think as I read in one article it can be both... along the long axis of the ellipse and also along the short axis... it depends on the V-number value... I don't know actually the exact physical reason why should the lobes change the alignment...

## 1. What is polarization of elliptical fiber modes?

Polarization of elliptical fiber modes refers to the orientation of the electric field vector of a light wave as it propagates through an elliptical fiber. It can be either linear or circular, depending on the shape of the fiber's cross-section.

## 2. How does polarization affect the transmission of light through an elliptical fiber?

The polarization of light can affect the transmission of light through an elliptical fiber in several ways. For example, if the fiber is birefringent (has two different refractive indices for different polarizations), the polarization of the light can determine which path it takes through the fiber and thus affect its transmission. Additionally, the polarization can also affect the coupling efficiency of light into and out of the fiber.

## 3. What are the different types of polarization in elliptical fiber modes?

The two main types of polarization in elliptical fiber modes are linear and circular. Linear polarization refers to the orientation of the electric field vector being either parallel or perpendicular to the long axis of the elliptical fiber. Circular polarization refers to the orientation of the electric field vector being either right-handed or left-handed as the light propagates through the fiber.

## 4. How is the polarization of elliptical fiber modes measured?

The polarization of elliptical fiber modes can be measured using a polarimeter, which is a device that measures the polarization state of light. Another method is to use a polarizer, which only allows light of a certain polarization to pass through, and then analyze the light that passes through using a detector such as a photodiode.

## 5. What are the applications of controlling the polarization of elliptical fiber modes?

Controlling the polarization of elliptical fiber modes has many practical applications. For example, it is used in fiber optic communications to improve the transmission and reception of light signals. It is also important in fiber optic sensors, where the polarization can be used to measure changes in the fiber caused by external factors. Additionally, controlling the polarization can also be used in imaging and microscopy techniques to enhance image contrast and resolution.

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