## Modes

A set of guided electromagnetic waves is called the modes of an optical fiber.

Maxwell's equations describe electromagnetic waves or modes as having two components. The two components are the electric field, E(x, y, z), and the magnetic field, H(x, y, z). The electric field, E, and the magnetic field, H, are at right angles to each other. Modes traveling in an optical fiber are said to be transverse.

The transverse modes, shown in the picture below, propagate along the axis of the fiber. The mode field patterns shown in this illustration are said to be transverse electric (TE). In TE modes, the electric field is perpendicular to the direction of propagation.

The magnetic field is in the direction of propagation. Another type of transverse mode is the transverse magnetic (TM) mode. TM modes are opposite to TE modes. In TM modes, the magnetic field is perpendicular to the direction of propagation. The electric field is in the direction of propagation. The picture below shows only TE modes.

Transverse electric (TE) mode field patterns.

The TE mode field patterns shown in the picture above indicate the order of each mode. The order of each mode is indicated by the number of field maxima within the core of the fiber. For example, TE0 has one field maxima. The electric field is a maximum at the center of the waveguide and decays toward the core-cladding boundary. TE0 is considered the fundamental mode or the lowest order standing wave. As the number of field maxima increases, the order of the mode is higher. Generally, modes with more than a few (5-10) field maxima are referred to as high-order modes.

The order of the mode is also determined by the angle the wavefront makes with the axis of the fiber. The next picture shown below illustrates light rays as they travel down the fiber. These light rays indicate the direction of the wavefronts. High-order modes cross the axis of the fiber at steeper angles. Low-order and high-order modes are also shown in the picture below.

Low-order and high-order modes.

Before we progress, let us refer back to the illustration above on "Transverse electric (TE) mode field patterns".

Notice that the modes are not confined to the core of the fiber. The modes extend partially into the cladding material. Low-order modes penetrate the cladding only slightly. In low-order modes, the electric and magnetic fields are concentrated near the center of the fiber. However, high-order modes penetrate further into the cladding material. In high-order modes, the electrical and magnetic fields are distributed more toward the outer edges of the fiber.

This penetration of low-order and high-order modes into the cladding region indicates that some portion is refracted out of the core. The refracted modes may become trapped in the cladding due to the dimension of the cladding region. The modes trapped in the cladding region are called cladding modes. As the core and the cladding modes travel along the fiber, mode coupling occurs. Mode coupling is the exchange of power between two modes. Mode coupling to the cladding results in the loss of power from the core modes.

In addition to bound and refracted modes, there are leaky modes.

Leaky modes are similar to leaky rays. Leaky modes lose power as they propagate along the fiber. For a mode to remain within the core, the mode must meet certain boundary conditions. A mode remains bound if the propagation constant beta meets the following boundary condition:

where n1 and n2 are the index of refraction for the core and the cladding, respectively. When the propagation constant becomes smaller than 2pin2/lambda, power leaks out of the core and into the cladding. Generally, modes leaked into the cladding are lost in a few centimeters. However, leaky modes can carry a large amount of power in short fibers.

NORMALIZED FREQUENCY

Electromagnetic waves bound to an optical fiber are described by the fiber's normalized frequency.

The normalized frequency determines how many modes a fiber can support. Normalized frequency is a dimensionless quantity.

Normalized frequency is also related to the fiber's cutoff wavelength. Normalized frequency (V) is defined as:

where n1 is the core index of refraction, n2 is the cladding index of refraction, a is the core diameter, and lambda is the wavelength of light in air.

The number of modes that can exist in a fiber is a function of V. As the value of V increases, the number of modes supported by the fiber increases. Optical fibers, single mode and multimode, can support a different number of modes.

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