Generally light rays propagate within different media at different velocities. It seems too, as though different media resist light propagation with different strengths. The characteristic that describes this property of a medium is called the refractive-index which is the ratio of the velocity of light in a vacuum to the velocity of light in the medium. The mathematical expression is given by:
In
general, when a light beam strikes of boundary of two media, the incident beam
splits into two beams called reflected and refracted beams. Snell's law gives
the rules defining the directions of the incident reflected and refracted beams:
A
special case, when light travels from a medium with a higher refractive index
to a medium with a lower refractive index and it strikes the boundary at more
than the critical angle (at which the angle of refractive equals to 90 degree),
all light will be reflected back to the incident medium, meaning it will not
penetrate the second medium. This phenomenon is called total internal reflection,
what keeps light inside an optical waveguide. To meet this requirement, the
condition is often described in term of critical incident angle and critical
propagation angle [9].
The
critical propagation angle (αc) is the angle the beam makes with the centerline
of the optical waveguide. The critical incident angle (
At
this point, to save the light inside an optical waveguide, we need to have it
strike the core cladding boundary at the critical incident angle (θIC) or above it, in order to provide total internal reflection
of this light: to make light fall at or above that angle, we have to direct it
so that it is at or below the critical propagation angle (
There is another angle associated with the propagation of light through waveguides, known as the acceptance angle. The acceptance angle is the maximum allowable angle of the incident ray coming into the waveguide structure from outside with respect to the optical axis of the waveguide so that light rays can able to meet the total internal reflection conditions inside the waveguide. The well-known term numerical aperture describes the ability of an optical fiber to gather light from a source and then the ability to preserve this light inside the fiber because of the total internal reflection. The numerical aperture is closely related to acceptance angle and described as-
All the terms like critical
angle, critical propagation angle, acceptance angle, numerical aperture etc.
are associated with the coupling of light from optical source to the waveguide.
When the EM light rays enter
the optical waveguide, an EM wave propagating inside an optical fiber has to
meet the boundary conditions requirements (already have been illustrated).
Suppose the wave meets these requirements when it strikes the core-cladding
interface the first time. To meet these requirements at all other times, the
wave must repeat itself when striking the core-cladding boundary again. EM
waves that meet this requirement will exist as a stable pattern otherwise will
not appear. Therefore the EM waves can propagate within a light-guide structure
not as a continuum but as a set of discrete field patterns, naturally called
modes. The number of modes in a waveguide is determined by the normalized
frequency parameter V which is often called V number. This number is equal to
[10]:
Thus at a specific wavelength, one can control the
number of modes by choosing diameter(fiber) or dimension(rectangular waveguide)
a and n1-n2
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