The V-number, represented by V, is a dimensionless parameter used in optical fiber and waveguide technology. It is calculated as the ratio between the core radius of an optical fiber and its numerical aperture (NA). The V-number provides valuable information about the fiber's ability to capture and transmit light efficiently.
The V-number is also called a "normalized frequency" because it represents the frequency of light propagating through an optical fiber or waveguide in a normalized or dimensionless form. The V-number, or a normalized frequency, can be calculated using the formula:
where NA represents the numerical aperture and a denotes the radius of the fiber core.
For a step-index fiber,
Take,
Multiplying and dividing by 2 n1,
Substituting in the equation for V-number,
where a is the radius of the fiber core, λ is the free-space wavelength, n is the average refractive index of the core and cladding, i.e., n=(n1+n2)/2, and ∆ is the normalized index difference, that is
The V-number is directly proportional to the core radius, meaning that as the core radius increases, the V-number increases, and when the core radius decreases, the V-number decreases. Therefore, as the V-number is reduced by decreasing the core size, it eventually reaches a critical value of approximately 2.405.
When the V-number is less than 2.405, there is only one mode, the fundamental mode (LP01) that can propagate through the fiber core. As V is reduced further by reducing the core size, the fiber can still support the LP01 mode, but the mode extends increasingly into the cladding. The finite cladding size may then result in some of the power in the wave being lost. A fiber that is designed to allow only the fundamental mode to propagate at the required wavelength is called a single-mode fiber (SMF). Typically, single-mode fibers have a much smaller core radius and a smaller ∆ than multi-mode fibers (MMFs). If the wavelength λ of the source is reduced sufficiently, a single-mode fiber will become multimode as V will exceed 2.405; higher modes will also contribute to propagation. The cutoff wavelength λc above which the fiber becomes single mode is given by,
When the V-parameter increases above 2.405, the number of modes rises sharply. A good approximation to the number of modes M in a step-index multimode fiber is given by,
Significance of V-Number
Optimizing V-Number for Performance
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