The guided wavelength, also known as the wavelength in a waveguide, is a term used in the context of waveguide theory and electromagnetic wave propagation. It represents the effective wavelength of a wave traveling through a waveguide structure, which is different from the free-space wavelength.
In a waveguide, such as a coaxial cable or an optical fiber, electromagnetic waves propagate in a guided mode rather than a free-space mode. The guided mode confines the wave energy within the waveguide structure, allowing for efficient transmission of signals.
The formula for calculating the guided wavelength depends on the type of waveguide and the mode of propagation. Here are a few examples:
Rectangular waveguide: For the dominant mode (TE10 mode), the guided wavelength (λg) can be determined using the following formula:
λg = 2a / √(1 - (λ / λc)^2)
where a is the width of the waveguide and λc is the cutoff wavelength.
Circular waveguide: For the dominant mode (TE11 mode), the guided wavelength (λg) can be calculated using the following formula:
λg = λc / √(1 - (λc / λ)^2)
where λc is the cutoff wavelength and λ is the free-space wavelength.
Optical fiber: In an optical fiber, the guided wavelength depends on the refractive index of the fiber's core and cladding. The relationship between the guided wavelength (λg) and the free-space wavelength (λ) can be determined using the effective refractive index (neff) of the fiber:
λg = λ / neff
The value of neff is determined by the fiber's design and properties.
It's worth noting that these formulas provide approximate values for the guided wavelength, as the exact calculations can be complex and depend on various factors such as boundary conditions, mode profiles, and waveguide geometry. The formulas presented here are simplified versions for commonly used modes in waveguides.