About: Waveguide modes

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From Maxwell's equations, the field equation of a plane wave propagating along a waveguide can be derived, in terms of the spatial dimensions , and , and the temporal dimension , as where is the 2-dimensional cross-section of the distribution of the electromagnetic field, is the propagation constant, and is the angular frequency of the wave excitation in units of radians (with being the frequency in hertz). Technical names exist for each term in the equation: * is called the transverse term * is known as the phase term * is the harmonic term

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rdfs:label	Waveguide modes
rdfs:comment	From Maxwell's equations, the field equation of a plane wave propagating along a waveguide can be derived, in terms of the spatial dimensions , and , and the temporal dimension , as where is the 2-dimensional cross-section of the distribution of the electromagnetic field, is the propagation constant, and is the angular frequency of the wave excitation in units of radians (with being the frequency in hertz). Technical names exist for each term in the equation: * is called the transverse term * is known as the phase term * is the harmonic term
dcterms:subject	ELEC3115
abstract	From Maxwell's equations, the field equation of a plane wave propagating along a waveguide can be derived, in terms of the spatial dimensions , and , and the temporal dimension , as where is the 2-dimensional cross-section of the distribution of the electromagnetic field, is the propagation constant, and is the angular frequency of the wave excitation in units of radians (with being the frequency in hertz). Technical names exist for each term in the equation: * is called the transverse term * is known as the phase term * is the harmonic term Note that the wave propagation is in the -direction, and since the cross-sectional field pattern is normally assumed constant, it is therefore customary to express the wave equation without and dependence as where only the phase changes along the waveguide axis (-direction). By comparing this with the general equation for wave propagation , where is the velocity of the propagation, it is simple to define the propagation velocity of the wave as Recalling that the speed of light in a specific material (i.e. the waveguide) of refractive index is given by where m/s is the speed of light in free space, and is the free space wavenumber (with being the wavelength), we see that , or put another way, the effective refractive index of the waveguide is which always satisfies < < , where and are the refractive indices of the waveguide cladding and core, respectively.

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