No metal boundaries ==> hybrid modes beam waveguide

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# No metal boundaries ==> hybrid modes beam waveguide - PowerPoint PPT Presentation

No metal boundaries ==> hybrid modes beam waveguide. y. Waveguides. x. z. modes. E z = 0 and H z = 0 ==> TEM mode - plane wave - ideal coax or strip line E z = 0 and H z  0 ==> TE mode E z  0 and H z = 0 ==> TM mode E z  0 and H z  0 ==> hybrid mode.

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## PowerPoint Slideshow about 'No metal boundaries ==> hybrid modes beam waveguide' - terence-shirley

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Presentation Transcript

y

Waveguides

x

z

modes
• Ez = 0 and Hz = 0 ==> TEM mode - plane wave - ideal coax or strip line
• Ez = 0 and Hz 0 ==> TE mode
• Ez 0 and Hz = 0 ==> TM mode
• Ez 0 and Hz 0 ==> hybrid mode

Can we find a radial field distribution that will repeat itself? How about the phase?

z – zo

z

z + zo

r

j

Cylindrical Waves

Assume no j dependence

Jm is mth-order Bessel function

Propagation mainly along z axis.

z – zo

z

z + zo

Periodic means field distribution at z = -zo is the same as at z = + zo.

z – zo

z

z + zo

Identify this as the Hankel transform of.

z – zo

z

z + zo

Loss can be calculated by integrating from R to 

z – zo

z

z + zo

Periodic means field distribution at z = -zo is the same as at z = + zo.

z – zo

z

z + zo

Integral over g can be done.

z – zo

z

z + zo

Phase shift - lens or mirror

z – zo

z

z + zo

Normal wave propagation

z – zo

z

z + zo

Is there a function that is a Hankel transform of itself?

Is there a function that is a Fourier transform of itself?

Is there a function that is a Hankel transform of itself?

a Gaussian x Laguerre polynomial

Is there a function that is a Fourier transform of itself?

a Gaussian x Hermite polynomial

Weber function

Dielectric -- thickness d

Metal conductor

z

Surface wave guided by a dielectric above a conductorTM mode
• Obtain Ez in the dielectric and in the vacuum
• Assume Ez goes to 0 as y