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No metal boundaries ==> hybrid modes beam waveguide

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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No metal boundaries ==> hybrid modes beam waveguide

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  1. No metal boundaries ==> hybrid modes beam waveguide

  2. y Waveguides x z

  3. 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

  4. Can we find a radial field distribution that will repeat itself? How about the phase? z – zo z z + zo

  5. r j Cylindrical Waves

  6. Assume no j dependence Jm is mth-order Bessel function

  7. Due to no boundaries, g is not discrete. Continuous spectrum of g values. Propagation mainly along z axis.

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

  9. z – zo z z + zo Identify this as the Hankel transform of.

  10. z – zo z z + zo inverse Hankel transform leads to Loss can be calculated by integrating from R to 

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

  12. z – zo z z + zo Integral over g can be done.

  13. z – zo z z + zo

  14. Phase shift - lens or mirror z – zo z z + zo Normal wave propagation

  15. 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?

  16. a Gaussian

  17. 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

  18. z Surface wave guided by a dielectric above a conductorTM mode Dielectric -- thickness d Metal conductor

  19. 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

  20. Dielectric -- thickness d Metal conductor z Surface wave guided by a dielectric above a conductorTM mode

  21. Dielectric -- thickness d Metal conductor z Surface wave guided by a dielectric above a conductorTM mode

  22. Dielectric -- thickness d Metal conductor z Surface wave guided by a dielectric above a conductorTM mode

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