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Velocities in Uniform Dielectrics, Waveguides, and Fibers

This article explores pulse broadening, dispersion, and velocities in uniform dielectrics, metallic waveguides, and fibers. It also discusses the concept of slow light and superluminal pulse velocity in amplifiers.

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Velocities in Uniform Dielectrics, Waveguides, and Fibers

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  1. VELOCITIES 1. Uniform dielectrics, not absorbing 2. Waveguides • Metallic • Fibers 3. In uniform, isotropic saturable gain media 4. In uniform, isotropic saturable absorbers 5. Crystal velocity TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA

  2. Pulse broadening, dispersion, in a uniform dielectric E(t) Broadening and chirping time Electric field amplitude time z = v1t (fast) z = v2t (slow) z = ct

  3. Propagation through medium No change in frequency spectrum W Z=0 z Group delay in uniform dielectric Solution of 2nd order equation To make F.T easier shift in frequency Expand k value around central freq wl Expand k to first order, leads to a group delay:

  4. Group velocity dispersion Expansion orders in k(W)--- Material property

  5. In uniform lossless dielectrics Phase velocity Group velocity (delay) Group velocity dispersion Units mm/fs fs/mm fs2/mm In fibers: ps/(km/nm) Same definitions in transmission lines Not the same in waveguides

  6. VELOCITIES IN WAVEGUIDES a) Metallic b) Fibers

  7. E a) Velocities in metallic waveguides TE: f=0 H TM: f=p Phase velocity: Group velocity:

  8. V = 2.405 Propagation constantb a) Velocities in fibers Simple step index fiber

  9. VELOCITIES 1. Uniform dielectrics, not absorbing 2. Waveguides • Metallic • Fibers 3. In uniform, isotropic saturable gain media 4. In uniform, isotropic saturable absorbers 5. Crystal velocity TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA

  10. Usually described as Pulse velocities in uniform, isotropic saturable gain media k = k’ – i a Phase velocity Group velocity? Wrong! Numerous “slow light” papers dedicated to this concept! Basov – Soviet Physics JETP 23:16-22 (1966) Superluminal pulse velocity in an amplifier. Pulse generated by Q-switching: exponential rise. Pulse front amplified, pulse tail not because of saturation or depletion.

  11. VELOCITIES 1. Uniform dielectrics, not absorbing 2. Waveguides • Metallic • Fibers 3. In uniform, isotropic saturable gain media 4. In uniform, isotropic saturable absorbers 5. Crystal velocity TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA

  12. A B t1 z t =- z/c t = z/c t

  13. t2 t4 t5 A B t1 z t3 t =- z/c t = z/c t

  14. t3 A B t1 z t2 t =- z/c t = z/c t

  15. VELOCITIES 1. Uniform dielectrics, not absorbing 2. Waveguides • Metallic • Fibers 3. In uniform, isotropic saturable gain media 4. In uniform, isotropic saturable absorbers 5. Crystal velocity TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA

  16. Uniaxial crystals ne does not depend on j

  17. E Uniaxial crystals Walk-off angle: Equation of the index ellipse: z k no E ne (q) D q E x H = s b ne x, y or r

  18. qc z k no E ne (q) q b ne x, y or r E L Orienting Uniaxial crystals

  19. Velocities in Uniaxial crystals qc z E E no vp = c/ne (q) q k b ne vr = ray velocity x, y or r L

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