1 / 53

Michael Scalora U.S. Army Research, Development, and Engineering Center

OPTICS BY THE NUMBERS L’Ottica Attraverso i Numeri. Michael Scalora U.S. Army Research, Development, and Engineering Center Redstone Arsenal, Alabama, 35898-5000 & Universita' di Roma "La Sapienza" Dipartimento di Energetica. Rome, April-May 2004. BPM:Propagation in Planar Waveguides

moira
Télécharger la présentation

Michael Scalora U.S. Army Research, Development, and Engineering Center

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. OPTICS BY THE NUMBERS L’Ottica Attraverso i Numeri Michael Scalora U.S. Army Research, Development, and Engineering Center Redstone Arsenal, Alabama, 35898-5000 & Universita' di Roma "La Sapienza" Dipartimento di Energetica Rome, April-May 2004

  2. BPM:Propagation in Planar Waveguides Retarded Coordinate trasformation: time dependence, Raman scattering, self-phase modulation in PCFs

  3. Study the transmissive properties of guided modes. 5 mm air core 14 mm Propagation into the page fig.(4)

  4. Assuming steady state conditions…

  5. Wave front does not distort: Plane Wave propagation Diffraction is very important

  6. This equation is of the form: Where: Using the split-step BPM algorithm

  7. Example: Incident angle is 5 degrees b=1mm a=1.4mm Assume c(3)=0

  8. The cross section along x renders the problem one-dimensional in nature x

  9. Transmissive properties in the linear (low intensity) regime For two different fibers. We set c(3)=0

  10. Field tuning corresponds to High transmission state. Direction of propagation

  11. Same as previous figure.

  12. Same as previous figure.

  13. For the example discussed: 5-mm guide ~ 8 minutes on this laptop 3.2GHz, 1Gbts RAM

  14. If c(3) is non-zero, the refractive index is a function of the local intensity. Solutions are obtained using the same algorithm but with a nonlinear potential.

  15. Optical Switch 5 mm air core 14 mm fig.(4)

  16. The band shifts because the location and the width of each gap depends on the exact values of n2 and n1, and on their local difference.

  17. fig.(5a)

  18. Optical Switch on off fig.(5b)

  19. on off fig.(6)

  20. Retarded coordinate Transformation

  21. N.B.:An implicit and important assumption we have made is that one can go to a retarded coordinate provided the grating is shallow so that a group velocity can be defined unumbiuosly and uniquely. In other words, the effect of the grating on the group velocity is scaled away into an effective group velocity v. It is obvious that care should be excercised at every step when reaching conclusions, in order to properly account for both material index and modal dispersion, if the index discontinuity is large.

  22. Symplifying and Dropping all Higher order Derivatives…

  23. Now we look at the linear regime, by injecting a beam inside the guide from the left and then from the right.

  24. Input Spectrum ON-AXIS I 1013 W/cm2 n2  510-19 cm2/W L  8 cm t  100 fs Output Spectrum w/w0 Propagating from left to right the pulse is tuned on the red curve, igniting self-phase modulation, and the spectral shifts indicated on the graph. A good portion of the input energy is transmitted. Spectra are to scale. Fig. 4

  25. Propagation from right to left does not induce nonlinearities because the light quickly dissipates. The pulse is tuned with respect to the blue curve. Spectra are to scale. Fig. 4

  26. Initial pulse profile Final profile

  27. Spectrum of the pulse as it propagates. Note splitting. Initial profile

  28. Self-phase modulation A process whereby new frequencies (or wavelengths) are generated such that: Example: input 100fs pulse at 800nm is broadened by ~30nm

  29. Stimulated Raman Scattering

  30. The simplest case Raman Soliton: A sudden relative phase shift between the pump and the Stokes at the input field generates a “phase wave”, or soliton, a temporary repletion of the pump at the expense of the Stokes intensity

  31. The simplest case The Input Stokes field undergoes a p-phase shift The gain changes sign temporarily, For times of order 1/g; The soliton is the phase wave

  32. The Pump signal is temporarily repleted The Stokes minimum is referred to as a Dark Soliton

  33. PUMP FIELD z,t=0,0 z,t=L,0 z=0

  34. PUMP FIELD

  35. STOKES FIELD

  36. PUMP FIELD

  37. STOKES FIELD

  38. The onset of diffraction causes the soliton to decay… …almost as expected. Except that…

  39. … the Stokes field undergoes significant replenishement on its axis, as a result of nonlinear self focusing

  40. PUMP FIELD

  41. STOKES FIELD

  42. PUMP FIELD

More Related