1. Photonic Crystals: Controlling and Sensing Light for both Evanescent and Propagating Fields Shanhui Fan Department of Electrical Engineering Stanford University Stanford, CA 94305 http://www.stanford.edu/group/fan/ M. F. Yanik, W. J. Suh, X. Yu

2. Photonic Crystals: Background J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature, vol. 386, pp. 143 (1997) Yablonovitch, PRL, 58, 2059 (1987); John, PRL, 58, 2486 (1987).

3. Propagating light v.s. localizing light Wavevector (2  /a) Frequency (c/a)  XM   X M 0.0 0.2 0.4 0.6 0.8 Array of dielectric (Si or GaAs) rods surrounded by air a Operating Wavelength  Within the frequency range of the photonic bands, unusual propagation effects: Self-collimation; Guided Resonance Mirrors and Sensors.  Within the frequency range of the photonic band gap, strong localization of light: Stopping light all-optically.

4. Near-diffractionless propagation of light in a 2D photonic crystal r=0.35a Square array of air holes in Silicon Constant frequency contour, first band M. Notomi, PRB, 62, 10696 (2000)

5. Bends of self-collimated beams  Close to 100% bending efficiency over the entire self-collimation bandwidth.  No backward reflected pulse is observed in the pulse propagation study.  Preservation of beam shapes during the bending process  =45 o Frequency (c/a) Normalized Intensity

6. Splitting self-collimated beams Frequency (c/a) Normalized Intensity  No detailed structural tuning is required in order to accomplish either perfect bends or perfect splitters for self-collimated beams X. Yu and S. Fan, Applied Physics Letters, 83, 3251 (2003) (featured on cover, Oct. 20, 2003)

7. Guided Resonances in Photonic Crystal Slabs Singly degenerate resonance 0 0.1 0.2 0.3 0.4 G XM G Wavevector(2 p /a) 0 1 Intensity in E field Doubly degenerate resonance S. Fan and J. D. Joannopoulos, Phys. Rev. B, vol. 65, art no. 235112, (2002) r=0.2a

8. Direct and indirect transmission pathways r=0.2a Frequency (c/a) Timestep detection point

9. Direct pathwayResonant pathway Relative strength of the two pathways is completely determined by energy conservation and time reversal symmetry. S. Fan, W. Suh, and J. D. Joannopoulos, JOSA A, 20, 569, 2003. Temporal coupled mode theory for Fano resonance crystal slab

10. Broad band reflection from a single dielectric slab W. Suh, M. F. Yanik, O. Solgaard, S. Fan, Applied Physics Letters, 82, 1999 (2003). r=0.4a  >99% reflectivity over a bandwidth of 30nm accomplishable.  Strong in-plane scattering strength leads to wide angular range.  Robust against disorders. Frequency (c/a)

11. Extinction of transmission from a single dielectric slab: experiments and simulations O. Kinic, S. Kim, Y. -A. Peter, W. J. Suh, A. Sudbo, M. F. Yanik, S. Fan and O. Solgaard (submitted)

12. W. Suh, M. F. Yanik, O. Solgaard, S. Fan, Applied Physics Letters, 82, 1999 (2003). Double-slab structure for displacement sensing

13. Detection of lateral shift  Far field coupling insensitive to the lateral displacement  Near field coupling can be used to sense the relatively displacement.  Additional resonance feature introduced when the two slabs are misplaced, leading to sensitive detection of the lateral shift in the transmission spectrum.

14. Strong localization on point defect states Dielectric defect p-state Air defect s-state P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996) radius of defect (c/a) 0.00.10.20.30.4 0.2 0.3 0.4 0.5 Air defect Dielectric defect

15. Towards all-optical coherent stopping and storage of light L. Hau et al, “Light speed reduction to 17 meters per second in an ultracold atom gas”, Nature, vol. 397, pp. 594 (1999) Using electronic coherence Operation condition strongly constrained by atom properties Low temperature, ultra-high vacuum operations Very limited bandwidth, and wavelength flexibilities Can we use optical resonators to stop light? 1  m

16. 101 Gbit/s 10 -2 10 -3 v g /c Bandwidth-delay constraints in resonance structures Photon tunneling between nearest neighbor resonators  k Tunneling rate  Achievable minimum group velocity inversely related to bandwidth. Any meaningful way to stop light must overcome the fundamental bandwidth-delay constraints. Stopping light can not be achieved by static resonator systems. Coupled Resonator Optical Waveguide (CROW) Stefanou et. al. (1998), Yariv et. al. (1999)

17.  System bandwidth;    Photon bandwidth; Photon speed proportional to    General Criterion to Stop Light Tuning an optical system while the photon is in the system!   system photon Requires a system in which the bandwidth can be compressed coherently by an arbitrarily large order of magnitude. M. F. Yanik and S. Fan, Physical Review Letters, (in press, 2004).

18. Tunable Fano Resonance In Optical Resonators Interference between different photon pathways Unlimited bandwidth modulation with small refractive index variation (  n/n<10 -4 ) Frequency Transmission                BB AA

19. Caterpillar Resonator Systems Allows the entire photon pulse to be stored in the system. Bandwidth compression with small refractive index modulation. Exponential reduction in group velocity with linear increase in system complexity. AA BB ’B’B

20.       k    k         k  A B Adiabatic Bandwidth Compression Translationally invariant tuning, preserving the coherent information in the wavevector domain. Adiabatic tuning, preserving the coherent information in the frequency domain.

21. Implementation in photonic crystals

22. 0.8 t pass 2.0 t pass 5.0 t pass 6.5 t pass Input Output FDTD simulations and analytic model Intensity 

23. Immense potentials of stopping light all-optically With modulation rate of 1-10GHz, and with  n/n< 10 -4, assuming a short cavity loss lifetime of 50ns, a three-stage system allow bandwidth compression by 10 10. Enables the use of high-Q cavities to store large bandwidth pulse, greatly enhancing nonlinear effects for broad band pulse. Promise new possiblities for quantum engineering of photons. Complete spectral control of photon pulses, with potentials for novel tailoring of temporal and spectral properties of photons.

24. National Science Foundation David and Lucile Packard Fellowship in Science and Engineering DARPA Center for Integrated System at Stanford University 3M Untenured Faculty Award IBM Special University Research Award Army Research Office Summary  Photonic crystal enables new possibilities for engineering the properties of photons.  New dimensions for molding the spatial, spectral and temporal properties of photons are continuously being discovered, leading to completely novel possibilities for controlling and sensing with light.

25. Characterization of the inherent propagation properties of a self-collimated beam Frequency (c/a) Normalized Intensity crystal L=10*1.414a Dielectric waveguide Detection points (11) direction Number of time steps 0 100,000 Hz (a. u.) Signal pulse Boundary reflection

26. Exploit strong optical confinement for nonlinear applications 10 -3 W input power is sufficient to obtain bi-stable switching in a cavity with Q ~ 5,000 Sufficient for 10 Gbit/s applications For optical bi-stability: Power requirement reduced by ~ Q 2 /V M. Soljacic et al, Physical Review E, 66, 055601 (2002) Material constraints: Kerr nonlinearity: n = n 0 + n 2 * I Instantaneous nonlinearities are weak (AlGaAs, n 2 = 1.5*10 -17 m 2 /W) Maximum index shift allowed:  n/n < 10 -3 ~ 10 -4 Input Power (P 0 )

27. M. F. Yanik, S. Fan, M. Soljacic, Applied Physics Letters, vol. 83, pp. 2739-41 (2003) Ultra-high-contrast digital switching in photonic crystals Input Power (P 0 ) Time (  ) Low transmission state High transmission state

28. 3D Large-angle Self-Collimation Phenomena  3D image transfer. J. Shin and S. Fan, (unpublished)