Photonic Crystals: Controlling and Sensing Light for both Evanescent and Propagating Fields

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. 0.8 0.6 Frequency (c/a) a 0.4 M 0.2 X G 0.0 G X M G Operating Wavelength l Wavevector (2p/a) • 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. Propagating light v.s. localizing light Array of dielectric (Si or GaAs) rods surrounded by air

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

5. =45o Normalized Intensity Frequency (c/a) 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

6. Splitting self-collimated beams Normalized Intensity Frequency (c/a) • 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 Doubly degenerate resonance r=0.2a 1 0.4 0.3 Singly degenerate resonance 0.2 0 0.1 0 G X M G Wavevector(2p/a) Intensity in E field S. Fan and J. D. Joannopoulos, Phys. Rev. B, vol. 65, art no. 235112, (2002)

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

9. Temporal coupled mode theory for Fano resonance crystal slab Direct pathway Resonant 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.

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

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

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 0.5 Air defect Dielectric defect 0.4 0.3 0.2 0.0 0.1 0.2 0.3 0.4 radius of defect (c/a) Air defect Dielectric defect s-state p-state P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996)

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

16. k 10-2 10-3 Gbit/s 1 10 Bandwidth-delay constraints in resonance structures Photon tunneling between nearest neighbor resonators w Tunneling rate vg/c Coupled Resonator Optical Waveguide (CROW) Stefanou et. al. (1998), Yariv et. al. (1999) • 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.

17. General Criterion to Stop Light • Tuning an optical system while the photon is in the system! dw dW photon system dW:System bandwidth; d:Photon bandwidth; Photon speed proportional to d. • 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. wB A< B wA Transmission A= B A> B Frequency Tunable Fano Resonance In Optical Resonators • Interference between different photon pathways • Unlimited bandwidth modulation with small refractive index variation (dn/n<10-4)

19. Caterpillar Resonator Systems w’B wB wA • 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.

20. B A + A=B ~ A-B 2b - k k Adiabatic Bandwidth Compression • Translationally invariant tuning, preserving the coherent information in the wavevector domain. • Adiabatic tuning, preserving the coherent information in the frequency domain. + ~ B-A - k

21. Implementation in photonic crystals

22. Input Output 0.8 tpass 2.0 tpass 5.0 tpass 6.5 tpass FDTD simulations and analytic model Intensity dw/b

23. Immense potentials of stopping light all-optically • With modulation rate of 1-10GHz, and with dn/n< 10-4, assuming a short cavity loss lifetime of 50ns, a three-stage system allow bandwidth compression by 1010. • 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. 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. National Science FoundationDavid and Lucile Packard Fellowship in Science and EngineeringDARPACenter for Integrated System at Stanford University3M Untenured Faculty AwardIBM Special University Research AwardArmy Research Office

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

26. Exploit strong optical confinement for nonlinear applications Material constraints: Kerr nonlinearity: n = n0 + n2 * I Instantaneous nonlinearities are weak (AlGaAs, n2 = 1.5*10-17 m2/W) Maximum index shift allowed: dn/n < 10-3 ~ 10-4 For optical bi-stability: Power requirement reduced by ~ Q2/V 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 Input Power (P0) M. Soljacic et al, Physical Review E, 66, 055601 (2002)

27. Ultra-high-contrast digital switching in photonic crystals High transmission state Input Power (P0) Low transmission state Time (g) M. F. Yanik, S. Fan, M. Soljacic, Applied Physics Letters, vol. 83, pp. 2739-41 (2003)

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