Some of the applications of Photonic Crystals by

Some of the applications of Photonic Crystals (by no means a complete overview) Prof. Maksim Skorobogatiy École Polytechnique de Montréal

Hollow planar waveguides, resonators

Planar antiresonant reflecting optical (ARROW) waveguides, Si. N/Si. O 2 (2. 1/1. 46) dc~3. 7 mm 12 mm 1 l Ca pil lar ay Sensor applications - putting the light where the analyte (gas) is er 2 l ay ers 3 l ay e rs D. Yin et al. 14 June 2004 / Vol. 12, No. 12 / OPTICS EXPRESS 2710 y

Tunable multichannel optical filter based on silicon photonic band gap materials actuation Elastic deformation of a membrane by applying voltage Membrane Tuneable air gap Si Si. O 2 PBG Excitation of a defect mode in the air gap Y. Yi Et Al. , Applied Physics Letters Volume 81, Number 22 25 November 2002

Coupling to PC components from conventional WG and fibers

Coupling to photonic crystals from conventional WG and fibers External focused beam ( e = 12, r=0. 2 a, h=2 a) Extended field coupling, external beam - PCWG 0. 6 light cone 0. 5 Fiber mode Direct coupling Fiber mode PCWG mode frequency (c/a) Extended field coupling 0. 4 0. 3 0. 1 0 PCWG mode Evanescent field coupling Evanescent field, and direct coupling, fiber - PCWG 0. 2 odd (TM-like) bands even (TE-like) bands G X M TM-like gap G

Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals Wrong taper, tapered PC mirror has a PBG at the WG transmission frequency Correct taper, an “unzipping” PC Mirror Butt coupled waveguide and a 2 D Pxtal S. G. Johnson et al. PHYSICAL REVIEW E 66, 066608 2002

Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high -Q cavities Point where fiber mode is phase matched with a PC WG mode Barclay et al. , J. Opt. Soc. Am. B/Vol. 20, No. 11/November 2003

Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal Position of a waveguide has to be chosen accordingly as to guarantee a high quality factor of the WG – resonator system Line defect (removed rod) and a point defect are designed to operate at a common frequency of interest M. Okano et al. , PHYSICAL REVIEW B 68, 235110 ~2003!

Anomalous PC Refraction

Ultracompact high-efficiency polarizing beam splitter with a hybrid photonic crystal and conventional waveguide structure Ez(TM) No phase matching between an incident WG mode and an extended PC mode. Hz(TE) Incident WG mode is phase matched to an an extended PC mode + Brewster angle kin Constant frequency contours kparallel S. Kim et al. , OPTICS LETTERS / Vol. 28, No. 23 / December 1, 2003

Aperiodic nanophotonic design - do we really need a PC to stay cool PC’s can be designed to refract the beam in a complex way Aperiodically positioned scatterers can do the same job even better I. L. Gheorma Et Al. , Journal Of Applied Physics Volume 95, Number 3 1 February 2004

Resonant leaky modes above the cladding light line. Lasing. ( e = 12, r=0. 3 a, h=0. 5 a) light cone Truly guided modes below the light line Resonant leaky modes above the light line odd (TM-like) bands even (TE-like) bands G M K TE-like gap G

Waveguide tapers and waveguide bends in Al. Ga. Asbased two-dimensional photonic crystals (e-beam) He. Ne Propagation in resonant modes above the light line ecore=3. 4 quantum dot with a broad band emission exp theory exp 2 mm PBG Dinu et al. Appl. Phys. Lett. , Vol. 83, No. 22, 1 December 2003 theory

Laser action from two-dimensional distributed feedback in photonic crystals (laser dye in organic layer, core) light cone Two guided modes in a slab (cladding) Symmetry points of zero group velocity due to band splitting. Standing waves distributed feed back lasing Lasing at M point M. Meier et al. , Applied Physics Letters Volume 74, Number 1 4 January 1999

Evidence for bandedge lasing in a two-dimensional photonic bandgap polymer laser resonant leaky modes above the light line TE TM (organic gain media, core) clad N. Moll Et Al. , Applied Physics Letters Volume 80, Number 5 4 February 2002

Slow Light

Two-dimensional coupled photonic crystal resonator arrays Very flat bands - considerably reduced group velocity for all directions. Application in optical delay lines, lowtreshold lasers, non-linear phenomena. H. Altug and J. Vuckovic, Applied Physics Letters, Volume 84, Number 2 12 January 2004