PHOTONIC STRUCTURES FROM LCPOLYMER COMPOSITES Photonic crystals general

PHOTONIC STRUCTURES FROM LC/POLYMER COMPOSITES • Photonic crystals (general properties) • Photonic crystal optical fibers • Photonic quasicrystals • Switchable diffraction gratings from liquid crystal/polymer (LC/P) composites • Optical amplification in periodic LC/P structures • Switchable photonic crystals and quasicrystals from LC/P composites • Photonic bandgap fibers from LC composites

Photonic crystals-general properties • Photonic crystals are 1 D, 2 D and 3 D periodic structures of dielectric media with periodicity (lattice distance) on the scale of visible light. • Multiple optical reflection and refraction phenomena in such structures result in dispersion relations (k) similar to electronic band structure E(k) in crystals. 1 2 ( e=je=0; =1) + Maxwell equations H(r) These equations have to be fulfilled taking into account the structural periodicity: Due to the periodicity monochromatic EM fields propagating in such medium have the form Bloch waves : with complicated dispersion relation (k). If for some interval of all possible solutions have nonzero imaginary part of k, waves with these can not propagate in the photonic crystal (PC). Such interval of is called the photonic bandgap.

EXAMPLE OF 1 D STRUCTURE Sinusoidaly modulated refractive index: Propagation of EM field along the z axis: E(z)=ey. E(z) by substitution: y z and Maxwell equations it follows: Solutions of this equation have a form and are known as Mathieu functions. white regions: nonpropagating waves ( =a+ib) shadowed regions: propagating waves ( =±ib) Stability diagram of Mathieu functions.

BAND STRUCTURE of 1 D LATTICES sinusoidal lattice band gaps A(z) z E(z) Reduction to the 1 st Brillouin zone. Periodic dielectric layers Ga. As/Ga. Al. As Ga. As/air In 1 D periodic dielectric structures complete photonic band-gaps exist for any value of refractive index contrast ( 1/ 2) 1. In 2 D and 3 D this happens only in special cases.

2 D PHOTONIC CRYSTALS = (y, z) E Example: quadratic lattice of dielectric cylinders TE Different behaviour for TE and TM modes! TE modes TM modes Band-gap only for TM modes TE modes TM modes Complete band-gap J. D. Joannopolos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the flow of light (Princeton Uni. Press, 1995)

EXAMPLE OF A 2 D PHOTONIC CRYSTAL A-C: H = Amorphous Hydrogenated carbon Holographic patterning via photoresist coating. band-gap regions F. Quinonez et al. , Optics Express 14, 4873 (2006).

3 D PHOTONIC CRYSTALS To obtain band-gap structures in 3 D a very high refractive index contrast is required ( 2/ 1>10). Besides this only some lattices exhibit complete band-gaps. One such example is Yablonovitch construction (E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987)) Self-assembled 3 D FCC photonic structure from dielectric spheres (artificial opals)

DEFECTS IN PHOTONIC CRYSTALS Defects in PC structures provide localization and guiding of optical waves. g( ) A cavity (defect) within the PC structure can act as an optical resonator! New states appear witin the bandgap Such a PC acts as an extremly narrow band otical filter (dielectric Fabry-Perot filters) Extended defects in 2 D and 3 D provide waveguiding effects = bending of light around sharp edges. . .

Photonic crystal optical fibers PC optical fibers are a new technological chalange for improoved optical communication lines. Compared to standard quarz glass fibers they exhibit reduced optical loss, they can transmit higher optical power, they exhibit lower optical nonlinearities, they can be used also out from the conventioanl spectral region ( ~1. 5 m), their dispersion properties can be tuned to the desired needs. . . cladding core http: //ab-initio. mit. edu/photons/tutorial/ Basic idea of the PC fibers: Reflection at the surface of an „air core“ is obtained by surrounding it with a cladding of the PC band-gap medium. Number of guided modes at selected bandgap region (2 D):

EXAMPLES OF STRUCTURES a) Bragg reflection fibers: cladding is made from periodic cylindrical layers of two dielectric materials. The first example of optical fiber for CO 2 laser light. (Omni. Guide, MIT) B. Temelkuran et al. , Nature 420, 650 (2002) b) PC fiber based on 2 D periodic arrangement of air channels in fused silica. J. F. Cregan et al. , Science 285, 1537 (1999)

Photonic quasicrystals • Quasicrystals are structures with long-range positional order, but no regular periodicity (no Bloch waves and Brillouin zone concepts, effective Brillouin zones are called (pseudo)Jones zones ). • To desribe their structure a basic set of more than 3 lattice vectors is needed (4 D, 5 D. . . ). • They posses 5, 7, 8, 9 10, 12. . . fold rotational symmetry axes, which are not possible in regular crystals. • They can exhibit complete photonic bandgaps (actually pseudogaps!!) more readily and at much lower refractive index contrasts than 3 D photonic crystals. Effective „Brillouin zone“ image http: //www. physics. princeton. edu/~steinh/quasiphoton/ W. Man et al. , Nature 03977, 2005 Hand-made icosahedral quasicrystal for microwave radiation

PENROSE QASICRYSTAL STRUCTURE R. Penrose and R. Ammann Penrose tiling is based on two elements: 1) Thick rombus (angles of (2/10) and (3/10)*360 deg) 2) Thin rombus (angles of (1/10) and (4/10)*360 deg) Basic rule: no two tiles can be touching so as to form a single parallelogram! Optical structures composed of such tailings can be made by appropriate drilling and/or etching processes of dielectric films. Example of structure fabricated by electronic-beam litography. M. A. Kaliteevski et al. , Nanotechnology 11, 274 (2000).

PENROSE QC – band structure and density of modes The reciprocal wavector space of QC structures in in principle full. Nevertheless, some diffraction peaks have much higher intensity than the others. So in practice we always „see“ only a finite number of diffraction peaks. Optical diffraction pattern reduced to 3 most intense classes of peaks Band structure calculation with 2 different sets of RWVs M. A. Kaliteevski et al. , Nanotechnology 11, 274 (2000) b 1=(1, 0)=(10000) b 2 =(cos( /5), sin( /5))=(01000) b 3 =(cos(2 /5), sin(2 /5))=(00100) b 4 =(cos(3 /5), sin(3 /5))=(00010) b 5 =(cos(4 /5), sin(4 /5))=(00001) Reciprocal wave vectors of the internal „ring“.

Switchable diffraction gratings from LC/polymer composites Polarization optical microscopy image of a H-PDLC transmission grating. 100 mm grating L=1. 8 mm Optical diffraction from a H-PDLC transmission grating Optical grating structures from LC/P media can be obtained by: • periodic configuration of the external electric field (patterned electrodes) • periodic modification of the alignment layers (patterned alignment layers) • filling of a periodic polymeric host by the liquid crystalline material • periodically modulated photopolymerization induced phase separation process

GRATINGS BASED ON PERIODIC ELECTRODES probe beam w 0<< Optical microscopy, =50 m, L=5 m Field induced in-plane birefringence. 800 V (RMS) 100 V (RMS)

DIFFRACTION PROPERTIES p polarization probe beam w 0 >> I. Drevensek-Olenik at al. , J. Appl. Phys. 96, 6207 (2004) Ivp 0. 1. 2. 3. Diffraction efficiency: N (U)=IN(U)/(T(U)Ivp)

FORMATION OF HOLOGRAPHIC PDLC GRATINGS I(z) LC+polymer precursor laser beam 1 Polymer rich regions LC rich regions laser beam 2 z z Inhomogeneous phase separation process Spatially inhomogeneous polymerization-induced phase separation process. H-PDLCs are electrically switchable holographic media with contrast of refractive index ( 1/ 2) 1. 3. Examples of H-PDLC transmission gratings with different values of the grating pitch (SEM images). = 0. 8 m = 1. 6 m = 3. 1 m

SWITCHING PROPERTIES of H-PDLC GRATINGS + Bragg reflection - U s nlc npol nlc~ npol Diffraction efficiency p Time (s) Switching field Eth~10 V/ m, switching times are in the ms region.

REFLECTION AND TRANSMISSION GRATINGS n=n 0+n 1(r); n 1 0. 1 Reflection grating Transmission grating • switchable 1 D photonic band-gap reflectors. • selectively reflect light of specific wavelengths • applications in reflective display devices, color filters. . . • switchable deflectors for monocromatic light • voltage controled grating structures for spectral analysis • applications in beam steering units, optical interconnects. . .

Optical amplification in periodic LC/polymer composite structures band gap k N(E 2) N(E 1) • Near band edges cg=d /dk 0, therefore effective refractive index c 0/cg= ng , which results in high reflectivity R at surfaces. • Consequently an optical beam makes many roundtrips in the medium before it escapes out from the structure! • This effect is the basis of Distributed Feed-Back (DFB) laser systems. =(E 2 -E 1)/h z G= G 0/(1+ P/Ps) Gain coefficiet Optical d. P=2 GPL- P power Gain Loss ( (1 -R)) • If in such a structure there exist an atomic transition with inverted population of energy levels (N(E 2)/N(E 1))>1, optical amplification via stimulated emission will occur. • Due to large reflectivity R at sample surfaces optical gain per round-trip can become stronger than optical losses per round trip, therefore lasing takes place.

LASING FROM dye-doped H-PDLC GRATINGS To achieve stimulated emission, specific dyes are added to the LC/polymer mixture. The dye molecules are brought to excited state via usual absorption of a VIS or two photon absorption of an IR pump beam. Lasing builds up out from the fluorescence spectrum. noradiative decay absorption lasing The output wavelenght of such a laser depends on the type of the dye and the grating period of the H-PDLC. Y. J. Liu et al. , Appl. Phys. Lett. 88, 061107 (2006)

SWITCHABLE LASING V. K. S. Hsiao et al. , Optics Express 13, 3787 (2005) Laser emission power can be modulated by voltage applied to the H-PDLC grating. Voltage reduces the width of the band-gap and the effective refractive index ng.

Switchable photonic crystals and quasicrystals from LC/P composites • By appropriate orientaion of 4 or more curing laser beams 3 D periodic interference patterns can be formed within the H-PDLC structures. • In photopolymerization induced phase separation process LC material concentrates in the intensity minima. • The specific feature of these PCs is that their optical properties can be modulated by low voltage external fields. • The main problem is relatively low contrast of the refractive index • The feld-induced changes are affected by anisotropy of the droplet shapes. example of a 2 D intereference pattern

FCC H-PDLC PHOTONIC CRYSTAL Optical interference of 4 above described coherent laser beams produces intensity profile with FCC lattice in the 3 D space. p External voltage modifies the widths as well as the positions (with respect to k and ) of the band-gaps. M. Escuti et al. , Opt. Lett. 28, 522 (2003).

PHOTONIC QUASICRYSTALS Five beam interference pattern j=1. . 5 calculation for • TM polarized beams • wavelength = 532 nm, • angle of incidence with respect to the xy plane = 30 o. • Ai = A, i = 0, i = 1. . 5

H-PDLC PHOTONIC QUASICRYSTAL Expected refractive index profile n(x, y) for synchronized phases Ai = A, i = 0, i = 1. . 5 Calculated Fraunhoffer diffraction pattern. square=10 x 10 m 2

H-PDLC PHOTONIC QUASICRYSTAL Expected refractive index profile: n(x, y) Ai=A, i=1. . 5, 1 =0. 55, 2 =5. 99, 3 =1. 89, 4 =1. 90, 5 =1. 82 asynchronized phases (usual case!!) Fraunhoffer diffraction square=10 x 10 m 2

EXAMPLE OF QUASICRYSTAL STRUCTURE SEM-image of broken and etched H-PDLC morphology. The structure is very irregular. Volume fraction of the phase separated LC seems to be very low (small isolated droplets) Images of diffraction pattern observed on a far field screen: a) E=0, b) E=100 V/ m. a) b)

IRREGULARITY OF DIFFRACTION EFFICIENCY nomenclature 2 nd order diffraction efficiency: hn, N= In, N/Iin 3 rd order 1 st order 4 th order 1 st diffraction order Irregularities are correlated over the entire sample region. They result not from local sample imperfections, but from the imperfect holographic writing process. Various peaks within the 1 st diffraction order Electric field induced effect are very dispersed.

Photonic bandgap fibers from LC composites If usual air core in the PC fibers is filled with the LC, fiber properties can be tuned by temperature or external electric and magnetic fields. This property is important for waveguide modulators, couplers, filters, sensors and similar elements. . . T. T. Larsen at el. , Optics Express 11, 2589 (2003) PC fiber filled with cholesteric LC. Transmitted light at different temperatures.

CONCLUSIONS Photosensitive polymer/LC composites provide a simple way to make switchable PC structures All the structures reported during the last years are typically very imperfect. Extended work is needed in order to optimize appropriate material compositions, curing parameters and switching properties. What about other (besides the electrooptic effect) nonlinear optical properties of such structures? These are for the moment completely unexplored and will very probably be the topic of many near future Ph. D theses. .