Vladimir Bordo NanoSyd, Mads Clausen Institute Syddansk Universitet, Denmark Waveguiding in nanofibers

Contents Introduction Fundamentals Experiments Theory Conclusion

Introduction photoluminescence waveguiding optical confinement InP nanowires / SiO 2 p-6P nanofibers / mica

Fundamentals elementary wavesboundary conditions at r = a arbitrary wave normal modes  (  ) z 2a 11 22 x r 

Fundamentals cutoff fundamental mode (HE 11 ) aa  a/c A.V. Maslov and C.Z. Ning, Appl. Phys. Lett., 83, 1237 (2003)

Fundamentals space-decaying (SD) modes time-decaying (TD) modes waveguide modes V.G. Bordo, J. Phys.: Condens. Matter 19, (2007)

Experiments Photoluminescence images of para- hexaphenyl nanofibers excited by a mercury lamp ( = 365 nm). Measurements of the intensity decay with a fluorescence microscope F. Balzer, V.G. Bordo, A.C. Simonsen and H.-G. Rubahn, Phys. Rev. B 67, (2003) d,  m

Experiments Measurements of the intensity decay with a SNOM set-up distance dependence T. Tsuruoka, C.H. Liang, K. Terabe and T. Hasegawa, J. Opt. A: Pure Appl. Opt. 10, (2008) influence of local defects

Experiments Waveguiding at different wavelengths T. Tsuruoka, C.H. Liang, K. Terabe and T. Hasegawa, J. Opt. A: Pure Appl. Opt. 10, (2008)

Experiments Waveguiding & Spatially resolved fluorescence microscopy K. Takazawa, J. Phys. Chem. C, 111, 8671 (2007) thiacyanine dye molecule

Experiments Waveguiding & Spatially resolved fluorescence microscopy K. Takazawa, J. Phys. Chem. C, 111, 8671 (2007) reabsorption

Experiments Optical cavity effects K. Takazawa, J. Phys. Chem. C, 111, 8671 (2007) L Fabry-Perot modes J-band => anomalous dispersion

Experiments Optical cavity effects ZnSe nanowire PL spectra from nanowires of different lengths L.K. van Vugt, B. Zhang, B. Piccone, A.A. Spector and R. Agarwal, NanoLett.. 9, 1684 (2009)

L.K. van Vugt, B. Zhang, B. Piccone, A.A. Spector and R. Agarwal, NanoLett., 9, 1684 (2009) Experiments TE 01 mode excitationHE 11 mode excitation

L.K. van Vugt, B. Zhang, B. Piccone, A.A. Spector and R. Agarwal, NanoLett., 9, 1684 (2009) Experiments two-mode excitation ”slow light” (v g = c/8) near the band-edge (2.69 eV) strong coupling between excitons and photons

Coupling of external light into a nanofiber T. Voss, G.T. Svacha, E. Mazur, S. Müller, C. Ronning, D. Konjhodzic and F. Marlow, NanoLett., 7, 3675 (2007) ZnO nanowire silica fiber tuning the fiber-nanowire distance tuning the fiber alignment Experiments

Optical mode launching in nanofibers set-up light scatteringphotoluminescence J. Fiutowski, V.G. Bordo, L. Jozefowski, M. Madsen and H.-G. Rubahn, Appl. Phys. Lett., 92, (2008) Experiments

Optical mode launching in nanofibers J. Fiutowski, V.G. Bordo, L. Jozefowski, M. Madsen and H.-G. Rubahn, Appl. Phys. Lett., 92, (2008) phase matching Experiments

Rectangular anisotropic nanofiber on a substrate 11 22 33 a TE waves do not exist TM waves: - dispersion -cutoff wavelengths -number of modes F. Balzer, V.G. Bordo, A.C. Simonsen and H.-G. Rubahn, Phys. Rev. B 67, (2003) Theory

Semi-cylindrical isotropic nanofiber on a substrate ideally reflecting substratetheory of images V.G. Bordo, Phys. Rev. B, 73, (2006)

Theory Semi-cylindrical isotropic nanofiber on a substrate V.G. Bordo, Phys. Rev. B, 73, (2006) total scattered intensity vs incidence angle phase matching with a radiative mode angular distribution of scattered light vicinity of exciton resonance

Semi-infinite cylindrical isotropic nanofiber incident waveguide mode boundary conditions => fictitious current sheets V.G. Bordo, Phys. Rev. B, 78, (2008) => + Theory

Numerical calculations silicon nanowire, = 1.5  m L. Tong, J. Lou and E. Mazur, Opt. Express, 12,1025 (2004)

Theory Numerical calculations L. Tong, J. Lou and E. Mazur, Opt. Express, 12,1025 (2004) fractional power inside the core fundamental mode, = 1.5  m silica nanowire n = 1.45 silicon nanowire n = 3.5

Numerical calculations => FDTD calculations top facet bottom facet A.V. Maslov and C.Z. Ning, Appl. Phys. Lett., 83, 1237 (2003) 11 22 n  1 = 1  2 = 6 n = 1.8 Theory

Conclusion Waveguiding is characterized by optical confinement. Electromagnetic fields in a nanofiber can be described in terms of wavegiude modes as well as transient modes. The latter ones can be radiative. Waveguide modes have frequency cutoffs below which they can not propagate to the exclusion of the fundamental mode. Waveguiding in nanofibers can be observed in both photoluminescence and propagation of incident light. A nanofiber can act as an optical resonator. The waveguide modes can be enhanced if the waves travelling back and forth interfere constructively. The launching of the nanofiber modes can be observed in the far field as peaks in light scattering or photoluminescence. As the nanofiber diameter increases, the optical confinement becomes better.