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Zhang Gsas.Harvard 0084L 10989.Pdf (11.58Mb) Manipulating Light on Wavelength Scale The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Zhang, Yinan. 2012. Manipulating Light on Wavelength Scale. Doctoral dissertation, Harvard University. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:11051175 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Manipulating Light on Wavelength Scale Y Z T S E A S D P E E H U C, M D © - Y Z A . esis advisor: Marko Loncar Yinan Zhang Manipulating Light on Wavelength Scale A Light, at the length-scale on the order of its wavelength, does not simply behave as “light ray”, but instead diffracts, scaers, and interferes with itself, as governed by Maxwell’s equations. A profound understanding of the underlying physics has inspired the emergence of a new frontier of materials and devices in the past few decades. is thesis explores the concepts and approaches for manipulating light at the wavelength-scale in a variety of topics, including anti-reective coatings, on- chip silicon photonics, optical microcavities and nanolasers, microwave particle accelerators, and optical nonlinearities. In Chapter , an optimal tapered prole that maximizes light transmission be- tween two media with different refractive indices is derived from analytical theory and numerical modeling. A broadband wide-angle anti-reective coating at the air/silicon interface is designed for the application of photovoltaics. In Chapter , a reverse design method for realizing arbitrary on-chip optical l- ters is demonstrated using an analytical solution derived from Chapter . Example designs are experimentally veried on a CMOS-compatible silicon-on-insulator (SOI) platform. Among this device’s many potential applications, the use for ul- trafast on-chip pulse shaping is highlighted and numerically demonstrated. In Chapter , the concept of tapering is applied to the design of photonic crystal cavities. As a result, the scaering losses of cavities are suppressed, and light can be localized in a wavelength-scale volume for a long life-time. iii esis advisor: Marko Loncar Yinan Zhang In Chapter , photonic crystal cavity-based nanolasers with low power con- sumptionaredemonstratedwithtwodifferentprototypes-photoniccrystalnanobeams and photonic crystal disks. e use of graphene is also explored in this chapter for the purpose of electrically-driven nanoscale light-emiing devices. In Chapter , photonic crystal cavities at millimeter wavelength for particle ac- celeration applications are developed. In Chapter , a novel design of dual-polarized mode photonic crystal cavities, and its potential for difference-frequency generations are examined. iv Contents O . Introduction to impedance matching . . Derivation of Maxwell’s equations . . Optimal taper function . . Design and performance . A - I -Q/V - . Ultrahigh-Q/V cavities based on nanowires . . Ultrahigh-Q/V micropillar cavities . P . Introduction . . Lasing threshold of photonic crystal lasers . . Photonic crystal nanobeam lasers . . Photonic crystal disk lasers . . Graphene-contacted micro-LED . . Conclusion and outlook . P . Introduction . v . Design . . Fabrication and measurement . . Summary . D- - . Introduction . . Design . . Application for nonlinear optics . . Summary . vi Included publications Chapter includes: Y. Zhang, C. Li, M. Loncar, “Optimal broadband anti-reective taper,” Optics Let- ters Vol. , pp. () Chapter includes: I. Frank*, Y. Zhang*, M. Loncar, “Arbitrary on-chip optical lters for ultrafast pulse shaping,” in preparation to submission () (*Equal contribution to the work) Chapter includes: Y. Zhang, M. Loncar, “Submicrometer diameter micropillar cavities with high Quality factors and ultrasmall mode volumes,” Optics Leers, Vol. , () [Selected for the April , issue of the Virtual Journal of Nanoscale Science and Technology] Y. Zhang, M. Loncar, “Design and simulation of nanowire-based high Quality fac- tor nanocavities,” Proc. SPIE, Vol. , W () Y. Zhang, M. Loncar, “Ultra-high quality factor optical resonators based on semi- conductor nanowires,” Optics Express, Vol. , pp. - () vii Chapter includes: Y. Zhang, M. Loncar, “Photonic crystal lasers,” in Alexei Baranov and Eric Tournie, Semiconductor lasers: fundamentals and applications, Cambridge, Woodhead Pub- lishing (). Y. Zhang, M. Khan, Y. Huang, J. H. Ryou, P. B. Deotare, R. Dupuis, M. Lon- car, “Photonic crystal nanobeam lasers,” Applied Physics Leers, Vol. , () [Selected for the August , issue of the Virtual Journal of Nanoscale Science and Technology] Y. Zhang, C. Hamsen, J. T. Choy, Y. Huang, J. H. Ryou, R. Dupuis, M. Loncar, “Photonic crystal disk lasers,” Optics Leers, Vol. , pp. - () Chapter includes: Y. Zhang, I. Bulu, T. Boo, W. M. Tam, B. Levi, M. Loncar, “High Q/V air-mode photonic crystal cavities at microwave frequencies,” Optics Express, Vol. , pp. - () Chapter includes: Y. Zhang, M. W. McCutcheon and M. Loncar, “Ultra-high-Q dual-polarized pho- tonic crystal nanocavities,” Optics Leers, Vol. , () [Selected for the September , issue of the Virtual Journal of Nanoscale Science and Technology] I. B. Burgess*, Y. Zhang*, M. W. McCutcheon*, A. W. Rodriguez, J. Bravo-Abad, S. G. Johnson, and M. Loncar, “Efficient terahertz generation in triply resonant nonlinear photonic crystal microcavities,” Optics Leers, Vol. , () (*Equal contribution to the work) viii Listing of gures .. Comparison of different window functions p(u) [] for anti-re- ective coatings at silicon/air interface, and their respective re- ectance R = jr()j predicted by the Fourier model. .. Comparison of power reectance between that predicted by the Fourier model and that calculated by solving Maxwell’s Equa- tions. e Dolph-Chebyshev function in this Figure is optmized for a cutoff frequency of L=λmax = and has a sideband re- − ectance of Rsb = dB. .. Comparison of different taper functions’ performance, for sili- con/air interface as an example. .. Example of a broadband wide-angle anti-reective coating be- tween air and silicon. (b)(c) Reectance dependence on inci- dent angle, at different wavelengths across the solar spectrum, for TE-and TM-polarized light. ix .. (a) A cartoon representation of the lter in action. e red light is transmied through the width modulated region, whereas the blue light is reected back. (b) An SEM micrograph of a fabri- cated waveguide showing the W(x) prole. (c) An example target R(λ). (d) e width prole W(x) that is obtained by applying the inverse Fourier transform obtained from Eq. to the spectrum from (c). (e) e solid lines are target amplitudes of labeled val- ues A. e dashed lines show the resulting reectance when the W(x) prole is checked by solving the exact Maxwell’s equations numerically. For small values of A the agreement is excellent, but increasingly larger values lead to distortion of the shape and dis- crepancies in the amplitude. .. (a) Time domain Gaussian input pulse. (b) e wavelength do- main reectance lter shapes. Eq. is used turn these lter shapes into W(x) for the waveguides. (c) Time domain readout of the input pulse reected off the lters. e results are a Ham- ming and linear pulse shape, respectively. .. (a) SEM micrograph of example device; the inset shows a mag- nication of the width modulated region. Cartoons show ow of experiment. (b) A set of ve target spectra. e intensity is in a linear saw-tooth paern. (c) Normalized, measured reec- tions from fabricated devices. e dashed lines indicate the un- certainty in the normalization. .. (a) Schematic of nanowire and mode prole (Ex components) for fundamental HE mode with d = nm and nclad = . (b) Reectance of nanowire facets with air and PMMA cladding (HE mode). .. (a)SchematicofasemiconductornanowirewithDPhCdened at its end. (b) Transmiance and reectance spectra for nanowire with PhC consisting of PMMA/air pairs. x .. (a) Schematic of guided-mode cavity. (b) Schematic of Bloch- mode cavity. (c) Dispersion line of Bloch mode with periodic- ity of :a (blue solid), Bloch mode with periodicity of a (pink solid), and guided mode of nanowire embedded in PMMA (red dash-dot). .. (a) Schematic of photonic band tapering. (b) Quality factor and mode volume as a function of number of taper segments. In all cases, the cavity was designed to support one resonance position at the mid-gap wavelength of nm. (c) Mode prole of cav- ity modes (Eφ component) with taper segments and mir- ror pairs. Conguration of the tapered gratings is also mapped as background. .. Fourier transform of Eφ along wire axis. k-space zones within the light line are shown in green (light green within PMMA light line, dark green within air light line). .. Quality factor (red-square) as a function of imaginary part of re- fractive index (κ). e Q value with lossless cladding is indi- cated in black line. e dash lines represent estimation of Q using Eq. ., while η = : (blue) and (magenta), respectively. .. (a) Schematic of hexagonal cross-section nanowire embedded in air/PMMA grating. (b) Mode prole of Ex component of hexag- onal cross-section nanowire embedded in PMMA cladding. (c) Mode prole of cavity modes (Ex component) with taper seg- ments and mirror pairs. .. (a) Traditional design of micropillar cavities and (b) modied
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