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Introduction to nanophotonics

This document provides an introduction to the field of nanophotonics. It defines nanophotonics as the science and engineering of light-matter interactions that take place on wavelength and subwavelength scales. Examples of nanophotonics in nature are discussed. The foundations of nanophotonics are explored, including similarities between the propagation of photons and electrons. Computational methods for modeling nanophotonic structures like finite difference time domain are also summarized. The effects of quantum confinement on the optical properties of nanostructures are described.

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Introduction to Nanophotonics Logan Liu Micro and Nanotechnology Lab Department of Electrical & Computer Engineering University of Illinois
What is Nanophotonics? This area of nanoscience, called nanophotonics, is defined as “the science and engineering of light matter interactions that take place on wavelength and subwavelength scales where the physical, chemical or structural nature of natural or artificial nanostructured matter controls the interactions” -‐‐National Academy of Science
Early Examples of Nanophotonics
Nanophotonics in Mother Nature
Foundation of Nanophotonics • Photon-Electron Interaction and Similarity “There’s Plenty of Room at the Bottom” (Feynman, 1961)
Foundation of Nanophotonics Basic Equations describing propagation of photons in dielectrics has some similarities to propagation of electrons in crystals Similarities between Photons and Electrons Wavelength of Light, Wavelength of Electrons,
Foundation of Nanophotonics Maxwell’s Equations for Light 1 D 1 B H  E  c t c t   [  1  E ( r )]   2 E ( r ) Eigenvalue Wave Equation:   [ 1  H ( r )]   2  H ( r ) For plane wave   E ( r )   k0 2 E ( r ) Describes the allowed frequencies of light Schrodinger’s Eigenvalue Equation for Electrons: h2 Describes allowed ( 2 ) 4 [    V ( r )] ( r )  E ( r ) Energies of Electrons 2m
Foundation of Nanophotonics Free Space Solutions: Photon Plane Wave: EE e 0  ik .r t e  ik .r t  Electron Plane Wave:   ce ik .r t e  ik .r t  Interaction Potential in a Medium: Propagation of Light affected by the Dielectric Medium (refractive index) Propagation of Electrons affected by Coulomb Potential
Foundation of Nanophotonics Photon tunneling through classically forbidden zones. E and B fields decay exponentially. k-vector imaginary. Electron Wavefunction decays exponentially in forbidden zones
Foundation of Nanophotonics Confinement of Light results in field variations similar to the confinement of Electron in a Potential Well. For Light, the analogue of a Potential Well is a region of high refractive-index bounded by a region of lower refractive-index. Microscale Confinement of Light Nanoscale Confinement of Electrons
Foundation of Nanophotonics • Free space propagation of both electrons and photons can be described by Plane Waves. • Momentum for both electrons and photons, p = (h/2π)k • For Photons, k = (2π/λ) while for Electrons, k = (2π/h)mv • For Photons, Energy E = pc =(h/2π)kc while for Electrons,
Near Field Optics    In Far-Field Microscopy, Re solution  1.22   2 NA  This can be overcome with Near-Field Techniques by having nanoscale apertures or by using aperture-less techniques which enhance light interaction over nanoscale dimensions with the use of nanoscale tips, nanospheres etc. The idea of using sub-wavelength aperture to improve optical resolution was first proposed by Synge in a letter to Einstein in 1928. These ideas were implemented into optics much later in 1972 [Ash and Nicholls] Schematic set-ups for Near-Field Scanning Optical Microscope (NSOM) Aperture-less Near-field light decays over a Technique: Near-Field distance of 50 nm from aperture. Tapered Optical-Fiber around Nano-Tip
Near-Field Optics SNOM PSTM Tip collects the evanescent light created by laser illuminating the sample from the Tip illuminates the sample; back Scattered light is collected
Near Field Optics (Paesler, <Near-field Optics>)  2  x )1/2 Z 2 f ( x, z  Z )   d x e  i 2 x x F ( x , z  0)e i 2 (  (1)  For far field only need to integrate over k   / c, i.e.   2 C  i 2 x x  i 2 (  2  x )1/ 2 Z 2 f ( x, z  Z )    d x e F ( x , z  0)e  (2)  2 C z      , T h e n E q n . (1 ) is re c a p tu re d b y Z   Then taking at aperture, f ( x, z   )  rect ( x )   2 2 2 C  i 2 x x  i 2   x ( Z  ) Now far field: f ( x, z  Z )    d x {e e   2 C "  "  i 2 " x " sin(( x   x ) w) 2  2  "2   d ex x F ( , z  0) x " e x }   (3)  x  x F ( x , z  0)  Eo ( x  K ), with K one spatial frequency
Near Field Optics Continued from the previous page  2 K 2 Z Eqn.(1)  f ( x , z  Z )  Eo e i 2 Kx  e i 2 for K   / C  0, for K   / C  (4)   i 2  2  K 2   i 2  2  x ( Z  ) 2 sin( x  K ) w Eqn.(3)  f ( x, z  Z )  Eo e 2 C  d  x e  i 2 x x e   (5)  2 C x  K Notes: Eqn. (4) fulfills all our notions about far-field microscope and its inability to carry information beyond certain spatial frequency Eqn. (5) integral doesn’t vanish for K   / C , such that high-frequency elements still contribute to the signal arriving at z=Z (far field). sin( x  K ) w Eqn. (4) collapses to (5) when w (aperture width) is large, i.e.   ( x  K ) x  K In the near-field, evanescent terms must be taken into account, due to the convolution of the tip and the sample.
Quantum confinement Quantum-confined materials refer to structures which are constrained to nanoscale lengths in one, two or all three dimensions. The length along which there is Quantum confinement must be small than de Broglie wavelength of electrons for thermal energies in the medium. Thermal Energy, E = de Broglie Wavelength, For T = 10 K, the calculated λ in GaAs is 162 nm for Electrons and 62 nm for Holes For effective Quantum-confinement, one or more dimensions must be less than 10 nm. Structures which are Quantum- confined show strong effect on their Optical Properties. Artificially created structures with Quantum-confinement on one, two or three dimensions are called, Quantum Wells, Quantum Wires and Quantum Dots respectively.
Quantum Confinement Quantization of energy into discrete levels Nanoscale Confinement in 1-Dimension has applications for fabrication of new solid- results in a “Quantum Well” state lasers. Two or more Quantum wells side-by-side give rise to Multiple Quantum Wells (MQM) structure. Motion is confined only in the Z- Z direction. For electrons and holes moving in the Z-direction in low bandgap material, their motion can be described by Particle in a Box. If the At 300 K, The band gap of GaAs is 1.43 eV while it is 1.79 eV for AlxGa1-xAs (x=0.3). Thus the electrons and depth of Potential Well is V, for holes in GaAs are confined in a 1-D potential well of energies E<V, we can write, length L in the Z-direction. 2 2 2 nh 2 h 2 (k x  k y ) En ,k x ,k y  EC   2   8me L 8 2 me n = 1, 2, 3,…..
Quantum Confinement Quantum Well: 1D Confinement Due to 1-D confinement, the number of continuous energy states in the 2-D phase space satisfy 2 2 2mE2D xp p y Quantum Wire: 2D Confinement 2D confinement in X and Z directions. For wires (e.g. of InP, CdSe). with rectangular cross-section, we can write: 2 2 n1 h 2 2 n2 h 2 h2k y En1 ,n2 ,k y  EC   2   2  2  8me Lx 8me Lz 8 me Quantum Dot: 3D Confinement For a cubical box with the discrete energy levels are given by: 2 2 2 h 2 n1 n2 n3 En1 ,n2 ,n3  EC   ( 2  2  2 ) 8me Lx Ly Lz
Quantum Confinement Size Dependence of Optical Properties In general, confinement produces a blue shift of the band-gap. Location of discrete energy levels depends on the size and nature of confinement. Increase of Oscillator Strengths This implies increase of optical transition probability. This happens anytime the energy levels are squeezed into a narrow range, resulting in an increase of energy density. The oscillator strengths increase as the confinement increases from Bulk to Quantum Well to Quantum Wire to Quantum Dot.
Computational Nanophotonics • Analytical approach hampered by over-simplifying assumptions – Perfect conductivity, zero thickness materials, semi-infinite structures, … • Frequency vs. Time domain? • Computational resources becoming less constraining – Very complex problems being tackled • Finite Difference Time Domain (FDTD) • Frequency Domain Integral-differential
Computational Nanophotonics Time Domain Frequency Domain • Numerical integration of • Time harmonic excitation Ampere/Faraday (steady state) • Impulse excitation • Boundary value problem based • Numerical integration to get steady on integro-differential equation state • Big things to invert • Relate time series to frequency domain (stability/accuracy issues via F.T. possible) • Some problems with highly dispersive • Relate to time domain by F.T. media (convolutional response) • No big things to invert but lots of memory • Sophisticated variable mesh
Finite Difference Time Domain (FDTD) Yee Cell – Space/Time t  E x ( n  1, i, j, k )  E x ( n, i, j , k )    (i, j , k )  H z ( n  1 2 , i, j  12 , k )  H z ( n  1 2 , i, j  1 2 , k )  y H y ( n  1 2 , i, j , k  1 2 )  H y ( n  1 2 , i, j , k  1 2 )   z  E(0) H(1/2) E(1) 0 1/2 1 t
Static State Computation Electrostatic Approximation Finite Element Simulation 16 (b) 4dB  y x z |E|/|E0| at 785 nm (, ) 0 Solve Harmonic Wave Equation 9 dB Solve Laplace equation   (  1  E )   2E  0 1     1   2   ( 1  H )   2 H  0   0       2  2   For Plane Wave 2   E z  k 0 E z  0 30 dB Charge density 2  a (  /  ) 1    (H z )  k 0 H z  0  (  )   E  , 0     Low-reflecting Boundary Condition Singularity near the sharp tip n   H   E z  2  E0 z      (   0)   n   E   H z  2  H 0 z dB 30 20 10 0 -10 -20
Plasmonics Transverse EM wave coupled to a plasmon (wave of charges on a metal/dielectric interface) = SPP (surface plasmon polariton) Note: the wave has to have the component of E transverse to the surface (be TM-polarized). Polariton – any coupled oscillation of photons and dipoles in a medium 10 µm 1 µm
Plasmonics Research Details in Prof. Nick Fang’s Lecture
Metamaterials Hormann et al, Optics Express (2007) Details in Prof. Nick Fang’s Lecture
Photonic Crystal The most striking similarity is the Band-Gap within the spectra of Electron and Photon Energies Likewise, diffraction of light within a Photonic Crystal is forbidden for a range of frequencies which gives the Solution of Schroedinger’s equation in a 3D concept of Photonic Band-Gap. The forbidden range of periodic coulomb potential for electron frequencies depends on the direction of light with respect crystal forbids propagation of free to the photonic crystal lattice. However, for a sufficiently electrons with energies within the Energy refractive-index contrast (ratio n1/n2), there exists a Band- Band-Gap. Gap which is omni-directional.
Photonic Crystal
Photonic Crystal
All-Optical Processor
Molecular Nanophotonics
Molecular Nanophotonics Photosynthetic Solar Cell Molecular Nano Antenna
Molecular Nanophotonics Coupled Spring Model r r ωex ωvib Excitation electric field Nuclear displacement Polarizonbility    E  E 0 cos(  ex t ) r  r0 cos(  vib t )   0    r   r  0 Dipole moment       E   0 E 0 cos(  ex t )    r0 E 0 cos(  ex t ) cos(  vib t )  r  0 1      0 E 0 cos(  ex t )    r0 E 0 cos ( ex   vib )t  cos ( ex   vib )t  2  r  0 Rayleigh Scattering Anti-Stokes line Stokes line
Nanophotonic Interaction Raman Spectra of DNA Bases Optical Cross Section -14 150 10 A -16 10 C SERRS Geometrical Rayleigh cross-section G -18 10 Scattering of a single Optical Cross Section [cm ] 2 100 T Fluorescence biomolecule Intensity [a.u] -20 10 SERS -22 12 orders 10 of magnitude 50 -24 10 FTIR -26 Resonance Raman 10 -28 0 10 -30 10 Raman scattering 500 1000 1500 -1 Raman Shift [cm ] Electromagnetic Enhancement Chemical Enhancement LUMO hωinc hωinc±hωvib hω hω’ EFermi HOMO
Nanophotonic Field Enhancement Cresyl blue SERS spectra. Adapted from Stöckle et al., Chem. Phys. Lett. 2000, 318, 131.
Hybrid Nanophotonics • Inorganic-organic hybrid structures
Fabrication of Nanophotonics
Nanophotonic Bioimaging Nanoparticles are also used for bioimaging by non-optical techniques like Magnetic Resonance Imaging (MRI), Radioactive Nanoparticles as tracers to detect drug pathways or imaging by Positron Emission Tomography (PET), and Ultrasonic Imaging. For MRI, the magnetic nanoparticles could be made of oxide particles which are coated with some biocompatible polymer. Newer Nanoparticle Heterostructures have been investigated which offer the possibility of imaging by several techniques simultaneously. An example is Magnetic Quantum Dot.
Nanophotonic Bioimaging Dual-Functional Nanoprobes for Dual-Modality Animal Imaging Fluorescence Photoacoustic T2 MRI T1 MRI Bouchard and Liu et al, PNAS 2009
Nanophotonic Energy Conversion Joule Heat due to Plasmon Current Q  j plasmon (t )  E plasmon (t ) t 2   1 3 medium  PRET   Re i NP E 02   8 2 medium   NP    Chemical/Biomolecules 2 Electron-Lattice Collision  2 3 medium  E0 Im  NP (Electron-Phonon Relaxation) 8 2 medium   NP Temperature Increase due to E0e-jωt Photothermal Conversion Metal lattice At steady state Light Intensity 2 a Q Conduction Electron  T  NP I 0  cE 02  0 / 8 3 2 2  I 0 a NP 3 medium T  Im  NP 3c  0 2 medium   NP NRL 1, 84-90 (2006)
Nanophotonics Therapy H. Atwater, Scientific American 2007
Nanophotonic Molecular Manipulation Steady State 57 οC 52 οC 47 οC 42 οC 37 οC 32 οC 27 οC 60 Steady state 0 ns Temperature ( C) 1 ns 3 ns 50 32 ns 40 30 50 nm 0 50 100 150 Distance (nm) Lee et al, Nano Letter (2009)
Nanophotonic Fluidic Manipulation Liu et al, Nature Materials (2006)
Optofluidic Molecular Manipulation Light Ilumination Microfluidic Channel Optical Pre-Concentration of DNA Photothermal Nanofilm Biomolecule concentrating
Nanophotonic Particle Manipulation Conveyer Rotor Stirrer Liu et al. Manuscript in preparation
Nanophotonics Market
Nanophotonics Market
Research Trends