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 2 E()() r k0 E r Describes the allowed frequencies of light
Schrodinger’s Eigenvalue Equation for Electrons: 2 h Describes allowed ()2 4 [()]()() V r r E r Energies of Electrons 2m Foundation of Nanophotonics Free Space Solutions: Photon Plane Wave: E E 0 eik.rt eik.rt
ik.rt ik.rt Electron Plane Wave: ce e
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 2NA 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,
2 2 1/2 i2x x i 2 ( x ) Z f(,) x z Z dx e F (,0) x z e (1) For far field only need to integrate over k / c , i.e.
2 2 1/2 2C i2x x i 2 ( x ) Z f( x , z Z ) dx e F ( x , z 0) e (2) 2C
z , Then Eqn. (1) is recaptured by Z
Then taking at aperture, f ( x , z ) rect (x ) 2 2 2C i2x x i2 x ( Z ) Now far field: f ( x , z Z ) dx { e e 2C " " sin(( )w ) 2 2 "2 d"" ei2x x F ( , z 0) x x e x } (3) x x " x x
F(x , z 0) Eo (x K), with K one spatial frequency Near Field Optics Continued from the previous page i2 Kx i 2 2 K 2 Z Eqn.(1) f ( x , z Z ) Eo e e for K / C 0, for KC / (4)
2 2 2 2 i2 K 2C i2x x i2 x ( Z ) sin( x K ) w Eqn.(3) fxzZEe ( , ) o de x e (5) 2C 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 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 n 2h2 n 2h2 h2k E E 1 2 y n1 ,n2 ,k y C 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: h2 n 2 n 2 n 2 E E ( 1 2 3 ) n1 ,n2 ,n3 C 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 Ex (n 1,i, j,k) Ex (n,i, j,k) (i, j,k) H (n 1 ,i, j 1 ,k) H (n 1 ,i, j 1 ,k) z 2 2 z 2 2 y 1 1 1 1 H y (n 2 ,i, j,k 2) H y (n 2 ,i, j,k 2) z E(0) H(1/2) E(1) t 0 1/2 1 Static State Computation Electrostatic Approximation Finite Element Simulation 16 (b) 4dB y x |E|/|E | at 785 nm z 0 (, ) 0 Solve Harmonic Wave Equation 9 dB 1 2 Solve Laplace equation ( E) E 0 1 2 1 1 2 ( H ) H 0 2 2 0 For Plane Wave E k 2 E 0 z 0 z 30 dB Charge density (H ) k 2 H 0 a z 0 z ( ) E ,0 ( / )1 Low-reflecting Boundary Condition Singularity near the sharp tip n H Ez 2 E0z dB ( 0) n E H z 2 H 0z 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 E0 cos(ext) r r0 cos(vibt) 0 r r 0 Dipole moment E 0 E0 cos(ext) r0 E0 cos(ext) cos(vibt) r 0 1 0 E0 cos(ext) r0 E0 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 10-16 C SERRS Geometrical Rayleigh cross-section G 10-18 ] Scattering of a single 100 T 2 Fluorescence biomolecule 10-20 SERS -22 12 orders 10 of magnitude 50 -24 10 FTIR 10-26 Resonance Raman Intensity [a.u]Intensity -28 0 10 Optical Cross Section Optical Cross[cm 10-30 Raman scattering 500 1000 1500 Raman Shift [cm-1] 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 (t) E (t) plasmon plasmon t 2 1 3 Rei NP E 2 medium PRET 8 0 2 medium NP Chemical/Biomolecules 2 Electron-Lattice Collision 3 E 2 medium Im (Electron-Phonon Relaxation) 0 NP 8 2 medium NP Temperature Increase due to E e-jωt Photothermal Conversion 0 Metal lattice At steady state Light Intensity 2 aNP Q 2 Conduction Electron T I 0 cE0 0 / 8 3 2 2 I 0aNP 3 medium T Im NP 3c 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 1 ns 50 3 ns 32 ns 40 Temperature ( Temperature C) 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