Advanced techniques Local probes, SNOM Principle Probe the near field electromagnetic field with a local probe near field probe propagating field evanescent
Advanced techniques Local probes, SNOM Principle Different configurations Illumination Collection b) a) fiber tip sample detector c) d) Apertureless Evanescent (TIR) V. Sandogdhar et al.,"photonic crystals..." Wiley-VCH Berlin,15, (2003)
Advanced techniques Local probes, SNOM Principle Tricks are in : Tip position control, as in STM, AFM Tip fabrication
Advanced techniques Local probes, SNOM Principle Tricks are in : Tip position control, as in STM, AFM Tip fabrication (a) quartz tuningfork sample piezo scanner (b) fast z-piezo fiber probe 500nm translation stages Metallized tapered fibre tip. SEM, H. Gersen V. Sandogdhar et al.,"photonic crystals..." Wiley-VCH Berlin,15, (2003)
Examples, bends SNOM S.I. Bozhevolnyi et al., Phys. Rev. B, 66, 235204, (2002) with increasing shear force feedback (increasing tip distance)
Examples, cavities SNOM K. Okamoto et al., Appl. Phys. Lett., 82, 1676, (2003) Nice images, but difficult to be quantitative
Examples, opals SNOM vs. tip separation vs. light wavelength E. Flück et al., Phys. Rev. E, 68, 015601R, (2003)
SNOM Examples, 2D macroporous PhC a) b) detector a b c 1 z fiber tip#2 0 x d e f fibertip#1 1.5μm incident beam 100μm x z y detector g h i n vs. tip 1 distance V. Sandogdhar et al., Phys. Rev. Lett., 92, 113903, (2004)
T-SNOM Mode field pattern mapping or modification with AFM tip Calculated +AFM tip scanning tip smaller, lower perturbation for small high Q cavities Calculated - unperturbed tip change in Q factor or resonance wavelength R. De Ridder, Twente, ECIO 2007 and Opt. Exp., 14, 8745 (2006) Measured
Advanced techniques Heterodyne SNOM Usual SNOM measures intensity, what about amplitude? (i.e. intensity and phase) Insert the SNOM set-up in an interferometer (e.g. Mach-Zender) Note : amplitude information is necessary e.g. for numerical Fourier transform
Advanced techniques Heterodyne SNOM Topography Intensity Topography Intensity Phase E. Flück et al., J. Ligtht. Tech., 21, 1384, (2003)
Advanced techniques Heterodyne SNOM Amplitude Phase Phase 0 5 10 15 20 Length, μm Courtesy I. Märki, Uni Neuchâtel scan area of 35X35μm 2
Heterodyne SNOM Once amplitude is known, Fourier transform gives information on the Bloch wave Dispersion curves A.cos(ø) A R.J.P. Engelen et al., Opt. Exp., 13, 4457, (2005) Fourier transform
a) Optical delay line Interference signal Fiber probe Advanced techniques Time resolved SNOM 0.5μm b a b c d e f g 0 ps h) 160 0.4 ps 0.8 ps Position ( μ m) 120 80 40 0 126.0 x 8.1 μm2 k = 0.607 k = 0.728 k = 0.849 k = 1.054 0 0.8 1.6 Delay (ps) 2.4 1.2 ps 1.6 ps 2.0 ps In Evanescent field-tail Si SiO 2 Al Glass W3 waveguide ~10nm 3 μm a b c d e f g h i j 121.1 x 8.1 μm2 0 ps 0.6 ps 1.2 ps 1.8 ps 2.4 ps 3.0 ps 3.6 ps 4.2 ps 4.8 ps k 5.4 ps H. Gersen et al., Phys. Rev. Lett., 94, 073903, (2005)
Principle Advanced techniques High Numerical Aperture Fourier Space Imaging of Planar Photonic Crystals Single point in the Fourier image (back focal plane) optics unique direction of emission k// conservation unique inplane wavevector
Principle Fourier imaging Make use of the light scattered off the propagation axis or plane intrinsically (above the light line) via imperfections / defects (below the light line) additional probe structures How? with "well-known" and "old-fashioned" classical optics
Real space imaging of Bloch Waves propagating in PhCs CCD L 3 L 2 x L 1 =1.48 m O injection InP Sample collection 36 m 3μm
Imaging of the scattered light Propagation losses and defect characterization W3 on InP 640a=250.8μm =1.485 m =1.495 m a=60cm -1 a=140cm -1 Propagation losses 2μm 2μm W1 on InP 160 a = 62.7μm Defect 10μm =1.5μm =1.55μm u = 0.261 u = 0.253
Fourier space imaging of Bloch wave emission diagram CCD L 3 L 2 x L 1 =1.48 m O injection InP Sample collection k y (2 /a) 0.2 0.1 0-0.1 r v g Y X 3μm -0.2 36 m -0.2-0.1 0 0.1 0.2 k (2 /a) x
Equi-Frequency surfaces mapping in PhCs Real space =1.48 m =1.51 m =1.55 m =1.63 m Fourier space 0.2 0.2 0.2 0.2 k y (2 /a) 0.1 0-0.1 k y (2 /a) 0.1 0-0.1 k y (2 /a) 0.1 0-0.1 k y (2 /a) 0.1 0-0.1-0.2-0.2-0.2-0.2-0.2-0.1 0 0.1 0.2 k (2 /a) x -0.2-0.1 0 0.1 0.2 k (2 /a) x -0.2-0.1 0 0.1 0.2 k (2 /a) x -0.2-0.1 0 0.1 0.2 k (2 /a) x
Reduced frequency u =a/ 0.30 0.29 0.28 Dispersion curves TM TE 0.10 0.15 0.20 0.25 Wave vector k (2 /a) 0.30 Objective light line coming soon
Intuitive image what is going on or avoiding some misinterpretations Why do we observe emission in a direction determined by the in-plane wave vector conservation rule? Ideal guided mode e ikr r = kr No time averaged structures, just a permanent phase relation due to wave propagation
Intuitive image what is going on or avoiding Random defects scattering some misinterpretations No structures in k-space = kr + r Each defect has a different emission pattern in intensity and phase No constructive interferences between scatterers, scattered emission loses phase information
Intuitive image what is going on or avoiding Identical defects scattering some misinterpretations Structures in k-space at k=k// e ikr = kr r Constructive interferences between scatterers
Intuitive image what is going on or avoiding some misinterpretations Periodic identical defects scattering (a grating) = kr + 2m m+1 m = kd Structures in k-space at k=gk//+mg e ikr d Constructive interferences between scatterers and possibly other diffraction orders
Intuitive image what is going on or avoiding some misinterpretations k y (2 /a) 0.2 0.1-0.1-0.2 The fringes are not an image of the Bloch mode. They originate from the interference between the forward and backward propagating mode, which are different modes at +k+mg and -k+mg 0-0.2-0.1 0 0.1 0.2 k (2 /a) x
Imaging of defect W3 PhC waveguide 1.5 m Y X Real space InP 1.1 m k y (2 /a) k y (2 /a) Fourier space 0.24 0.16 0.08 0-0.08-0.16-0.24-0.24-0.16-0.08 0 0.08 0.16 0.24 k x (2 /a) 0.24 0.16 0.08 0-0.08 u=0.266 u=0.266 Y X -0.16-0.24-0.24-0.16-0.08 0 0.08 0.16 0.24 k x (2 /a)
Experimental dispersion curves of a W3 PhC waveguide 0.270 Above the mini-stopband even odd In Out 0.265 u=a/ 0.260 odd 0.255 odd Inside the mini-stopband 0.250 even In Out 0.12 0.14 0.16 0.18 0.20 0.22 k (2 /a)
Optical and numerical FFT Because the phase information is still present during the formation of the Fourier image, there is no DC component and forward and backward propagation can be distinguished. k y (2 /a) 0.24 0.16 0.08 0-0.08 backward 0 forward backward 0 forward -0.16-0.24-0.24-0.16-0.08 0 0.08 0.16 0.24 k x (2 /a) Optical Fourier transform Numerical 2D-FFT
Comparison SNOM high NA imaging Near-field Far-field 1550 nm Real image 1524 nm Simulation Courtesy I. Märki, Uni Neuchâtel
In-situ characterization of a polarization splitter
In-situ characterization of a polarization splitter TM polarized light TE polarized light f45 f25 InP 18μm T=35% R=3% R=25% T=0.2%
In-situ characterization of a polarization splitter TE polarized light 0.2 k y (2 /a) 0.1 0.0-0.1-0.2 InP 18μm -0.2-0.1 0.0 0.1 0.2 k x (2 /a)
Fourier space imaging with filtering in real space TE polarized light 0.2 k y (2 /a) 0.1 0.0-0.1-0.2 InP 18μm -0.2-0.1 0.0 0.1 0.2 k x (2 /a)
Fourier space imaging with filtering in real space TE polarized light 0.2 k y (2 /a) 0.1 0.0-0.1-0.2-0.2-0.1 0.0 0.1 0.2 k x (2 /a) InP 18μm R 0.30 0.25 0.20 0.15 0.10 1480 1520 (nm) 1560 1600
but... Problem: most of the interesting structures work below the light line How to go beyond the light cone limit or how to convert evanescent waves into propagating waves for imaging?
1 Make use of fabrication imperfections
Imaging of Bloch wave propagating below the light cone 3 m SOI SC Self-collimation regime Stitching errors 240 m Reduced energy u=a/ Objective line Light line SC 0.2236 B Wave vector 3 m 10-6 6 4 2 10-7 6 SOI 4 I (W) 1520 SC B REF 1560 1600 1640 (μm)
2 Make use of finite size effects
Dispersion curves and super-resolution: Size effect 5μm 1 Fourier space 9μm 2.0 100 u=0.283 18μm 3 2 Intensity (norm.) 1.5 1.0 1 I (arb.units) 10 1 4 2 4 2 4 2 0.00 0.05 2 0.10 0.15 k ( 2 /a) 0.20 0.25 0.5 2 36μm 0.0 3-0.2-0.1 0.0 0.1 0.2 k (2 /a)
Dispersion curves and super-resolution: Size effect Reduced frequency u =a/ 0.30 0.29 0.28 TM TE Objective light line Light line 0.10 0.15 0.20 0.25 Wave vector k (2 /a) 0.30 Light line Intensity (arb.units) 100 10 1 =1.550μm -0.2-0.1 0.0 0.1 0.2 k (2 /a) Intensity (arb.units) 100 10 1 =1.630μm -0.2-0.1 0.0 0.1 0.2 k (2 /a)
Dispersion curves and super-resolution: Size effect and analytical prolongation 2 nd BZ 1 st BZ 2 nd BZ 9.7μm b) Intensity (arb. units) BW FW BW FW u=a/ 0.300 0.295 0.290 0.285 light line 0.280 0.275-0.5 0.0 0.5 k (2 /a) 0.1 0.2 0.3 k (2 /a) 0.4 0.5 T (arb. units) Effective NA = 2.5
Fourier space imaging with filtering in real space Characterisation below the light cone TE polarized light 0.2 k y (2 /a) 0.1 0.0-0.1-0.2 InP 18μm -0.2-0.1 0.0 0.1 0.2 k x (2 /a)
3 Fold back the band structure into the light cone with an extra periodicity just a small amount to enable measurement
Imaging of Coupled Cavities based Waveguides SEM Optical microscope 5.76μm 5.76μm a 1 a 2 581μm 5.76μm
Imaging of Coupled Cavities based Waveguides SEM Optical microscope 5.76μm a 1 a 2 k y (2 /a) 0.27 0.18 d 4 d 3 d 2 d 1 0.09 0-0.09 G sc -0.18-0.27-0.27-0.18-0.09 0 0.09 0.18 0.27 k (2 /a) x u=a/ 0.295 0.290 0.285 G sc d 1 d 2 d 3 d 4 Objective light line light line 0.280 0.275 0.0 0.1 0.2 k (2 /a) 0.3 0.40 20 40 60 T (arb. units) 80
Imaging of slow light propagating below the light cone regime I regime II G = 2 N. Le Thomas et al.,phys. Rev. B, in print (2007)
Imaging of slow light propagating below the light cone 100μm Y X 0.2 0.1 c) =1514nm k y (2 /a) 0-0.1 D1 Dr1 D2 N. Le Thomas et al.,phys. Rev. B, in print (2007) -0.2-0.2-0.1 0 0.1 0.2 k (2 /a) x
Imaging of slow light propagating below the light cone regime I regime II N. Le Thomas et al.,phys. Rev. B, in print (2007)
Imaging of slow light propagating below the light cone Theory Experiment N. Le Thomas et al.,phys. Rev. B, in print (2007)
Techniques outline Lithographic tuning External light source Reflectivity End fire Internal light source Internal light source Luminescence spectroscopy Advanced techniques Local probe, SNOM Time resolved Fourier imaging