Presentation on theme: "Squeezing Light Through Small Holes"— Presentation transcript:
1 Squeezing Light Through Small Holes Taco D. VisserVU University AmsterdamTexPoint fonts used in EMF: AAAAAAA
2 How much light is transmitted by a small aperture in a metal plate? 10 mm2 mmMetal10 incident rays20 % of the metal plate is open, so only 2 out of 10 rays canpass through. The others are reflected or absorbed.Geometrical optics predicts a transmission of 20%.
3 But what about nano-holes? 100 nanometer20 nanometerMetalFor holes that are smaller than the wavelengthgeometrical optics is no longer valid.So what happens to the transmission? Is it still 20%?
4 Extraordinary Optical Transmission T.W. Ebbesen et al., Nature 391, 1998.The round holes are 20% of the surface.But the transmission is more than 20%!How is this extraordinary transmission possible?
5 Hole Shape Influences the Transmission Three types of holes:a. Circular holes, with an area of 28,000 nm2b. Rectangular holes with an area of 16,000 nm2c. Rectangular holes with an area of 32,000 nm2Klein Koerkamp et al. Physical Review Letters 92, 2004.
6 Influence of the hole shape Surprisingly, at 900 nm the small rectangular holes transmits more light than the larger holes!This again shows that geometrical optics is not a goodmodel for this situation.The circular holes always transmit less.
7 Slit in a Metal PlateDepending on the slit width w, zero, one, two or more guided modes can exist in the hole. Their number influences the transmission.
8 A Scattering Approach = field around metal plate without slit Split field into two parts:= field around metal plate without slit= scattered field due to slit2. Convert Maxwell’s equation into anintegral equation:3. Solve integral equation numerically
9 Transmission vs. Slit Width for Silver Plate w/lSilver (n = i 2.87)l = 500 nmthickness = 100 nmQuestion:How can transmission be > 1 ?
10 Effective index of first TE mode in silverWhen the width w = 0.4 l, the first TE mode kicks in.
13 More Topological Structures source sink vortexsaddle monkey saddle dipole
14 Many AnnihilationsIf we increase the slit width a little, a host of structures annihilate, leading to a smoother power flow and thus an enhanced transmissionThis annihilation of vortices and saddle pointscoincides with the onset of the first guided modePRE 67, (2003)
15 Optical VorticesIn the example of a narrow slit in a silver film, the vortices seem to concentrate the power flow and that way more light is `pushed through’ the slit than you would expect.But what happens when we change the material from a metal into a semiconductor such a silicon?
16 Silver vs. Silicon red = silicon (n = 4.3 – i 0.74) l = 500 nm Tw/lred = silicon (n = 4.3 – i 0.74)blue = silver (n = 0.05 – i 2.87)l = 500 nmthickness = 100 nmTransmission for a slit in a silicon plate is less than expected.
17 Changing the handedness of the vortices: Silicon A narrow slit in a silicon plate has a low transmission, i.e. T< 1it transmits less light than you would expect.This anomalously low transmission coincides with achange in handedness of the optical vortices (b and c) .Notice the two saddles (a and d) and the two sinks.J. of Optics A 6, S277 (2004).
18 Creating a monkey saddle The two saddle points have joined to form a monkey saddle (e).The two vortices (b and c) have moved sideways, but still pushthe light “the wrong way.”
19 Surface Plasmons - IWhen an incident TM field hits the slit, surface plasmons aregenerated.They travel away from the slit to the left and to the right.Eventually the plasmons are absorbed by the metal.surface plasmonsurface plasmonincident TM wave
20 Surface Plasmons - II Until now we have only analyzed a single slit. If we have two slits, are they independent?dIncident TM waveWhat is the influence of the two slits on each other?
21 Surface Plasmons - III Transmitted plasmon field Incident TM wave A part of the incident field at the left slit is converted intosurface plasmons that travel to the right.There the surface plasmons can change back into a free field again.The same thing happens at the right slit.So, in each slit there are two fields: the directly transmitted fieldand the surface plasmons from the other slit.
22 Surface Plasmons Interference dinterferenceincident TM waveAt each slit the total field consists of two contributions:1. The directly transmitted field.2. The surface plasmon field coming from the other slit.The two fields can interfere in a constructive or in adestructive manner.
24 Plasmon Interference (changing d ) Maximum intensity at the slitsMinimum intensity at the slits
25 Experiment (changing l) The total transmission varies strongly with the wavelength,just as predicted.Distance between slits = 25 mm, Width slit = 200 nmThickness plate (gold) = 200 nm, TM polarizationPhys. Rev. Lett., 94, , 2005.
26 Steering the PlasmonsSurface plasmons generated at the slit travel to left and to the rightCan we control the direction in which the plasmons are launched?Until now only static schemes (built-in asymmetry) have been proposed.surface plasmonsurface plasmonincident TM beam
27 piezoA narrow slit in a gold film allows only two TM modes,one is symmetric (TM0), the other anti-symmetric (TM1).Beam B only excites the even mode.Beams A and –A have the same amplitude but are p phase shifted.Together they only excite the odd mode.By varying the phase of beam B with a piezo we can control thesuperposition of the two guided modes.
28 -- Total magnetic field on interfaceBy tuning the superposition of the two modes we can get completecancellation of the field at one side of the slit exit.Plasmons will only be generated on the opposite side:Unidirectional plasmon launching
29 By simply changing the phase of the normally incident beam, we get dynamic plasmon switchingOptics Express 20, (2012).
30 Steering the Radiation Field The transmitted light is radiated symmetrically.Can we also control the direction of radiation?incident laser beam
31 Minima of the far-zone radiation of a slit coincide with phase singularities in the near-field along the line of sight.Physical Review Letters, vol. 93, (2004).
32 Using the same method of selective mode excitation, we can steer the radiation continuously from left to rightby varying the voltage across the piezo.
33 Two different voltage settings across the piezo give radiation to the left (blue) or to the right (red).Physical Review Letters, vol. 111, (2013).
34 ConclusionsThe extraordinary transmission of light through nano-apertures is accompanied by optical vortices that funnel the light.Very low transmission (as in silicon) is accompanied by optical vortices steering the light away from the slit.The onset of guided modes is accompanied by the annihilation of vortices and saddles.Surface plasmons generated at one hole can travel to another holewhere they interfere with the directly incident field.Depending on the hole separation this eitherincreases or decreases the transmission.There is a connection between the direction of minimal radiationand the presence of phase singularities near the slit.By selective excitation of the guided modes we can dynamically steer both the plasmons and the radiated field.and finally….
35 Thanks to Shreyas Raghunathan (Delft) Hugo Schouten (Amsterdam) Thomas van Dijk (Urbana Champain)Greg Gbur (Charlotte)Wim Ubachs (Amsterdam)Erik Eliel (Leiden)Dave Fischer (NASA, Cleveland)Phillipe Lalanne (Paris/Bordeaux)