Presentation on theme: "Squeezing Light Through Small Holes Taco D. Visser VU University Amsterdam TexPoint fonts used in EMF: AAAAAAA."— Presentation transcript:
Squeezing Light Through Small Holes Taco D. Visser VU University Amsterdam TexPoint fonts used in EMF: AAAAAAA
How much light is transmitted by a small aperture in a metal plate? 20 % of the metal plate is open, so only 2 out of 10 rays can pass through. The others are reflected or absorbed. Geometrical optics predicts a transmission of 20%. Metal 10 incident rays 2 mm 10 mm
But what about nano-holes? For holes that are smaller than the wavelength geometrical optics is no longer valid. So what happens to the transmission? Is it still 20%? Metal 20 nanometer 100 nanometer
T.W. Ebbesen et al., Nature 391, The round holes are 20% of the surface. But the transmission is more than 20%! How is this extraordinary transmission possible? Extraordinary Optical Transmission
Three types of holes: a. Circular holes, with an area of 28,000 nm 2 b. Rectangular holes with an area of 16,000 nm 2 c. Rectangular holes with an area of 32,000 nm 2 Klein Koerkamp et al. Physical Review Letters 92, Hole Shape Influences the Transmission
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 good model for this situation. The circular holes always transmit less.
Slit in a Metal Plate Depending on the slit width w, zero, one, two or more guided modes can exist in the hole. Their number influences the transmission.
A Scattering Approach 1.Split field into two parts: = field around metal plate without slit = scattered field due to slit 2. Convert Maxwell’s equation into an integral equation: 3. Solve integral equation numerically
Transmission vs. Slit Width for Silver Plate Silver (n = i 2.87) = 500 nm thickness = 100 nm w/ T Question: How can transmission be > 1 ?
Effective index of first TE mode in silve r When the width w = 0.4, the first TE mode kicks in.
Many Annihilations This annihilation of vortices and saddle points coincides with the onset of the first guided mode PRE 67, (2003) If we increase the slit width a little, a host of structures annihilate, leading to a smoother power flow and thus an enhanced transmission
Optical Vortices In 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?
Silver vs. Silicon red = silicon (n = 4.3 – i 0.74) blue = silver (n = 0.05 – i 2.87) w/ T = 500 nm thickness = 100 nm Transmission for a slit in a silicon plate is less than expected.
Changing the handedness of the vortices: Silicon A narrow slit in a silicon plate has a low transmission, i.e. T 1 it transmits less light than you would expect. This anomalously low transmission coincides with a change 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).
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 push the light “the wrong way.”
Surface Plasmons - I When an incident TM field hits the slit, surface plasmons are generated. They travel away from the slit to the left and to the right. Eventually the plasmons are absorbed by the metal. incident TM wave surface plasmon
Surface Plasmons - II Until now we have only analyzed a single slit. If we have two slits, are they independent? What is the influence of the two slits on each other? d Incident TM wave
Surface Plasmons - III A part of the incident field at the left slit is converted into surface 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 field and the surface plasmons from the other slit. Incident TM wave Transmitted plasmon field
Surface Plasmons Interference At 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 a destructive manner. incident TM wave d interference
Changing the phase of the Surface Plasmons
Plasmon Interference (changing d ) Minimum intensity at the slits Maximum intensity at the slits
Experiment (changing ) The total transmission varies strongly with the wavelength, just as predicted. Distance between slits = 25 m, Width slit = 200 nm Thickness plate (gold) = 200 nm, TM polarization Phys. Rev. Lett., 94, , 2005.
Steering the Plasmons Surface plasmons generated at the slit travel to left and to the right Can we control the direction in which the plasmons are launched? Until now only static schemes (built-in asymmetry) have been proposed. incident TM beam surface plasmon
A narrow slit in a gold film allows only two TM modes, one is symmetric (TM 0 ), the other anti-symmetric (TM 1 ). Beam B only excites the even mode. Beams A and –A have the same amplitude but are phase shifted. Together they only excite the odd mode. By varying the phase of beam B with a piezo we can control the superposition of the two guided modes. piezo
By tuning the superposition of the two modes we can get complete cancellation of the field at one side of the slit exit. Plasmons will only be generated on the opposite side: Unidirectional plasmon launching -- Total magnetic field on interface
By simply changing the phase of the normally incident beam, we get dynamic plasmon switching Optics Express 20, (2012).
Steering the Radiation Field The transmitted light is radiated symmetrically. Can we also control the direction of radiation? incident laser beam
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).
Using the same method of selective mode excitation, we can steer the radiation continuously from left to right by varying the voltage across the piezo.
Two different voltage settings across the piezo give radiation to the left (blue) or to the right (red). Physical Review Letters, vol. 111, (2013).
Conclusions The 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 hole where they interfere with the directly incident field. Depending on the hole separation this either increases or decreases the transmission. There is a connection between the direction of minimal radiation and 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….
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)