How does light emerge from a small hole?  (accepted for publication in Optics Express)

(voor Nederlandse versie klik hier)

When holes are smaller than half-a-wavelength, conventional wisdom says that the transmission of light by such a hole becomes very difficult. Exactly how light passes through a small hole is not well-known. This is because any experimental technique to measure this requires a spatial resolution much smaller than the diameter of the hole, which is itself already smaller then the wavelength. In conventional optics, the diffraction limit imposes a lowest value of half-a-wavelength on the smallest feature that can be observed using imaging techniques. To obtain a higher spatial resolution, one has to resort to near-field techniques. Here, we show measurements of the THz electric near-field of small, sub-wavelength sized, apertures. A schematic setup is shown in the figure below.

A THz pulse is incident on a small aperture in a gold film. Key to measuring the electric near-field of the hole is the integration of the hole with the detector. The detector consists of a (100)-oriented GaP electro-optic crystal in which the THz electric field induces a refractive-index change in the GaP crystal, which is sampled by a focused probe laser pulse. Our choice of the EO crystal ensures that we are only sensitive to the z-component of the THz electric field. This is the component perpendicular to the metal surface. In the picture below, we plot this component at the shadow side of a 150 micron diameter aperture, at 4 different times after the THz pulses impinges on the aperture. Blue indicates negative electric field, red positive.

One can clearly see how the field is localized near the edges of the hole and spreads out radially as time increases. On the right, the field incident on the hole (bottom), the time-differentiated incident field and the the measured near-fields for three aperture sizes are shown. The image shows that for decreasing hole size, the THz electric near-field increasingly resembles the time-differentiated incident field. This behavior was actually predicted, but has never been measured until now, by Bouwkamp in 1950.

Interestingly enough, recent results show how we are capable of measuring the transmission of a small hole, even for wavelengths fifty times larger than the hole diameter!

Square apertures

Results for square holes are shown in the figure below. Again, the field is localized near the edges. Blue indicates a negative z-component, red indicates a positive z-component. The scanned area here is larger than for the round holes, showing the creation and spreading out of the THz electric field as time progresses.

One of the clear advantages of these experiments is the use of broadband  THz pulses, allowing us to show how the field behaves for many different frequencies. Below, four movies are shown, for four different frequencies. Each movie shows the time-evolution of the near-field, during one oscillation period of the near-field at that frequency. At the highest frequency of 537 GHz, the bands of light spreading out from the hole are more closely spaced compared to those at 98 GHz. This is because the wavelengths are longer in the latter case. The movies provide a clear illustration of how light emerge from a small hole.