Creation and Annihilation of Optical Phase Singularities H.F. Schouten 1 , T.D. Visser 1 , D. Lenstra 1 and H. Blok 2 1 Dept. of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam 2 Dept. of Electrical Engineering, Technische Universiteit Delft, Mekelweg 4, 2628 CD, Delft Using a rigorous scattering model we study the electromagnetic field around a subwave- length slit in a metal plate with finite conductivity and finite thickness. It is found that the transmission can be strongly enhanced when the phase singularities (“optical vortices”) of the Poynting vector field have a certain position. We examine the creation and anni- hilation of different kinds of phase singularities as a function of the incident wavelength and slit width. The analysis of light transmission through a slit with a sub-wavelength width in a thin plate is a subject with a venerable history [1, 2, 3], dating back to Lord Rayleigh. Be- cause of its importance for near-field optics and semiconductor technology, it continues to attract attention. Recently Ebbesen et al. observed extraordinary light transmission (i.e., more than 100%) through an array of sub-wavelength holes [4], which led to a new wave of interest in the subject. In this paper we study the light transmission through a single sub-wavelength slit in a metal plate of finite conductivity for the TE-polarization case. A rigorous computation of the field [5] demonstrates that for certain widths, there is an enhanced transmission through the slit. To understand this anomalous transmission, we have analysed the field of power flow (i.e. the time-averaged Poynting vector) near the slit. It is found that this field exhibits optical vortices and other kinds of phase sin- gularities [6, 7], which are arranged in an array-like pattern. We find that the location and annihilation/creation of these phase singularities are intimately connected with the phenomenon of enhanced transmission. A typical example of the calculations of the field of power flow near a slit is shown in Fig. 1, where the field is seen to exhibit phase singularities, i.e. points were the amplitude of the time-averaged Poynting vector is zero and as a consequence its direction, or equiv- alently its phase, is undetermined. It is seen that the anomalous transmission (namely T 1 11) coincides with the presence of two optical vortices (a and b) within the plate, and a “funnel-like” power flow into the slit. This “funnel-like” effect corresponds to a transmission coefficient of more than one. In addition, four other phase singularities are visible just below the slit (c,d,e and f; two saddle points and two vortices). In Fig. 2 the location of the phase singularities is shown on a larger scale. It is seen that they are ar- ranged in an array-like pattern. It is to be noted that only part of the phase singularities are shown—the pattern is continuous in a periodic way to the left and right, and also downwards. Changing the slit width in a continuous manner causes the phase singularities to move through space. Near w 0 45λ the array of phase singularities along the symmetry-axis annihilate, each annihilation consisting of two vortices (one left-handed and one right- handed) and two saddle points. In Fig. 3 the resulting arrangement for w 05λ is shown. Because the annihilation of phase singularities leads to a smoother field of power flow,