Fig. 1. Illustrating the relation between phase singularities (a), stationary points of the phase (c,e), and the corresponding singularities of the power flow (b,d,f). The arrows in the left-hand column indicate the direction of increasing phase Φ _E .

Fig. 2. Illustrating the notation relating to transmission through a slit.

Fig. 3. Illustration of the power flow in the neighborhood of a 200 nm wide slit in a 100 nm thick plate of evaporated silver, with wavelength λ = 500 nm and n = 0.05+i2.87 (the value of the refractive index wastak en from [11]). Features (a) and (d) are left-handed centers, (b) and (c) are right-handed centers, and (e) and (f) are saddles. For this example the transmission coefficient T = 1.11. The color coding indicatesthe modulus of the (normalized) Poynting vector. The dashed box indicatest he region illustrated in Movie 1.

Fig. 4. (186 KB) The field of power flow asa function of the slit width w in the region indicated in Fig. 3. The four phase singularities move together as the slit width is increased, and finally annihilate, leaving a smoother field of power flow corresponding to a higher transmission coefficient T.

Fig. 5. Array of singularities in the field of power flow in the neighborhood of the slit. All parametersar e as given in Fig. 3. Left-handed vortices(cen ters) and righthanded vortices (centers) are denoted by LV and RV, respectively, and saddles are denoted by S.

Fig. 6. (212 KB) Schematic of the position and type of singularities of power flow near a sub-wavelength slit. It is to be observed that multiple creation and annihilation events occur as the slit width is gradually increased. Left-handed vortices (centers) and right-handed vortices (centers) are denoted by LV and RV, respectively, and saddlesar e denoted by S. U denotesa vortex (center) very close to a saddle point which cannot be spatially resolved by the particular grid used for these calculations; it can be seen that eventually the singularities separate sufficiently to be distinguishable.