OBSERVATION OF THE OPTICAL ANALOG OF QUANTIZED CONDUCTANCE OF A POINT CONTACT

DIFFRACTION of light by an aperture is a well-known manifestation of the wave nature of light. The most familiar case is that of an incident plane wave, which is diffracted into a spatial pattern that is sensitive to the properties of the aperture: the ratio of transmitted power to incident flux (the transmission cross-section-sigma) depends in a complicated way on the aperture area A (refs 1-3). For diffuse (that is, isotropic rather than plane-wave) illumination, however, the situation is much simpler 4: in three dimensions, sigma increases with A in a series of steps of equal height lambda-2/2-pi (where lambda is the wavelength of the light), and is thus independent of the detailed aperture shape. A similar simplification occurs for two-dimensional diffuse illumination of a slit: the transmission cross-section per unit slit length increases in stepwise fashion as a function of the slit width W, with steps of height lambda/2 occurring whenever W = n-lambda/2 (n = 1, 2, 3,...) - that is, whenever a new mode is enabled in the slit. Although the optical transmission characteristics of slits have been studied extensively for plane-wave illumination 5-8, we know of no investigation of this predicted staircase dependence for diffuse illumination. Here we report the observation of such an effect, and suggest that it may play a part in any process of wave propagation through a constriction.