Photonic crystal (PhC) based integrated optical circuits have attracted a great deal of interest within the last decade. These artificially designed materials allow for a wide ranging control of the optical properties and thus the realization of devices with smaller footprint or new functionality. Recently nonlinear optical effects in PhCs raised much attention because their efficiency can be enhanced [1].One critical issue of PhC components is still their considerable propagation loss. Material absorption and scattering losses can be reduced using cleaner materials and better production processes, but radiation losses remain problematic even for ideal structures. Therefore, the control of losses, which are due to coupling to radiation modes of the surroundings, is already important at the design stage.Here we investigate the most prominent source of radiation losses, the radiation into the substrate in slab based geometries. These PhC slabs are experimentally most studied and best adapted to contemporary lithographic technologies. More specifically, we investigate line defect waveguides in PhC membranes suspended over a substrate at a finite distance. There is evidence for a resonance mechanism in the air gap exploited earlier elsewhere without further systematic investigation or confirmation [2][3][4]. In order to obtain an appropriate photonic bandgap for TE polarized light we use a hexagonal lattice of air holes as PhC. We focus on a W1 waveguide, defined by removing one row of holes in ГK direction (see Fig. 1). We show how the radiation losses depend on the system parameters and how they can be reduced by simple means. 0 0.1 0.2 0.3 0.4 0.5 Bloch vektor kΛ -1 0.36 0.4 0.44 0.48 frequency Re(ω)(cΛ) -1 light line 0.4 0.42 0.44 frequency Re(ω)(cΛ) -1 0.1 0.2 0.4 0.6 0.08 0.06 0.04 normalized loss dBa -1 da -1 =0.6 da -1 =0.8 da -1 =1.2 membrane Fig. 1. W1 waveguide in a PhC membrane suspended over a substrate with a finite air gap (left), dispersion relation (middle), and loss spectra for different air gap widths (right) of the waveguide. dWe assume a refractive index of , corresponding roughly to lithium niobate (neglecting the birefringence), a common quadratically nonlinear and electrooptic material (on its patterning see, e.g. [5]). The hexagonal lattice of cylindrical air holes of radius and pitch is patterned into a membrane of height . In the following we use a normalized radius 2.211 n = r a h 0.317 r a = and height 0.833 h a = . The dispersion relation of the fundamental mode of the waveguide is shown in Fig. 1. We calculate the propagation losses from three-dimensional finite-difference time-domain transmission simulations of long waveguides for different air gap widths (see Fig. 1). The non-monotonic and wavelength dependent losses can clearly be identified and the curves intersect. There is even a loss reduction forcompared to the pure membrane case ( ). This altogether is clear evidence for a wavelength dependent resonance mechanism obtained when a substrate layer is brought in optical proximity t...