  Stochastic computing allows a drastic reduction in hardware complexity using
serial processing of bit streams. While the induced high computing latency can
be overcome using integrated optics technology, the design of realistic optical
stochastic computing architectures calls for energy efficient switching
devices. Photonics Crystal (PhC) nanocavities are $\mu m^2$ scale devices
offering 100fJ switching operation under picoseconds-scale switching speed.
Fabrication process allows controlling the Quality factor of each nanocavity
resonance, leading to opportunities to implement architectures involving
cascaded gates and multi-wavelength signaling. In this report, we investigate
the design of cascaded gates architecture using nanocavities in the context of
stochastic computing. We propose a transmission model considering key
nanocavity device parameters, such as Quality factors, resonance wavelength and
switching efficiency. The model is calibrated with experimental measurements.
We propose the design of XOR gate and multiplexer. We illustrate the use of the
gates to design an edge detection filter. System-level exploration of laser
power, bit-stream length and bit-error rate is carried out for the processing
of gray-scale images. The results show that the proposed architecture leads to
8.5nJ/pixel energy consumption and 512ns/pixel processing time.
