This paper presents a new petabit photonic packet switch architecture, called PetaStar. Using a new multidimensional photonic multiplexing scheme that includes space, time, wavelength, and subcarrier domains, PetaStar is based on a three-stage Clos-network photonic switch fabric to provide scalable large-dimension switch interconnections with nanosecond reconfiguration speed. Packet buffering is implemented electronically at the input and output port controllers, allowing the central photonic switch fabric to transport high-speed optical signals without electrical-to-optical conversion. Optical time-division multiplexing technology further scales port speed beyond electronic speed up to 160 Gb/s to minimize the fiber connections. To solve output port contention and internal blocking in the three-stage Clos-network switch, we present a new matching scheme, called c-MAC, a concurrent matching algorithm for Clos-network switches. It is highly distributed such that the input-output matching and routing-path finding are concurrently performed by scheduling modules. One feasible architecture for the c-MAC scheme, where a crosspoint switch is used to provide the interconnections between the arbitration modules, is also proposed. With the c-MAC scheme, and an internal speedup of 1.5, PetaStar with a switch size of 6400 × 6400 and total capacity of 1.024 petabit/s can be achieved at a throughput close to 100% under various traffic conditions.