Abstract: Based on the system Hamiltonian and Heisenberg equation of motion for system operators, we derived the input-output relations of the optical modes. Moreover, using the Green function theory, the coupling rate between the cavity and waveguide is analytically defined. Based on the above, we derived the analytic solution of the transmission spectra. By numerical calculation, the transmission spectra of the whole system are investigated with varying optical length (which induces the phase separation between the two cavities) and detuning factor between the two cavities. The results reveal that the transmission spectra are closely dependent on the distance and detuning of the two cavities. This structure has potential applications in quantum information, quantum computation and optical switch.

Key words: Quantum Optics；Analytic transmission spectra; Green function theory; Waveguide-cavities-quantum dot system