Coherent optical receiver using phase modulation detection

We propose a coherent receiver scheme based on phase modulation (PM) detection that recovers the in-phase (I) and quadrature (Q) components of the optical signal and potentially simplifies the front-end of a coherent optical receiver [1]. The scheme has been demonstrated for a differentially coherent, self-heterodyne receiver via simulations for DQPSK and experimentally for DBPSK. Fig. 1 shows the experimental setup in which the upper arm of the interferometer has a one-symbol delay and the lower arm is phase modulated by a sine wave. The incident E-field on the photo-detector can be written as equation where equation is the received optical E-field with optical frequency ω_o and power P. ø(t) and T_s respectively are the symbol phase modulation and duration (at 2 GSps symbol rate), a(t) is the normalized symbol amplitude modulation. For brevity we have omitted the laser phase and intensity noises. The input signal to the phase modulator is bsin(ω_ct + ø_c) where b is the PM index, É_c and ø_c are the angular frequency and phase of the modulating carrier at 2 GHz, respectively. The output current of the photo-detector with responsivity ℜ is proportional to the intensity of the incident field: equation Ignoring the first two terms (which can be cancelled using balanced photo-detectors) and expanding the third term: equations Using the Bessel coefficient expansions: equations where J_k(b) is the Bessel function of the first kind with integer order k, we find that the I and Q components of the complex differential optical modulation envelope, a(t)a(t-T_s)e^{j[ø(t)-ø(t-Ts)]}, can be found at the even and odd harmonics of i(t). In particular, we have at the first and second harmonics: Q(t)~2J₁(b)a(t)a(t-T_s)sin[ø(t)-ø(t-T_s) + ω_oT_s]sin(- ω_ct + ø_c) I(t)~-2J₂(b)a(t)a(t-T_s)cos[ø(t)-ø(t-T_s) + ω_oT_s]cos[2(ω_ct + ø_c)] and at base-band: I(t)~-J_o(b)a(t)a(t-T_s)cos[ø(t)-ø(t-T_s) + ω_oT_s].