Schematic diagrams of heterodyne phase-locking configurations. (a) A typical diode laser phase synchronization system. (b) A simplified phase synchronization configuration that takes advantage of an in-loop frequency divider and eliminates the microwave synthesizer.
Spectra of optical beat notes at 6.8 GHz (1) and at 212 MHz (2). The PLL is off.
Spectra of optical beat notes of two phase-locked lasers. PLL with microwave synthesizer (1); PLL with frequency divider (2) (n = 8).
Spectra of optical beat notes with the PLL enabled for various frequency division ratios. Resolution bandwidth = 30 kHz.
Spectra of optical beat notes at 6.8 GHz and 850 MHz. The PLL is on. Resolution bandwidth = 30 kHz.
Effect of PLL on phase noise spectra: PLL is disabled (1); “narrow-band” PLL is on (2); “medium-band” PLL is on (3); and “broad-band” PLL is on (4). A power law fit to the “free-running” spectrum gives S ϕ(F) ≃ 3 × 105/F 4 + 100/F 2 rad2/Hz. The filtered spectra are truncated at low frequency, since it was not possible to correctly reproduce them without increasing T obs and N.
Effect of the PLL on the power spectra of simulated beat notes in the case of a purely random phase modulation (a) and a mixture of random phase noise and low-frequency sinusoidal modulation (b): PLL is disabled (1), “narrow-band” PLL is enabled (2), “medium-band” PLL is enabled (3), and “broad-band” PLL is enabled (4).
Simulated power spectra of frequency-multiplied beat notes: PLL is disabled (1), “narrow-band” PLL is enabled (2), “medium-band” PLL is enabled (3), and “broad-band” PLL is enabled (4). The carrier frequency was 800 kHz, N was 221, and the number of averages was 128. Phase locking with a narrow carrier is observed only in the cases 3 and 4.
Dynamics of the PLL based on the first-order low-pass filter. (a) Frequency difference Δω and phase difference ΔΦ. (b) PLL amplifier output voltage u amp as a function of time.
Dynamics of the PLL based on an ideal integrator. (a) Frequency difference between two oscillators Δω (open- and close-loop control). (b) Closed-loop phase difference ΔΦ and voltage at the output of the PLL amplifier u amp as a function of time.
Effect of PLL bandwidth on the magnitude of phase disturbances caused by large-scale variations of Δω. Curves 1, 2, and 3 correspond to the “locked” phase difference computed for progressively increasing bandwidth of the phase control loop.
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