Detection of Mode-Locked Laser Signals

Citation

D'Orazio, Robert Joseph (1973) Detection of Mode-Locked Laser Signals. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/26D2-8776. https://resolver.caltech.edu/CaltechTHESIS:11122019-160113596

Abstract

In this work we describe our approach to matched-filtering for mode-locked laser signals. Our optical receiver consists of a passive laser cavity controlled in length and a photodetector with its associated electronics. The length of the passive Fabry-Perot cavity is chosen roughly equal to the cavity length of the transmitting laser, but with provision for fine fractional wavelength control of its length. In addition to the selective filtering characteristics of the passive cavity (passbands of unity transmission matching the frequencies of the multi-mode laser), a readout of the vernier length control, peaking the output, provides for an extremely wide range of velocity measurements with either an active or passive vehicle moving relative to the receiver.

In studying the mode-locked laser we use the matched-filter criterion resulting from the optimization of the signal-to-noise ratio. This criterion specifies that the amplitude transmission function be T_m(ω) = AE*(ω)/S_n(ω); where E(ω) is the Fourier transform of the laser signal E₁(t); S_n(ω) is the power spectral density of the additive input noise; the asterisk denotes the complex conjugate; and A is any nonzero complex constant. For an actual laser signal, writing E(ω) for the multi-tone laser with finite linewidths Δω_ℓ yields an expression which is comparable on a mode by mode basis to the transmission function for a Fabry-Perot cavity. The resulting matching conditions are that Δω_p = Δω_ℓ and h_o = h in which Δω_p is the linewidth of the receiver cavity of length h_o, and h is the length of the transmitter cavity.

The Fabry-Perot cavity is probably as close a physical realization to a matched-filter for the multi-toned laser as can be attained in a passive system. Even so, gain narrowing invariably results in Δω_ℓ < Δω_p, thereby limiting the observed improvement in signal-to-noise ratio from its optimal value. For high gain lasers with cavities of low finesse, the receiver can be made closer to the ideal, while greater departures are to be expected in the case of low gain.

Further study of the use of the passive cavity in contrast to no cavity shows that the signal-to-noise ratio improves approximately by the finesse of the cavity which is typically 150. Considering the improvement in signal-to-noise ratio as a function of the number of oscillating modes N we find that the peak value of the temporally varying detected output has a signal-to-noise ratio proportional to N², i.e., it varies as the peak power of the mode-locked laser.

Now, suppose that the mode-locked laser is moving toward our receiver with a velocity v. For TEM waves, an emitted frequency ω' will be observed shifted to ω given by ω = γ(1 + v/c)ω' in which γ = [1 - (v/c)²]^-l/2 and c is the speed of light. In this case where there is relative motion, we find that optimal detection of the mode-locked laser signal requires a receiver with a cavity length h_o given by h_o = h/[γ(1 + v/c)]. Similarly, if the mode-locked laser and the passive cavity were on a common platform, then the echo from a vehicle moving toward this platform with velocity v would be shifted to ω = (1 + 2v/c)ω', where we have set γ = 1. So by vernier adjustments of the passive cavity length we can read a large range of approach velocities with a resolution independent of the velocity.

Thesis Files