Nonlinear heterodyne detection with two independently stabilized cw CO2

lasers Denis Vincent and Gabriel Otis

Defence Research Establishment Valcartier, P.O. Box 8800, Courcelette, P.Q. GOA 1R0. Received 14 July 1982. 0003-6935/83/010013-03$01.00/0. While working on cw CO2 rangefinders with amplitude

modulation in homodyne configuration, it became clear that optical isolation between the transmitter and local oscillator paths was a major problem.1 In the case of moving targets with Doppler shifts much larger than the modulation fre­quency (fm = 15 kHz), adequate isolation was achieved through use of an electronic high-pass filter (fcutoff ≥ fm )• But then the system is unable to range on stationary targets. We, therefore, looked at a heterodyne configuration with two in­dependently stabilized CO2 lasers. While this should elimi­nate the isolation problem, questions arise about the behavior of the SNR with respect to Doppler shifts and to variations of the relative frequency between the two lasers. Provided that the detector has a sufficient bandwidth, this problem of intermediate-frequency shifts should be treated as in the single-laser case with moving targets. To test this statement, we used a laboratory setup (Fig. 1) with a conventional low-pressure (2.7-kPa) cw CO2 laser as transmitter and a dc-ex-cited waveguide CO2 laser as local oscillator.2 Both lasers are dither-stabilized to the peak of the P20 line. The waveguide laser is made of a BeO tube (2-mm bore diameter, 20 cm long), has a Littrow-mounted grating (135 lines/mm), and uses a gas mixture (8.8 kPa) containing Xe so that it produces ~1 W on P20 in the lowest-order transverse mode. The conventional laser also has a grating and emits ~1 W on the TEM00 mode.

Fig. 1. Experimental setup: T, transmitter; LOC, local oscillator; SPEC, spectrum analyzer; STAB, stabilization loop; OSC, oscillator at 15 kHz; P1, P2, polarizers; CYL, rotating cylinder (target); MON, power monitor; M signal magnitude; φ, signal phase; L, converging

lenses.

1 January 1983 / Vol. 22, No. 1 / APPLIED OPTICS 13

The range-measurement technique is based on amplitude modulation, envelope recovery, and coherent detection of the transit-time induced phase shift of the envelope. The enve­lope detector is a diode with a square-law characteristic. The electrooptic amplitude modulator is driven by the oscillator of the coherent amplifier (PAR 5204) whose output is ampli­fied by an audio amplifier (RCA HC2000H) and fed to the crystal via the HV transformer. At the resonant frequency of ~15 kHz, the modulation depth is ~80%. The rotating cylinder (sandblasted aluminum) induces a maximum Dop-pler shift of ~1 MHz. The local oscillator and signal beams are mixed on a SAT HgCdTe photodiode with an area of 4 X l0 - 4 cm2, a D*10.6 of 1.4 X 1010 cm-Hz½-W-1, and a measured quantum efficiency η of 0.2. This detector is reverse biased at 200 mV and its output fed to Avantek amplifiers via an RF transformer. The overall spectrum is displayed on a Tek­tronix 7L12 spectrum analyzer. The signal then passes through a 20-MHz low-pass filter to reduce the noise band­width at the input of the square-law detector (HP 8471A). The signal is read by the coherent detector (PAR 5204), whose output gives the magnitude and phase of the signal. The noise is read by the wave analyzer (HP 310A) tuned 2 kHz below fm, since, in square-law detection at high SNR, the noise depends on the signal magnitude and so cannot be read by blocking the signal.3

Although stabilized at the peak of the P20 line, the wave­guide laser produces an output frequency which is offset by several megahertz from the transmitter laser frequency. Figure 2 shows clearly that the peak of the transmitter laser (upper trace) does not correspond to the zero-frequency beat (lower trace). These traces were taken by sweeping the low-pressure (conventional) laser cavity. The maximum fre­quency excursion is ~45 MHz, which is the apparent width of the low-pressure line. When both lasers are actively sta­bilized, the beat frequency is ~10 MHz. The same phe­nomenon has been observed by other workers4 who have noted a beat frequency of 12 MHz at 13.3 kPa with a different gas mixture. We are currently making a thorough investigation of this effect.

To simulate frequency independence between the two lasers while taking SNR measurements, we increased the dithering amplitude on the waveguide laser cavity. Although the in­stantaneous beat frequency was unique, it was found to vary in time between 5 and 15 MHz.

Fig. 2. Beat between the conventional CO2 laser at 2.7 kPa and the waveguide CO2 laser at 8.8 kPa: upper trace—P20 line shape of the low-pressure laser (measured with Coherent 201 power meter); lower trace—beat between the peak-stabilized waveguide laser and the swept low-pressure laser. The horizontal arrow on the lower trace indicates the beat frequency when both lasers are peak-stabilized. The frequency was read with a counter (HP5328A) plus digital-to-

analog converter (HP59303A).

Fig. 3. Measurements and theoretical curves of SNR vs Pr (received power).

The low-frequency spectrum measured after the square-law detector with the wave analyzer exhibited the following fea­tures. The total noise which comprises the local-oscillator-induced shot noise (»electronic noise) and the signal carrier X noise term without modulation had the characteristic tri­angular form of quadratic detection.3 The signal's strongest harmonic was at 2fm but was 20 dB lower than the funda­mental as is normal for a modulation depth of 80%. The av­erage signal was constant at ±30% for any rotation rate of the cylinder. Increasing the rotation rate from zero increased the noise up to a maximum when the Doppler spreading was comparable to fm. Then a further increase in rotation rate decreases the noise. This part of the noise comes from fluc­tuations due to the target.1

Assuming that the fluctuation noise is negligible due to proper target rotation rate, the SNR of such a detection sys­tem in the shot-noise-limited regime is given by1

where K = (fn/B)(ξ/1 + ξ2)2, ξ2 = 2J2

1(β/2), J1 = Bessel function of first order, β = modulation depth (0.8),

Q I F = ηPr/hvfn, Pr = received optical power measured with the

same calibrated detector but with a resistive bias circuit in direct detection,

hv = photon energy (0.12 eV), fn = noise bandwidth before the electronic de­

tector, γ = fields overlap on detector surface (0 ≤ 7 ≤ 1),

and B = analysis bandwidth.

This is the same equation that has been derived for a ho-modyne system with Doppler shifts.

In the present case, fn = 20 MHz, fm = 15 kHz, B = 1 Hz, and 7 varies between 0.2 and 0.4. With these parameters, the equation yields the curves shown on Fig. 3. The experimental points correspond to measurements made at different times and with different optical adjustments. A typical value of 7 is 0.3. From the curves, as is characteristic of envelope de­tection, two regions can be identified: SNR pr and SNR

P2r. The experimental points follow the curves up to a SNR

of ~80 dB where they tend to level off to a plateau, which gives an indication of the dynamic range (~85 dB) of the mea-

14 APPLIED OPTICS / Vol. 22, No. 1 / 1 January 1983

surement system. The fit between the measurements and the theory is close enough to permit reliable prediction for the design of a rangefinder based on this model. It also shows that the intermediate frequency after heterodying is unim­portant in this detection scheme as long as the optical detector bandwidth is large enough.

References 1. D. Vincent, P. Lavigne, and G. Otis, DREV Report 4201/81. 2. P. Lavigne, G. Otis, and D. Vincent, DREV Report 4150/79. 3. M. C. Teich and R. Y. Yen, Appl. Opt. 14, 666 (1975). 4. A. Van Lerberghe, S. Avrillier, and C. J. Bordé, IEEE J. Quantum

Electron. QE-14, 481 (1978).

1 January 1983 / Vol. 22, No. 1 / APPLIED OPTICS 15