Optical Sources, Detectors, and Systems

130 Chapter

6

Heterodyne or Coherent Detection and Optical Amplification

Heterodyne detection approaches photon-noise-limited perform-

ance, but the beamwidth and required frequency purity of the signal and

local oscillator usually restrict its application to systems such as Doppler

radar, where the frequency of the return signal must be measured.

Example. A laser radar receiver operating at a wavelength of

10

imi uses a carbon dioxide laser as a local oscillator. The radar

pulsewidth is 1

msec,

the receiver aperture diameter is I m, and the

required preamplifier bandwidth 1 GHz for satellite Doppler

velocity shifts, which results in a required i?,„ of 50 Q, because of

the capacitance of the available junction photodiode.

Receiver

beamzvidth:

From the antenna theorem and Section 3.4,

the full beam angle at half-power for a uniform circular plane wave

is A/d =

10"^

rad

or approximately

2 arc

sec.

Local oscillator frequency

stability:

For optimum processing of a

1 ms pulse, the matched bandwidth is I kHz. Frequency fluctu-

ations must be much less than

1

kHz.

Local oscillator

power:

We want the local oscillator induced shot

noise to be much greater than the effective amplifier input

noise,2q(rjqPioIhv)B»4kT^B/Riri or Pio»(2/7])(hv/q)(kT^/q)/Rin.

With

7]

= 0.5 and T^ = 300K P

L

o» (4)(0.U4)(0.026)/50 = 0.26

mW.

6.4 Optical Amplification with Heterodyne Detection

In our detailed discussions of laser action in Chapters 3 and 4, we

considered only the onset and development of oscillation in the laser

cavity. But if the laser medium can amplify an incoming optical wave,

can we use this mechanism to introduce gain in the received optical

signal power prior to detection and thus improve the sensitivity? The

answer is a qualified yes for a coherent or heterodyne detector but the

resultant performance, dependent on the optical amplifier bandwidth, is

the same as that of an unamplified heterodyne system with a detector

quantum efficiency between

507o

and

1007o.

For a direct detection

system, where we are only measuring power, we shall find that the ap-

plicability depends on the relative magnitudes of the system bandwidth

(or data rate) and the optical bandwidth of the amplifier. In addition.

6.4 Optical Amplification with Heterodyne Detection

131

the noise introduced in the amplification process will be found to be

proportional to the number of diffraction-limited modes amplified and

then detected by a single detector. We first consider the coherent or

heterodyne case.

Figure 6.3 shows a coUimated signal beam passing through a laser

medium, an optical spectral filter, and impinging on a heterodyne de-

tection system to the right of the medium. The field distribution or

mode of the beam is defined by the local oscillator beam as discussed

earlier. We call this a

diffraction-limited

mode,

indicating that it is the

same as the radiated pattern associated with a specific field configuration

on a source plane. As derived in Eq. (3.19) for a Gaussian mode, the

area-solid angle product AQ is equal to the square of the wavelength

X^,

and this relation is generally true for any type of mode (see King-

ston,

1978,

p.

35 et

seq.)

Such modes are

orthogonal

in the sense that the

integral of the product of any two different modes over the plane is equal

to zero. An example of such modes is the familiar Hermite-Gaussian set

(Boyd

and

Gordon,

1961), the

TEM^^^

modes of a confocal cavity gas

laser such as helium-neon. A heterodyne system only "sees" the mode,

which matches that of the local oscillator in amplitude, phase, and

polarization, as can be deduced from the mixing efficiency in Eq. (6.7).

We use a heterodyne detection system not only to determine its overall

performance but mainly as a method of calculating the noise contrib-

ution in each mode of free space.

Optical

filter

- Av

dx

Laser medium

(n^ nj

B

Figure 6.3 Laser amplifying medium with optical spectral filter and heterodyne detection.