1. On the use of optical amplifiers in coherent receivers
M. C. Welliver, P. J. Suni, C. S. Tuvey
Lockheed Martin Coherent Technologies
135 S. Taylor Ave., Louisville, CO 80027
marc.welliver@me.com
paul.suni@lmco.com
stewart2v@gmail.com
1. Summary
Heterodyne detection represents an optimal detection method theoretically achieving the standard quantum limit, and
Lockheed Martin Coherent Technologies (LMCT) is interested in developing multi-pixel receivers for optical remote
sensing applications. Practical realization of large array optical heterodyne receivers (many independent measurement
channels) represents an ongoing challenge on a number of technical fronts, among which is power-scaling of a high-
quality local oscillator laser (LO) to be mixed with the return optical signal from a remote target. Typical coherent
receiver designs require per-channel generation of tens of milliWatts of optical power for the LO so scaling to 100 pixel
coherent array requires on the order of 1 W or more of continuous-wave local oscillator power for the reference beam.
One potential solution to this issue involves the use an Erbium-Doped Fiber Amplifier (EDFA) to boost the power of a
lower power LO laser in order to achieve shot-noise limited optical detection in a multi-channel heterodyne receiver. It
is well known, however, that EDFAs (or indeed any known phase-insensitive optical amplifier technology) produce
optical fields with significant noise in excess of the fundamental shot-noise floor of classical optical fields. Such excess
noise in an LO represents a direct reduction in mean coherent receiver signal-to-noise ratio (SNR). We measured the
noise characteristics of an LO created by a shot-noise limited seed laser undergoing amplification followed by
attenuation and found that when gain and attenuation are equal the excess noise factor is >6 dB. When the EDFA is
seeded with significantly more power than is required for single-pixel shot-noise limited performance, however, the
excess noise factor approaches unity. Hence, ideal coherent receiver performance can be achieved with an EDFA-based
LO, enabling LO power scaling for large coherent receiver arrays.
2. Theoretical and system studies
Background: Optical heterodyne detection is a powerful measurement technique in which the received optical signal
is mixed with a reference laser beam known as a local oscillator. Among the benefits of mixing optical fields prior to
detection are: amplification of the (typically very weak) signal, spectral filtering (which reduces susceptibility to
background light and countermeasures), polarization selection, and preservation of amplitude and phase information,
thereby increasing the number of possible measurands (e.g. range, vibrometry, etc.). From a laser radar design
perspective the key benefit of heterodyne detection is its ability to achieve of the standard quantum limit for optical
signal detection in the presence of noise, but this ideal performance is only realized if the LO is shot-noise limited.1 In a
coherent detection receiver laser light reflected from an object of interest is combined with a reference LO laser beam
through the two ports of a beamsplitter (typically 80:20 or 90:10 mixing ratio for a single-arm receiver). When spatially
matched with proper phase fronts, the co-propagating signal and LO optical fields interfere with one another temporally
on a photodetector, creating a periodic current at the beat frequency of the optical fields with amplitude proportional to
the square of the superposed field strengths:1
ηe 2
i( t ) = iDC + ih ( t ) = E s ( t ) + E LO ( t )
hν
. (1)
ηe
≅
hν
PLO 1+ 2( Ps
PLO
cos(2π Δf t + Δϕ ) )
Here, η is the overall coherent receiver efficiency, e is the charge of an electron, h is Planck’s constant, ν is the optical
frequency, P is the optical power incident on the detector, and Δf and Δφ are the differences in optical frequency and
phase of the signal and LO optical fields. We have also assumed PLO >> Ps. The DC photocurrent gives rise to wide-
band shot-noise due € the discrete nature of photoelectric conversion at the detector, and this noise power represents
to
the minimum possible fluctuation in measured signal (at least for classical light). We identify the mean SNR as the
ratio of the mean signal power < ih > to the in-band shot-noise power given by 2eiDC Be :
2
ηe 2
SNRh ≡
2
ih
≅
2( )Phν LO Ps
≅
η Ps n
=η s . (2)
2e ( ) P
ηe
2eiDC Be hν LO Be
hν Be Be
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2. The shot-noise limited mean heterodyne SNR is the product of the number of photons per unit bandwidth and the
overall receiver efficiency, and is independent of LO power (so long as the LO shot noise dominates all other noise
sources in the coherent receiver measurement chain). Excess noise on the LO directly reduces mean heterodyne SNR,
so we now turn to the noise characteristics of an EDFA-based LO operating in a real coherent receiver system.
Amplification and attenuation of a shot-noise limited LO laser source: Having identified the ideal performance of
a coherent optical receiver, we now turn our attention to the case of coherent receivers with excess noise on the LO.
Suppose a light beam with n0 photons per unit bandwidth is incident on an optical amplifier with gain G. For a shot-
noise limited input beam the mean photon number and photon number variance per unit bandwidth at the output are:2
n1 = Gn 0 + f sp (G −1)
2. (3)
σ n1 = Gn 0 + f sp (G −1) + 2Gn 0 f sp (G −1) + [ f sp (G −1)]
2
The photon number variance per unit bandwidth has four contributions: the first two are shot noise from the amplified
input and amplified spontaneous emission (the latter is typically small and can be ignored, as can the fourth term arising
from spontaneous-spontaneous mixing). The third term is the trouble and represents amplified spontaneous emission
(ASE) beating with the amplified input field, resulting in excess intensity noise at the output of the EDFA. The ratio of
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this expression to the variance of a shot-noise limited field with mean photon number Gn0 gives the multiplicative
excess noise factor for the output field, neglecting terms of order (fsp/n0)<<1:2
2 2
σ n1 σ n1
Fex ≡ 2
= ≅ [1+ 2 f sp (G −1)] . (4)
σ shot−n1 Gn 0
The spontaneous emission noise factor in Eq. 4 is unity for a 4-level system (like Nd), whereas in 3-level or quasi-3-
level systems (like erbium) it is worse than unity unless the gain medium is completely inverted.3 Real fiber amplifiers
tend to have noise figures in excess of 3 dB.
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Next we consider the case of multi-pixel coherent receivers where the amplified LO is attenuated prior to detection.
Attenuation occurs due to the heterodyne mixing beamsplitter as well as spreading the amplified LO over many pixels.
For the purpose of this analysis, we will consider a single effective attenuation factor that accounts for the partial
reflectivity of the signal-LO beamsplitter (typically 10-20%) and the effective attenuation due to spreading the LO over
multiple pixels (potentially 64 or larger for arrays where optical amplification of the LO becomes relevant). Hence, a
typical value of the attenuation factor may be 640. Under attenuation the mean number of photons per unit bandwidth
and the shot-noise variance in the photon number scale inversely with attenuation factor, resulting in the well-known
result of degradation in signal-to-shot-noise ratio with attenuation. The photon number variance due to excess intensity
noise contributions scales inversely with the square of the attenuation factor, conserving signal-to-excess-noise ratio
under attenuation. The resulting expressions, again neglecting terms of order (fsp/n0) compared to 1, become:
n 2 ≅ (G A ) n 0
σ n 2 ≅ (G A) n 0 [1+ 2(G / A) f sp ] .
2
(5)
Fex ≅ [1+ 2(G A) f sp ]
The total noise spectral density of the resulting LO field is obtained by adding the shot- and excess noise contributions
in quadrature. Figure 1 (left) shows the various contributions of noise photons (integrated over the spectral band) from
an amplified-attenuated optical field for two different spontaneous noise factors. We see that with significant
attenuation (G/A << 1) this excess noise term can become relatively unimportant compared to the unavoidable shot
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noise (assuming ordinary laser light), and that the dependence on the assumed spontaneous noise rate diminishes as the
resulting optical field becomes weaker. In regions of G/A > 1 we see that the excess intensity noise dominates.
Coherent receiver system considerations and results: Now that we have demonstrated that attenuation consistent
with realistic multi-pixel system configurations can alleviate the excess intensity noise issues associated with optical
amplification of the local oscillator, we turn to system-level considerations of the implementation. It is well known that
filtering the amplified light with an optical cavity also removes the excess intensity noise due to ASE, but the point here
is that for large coherent receiver arrays the same effect can be recovered through passive system-level attenuation of
the noisy, amplified LO. This greatly simplifies system design and reliability. Additionally, while it is advantageous to
attenuate an amplified optical field to recover shot-noise limited statistics, coherent detection systems still require
sufficient optical power on the detector to overcome electronic noise in the first electronic gain stage (typically a

3. transimpedance amplifier). Hence, there will be an optimal regime for system design based on the single-pixel LO
power required to overcome all subsequent measurement noise sources.
Figure 1: (Left) Number of shot-noise and excess noise photons (normalized to number of input beam photons) versus G/A for fsp =
2 and fsp = 4. (Right) Coherent Detection excess noise factor versus G/A for various input optical seed powers. m_seed indicates the
ratio of EDFA seed power to shot-noise limited single-pixel LO power, defined by 10 dB above the TIA noise floor, and fsp = 2 is
assumed.
Modification of the mean heterodyne SNR from Eq. 2 to include excess noise on the LO optical field and electronic
amplifier noise results in:
−1
ηe 2  
SNRh ≅
( ) (G / A)P P
2 hν LO s
≅
η Ps 
Fex +
σA 2
 , (6)
2e ( ) P F B + σ B
ηe
hν LO ex e
2
A e
hν Be 
 h
e
( )
2e ην PLO 

where σA2 is the input-referred noise power spectral density of all measurement electronics, Ps is the signal power
incident on a single photodetector, and PLO is the local oscillator power incident on a single detector following all gain
and amplification processes. The ratio of this overall mean heterodyne SNR to that for an ideal LO shot-noise limited
system gives the overall coherent receiver excess noise factor for an EDFA-based LO design. With the definition
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PLO=(G/A)PIN analytically we find:
2
SNRh σA 1
F (G A,PIN ) = SNL
≅ 1+ 2(G A) f sp + . (7)
SNRh 2e ( )
ηe
hν PIN G A
The competing trends of the two excess noise terms as a function of (G/A) are evident in the data plotted in Figure 1
(right). In the figure m_seed is the ratio of the EDFA input optical power to the single-pixel LO power required such
that the LO shot-noise power is 10σA2. F=1 represents ideal performance.
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3. Experimental investigation
We performed spectrally-resolved noise power measurements for a commercial EDFA designed for gain at a
wavelength of 1617 nm. The output power could be adjusted over the range 0.2-1.2 W, while the minimum seed power
was 7 mW. For the present study our source was a 1617 nm DFB laser capable of up to 50 mW CW power, and our RF
measurement band spanned 100 MHz to 3.0 GHz. For detection we used an AC-coupled Discovery InGaAs PIN
photoreceiver with integrated TIA, the combined bandwidth of which is approximately 9.5 GHz. A Miteq post-amplifier
with 30 dB of gain and a noise figure of <1 dB followed the photoreceiver, providing input for spectrally-resolved AC
measurements on a Rohde & Schwarz 20 GHz RF Spectrum Analyzer. DC measurements were made at the photodiode
using a Keithley source meter, which also biased the photodetector. Figure 2 (left) shows the noise spectral density under
dark and CW illuminated conditions for (G/A) = 1 with the EDFA operating at different gain settings and compensating
adjustment in the post-EDFA attenuation. The lowest blue curve represents the post-detection electronics noise power
under dark conditions. The red line shows the noise power spectrum of the input optical field to the EDFA, while the
dashed line represents the calculated shot-noise floor based on the measured 9 mA DC photocurrent. The EDFA seed
laser source is shot-noise limited and post-detection electronics are suppressed by >10dB relative to this level. For
(G/A) = 1 the noise spectrum of the amplified LO is a factor 4-5 larger than that of the seed laser itself, resulting in a
direct degradation to heterodyne receiver sensitivity.
Figure 2 (right) shows the mid-band spectrally averaged excess noise factor versus (G/A). The spectral average is taken

4. from 900-1100 MHz for various seed powers and gain settings. The solid line corresponds to Eq. 4 with fsp = 2, but the
spontaneous emission factor may be a function of seed power and/or gain setting, so this should not be interpreted as a
measurement of fsp. Rather, the excess noise factor of the resulting optical field is measured directly and of the greatest
importance since it directly affects heterodyne receiver performance. For the smallest values of (G/A) our optical shot-
noise was not 10 dB above the post-detection electronics noise floor, but differential data analysis allowed extraction of
the excess noise.4 For (G/A)<0.05 the excess noise factor is <1.1 and ideal performance is approached.
Figure 2: (Left) Noise Power Spectra for TIA, seed laser, and amplified laser fields for multiple gain settings and G/A=1. All
optical fields were attenuated such that the DC photocurrent measured at the detector was 9 mA. (Right) Excess noise factor vs.
(G/A) for multiple gain settings and DC photocurrents. Data demonstrate that given large seed power and enough attenuation, shot-
noise limited performance can be achieved.
4. Conclusions
Physically the analysis means that one cannot reduce shot-noise by manipulating gain and attenuation since it is a
quantum statistical effect, but one can alter the contribution of excess noise due to amplification by spreading it out
over many receiver channels or throwing light away. ASE noise is fixed in the sense that adding 10 noise photons to a
time slot and then dividing those photons among 100 channels produces on average only 0.1 noise photons per channel.
In the limit of large effective attenuation this confirms the accepted notion that sufficient attenuation will make any
source shot-noise limited. The trouble, of course, is that while dividing up the noise photons one also decreases the LO
power, so for practical designs two constraints have to be met: First (G/A) must be small enough that shot-noise
dominates ASE for any given detector; second, one must ensure that there is still sufficient LO power impinging on
each pixel that its shot-noise dominates post-detection electronics noise. To reiterate the point, from Eq. 5 it is clear
that amplifying by a factor larger than the subsequent effective attenuation is not useful since the noise variance is still
degraded by a factor of at least [1+2fsp] or >3. For amplifiers to be useful in the LO arm of a coherent detection system
the quantity (G/A) must be small. In order to still have sufficient LO power on the detector the seed power at the
amplifier input must exceed that required for shot-noise limited detection on a single pixel. If one needs 1 mW to
produce ideal performance for a single detector, it is not useful to amplify that same power level and subsequently
attenuate it by division across multiple detectors. However, if one starts with e.g. 100 mW, amplifies by 10 X and
divides the resulting noisy field among 100 detectors (and uses a 10% heterodyne beam splitter) the result is still 1 mW
on each detector, while the excess noise factor is negligible. The shot-noise variance is unaffected as expected. The
same system without an optical amplifier would require 1 W of clean LO power, so this appears to be a situation in
which amplification of the LO is a net win.
References
[1] S. Henderson, P. Gatt, et al., Wind LIDAR in Laser Remote Sensing, CRC Press Taylor & Francis Group, Boca
Raton, FL, Ch. 12 (2005).
[2] Tulloch et al., “Quantum noise in a continuous-wave laser-diode-pumped Nd:YAG linear optical amplifier,” Opt.
Lett. 23, p.1852 (1988).
[3] Desurvire, E., Erbium-Doped Fiber Amplifiers, Principles and Applications, Wiley-Interscience (1994).
[4] Obarski, G., “Precise calibration for optical amplifier noise figure measurement using the RIN subtraction method”,
Proc. IEEE Opt. Fib. Comm., p. 601-603 (2003).