Optical receivers are devices that convert light signals into electrical signals using photodetectors, which come in various types such as photodiodes and avalanche photodiodes. The document covers key concepts such as the operating principles of these detectors, noise types, signal-to-noise ratio, error rates, and the impact of parameters like wavelength and receiver sensitivity. It also discusses practical considerations in optical communications, including burst-mode receivers and testing measures such as eye diagrams.

1. Optical Receivers
Theory and
Operation
Amitabh Shukla

2. Photo Detectors
• Optical receivers convert optical signal (light) to electrical signal
(current/voltage)
 Hence referred ‘O/E Converter’
• Photodetector is the fundamental element of optical receiver,
followed by amplifiers and signal conditioning circuitry
• There are several photodetector types:
 Photodiodes, Phototransistors, Photon multipliers, Photo-resistors etc.

3. Requirements
• Compatible physical dimensions (small size)
• Low sensitivity (high responsivity) at the desired wavelength
and low responsivity elsewhere  wavelength selectivity
• Low noise and high gain
• Fast response time  high bandwidth
• Insensitive to temperature variations
• Long operating life and low cost

4. Photodiodes
• Photodiodes meet most the requirements, hence widely used as
photo detectors.
• Positive-Intrinsic-Negative (pin) photodiode
 No internal gain, robust detector
• Avalanche Photo Diode (APD)
 Advanced version with internal gain M due to self multiplication process
• Photodiodes are sufficiently reverse biased
during normal operation  no current flow
without illumination, the intrinsic region is fully
depleted of carriers

5. Physical Principles of
Photodiodes
• As a photon flux Φ penetrates into a semiconductor, it will
be absorbed as it progresses through the material.
• If αs(λ) is the photon absorption coefficient at a wavelength
λ, the power level at a distance x into the material is
Absorbed photons
trigger photocurrent
Ip in the external
circuitry

6. Examples of Photon Absorption

7. pin energy-band diagram
Cut off wavelength depends on the
band gap energy
μm
)(
24.1
eVEE
hc
gg
c ==λ
Cut off wavelength:

8. Quantum Efficiency
• The quantum efficiency η is the number of the
electron–hole carrier pairs generated per incident–
absorbed photon of energy hν and is given by
Ip is the photocurrent generated by a steady-
state optical power Pin incident on the
photodetector.

9. Avalanche Photodiode
(APD)
• APD has an internal gain M, which is
obtained by having a high electric field that
energizes photo-generated electrons.
• These electrons ionize bound electrons in the
valence band upon colliding with them
which is known as impact ionization
• The newly generated electrons and holes are
also accelerated by the high electric field and
gain energy to cause further impact
ionization
• This phenomena is the avalanche effect

10. APD Vs PIN

11. Responsivity (ℜ)
Quantum Efficiency (η) = number of e-h pairs generated /
number of incident photons
APD’s have an internal gain M, hence
where, M = IM/Ip
IM : Mean multiplied current
0
/
/
pI q
P h
η
ν
=
0
pI q
P h
η
ν
ℜ = = mA/mW
APD PIN Mℜ = ℜ
M = 1 for PIN diodes

12. Responsivity
c
g
hc
E
λ =When λ<< λc absorption is low
When λ > λc; no absorption

13. Light Absorption Coefficient
• The upper cutoff
wavelength is
determined by the
bandgap energy Eg of
the material.
• At lower-wavelength
end, the photo response
diminishes due to low
absorption (very large
values of αs).

14. Photodetector Noise• In fiber optic communication systems, the photodiode is
generally required to detect very weak optical signals.
• Detection of weak optical signals requires that the
photodetector and its amplification circuitry be optimized to
maintain a given signal-to-noise ratio.
• The power signal-to-noise ratio S/N (also designated by
SNR) at the output of an optical receiver is defined by
SNR Can NOT be improved by amplification

15. Notation: Detector Current
• The direct current value is denoted by, IP (capitol
main entry and capital suffix).
• The time varying (either randomly or periodically)
current with a zero mean is denoted by, ip (small
main entry and small suffix).
• Therefore, the total current Ip is the sum of the DC
component IP and the AC component ip .
ppP iII +=
∫−
∞→=
2/
2/
22
)(
1
Lim
T
T
pTp dtti
T
i

16. Quantum (Shot Noise)
)(2 22
MFBMqIi pQ =
F(M): APD Noise Figure F(M) ~= Mx
(0 ≤ x ≤ 1)
Ip: Mean Detected Current
B = Bandwidth
q: Charge of an electron
Quantum noise arises due optical power fluctuation
because light is made up of discrete number of photons

17. Dark/Leakage Current Noise
)(2 22
MFBMqIi DDB =
BqIi LDS 22
=
Bulk Dark Current Noise
Surface Leakage
Current Noise
ID: Dark Current
IL: Leakage Current
There will be some (dark and leakage ) current without any
incident light. This current generates two types of noise
(not multiplied by M)

18. Thermal Noise
LBT RTBKi /42
=
The photodetector load resistor RL contributes to
thermal (Johnson) noise current
KB: Boltzmann’s constant = 1.38054 X 10(-23)
J/K
T is the absolute Temperature
• Quantum and Thermal are the significant noise
mechanisms in all optical receivers
• RIN (Relative Intensity Noise) will also appear in
analog links

19. Signal to Noise Ratio
2 2
2
2 ( ) ( ) 2 4 /
p
p D L B L
i M
SNR
q I I M F M B qI B k TB R
=
+ + +
Detected current = AC (ip) + DC (Ip)
Signal Power = <ip
2
>M2
Typically not all the noise terms will have equal weight.
Often thermal and quantum noise are the most significant.

20. Noise Calculation Example

21. Limiting Cases for SNR
• When the optical signal power is relatively high, then
the shot noise power is much greater than the thermal
noise power. In this case the SNR is called shot-noise or
quantum noise limited.
• When the optical signal power is low, then thermal
noise usually dominates over the shot noise. In this
case the SNR is referred to as being thermal-noise
limited.

22. Limiting Cases of SNR
In the shot current limited case the SNR is:
For analog links, there will be RIN (Relative Intensity
Noise) as well
2
2 ( ) ( )
p
p
i
SNR
q I F M B
=
2 2
2 2
2 ( ) ( ) 4 / ( )
p
p D B L p
i M
SNR
q I I M F M k T R RIN I B
=
 + + + 

23. Typical SNR vs. Received
Power
• Note, APD has an
advantage only at
low received power
levels

24. Noise-Equivalent Power
• The sensitivity of a photodetector is describable in terms of
the minimum detectable optical power to have SNR = 1.
• This optical power is the noise equivalent power or NEP.
• Example: Consider the thermal-noise limited case for a pin
photodiode. Then
To find the NEP, set the SNR = 1 and solve for P:

25. Response Time in pin
photodiode
Transit time, td and carrier drift velocity vd are related by
/d dt w v= For a high speed Si PD, td = 0.1 ns

26. Rise and fall times
Photodiode has uneven rise and fall times depending on:
1. Absorption coefficient αs(λ) and
2. Junction Capacitance Cj
o r
j
A
C
w
ε ε=

27. Junction Capacitance
o r
j
A
C
w
ε ε=
εo = 8.8542 x 10(-12) F/m; free space permittivity
εr = the semiconductor dielectric constant
A = the diffusion layer (photo sensitive) area
w = width of the depletion layer
Large area photo detectors have large junction
capacitance hence small bandwidth (low speed)
 A concern in free space optical receivers

28. Various pulse responses
Pulse response is a complex function of absorption coefficient
and junction capacitance

29. Comparisons of pin
Photodiodes
NOTE: The values were derived from various vendor data
sheets and from performance numbers reported in the
literature. They are guidelines for comparison purposes.

30. Comparisons of APDs
NOTE: The values were derived from various vendor data sheets
and from performance numbers reported in the literature. They
are guidelines for comparison purposes only.

31. Optical receiver
Part B

32. Signal Path through an Optical
Link

33. Fundamental Receiver Operation
• The first receiver element is a pin or an avalanche photodiode, which produces
an electric current proportional to the received power level.
• Since this electric current typically is very weak, a front-end amplifier boosts
it to a level that can be used by the following electronics.
• After being amplified, the signal passes through a low-pass filter to reduce the
noise that is outside of the signal bandwidth.
• The also filter can reshape (equalize) the pulses that have become distorted as
they traveled through the fiber.
• Together with a clock (timing) recovery circuit, a decision circuit decides
whether a 1 or 0 pulse was received,

34. Optical receiver schematic
Bandwidth of the front end:
CT: Total Capacitance = Cd+Ca
RT: Total Resistance = Rb // Ra
Try Example 6.7 in Keiser
1 2 T TB R Cπ=

35. Noise Sources in a
Receiver
The term noise describes unwanted components of an electric signal that tend to
disturb the transmission and processing of the signal
• The random arrival rate of signal photons produces quantum (shot) noise
• Dark current comes from thermally generated eh pairs in the pn junction
• Additional shot noise arises from the statistical nature of the APD process
• Thermal noises arise from the random motion of electrons in the detector load
resistor and in the amplifier electronics

36. Probability of Error (BER)
• BER is the ratio of erroneous bits to correct bits
• A simple way to measure the error rate in a digital data
stream is to divide the number Ne of errors occurring over a
certain time interval t by the number Nt of pulses (ones and
zeros) transmitted during this interval.
• This is the bit-error rate (BER)
• Here B is the bit rate.
• Typical error rates for optical fiber telecom systems range
from 10–9
to 10–12
(compared to 10-6
for wireless systems)
• The error rate depends on the signal-to-noise ratio at the
receiver (the ratio of signal power to noise power).

37. Logic 0 and 1 probability distributions
1( ) ( /1)
thV
thP V p y dy
−∞
= ∫
0 ( ) ( / 0)
th
th V
P V p y dy
∞
= ∫[ ]1
1 02 ( ) ( )e th thP P V P V= +
Select Vth to minimize Pe
Asymmetric distributions

38. Deciding Threshold Voltage
0 ( ) ( / 0)
th
th
V
P V p y dy
∞
= ∫
1( ) ( /1)
thV
thP V p y dy
−∞
= ∫
[ ]1
1 02 ( ) ( )e th thP P V P V= +Probability of error assuming
Equal ones and zeros
Where,
Depends on the noise variance at on/off levels and the
Threshold voltage Vth that is decided to minimize the Pe
Question: Do you think Vth = ½ [Von + Voff] ?

39. Derived BER Expression
• A simple estimation of the BER can be calculated by assuming the
equalizer output is a gaussian random variable.
• Let the mean and variance of the gaussian output for a 1 pulse be
bon and σ2
on, respectively, and boff and σ2
off for a 0 pulse.
• If the probabilities of 0 and 1 pulses are equally likely, the bit error
rate or the error probability Pe becomes

40. Probability of Error
Calculation
• The factor Q is widely used to specify receiver performance, since
it is related to the SNR required to achieve a specific BER.
• There exists a narrow range of SNR above which the error rate is
tolerable and below which a highly unacceptable number of errors
occur. The SNR at which this transition occurs is called the
threshold level.

41. BER as a Function of SNR
BER as a function of SNR when the standard deviations are
equal (σon = σoff) and when boff = 0

42. Receiver Sensitivity
• A specific minimum average optical power level must
arrive at the photodetector to achieve a desired BER at a
given data rate. The value of this minimum power level
is called the receiver sensitivity.
• Assuming there is no optical power in a received zero
pulse, then the receiver sensitivity is
Where, including an amplifier noise figure Fn, the
thermal noise current variance is

43. Receiver Sensitivity
Calculation
The receiver sensitivity as a function of bit rate will change for a
given photodiode depending on values of parameters such as
wavelength, APD gain, and noise figure.

44. The Quantum Limit
• The minimum received optical power required for a specific bit-
error rate performance in a digital system.
• This power level is called the quantum limit, since all system
parameters are assumed ideal and the performance is limited only
by the detection statistics.

45. Eye Diagrams
• Eye pattern measurements are made in the time domain and
immediately show the effects of waveform distortion on the
display screen of standard BER test equipment.
 The eye opening width defines the time interval over which signals
can be sampled without interference from adjacent pulses (ISI).
 The best sampling time is at the height of the largest eye opening.
 The eye opening height shows the noise margin or immunity to noise.
 The rate at which the eye closes gives the sensitivity to timing errors.
 The rise time is the interval between the 10 and 90% rising-edge
points

46. Stressed Eye Tests
• The IEEE 802.3ae spec for testing 10-Gigabit Ethernet (10-GbE)
devices describes performance measures using a degraded signal.
• This stressed eye test examines the worst-case condition of a poor
extinction ratio plus multiple stresses, ISI or vertical eye closure,
sinusoidal interference, and sinusoidal jitter.
• The test assumes that all different possible signal impairments
will close the eye down to a diamond shaped area (0.10 and 0.25 of
the full pattern height).
• If the eye opening is greater than this area, the receiver being
tested is expected to operate properly in an actual fielded system.
46
The inclusion of all possible signal
distortion effects results in a
stressed eye with only a small
diamond-shaped opening

47. Architecture of a Typical PON
• A passive optical network (PON) connects switching equipment in
a central office (CO) with N service subscribers
• Digitized voice and data are sent downstream from the CO to
customers over an optical link by using a 1490-nm wavelength.
• The upstream (customer to central office) return path for the data
and voice uses a 1310-nm wavelength.

48. Burst-Mode Receivers
• The amplitude and phase of packets received in successive time slots
from different user locations can vary widely from packet to packet.
• If the fiber attenuation is 0.5 dB/km, there is a 10-dB difference in the
signal amplitudes from the closest and farthest users.
• If there are additional optical components in one of the transmission
paths, then the signal levels arriving at the OLT could vary up to 20
dB.
• A fast-responding burst-mode receiver with high sensitivity is needed
The guard time
provides a sufficient
delay time to
prevent collisions
between
successive packets
that may come
from different
ONTs.