V2CH12 Detecting Light

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Elements of Photonics, Volume II: For Fiber and Integrated Optics . Keigo IizukaCopyright 2002 John Wiley & Sons, Inc.

ISBNs: 0-471-40815-8 (Hardback); 0-471-22137-6 (Electronic)

12

DETECTING LIGHT

This chapter begins with a description of light detectors used in optics laboratories(Sections 12.1 through 12.3). Then, special purpose detectors used primarily for opticalcommunication systems are described. These include the PIN photodiode and APDdetectors (presented in Section 12.4).

The remaining sections deal with various methods of detection employed in ber-optic communication systems. Direct detection is a simple method that measures onlythe intensity of light, and this method is described in Section 12.5. Sections 12.6 to12.8 are devoted to coherent detection, which can measure not only the intensity butalso the phase and frequency of the light. Lastly, Section 12.9 looks at phase andpolarization jitters.

The signal to noise ratio (S/N) of the detection system will be presented in connec-tion with optical communication systems in Chapter 16.

12.1 PHOTOMULTIPLIER TUBE

Light detectors convert light energy into an electrical signal. The photomultiplier tube(PMT) has an ultrahigh sensitivity and is widely used in optics research laboratories.The sensitivity is so high that it can almost detect a single photon.

Figure 12.1 explains the structure of the photomultiplier tube. The photomultipliertube is a combination of the cathode, which is the photonelectron converter, and thedynodes, which act as ampliers of the converted electrons.

The photoelectric converter section consists of the cathode and the rst dynode.The cathode surface is coated with a low-work-function material, such as alkali metals.When the incident photons bombard the cathode, electrons are ejected from the surface.Emission, however, takes place only when a quantum h of the incident light is largerthan the work function of the cathode material:

< h 12 .1

796


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PHOTOMULTIPLIER TUBE 797

Photon

Photoelectricconverter

Electron multiplier

Electron

Cathode

Anode

Amplifier

to Bto A

Dynode

to C

A

K

B C

Figure 12.1 Photomultiplier tube. Points A, B, C . . . at the bottom are connected, respectively, tothe A, B, C, . . . dynodes at the top.

where h is Plancks constant 6 .63 10 34 J s. Thus, the coating material of thecathode determines the range of wavelength for usable light. A number of materials areavailable in the visible wavelength range but, unfortunately, high-sensitivity materialshave not been found in the infrared region, where the optical communication systemoperates.

The electrons ejected from the cathode are accelerated by the high voltage betweenthe cathode and the rst dynode and then strike the surface of the dynode with highenergy. Secondary electrons are emitted from the dynode in larger numbers. With a

series of dynodes operating at gradually higher voltages, the number of secondary elec-trons are multiplied at each dynode. The multiplied secondary electrons are collectedby the anode whose potential is typically a few kilovolts higher than the cathode.

Next, the sensitivity of the photomultiplier tube will be calculated. Let W be theenergy of the light entering the cathode of the photomultiplier tube. The number of photons in terms of the incident light energy is W/h .

Let be the quantum efciency, which is dened as the ratio of the number of gener-ated electrons to incident photons. Each electron carries charge e. The total amount of charge Q accumulated at the cathode is

Q D e

h W 12 .2

The current from the cathode is obtained by taking derivatives of both sides of Eq. (12.2),

icathode D e

hP 12 .3

where P is the incident light power.If in each dynode stage one electron generates secondary electrons, the total

multiplication M from the N dynodes is

M D N 12 .4


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798 DETECTING LIGHT

Thus, the output current from the photomultiplier tube is

i D e

h MP 12 .5

Finally, the responsivity R of the photomultiplier tube, which is the output current withunit incident light power, is

R D e

h M A/W 12 .6

where A/W is amperes/watt. The responsivity is used to characterize a photomulti-plier tube.

Typical values are inserted into Eq. (12.6) to calculate the responsivity of the photo-multiplier.

D 0.01

D 0.63 m or D 4.76 1014 Hz D 5 N D 10

R D 0.011.6 10 19 510

6.63 10 34 4.76 10145 10

4 A/W

The responsivity of a PIN photodiode is typically R

D 0.5 A/W and the photomultiplier

tube is signicantly more sensitive.The internal impedance of a photomultiplier being as high as 10 M , the matched

load impedance can be selected high so that a high output voltage can be achieved.For instance, for 1 pW ( 90 dBm) of input light, the output voltage across the 10-Mload resistance R L is

Vout D RPR L D 5 104 10 12 107 D 0.5 V

It should, however, be remembered that such a large load resistance raises the valueof the time constant CR L of the detector, where C is the capacitance of the tube, and

the response time of the tube becomes excessively slow.Despite the high sensitivity of the photomultiplier tube, it is not practical for use asa detector for optical communication systems. These systems operate in the D 1.3or 1.55 m regions where the photomultiplier sensitivity is low. Other disadvantagesof the photomultiplier tube when used for optical communication systems are poorfrequency response, large size, the necessity of a kilovolt power supply, the limitedlifetime of the tube, and the cost.

12.2 STREAK CAMERA

A streak camera is used to observe light variations with respect to time of the order of picoseconds (10 12 s). The structure of the streak camera, which is shown in Fig. 12.2a,


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STREAK CAMERA 799

3

2 1

t

Grating

Time0

S p a c e

Lens

Fiber

Sweep V (t )

Cathode Anode

Slit

Phosphor screen

Microchannelplate

DeflectionplateAnode

voltage

Streak camera

Fiber

Discretespectrafilter

(a)

Laserdiode

0t

V (t )

I

Time

1530

200ps/div

1525 1520

Wavelength (nm)

1515

(b)

Figure 12.2 Streak camera measuring (a) the dispersion during transmission in an optical ber and(b) chromatic dispersion in single-mode optical ber. (After Y. Tsuchiya [1].)


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800 DETECTING LIGHT

is quite similar to a cathode ray tube used for an oscilloscope. The major differenceis that the cathode ray tube uses a steady electron beam supplied by an electron guninstalled in the tube, while the streak camera uses the electrons that are generated by thebombardment of incident photons onto a low-work-function cathode and formulated

as a beam by the anode.Another feature is that even though the location of the electron gun of the cathoderay tube is xed, the photocathode of the streak camera is sensitive along the horizontalslit, and the location of the incident light is another piece of information that the streak camera can supply. Thus, the streak camera provides simultaneously three kinds of information: the intensity of the light, the time of arrival, and the location of theincidence.

For higher speed operation the sawtooth deector voltage is sometimes replaced bya high-frequency sinusoidal voltage.

The variation of the incident light intensity is observed as a function of time onthe uorescent screen. In order to enhance the electron density hitting the uorescent

screen, a microchannel plate is installed between the deector plate and the uorescentscreen. The microchannel plate is made up of a honeycomb of ne dynode tubes. Asthe wall bounces the electron beam, the electron beam is intensied.

Figure 12.2a shows an example of using the streak camera to measure the disper-sion phenomenon in an optical ber. A pulse having different wavelengths is launchedsimultaneously into a long optical ber. The difference in arrival time of the differentwavelength components is measured by the streak camera. The light componentsarriving at a later time see a higher deector voltage V t and are deected higher. Adisplay such as the one shown in Fig. 12.2b is obtained [1].

12.3 MISCELLANEOUS TYPES OF LIGHT DETECTORS

Other types of light detectors [24] are summarized here. When light illuminates suchmaterials as CdS or CdSe, the surface conductivity increases due to the photoconduc-tive effect. The device based on this phenomenon is known as the photoconductor cell or photocell . A special feature of the CdS photocell is that its spectral responsecharacteristics resemble that of the human eye. It is widely used as an exposure meterin photography.

Solar cells convert solar energy into electrical energy by a phenomenon known as the photovoltaic effect . Calibrated solar cells are also used as light meters for photography.

The phototransistor is the amalgamation of a photodiode, which will be explainedextensively in the next section, and an amplier transistor. It is like a photomultipliertube made of semiconductor material. It can provide a large signal output, but theresponse time is not as high as the photodiode alone.

Calorimetric methods use the temperature rise in a heat-absorbing strip that isexposed to light. The temperature rise is measured by a thermometer with as low a heatcapacity as possible. These thermometers include a thermocouple, which establishes thevoltage due to the temperature difference between the ambient and the heat-absorbingstrip, and a thermister or bolometer, which changes its resistance in accordance withits temperature.

As an example of a device based on the calorimetric method, Fig. 12.3 shows adiagram of a pyrometer that measures the temperature distribution inside a furnance


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PIN PHOTODIODE AND APD 801

Heat-absorbing strip

ThermocoupleShield againstdirect illumination

Real image of the objectObject

Moving concavemirror

Microscope to observethe real image on the strip

Figure 12.3 Pyrometer structure.

by measuring the radiating light intensity. The position of the concave mirror isadjustable so that the real image of the desired point of the radiation is focused onto theheat-absorbing strip. The attached microscope is used to observe the real image. Thetemperature rise of the strip is measured by a thermocouple. The measured intensityof light correlates with the temperature of the desired point in the furnace.

None of the devices in this section are suitable for ber-optic communicationbecause of the relatively slow response time. Detectors for ber-optic communicationare presented in the next section.

12.4 PIN PHOTODIODE AND APD

The basic principles of the PIN photodiode (PIN diode) and avalanche photodiode(APD) are quite similar to each other. Once the fundamental principles have been estab-lished for the PIN photodiode, the transition to understanding the avalanche photodiodewill be quite easy.

Figure 12.4 shows the basic structure of the PIN and APD photodetectors. Basically,a PIN photodiode consists of three layers of semiconductor material: the p-type, theintrinsic-type, and the n-type semiconductors.

The actual physical structures of the PN and PIN photodetectors and the APD arepresented in the next section; the PN and PIN photodetectors and the APD on anatomic scale are described in Appendix A of Volume II.

12.4.1 Physical Structures of PIN and APD Photodetectors

Figure 12.5a shows typical physical structures for the PIN and PN photodetectors [4,5].There is very little difference between PN and PIN diodes. A PN diode is a diodeformed by joining a p layer directly to an n layer, whereas a PIN diode is formed by joining a p layer to an intrinsic layer and then to an n layer. The p C-type windowlayer is made extremely thin ( 0.3 m) because the light is incident from this layerand any charge carriers (electrons and holes) produced in the p C layer are subjectedto a low electric eld because of the high conductivity of the heavily doped p C layer.The lower electric eld means slower response time and adds to the noise.


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802 DETECTING LIGHT

e

i

n

p

h n

Positive electrode

Negative electrode

Antireflection coating

Biasvoltage

OutputR L

S i

S i

S i

S i

S i

Figure 12.4 Basic structures of PN, PIN, and APD photodetectors.

p+

p+

n+

Positive electrode

nnp+i

i

n

p+ Guard ring

n

0E

E field

Light intensity

P

n+ cappingPositive electrode

Antireflection coatingNegative electrode

Field plate

Electronhole pair production

i Electronhole production region

SiO 2 insulator

Electronholeproduction

Avalancheregion

(a)

(b)

h n

h n

Figure 12.5 Structure of photodetectors. (a) PN and PIN photodiodes. (b) Avalanche photodiode(APD).


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PIN PHOTODIODE AND APD 803

The light aperture is usually circular (Fig. 12.5 shows the cross section in a planeperpendicular to that of the circular aperture). A circular electrode is deposited overan insulating layer of SiO 2 and the p C layer guard ring. The purpose of the guard ringis to prevent dielectric breakdown by spreading the electric lines of force from the

edge of the electrode. An antireection (AR) coating is deposited over the aperture tominimize the amount of incident light that is reected. Compared to a PN diode, thePIN diode has a thicker (a few m thick) intrinsic layer that increases the interactionregion for the incident photons with orbital electrons. An excessively long intrinsicregion, however, harms the response time because the transit time for the electrons toreach the electrodes becomes too long. The diameter of the electrode is made smallto minimize the capacitance. A metal eld plate is deposited in order to prevent straylight entering the diode.

On the bottom side of the substrate, a highly doped n C capping layer is depositedto ensure better adhesion to the electrode in order to minimize the series resistance.

Figure 12.5b shows the structure of the avalanche photodiode [4] (APD). An APDhas additional regions for accelerating the drift velocity of the carriers and multiplyingthe number of carriers by the avalanche effect. The bottom structure of the APD isidentical with that of the PIN photodiode. The top p-i-n layers are multiplier layers.The resistivity of the i-type layer is made much higher than the other layers so thatthe potential drop across all the layers in series is concentrated in this layer.

Incident light is rst converted into electric charge carriers in the n region. Thegenerated carriers drift upward into the n-type layer because of the moderate electriceld. The carriers then enter the highly resistive i-type layer. This i-type layer isnot a separately deposited layer. Rather, it is the depletion region formed when thepC layer is joined to the n layer. Because of the combination of high resistivity and

thinness, the eld intensity in the i layer is so large that the collisions of the acceleratedelectrons with the crystal lattice result in the creation of new carriers. The electric eldintensity reaches as high as 10 5 V/cm or even higher (the breakdown voltage of airis 3 104 V/cm), which is necessary to start the avalanche effect. The new carriersare also accelerated and collide with the crystal lattice in the avalanche region andgenerate even more carriers. The density of carriers multiplies as this snowball effectis triggered. Finally, the charge carriers exit from the top electrodes.

Thus, the bottom half of the APD has the function of converting the incident photonsinto electrons, and the top half has the function of amplifying the number of elec-trons generated. The APD performs the dual functions of photoelectric conversion andelectric amplication.

12.4.2 Responsivity of the PIN Photodiode and APD

Expressions will be derived for the output current from a PIN photodiode and APD dueto the incident light. The expressions are quite similar to those of a photomultiplier.Let W be the energy of the light entering the detector. The number of incident photonsexpressed in terms of the incident light energy is W/h . Let be the quantum efciency,which is dened as the ratio of the number of generated electrons to incident photons.Each electron carries a charge e and the total amount of charge Q after multiplicationdue to the avalanche effect is

Q D eh MW 12 .7


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804 DETECTING LIGHT

M is the multiplication factor due to the avalanche effect. The derivative of Eq. (12.7)with respect to time gives the output current from the diode

is D e

h MP s or is D

ehc

MP s 12 .8

where Ps is the incident light power.It should be noted that the above denition of includes (1) the nite transmission of

light into the surface with transmission coefcient Eq. (2.16), (2) the exponential decayof the light power inside the intrinsic region, and (3) the nite length of the intrinsicregion for generating electron-hole pair production over and above the probabilisticnature of electron-hole pair production.

Equation (12.8) indicates that the output current increases linearly with the wave-length of the incident light. There is, however, an upper limit on the wavelength. Forthe photon to ionize the atoms in the crystal lattice, the energy quantum h of theincident photon has to be larger than the bandgap energy E g of the semiconductor. Thequantum efciency has a rather abrupt cutoff wavelength in the longer wavelengthregion, as shown in Fig. 12.6a. In practice, the quantum efciency decreases faster

0

R e s p o n s

i v i t y

I n c r

e a s e

s w i t h

l

Wavelength l

Abruptdecrease at

E g = h n

(a)

(b)

C

L J

D

I

B F C

E

A

G H

K

M

190 300 400 500 600 700 800 900 1000 1100 1 200 1 300 1 400 1 5000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Visual sensitivity(relative value)

R e s p o n s

i v i t y

( A / W )

Wavelength (nm)

(Typ.at 25 C)

Si : AG GaAsP : H K

GaP : LInGaAs : M

Figure 12.6 Spectral response of the PIN photodiode and APD. (a) Generic spectral response ofthe PIN photodiode and APD. (b) Spectral response of photodiodes. (After Hamamatsu Photonicscatalog).


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DIRECT DETECTION SYSTEMS 805

than linearly at shorter wavelengths due to scattering and deviation from the centerfrequency of the designed antireection coating. Figure 12.6b shows the sensitivityof various semiconductor detectors. The wavelength dependence of varies with thesemiconductor material. The wavelength regions for optimum sensitivity are:

Ge 0.81.6 mSi 0.50.9 mInGaAs 1.01.6 m

As with the photomultiplier, the responsivity is used to characterize a photodiode.The output current with unit incident light power is the responsivity R, and R is

expressed as

R D e

h M 12 .9

or

i D RP 12 .10The responsivity of most PIN diodes is 0.5 A/W and a good rule of thumb is thatevery 1 watt of incident light power generates 12 ampere of output current.

The reasons why the PIN photodiode and APD are exclusively used for ber-optic communications are that both have (1) high photoelectric conversion efciency,(2) fast response time, (3) high reliability, (4) compactness as well as ruggedness,(5) longevity, (6) simple electronics, (7) moderate cost, and (8) high linearity of outputcurrent over a wide range of input light power.

The rest of the chapter concentrates on how to incorporate these photodiodes in

ber-optic communication systems that are broadly categorized as direct detectionsystems and coherent detection systems.

12.5 DIRECT DETECTION SYSTEMS

Figure 12.7 shows a very basic circuit employing a PIN photodiode for direct detectionin a ber-optic communication system. The photodiode is back-biased. The p layer isnegative, and the n layer is positive. The bias voltage is in the range of 715 volts. Thecapacitor C prevents the signal from going through the power supply. This particularcircuit is connected directly to a transistor amplier, but a more sophisticated couplingcircuit is required if impedance matching, frequency response, and signal to noise ratioare all to be considered. The details for these more sophisticated circuits are presentedin Chapter 16.

Let the instantaneous E eld of the light incident to the photodiode be

Es D S t cos c t C 12 .11where S t is the modulated amplitude, c is the carrier frequency of the light, and is either the modulated or unmodulated phase angle of the carrier. In order to calculatethe detected signal current is using Eq. (12.8), the input power Ps has to be calculated.

The peak energy per unit time crossing a unit area is, by the Poynting vector theorem,

S D E H 12 .12


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806 DETECTING LIGHT

Modulator

Fiber for transmission

+

Q

R L

PIN orAPD

C

P s

v s

715 V

i s a P s

Transmitterlaser

Figure 12.7 Direct detection system.

The magnitude of E and H have the relationship

E D 0 Hwhere 0 is the intrinsic impedance. The average energy per unit time crossing area s is

P s Ds

0 h E2s i

Ds

0S2 t hcos

2 c ti

Ds

2 0S2 t

12 .13

where h i is the time average over a length of time containing a large number of lightcarrier periods but not so large a number in modulation periods. The detected signalcurrent from the avalanche photodiode can be expressed in various ways:

is Deh

MP s

Deh

Ms

2 0S2 t

D Rs

2 0S2 t

D KS 2 t

12 .14

where

K Deh

Ms

2 0

Expressions in terms of the light amplitude S t rather than the power Ps are moreconvenient for explaining mixer operations. The amplitude constant K accounts forboth responsivity and sensor area and directly relates the amplitude square to theoutput current from the diode.

Note that is is proportional to the light intensity and does not contain information

about either the frequency c of the light carrier or the phase . Thus, direct detectioncannot be used for detecting frequency modulated or phase modulated signals.


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COHERENT DETECTION SYSTEMS 807

The mean square value of the direct detection signal is

hi2s i D

eh

M2

P 2s 12 .15

Next, coherent detection systems that can be used not only with intensity modulatedlight but also with phase and frequency modulated light are presented.

12.6 COHERENT DETECTION SYSTEMS

Four more schemes besides the direct detection scheme will be explained here. Thesefour are coherent detection schemes [6,7] and are so named because they require a localoscillator laser whose output light is either coherent or quasicoherent with the signallight. Making a comparison with a radio receiver set, direct detection is analogous to acrystal radio. The crystal radio is simple, but the sensitivity and station selectivity arepoor. Direct detection is primarily used for an onoff type of modulation. Coherentoptical detection is analogous to a superheterodyne radio. The superheterodyne radiois much more sophisticated, but its sensitivity and selectivity are far better than thecrystal radio.

volume Tuner

12.6.1 Heterodyne Detection

Optical heterodyne detection [8,9] uses the beat signal between the signal light and thelocal oscillator (LO) light.

Figure 12.8 shows a heterodyne detection circuit. The signal light from the trans-mitter laser passes through the ber-optic cable transmission line and prior to beingcombined with the local oscillator laser light, the signal light passes through a polariza-tion controller. The polarization controller adjusts the state of polarization of the signallight so that it is linearly polarized in the desired direction with respect to the local

oscillator laser light (parallel in the case of a single mixer). The frequency differencebetween the local oscillator laser and the signal light has to be maintained at a constant


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808 DETECTING LIGHT

Modulator

Transmitterlaser at ws

Fiber for transmission

Fiber-looppolarization

controller

Second detectorIF amplifierwp = ws wL

APD as amixer

i s

Local oscillator (LO)laser at wL

i s a P s P L

Figure 12.8 Heterodyne detection.

value. The output from the mixer is amplied by an IF amplier and then detected asecond time to recover the desired information from the IF signal.

The eld at the mixer surface is the sum of the received signal eld and the localoscillator laser eld. Let the incident light be the same as the case of direct detectiongiven by Eq. (12.11) and let the local oscillator laser light be

E L D E LO cos Lt C L 12 .16Both the signal and local laser light illuminate the APD diode used as a mixer diode.The resultant incident light power is obtained from the top equation of Eq. (12.13)replacing Es by E L C Es .

P Ds

0 h[S t cos c tL C ELO cos Lt C L ]2

i 12 .17

Using Eq. (12.8) and the identity cos x cos y D 12 [cos x y Ccos x Cy ], the outputcurrent from the mixer is

i IF

De

h M

fP s

CP L

C2

P sP L cos[ IF t

C c

L ]

g 12 .18

where

IF D c L, P s Ds

2 0S2 t , P L D

s2 0

E2LO 12 .19

and where L and IF are the local oscillator and IF frequencies, respectively. Theterms with c C L have been ignored. The phases of the signal and local oscillatorlight are c and L, respectively. Only the third term of Eq. (12.18) contains the signalat the intermediate frequency IF . The mean square value of the IF signal is, fromEq. (12.18),

hi2IFi D 2 eh M

2 P sP L 12 .20


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The mean square value of the IF signal is the product of the signal and local oscil-lator powers, while that of the direct detection system as given by Eq. (12.15) is thesquare of the signal power, which for weak signals is the square of an already smallquantity. Thus, the output from the heterodyne detection for the small signal case

is signicantly higher than that of direct detection. The selectivity of the heterodynesystem is also higher than that of direct detection because the bandwidth of the hetero-dyne is determined by the bandwidth of the IF amplier, which is a lower frequencyand can be tailored to the required bandwidth of the signal more easily, typically inthe gigahertz range. This not only improves the selectivity but enhances the rejectionof the noise power. Direct detection, on the other hand, has to rely on an optical band-pass lter (whose bandwidth is normally much wider than gigahertz) for wavelengthselectivity and noise power rejection.

12.6.2 Homodyne Detection

When the frequency of the local oscillator of the heterodyne detection system [10,11]is made equal to the frequency of the signal light, the system becomes homodyne.The homodyne system not only relaxes the frequency bandwidth requirement of theIF amplier but also improves the sensitivity by 3 dB over heterodyne detection. Thephase stability requirement of the local oscillator, however, is severe and an elaboratephase stabilization circuit is required for the local oscillator laser.

With

c D L or IF D 0Eq. (12.18) becomes

im Deh

M[P s CP L C2 P sP L cos c L ] 12 .21When P L is large in comparison to P s , the third term is the signal component. Thephase-lock loop assures c D L for the steady signal. The mean square value of thedesired signal is

hi2mi D 4

eh

M2

P sP L 12 .22

Compare this result with the heterodyne result in Eq. (12.20). There is a factorof 2 difference. This difference comes from averaging hcos 2[IF t C c L ]i inEq. (12.18), which is 12 and averaging hcos 2 c L i in Eq. (12.21), which is unityfor c D L. Thus, the signal to noise ratio and hence the sensitivity of the homodynesystem is better than the heterodyne system by 3 dB.

A disadvantage of homodyne detection is the stringent requirement on the phasestability of both the transmitting and local oscillator lasers. In Eq. (12.21), if c Luctuates between 0 and 90 , the output uctuates between its maximum value andzero, and communication becomes impossible. A phase-lock loop (PLL) can extractthe carrier frequency component from the amplitude modulated carrier. The extractedcarrier is used to lock the oscillation of the local oscillator signal.

Figure 12.9 shows a block diagram of the Costas PLL [12]. Inside the 90 opticalhybrid, the local oscillator signal is divided into two components, one of which is phase


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810 DETECTING LIGHT

Signal

E s , wc

LO E L, wL

90

Opticalhybrid

Polarizationcontrol

LO laseri e = K S de E

2LO sin 2( w t + q e )

Low-passfilters

i I i Q

MQ

MI Amplifier

Amplifier

iI

i Q

Basebandoutput

M m

1 2 (E s + E L)

1 2 (E s + jE L)

Figure 12.9 Homodyne detection with a phase-lock loop.

shifted by 90 . The component with the same phase as the original local oscillator signaland that with a 90 phase shift are expressed as

E L I D1

p 2 ELO cos Lt C L

E LQ D 1p 2 ELO sin Lt C L12 .23

The local oscillator power P L is assumed to be equally divided into the twocomponents. The subscripts I and Q stand for in-phase and quadrature, respectively.The two components of the local oscillator are separately mixed with the receivedsignal at mixers M I and M Q . When E L I is fed into M I with the received signal, theoutput from M I is similar to Eq. (12.18). The IF component of the output current isi I . Similarly, the output from M Q is iQ . The components of the outputs from M Iand M Q are called the in-phase and quadrature components of the IF signal. They aregiven by

i I Dp 2KS t E LO cos t C eiQ Dp 2KS t E LO sin t C e

12 .24

where

D c L, e D c Land K is given by Eq. (12.14). Now, both i I and iQ are fed into another mixer M m.The relevant component of the output from the mixer is

ie D 12 K02[S t E LO ]

2 sin 2 t C e 12 .25


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where K0 is a constant associated with the electronic mixer. [ S t ]2 can be rewritten as

[S t ]2 D Sdc CSac t 12 .26

where Sdc is the average component and Sac t is the ac component of [ S t ]2. The

frequency spectrum of Sac t is associated with the modulation by the signal and isnormally much higher (tens of gigahertz) than , provided L is close to c . Witha low-pass lter, Sac t can be removed. The output of the low-pass lter becomes

ie D K01 E2LO Sdc sin 2 t C e 12 .27

The output ie from the mixer is used as an error signal to control the frequencyand phase of the local oscillator laser diode. To explain the operation, assume rstthat the frequency is already matched but the phase is not: D c L D 0 and e D c L 6D 0. Figure 12.10 shows a plot of the error signal ie as a function of thephase mismatch e .

Consider only the region of / 4 < e < / 4. Let us say the operating point is atP in Fig. 12.10. A positive value of the error signal ie means e > 0 or c > L. Apositive error signal ie raises the local oscillator frequency higher so that L is increasedand reaches the value of c , thereby bringing the operating point P to the origin.

Next, suppose that c makes an abrupt increase at t D 0. In this case, e D tstarts to increase, and hence ie starts to increase, raising the local oscillator frequency L in order to catch up with the increase in c and bring the operating point back tothe origin. It is, however, crucial that the turnaround time of this feedback process befast enough to react before e goes beyond the range of

/ 4 radians.

0

P

p4

p4

E r r o r s i g n a l

i e

q c < q L q c > q L

q e

Figure 12.10 Error signal h i I i Q ierror as a function of phase error e D c L .


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812 DETECTING LIGHT

In the case of ASK (on off) modulation, either the in-phase or the quadraturecomponent alone of Eq. (12.24) could have been used directly as an error signal to thefeedback loop. For phase modulation, where S t takes on positive and negative values (or0 and 180 phases), the sign of the error signal changes as S t changes sign, and both

in-phase and quadrature components had to be used as the error signal.

In this way, the phase as well as the frequency of the local oscillator is locked to thereceived carrier frequency. In other words, the local oscillator is completely coherentwith the received signal, and in traditional communication theory, only homodyne iscalled coherent detection. In the eld of optics, both heterodyne and homodyne aregenerally called coherent detection.

12.6.3 Intradyne System

The intradyne system [10] is a hybrid of the heterodyne and homodyne systems.It enjoys the merits of both systems. The stringent requirements on the frequencybandwidth and phase stability are relaxed. The intradyne system normally incorporatesthe phase diversity technique in which the signal is rst divided into more than onechannel before detection. Signal processing circuits, such as squaring and differentiatingcircuits, are installed in each channel. After being processed, the signals from thedivided channels are added to render a nal signal that is free from phase jitter.

In the homodyne system shown in Fig. 12.9, if the local oscillator frequency isnot completely matched, both the in-phase, i I , and quadrature, iQ , components become

modulated at a frequency c L as shown in Figs. 12.11c and 12.11d. Such outputscan almost be used as the nal signal, but modulation of the amplitude at frequency D c L creates a problem.The intradyne system shown in Fig. 12.12 uses both in-phase and quadraturecomponents to remove the modulation of the amplitude. The sum of the squares of thein-phase component and the quadrature component, Eq. (12.24), gives the output

i2 D 2[KE LO S t ]2 12 .28

i2 is free from L c and . The quadrature current iQ is fed to the frequencydiscriminator, which keeps L

c within a given range. Such an intradyne detectoris sometimes called a phase diversity receiver because two phase components areused. It should be noted that the output being 2 K2 E2LO S

2 t , this detection system isnot suitable for either phase or frequency modulated signals.

It is also possible to split the signal into N components with equal phase spacingbetween components. But, the larger N is, the higher the local oscillator power isneeded. The loss in the circuit is also increased. An advantage of a larger N, however,is that uniformity among the channels is less critical.

As already mentioned, the frequency of the input light is converted into either an IFor baseband signal by mixing the incoming signal with the local oscillator light. Thequality of the mixer signicantly inuences the sensitivity of the heterodyne system

because the mixer is the rst element that the signal at its lowest power level sees.Because of this importance, the function of the mixer will be explained in detail here.


18/37


(d) i Q = KS (t ) sin( w t + q e )

(c) i I = KS (t ) cos( w t + q e )

(b) V I = cos( w t + q e )

(a) S (t )

t

t

t

t

0

i Q

i I 0

0

V I

0

(t )

Figure 12.11 Intradyne signal.

LO laser

Output

Polarizationcontrol

90 Opticalhybrid

Low pass filter

E s

E L

Frequencydiscriminator

(E s + E L)12

12 (E s + jE L)

i 2I

i 2Q

Figure 12.12 Intradyne detection.


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814 DETECTING LIGHT

12.7 BALANCED MIXER

There are two types of mixers: the single crystal mixer as shown in Fig. 12.13a, andthe double balanced mixer [13] as shown in Fig. 12.13b.

The most commonly used input elements to the mixer are optical ber couplersor prism couplers. The substrate optical coupler shown in (1) of Fig. 12.13b will betreated. Assume that inside the substrate optical coupler, the eld that crosses the guidefrom the upper to lower or from the lower to upper guide experiences a 90 phase shiftcompared to the eld that goes straight through. The input elds E1 to mixer M 1 and E2 to mixer M 2 will be calculated rst. The 90 phase shift will be accounted for bychanging the cosine function into a sine function. The input elds to the mixers areexpressed as

E1 D1

p 2 [S t cos c t C ELO sin Lt] 12 .29

E2 D1

p 2 [S t sin c t C ELO cos Lt] 12 .30

where S t and ELO are the signal and local oscillator elds, respectively. The factor1/ p 2 is necessary because the light power is split 5050.

++

E 1 =S + jL

E 2 = jS +L

S S

S

S

APD

APD

APDAPD

NBS

Nonpolarizingbeamsplitter

(NBS)Star fibercoupler

L

L

LL

I

I

Substrate fibercoupler

(1) Fiber coupling (2) Prism coupling

(2) Nonpolarizing beamsplitter coupling(1) Star fiber coupling

(b)

(a)

M1

M1

M2

M2

i 1

i 2

i 2

i 2

i 2 i 1

i 2 i 1

Figure 12.13 Comparison between (a) the single crystal mixer and (b) the double balanced mixer.


20/37


21/37

816 DETECTING LIGHT

12.8.1 Stimulated Effects

Detection associated with the nonlinear effect of the glass will be explained [1418].When a light beam with a diameter of a few millimeters is focused into the core of anoptical ber with a diameter of a few micrometers, the light intensity is increased by 10 6

times. When one compares the length of an optical ber with the lengths of other opticalcomponents, the ber is typically 10 4 times longer. The power density-interactionlength is used as a barometer of the enhancement of the nonlinear effect. An opticalber is 10 10 times more susceptible to nonlinear effects than a bulk optical component.

Close observation reveals that even when monochromatic incident light is used, thespectrum of the light reected back from inside the ber is no longer monochromatic.This phenomenon is quite different from the electrooptic effect that relates to thechange in the index of refraction but does not involve a change in frequency spectrum.

As shown in Fig. 12.14, on both sides of the spectrum of the incident light, twonew lines become observable as the intensity of the incident light is raised. Spectra

appearing on the lower frequency side are called lines of Stokes radiation, and thoseappearing on the higher frequency side are called lines of anti-Stokes radiation. Theratio of the intensity IS of Stokes radiation to the intensity Ia of anti-Stokes radiationobeys the Boltzmann distribution and

Ia /I S D e2h f/kT 12 .35

where f is the frequency shift of the Stokes wave. Thus, the intensities of the Stokeswaves are larger than those of the anti-Stokes waves.

Both Stokes and anti-Stokes waves consist of two sets of spectral lines. One isdue to Brillouin scattering and the other is due to Raman scattering. The mechanism

wa

wR wB w B w R w w

StimulatedBrillouin

scattering

Brillouinscattering

Incident light

Stokes lines Anti-stokes lines

Raman(in expanded scale)

Raman(in expanded scale)

Figure 12.14 Typical Stokes and anti-Stokes lines.


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DETECTION BY STIMULATED EFFECTS 817

of the frequency shift for Brillouin and Raman scatterings are different. While Ramanscattering is associated with vibrations of dipole moments formed by two ions in a unitcell of the crystal lattice, Brillouin scattering is the reection of light from acousticwaves (phonons) generated by the electrostrictive effect. The characteristics of the

Brillouin scattering are different from that of the Raman scattering.

12.8.2 Homodyne Detection by Stimulated Brillouin Scattering

Figure 12.15 shows a block diagram of a homodyne receiver that uses the wavegenerated by stimulated Brillouin scattering (SBS). The pump laser light with a powerof several milliwatts at frequency L is injected from the receiver end into the opticalber in the reverse direction from that of the signal ow. The signal light is muchweaker in intensity compared to the pump. A beat wave is generated between the pumplaser light at L and the signal wave whose carrier frequency s is set to be identical

with the frequency B of the Brillouin scattering. Two waves traveling in oppositedirections but with slightly different frequencies generate a moving standing wavein the ber in the direction of propagation of the higher carrier frequency light. Thismoving standing wave generates an acoustic wave due to the electrostrictive effect.The acoustic wave spatially modulates the index of refraction of the core. Consequently,a moving optical grating is formed in the core. If the Bragg condition is satised, themoving optical grating efciently scatters the pump beam into the same direction asthe signal, creating a second beam heading toward the receiver. The frequency of thesecond wave is shifted lower with respect to that of the pump beam due to the Dopplereffect of the moving scatterer (SBS). This second beam has the same frequency as thesignal light. The net result is an increase in the signal power.

f s = f b

f L = f b + f a

E s E L

Digitaldata

Isolator

Receiver

Pump f L

P u m p

l a s e r

Transmitter

E s

n (z )

Fiber

Laser

E L

E s

E L

z

M

E s (1 + G )

GE s

Figure 12.15 Homodyne receiver based on stimulated Brillouin scattering.


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818 DETECTING LIGHT

This amplication is immune to the phase jitter of the signal. If the phase of thesignal is delayed by radians, the peak positions of the grating shift by d D

12 /

toward the source. The local oscillator signal reected from the grating has to travelan extra distance 2 d , causing a phase delay of 2 d D . Thus, the reected localoscillator signal is delayed by the same amount. Thus, the secondary beam has boththe same frequency and the same phase. Two special features of this amplication arethe automatic synchronization of the phase of the pump beam with that of the signalbeam and the narrowness of the frequency bandwidth, typically 20 MHz. Thus, thisphenomenon can play the role of the synchronous homodyne receiver.

This scheme not only detects the signal but also has a power gain of G that is propor-tional to the pump power and is typically 1525 dB. The drawback is the difcultyin applying ASK modulation (on off modulation) because the stimulated Brillouinscattering tends to continue even during the light off period of the onoff modulation.

Let us nd the frequency relationships. The frequency f B of Brillouin scattering thatwill beat with a frequency f L of the pump light and generate the acoustic frequency

f a isf L f B D f a 12 .36

The grating has to satisfy the Bragg condition if the reected wave is enhanced byBrillouin scattering. If the acoustic wave propagates at velocity Va in the crystal, the

When two atoms in a unit crystal cell consist of positive and negative ions, these twoatoms form an electric dipole. Such a dipole oscillates when an oscillating external eld E isapplied. The oscillating dipole in turn reradiates an electromagnetic wave. Such a dipole has a

resonant frequency of oscillation that is determined, among other physical parameters, bythe atomic weight. When the frequency of the external eld coincides with this resonantfrequency, the intensity of the reradiation is greatly enhanced. If, as a start, a small-intensitysignal at R in the thermal noise spectrum is mixed with the frequency L of the externaleld in the nonlinear medium, beat waves are generated at the sum frequency L C R andthe difference frequency L R. Only the frequency R in the thermal noise spectrum thatsatises

L R D can effectively excite the dipole. The reradiated eld at from the dipole again mixeswith the incident wave at L and contributes to the signal eld at frequency R. The cyclic

reaction repeats and builds up the signal at R. To summarize, the incident energy at L istransferred into the Raman spectrum at R using the ionic dipole and the nonlinear propertiesof the medium.

The amplication based on the stimulated Raman scattering (SRS) goes through the sameprocedure but the difference is that the spectrum R is injected rather than that originatingfrom the thermal noise spectrum. The intensity of the output at R is larger than that of theinput power due to the enhancement of the Raman scattering. Such an enhancement can beused for a Raman amplier or a Raman oscillator [19,20].

The intensity of Stokes radiation due to Raman scattering in a SiO 2 ber is about twoorders of magnitude smaller than that of Brillouin scattering. The frequency shift of thespectrum due to Brillouin scattering is 11.4 GHz while that of Raman scattering is about afew hundred terahertz. The linewidth of Raman scattering is of the order of terahertz, whilethat of stimulated Brillouin scattering is of the order of tens of megahertz.


24/37

JITTER IN COHERENT COMMUNICATION SYSTEMS 819

wavelength a of the acoustic wave is a D V a /f a . For the pump wave to satisfy theBragg condition, a has to be one-half of the wavelength of the pump light:1

2

c

n 1

f L DVa

f a12 .37

Now, the value of f B that satises both Eqs. (12.36) and (12.37) is

f B D f L 12nc

Va 12 .38

Thus, the frequency of the Brillouin scattering is shifted by 2n/c V a f L, which ismuch smaller than f L because Va /c is quite small. For the case of a fused silica ber,Va

D 5960 ms 1 , L

D 1.5 m, and n

D 1.44. The frequency difference between the

signal and the local oscillator is 11.4 GHz.

12.9 JITTER IN COHERENT COMMUNICATION SYSTEMS

The two kinds of jitter (unpredictable change) that impact coherent communicationsystems are polarization jitter and phase jitter. The presence of these jitters will causethe output signal to wax and wane. If the jitter is severe enough, there will be timeswhen the signal fades completely, thus interrupting communication. Countermeasureshave to be incorporated.

12.9.1 Polarization Jitter Controls

When linearly polarized light is sent through a ber that does not preserve the stateof polarization of the input light, the received signal is generally elliptically polarized.For optimum mixing, the state of polarization of both the received signal and the localoscillator signal should match. A means of adjusting the state of polarization of oneor the other is required.

Polarization-maintaining bers could be used in place of polarization controllers;however, this is not always an option when using existing cables that have beeninstalled with non-polarization-maintaining ber.

The ber-loop polarization controller described in Chapter 6 can be used to convertthe polarization of the received light into a state that is linearly polarized parallel tothe local oscillator light. However, the ber-loop polarizer [21,22] cannot cope witha uctuating state of polarization. In ordinary optical bers, the polarization is apt tochange over time because of changes in stress caused by temperature changes or bymechanical vibration of the transmission ber [23]. An automatic polarization controlis necessary to dynamically correct for changes in polarization.

Example 12.1 Both the signal and the local oscillator signals are linearly polarized,

but they are not parallel to each other on the input surface of the mixer. What is theIF output current when they are angled spatially at as shown in Fig. 12.16?


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820 DETECTING LIGHT

E s

E L0

y

x

f

Figure 12.16 IF output current when E S and E L have a separation angle of .

Solution Let us say the input signal and local oscillator signal are

Es D S t cos c t C E L D E LO cos Lt

12 .39

The component of the signal parallel to the local oscillator is E s cos and that of theperpendicular component is Es sin .

The output from the mixer is proportional to the power or square of the resultant Eeld, which is the sum of the squares of resultant elds parallel and perpendicular to

the local oscillator eld.i D 2Kh[ ELO cos Lt CS t cos cos c t C ]

2

C[S t sin cos c t C ]2iD 2K

12 E2LO C

12

S2 t C ELO S t cos cos IF t C 12 .40

Thus, the IF current component is the third term in Eq. (12.40).

i IF D 2KE LO S t cos cos IF t C 12 .41In conclusion, only the eld component that is parallel to the local oscillator eld

contributes to the IF current.

There are two approaches for automatically correcting the state of polarization.These are the computer-controlled method and the polarization diversity method. Asevident from the name, the computer-controlled approach corrects the polarization of the received signal through computer control. The polarization diversity method usesan analog circuit that can process the signal independent of the state of polarization.

12.9.1.1 Computer-Controlled Method of Jitter Control

A designated computer either searches for the maximum output by interrogating thereaction to a small perturbation of the control signal, or actually monitors the state of


26/37


y 0 z x

x Electrode

y Electrode

Opticalguide

V g

V h

l4 Plate

l2 Plate

Lithium niobate

Control currentElectromagnetor piezocrystal

T 1T 2

T 3T 4Induced

stress

Peltierelements

Heatsink

b b = T

To servo +control

Polarization-maintainingfiber

(b)(a)

(d)(c)

V y V x

V y

Figure 12.17 Various types of automatic polarization controller elements. (a) Based on squeezingthe ber. (After A. S. Siddiqui and Y. Aihua [25].) (b) Based on heat. (After N. G. Walker andG. R. Walker [26].) (c) Based on the electrooptic effect. (After N. G. Walker and G. R. Walker [26].)(d) Electrically rotatable liquid crystal waveplates. (After T. Chiba, Y. Ohtera, and S. Kawakami [29].)

polarization at an intermediate stage and issues commands to the appropriate elements.

In either way, elements are needed whose birefringence can be computer controlled[24]. Figure 12.17 shows examples of such elements.The ber squeezer polarization controller [25] makes use of the stress-induced

birefringence created by squeezing the ber, as mentioned in Chapter 6. The ber issqueezed either by an electromagnet or piezoelectro mechanical transducers, as shownin Fig. 12.17a.

The heat-induced polarization controller in Fig. 12.17b uses the temperaturedependence of a short length of the birefringence of a polarization-maintaining ber[26]. The polarization-maintaining ber, as discussed in Chapter 11, is made of twotypes of glass having different amounts of shrinkage at the time the glass ber is set.The birefringence is zero at the temperature T s when the glass is set. As the temperature

T is decreased, the birefringence linearly increases [26] and

b D T 12 .42where

T D T s TThus, by changing the temperature, the birefringence can be controlled.

Another type of element is based on the electrooptic effect of an electrooptic [27,28]crystal. The birefringence is varied by an externally applied electric eld. An example

of an optical guide on a lithium niobate substrate is shown in Fig. 12.17c. The potentialV x between the center and both side electrodes controls the E x eld (vertical eld),


27/37


28/37


expression. The horizontally and vertically polarized signal and local oscillator eldsare represented by

E H Dp S t cos c t EV Dp 1 S t cos c t C

12 .43

E LH D E LV D1

p 2 ELO cos Lt 12 .44

The outputs from mixers M H and M V are

i H D 2K S t cos c t C ELOp 2 cos Lt

2

12 .45

iV D 2K 1 S t cos c t C C

ELO

p 2 cos Lt2

12 .46

After time averaging and ltering the signal currents from M H and M V , the IF frequencycomponents become

i H Dp 2K S t E LO cos IF t 12 .47iV Dp 2K 1 S t E LO cos IF t C 12 .48The outputs from the square operator after low-pass ltering are

i D H D [KE LO S t ]2 12 .49i DV D [KE LO S t ]

2 1 12 .50

It is good to remember that the square operator followed by low-pass ltering alwaysremoves the effect of carrier phase uctuation. Finally, the sum of i D H and i

DV gives

i D [KE LO S t ]2 12 .51

which is completely independent of uctuations in both and .

12.9.2 Phase Jitter

Besides polarization jitter, the other jitter to be concerned about is phase jitter, whichis generated not only in the laser diode but also in the ber due to temperatureuctuations and mechanical vibrations. For the amplitude or intensity modulated signal,the modulation information is extracted from only the amplitude of the signal, and thephase jitter does not show up in the output.

Phase jitter in the phase modulated system, however, is more difcult to remove,simply because the system has to identify the origin of the phase change and nd out if it is due to the intended phase change associated with the phase modulation, or due to

unwanted phase jitter of the system. The two-frequency method is one of the ways toremove the phase jitter and still retain the modulated phase information. The transmitter


29/37

824 DETECTING LIGHT

sends two light signals whose carrier frequencies are slightly different [31]. Only onelightwave is phase modulated. The frequency of the other unmodulated lightwave isshifted by a small amount . The unmodulated light is a tone signal used as reference.The two light signals are transmitted through the same ber, at the same time, under the

same conditions, and at the same state of polarization, and it is reasonable to expect thatboth suffer the same phase jitter during transmission. If the two phases are subtractedfrom each other at the receiver, only the intended phase modulation will be detected.

First, it is assumed that the polarization jitter is absent. Figure 12.19 shows thecircuit of a differential phase shift keying (DPSK) system. The transmitter laserlightwave is divided into two lightwaves. One is phase modulated as t , and theother is the frequency-shifted tone c C . In this example, the frequency shift is created by an acoustooptic modulator. Prior to entering the ber-optic cable, bothwaves are combined such that the two waves are polarized in the same direction. Atthe receiver end, both waves are mixed with the local oscillator and undergo detectionand signal processing. Both waves emerging from the ber will have undergone similarphase and polarization jitter. A ber-loop polarization controller [22] (FPC) is used toconvert the waves back to a linear polarization. Then, the waves are mixed with thelocal oscillator through a nonpolarizing beamsplitter (NPBS). Let denote the phase jitter from the ber during transmission. The output from the mixer M is

i D 2Khfcos[ c t C t C C p C ]Ccos[ c C t C C ] C ELO cos Lt C L g

2

i 12 .52where , p , and L are the phase jitters in the transmitter laser, the phase modulator,and the local oscillator laser, respectively. For simplicity, the wave amplitude S t hasbeen taken as unity.

The output is band-pass ltered so that the component is rejected. Only the IFand IF C components are retained, where 2 c , 2 L, and c C L) terms areignored.

( )2

Transmitter laser

(t )phase modulator

wc

MFilter Square Filter

operator

Delay and detect

NPBS

NPBS

NPBSFPC

Frequencyshifterwc + w

wc , wc + w

wL

i i IF

i s

Fiber cable

Transmitter Receiver

LO laser

i D t

Figure 12.19 Phase jitter removal from a DPSK system by a frequency shift delay- and-detectmethod.


30/37


The output current from the lter is

i IF D 2KE LOfcos IF t C t C L C p C ]

Ccos[ IF

C t

C

L

C ]

g 12 .53

After the square operator, the term with is selected by ltering. The ac output is

is D 4 KE LO2 cos[ t t p ] 12 .54

Equation (12.54) contains the desired phase modulation information t and is freefrom uctuations in , L, and . However, the phase jitter term from the phasemodulator itself is still present.

DPSK is the coding system that uses the change in the phase of the carrier. A 0 isrepresented by the absence of change; a 1 is represented by the presence of change.The means by which the delay-and-detect circuit interrogates the DPSK coding willbe explained. Besides the function of interrogation, the delay-and-detect circuit alsoremoves the p noise. The signal path of the delay-and-detect circuit is divided intotwo paths, one having a shorter length than the other. The output from the longer pathis time delayed from that of the shorter path by exactly one bit period. The sum of these two signals are squared, and all the terms except the product of these two signalsare ltered out. The result is

i D D K1 cos[ t t p ] cos[ t t p ] 12 .55

where K1 absorbs all the physical parameters, and is one bit period. The output isfed through a low-pass lter and

i D D 12 K 1 cos[ C t t ] 12 .56Imposing the condition that

D 2 N , where N is an integer 12 .57the 0 bit and the 1 bit of the phase modulation satisfy

t D t 0 bitt D t C 1 bit

12 .58

Thus, the output from the detector becomes

i D D K/ 2 for 0 bit

K/ 2 for 1 bit 12 .59

Therefore, all the phase jitter is removed from the detected signal. The signs of K/ 2in Eq. (12.59) are reversed if 2 N in Eq. (12.57) is replaced by 2 N C1.


31/37

826 DETECTING LIGHT

It may be added that even though the delay-and-detect circuit has the merit of simplicity, there is a restriction on the choice of the bit rate, as specied by Eq. (12.57).Equation (12.57) can be rewritten in terms of the bit rate B D 1/ as

B Df N 12 .60

where f D / 2 and N D 1, 2, 3. . . . The delay-and-detect circuit cannot function(See Problem 12.3) when B D

42 N 1

f 12 .61

where N D 0, 1, 2, 3 . . . .

12.10 COHERENT DETECTION IMMUNE TO BOTH POLARIZATION AND PHASE JITTER

Two systems that are free from both polarization and phase jitter will be presentedhere. Both systems combine a circuit designed to eliminate phase jitter with a circuitdesigned to get rid of polarization jitter, but they combine them in different ways. Therst example uses the two diversities separately while the second example uses thetwo diversities in a more comprehensive manner.

Figure 12.20 shows a block diagram of the rst example [32]. Phase diversityis applied to the horizontal and vertical waves separately and polarization diversity

wL

wL

E H

E V

wL

i HI i D HI

i D HQ

i D VI

i D VQ

i HQ

D HI

D HQ

D VI

D VQ

i VI

i VQ

wc , (t )

wc , (t )

V channel

H channel

90 opticalhydbridcoupler

90 opticalhybrid

couplerFilter

Signalwc , (t )

laserLO

PBS

PBS

t

t

t

t

Figure 12.20 Block diagram of DPSK that is free from both polarization and phase jitter. (AfterY. H. Cheng, T. Okoshi, and O. Ishida [32].)


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COHERENT DETECTION IMMUNE TO BOTH POLARIZATION AND PHASE JITTER 827

is applied to these two phase-jitter-free waves. This example again uses DPSKmodulation. The received signal is rst fed to the polarization beamsplitter. Thehorizontal and vertical wave outputs from the beamsplitter are

E H D S t cos[ c t C t C H ] 12 .62

EV D 1 S t cos[ c t C t C V ] 12 .63where the uctuating quantities are , H , and V . They are fed to separate 90 opticalhybrid couplers together with the local oscillator light. The output from the 90 opticalhybrid is similar to the one in Fig. 12.9 described in connection with the optical Costasloop in Section 12.6.2. The in-phase and quadrature phase IF frequency outputs forthe horizontal wave components are

i HI D

p 2K

E

LOS t cos[

IFt

Ct

C H

] 12 .64

i HQ Dp 2K E LO S t sin[ IF C t C H ] 12 .65where the local oscillator power is equally divided into each 90 hybrid coupler andits amplitude is 1/ p 2 E LO .

Similarly, the outputs from the 90 hybrid coupler for the vertical wave compo-nents are

iVI Dp 2K

1 E LO S t cos[ IF t C t C V ] 12 .66

iVQ Dp 2K 1 ELO S t sin[ IF t C t C V ] 12 .67

These IF signals are separately amplied and then fed to sets of delay-and-detectcircuits. The delay-and-detect circuit performs the operation of the product betweenthe present and previous bits, as described in Section 12.9.2.

Now let us obtain the horizontal wave output from the top delay-and-detect circuits.Note that the delay-and-detect circuit in Fig. 12.20 does not employ a low-pass lter ascompared to that in Fig. 12.19. The output for the in-phase component is the productof i HI at t D t and t D t with t D for 0 and t D t Cfor 1.

i D HI D K m[KE LO S t ]2 cos 2[ IF t C t C H ] 12 .68where the C sign corresponds to the 0 bit and the sign to the 1 bit, and whereK m is a constant associated with the electronic mixer and IF D 2 N . Similarly, theoutput for the quadrature phase component is

i D HQ D K m[KE LO S t ]2 sin 2[ IF t C t C H ] 12 .69

The sum of Eqs. (12.68) and (12.69) is independent of IF , t , and H .

i H D K m[KE LO S t ]2 12 .70


33/37

828 DETECTING LIGHT

The components for the vertically polarized waves are

i DVI D 1 K m[KE LO S t ]2 cos 2[IF t C t C V ] 12 .71

i DVQ

D 1 K m[KE LO S t ]2 sin 2[IF t

Ct

C V ] 12 .72

Addition of Eqs. (12.71) and (12.72) gives

iV D 1 K m[KE LO S t ]2 12 .73

Finally, the sum of Eqs. (12.70) and (12.73) removes the uctuation of inpolarization, and gives a completely jitter-free signal:

i D K m[KE LO S t ]2 12 .74

The system with the square operation that also achieves jitter-free operation forDPSK modulation is shown in Fig. 12.21. This system combines the two diversitymethods more comprehensively [33]. This system uses the frequency shift methodfor phase jitter cancellation, and the square and addition operation for polarizationdiversity. This system is simpler than the previous system in that both the unshiftedsignal and the frequency-shifted signal share the same circuit, but it requires afrequency-shifted signal light. The transmitting light consists of two waves. One isat frequency c and is phase modulated by t of the DPSK data. The other isfrequency shifted to c C but is not modulated. Both of these waves are linearlypolarized and the directions of polarization of the two waves are collinear.

Just the same as the system in Fig. 12.19, during the traversal of the ber, bothwaves experience the same phase jitter and change of state of polarization because the

MH

MV

Filter Square Filter

Filter( )

2

( )2

Transmitter laser

NPBS

NPBS

NPBS

Frequencyshifter w

wIF, wIF + w

wIF, wIF + w w, (t )

w, (t )

Fiber cable

Delay and detect

PBS

LO laser

i t

wc

wc , wc + w

(t )

Figure 12.21 System with the square operation for the removal of both polarization and phase jitterfrom DPSK.


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COHERENT DETECTION IMMUNE TO BOTH POLARIZATION AND PHASE JITTER 829

only difference between the two waves is that one is frequency shifted by . Thereceived signals become

E H D1

p 2

S t fcos[ c t C t C C p C H ]

Ccos[ c C t C C H ]g 12 .75 EV D

1p 2 1 S t fcos[ c t C t C p C V ]Ccos[ c C t C C V ]g 12 .76

where p is the jitter in the phase modulator and , H , and V are the same as beforeand are the phase jitters of the source, the horizontal wave, and the vertical wave.The received wave is separated into horizontal and vertical wave channels. The localoscillator signal is

E L D E LO cos Lt C L 12 .77which is polarized at 45 to the horizontal direction, providing an equal-amplitudeE LO / p 2 local oscillator eld to each channel, where ELO , L, and L are the localoscillator amplitude, frequency, and phase jitter. The analysis of the operation isquite similar to that of the phase diversity without polarization diversity describedin Section 12.9.1.2 and will be repeated only briey. In each channel, the signal isconverted down to the IF frequency by the mixers M H and M V . In each channel, aband-pass lter follows the mixer and lters out the component, keeping only IFand IF

C components. These two components experience the same phase jitter,

and the next processing step consisting of the square operation followed by summationserves to cancel the phase jitter. Thus, signals in both the H and V channels becomefree from phase jitter. Using results similar to Eq. (12.53) as the input to the squareoperator, the squared results of the H and V channels are

i H D 2[KE LO S t ]2 cos[ t t p ] 12 .78

iV D 2[KE LO S t ]2 1 cos[ t t p ] 12 .79

Addition of the two outputs becomes independent of uctuating and

i D 2[KE LO S t ]2 cos[ t t p ] 12 .80Finally, the signal from the delay-and-detect of Eq. (12.80), followed by a low-pass

lter, becomes

i DK12

cos[ C t t ] 12 .81where K 1 absorbs all the physical parameters. The output is completely free from bothphase and polarization jitter. An advantage of this system over the previous system isthat the lightwaves of c and c C share the same paths, and the receiving systemis simpler in this regard. The disadvantage is the requirement of a more elaboratetransmitting system.


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830 DETECTING LIGHT

The existing PBS in Fig. 12.21 cannot be used to mix the local oscillator beam withthe signal beam, thereby sparing a NPBS, because the direction of the polarizations of the emergent signal and the local oscillator beams become perpendicular to each other.

12.11 CONCLUDING REMARKS

At the receiving end, the transmitted light signal is converted back into the originalencoded electrical signal. Receiving systems can broadly be categorized into thefollowing ve systems:

1. Direct detection (or video detection).2. Heterodyne detection.3. Homodyne detection.4. Intradyne detection.5. Detection by stimulated effects.

The advantages and disadvantages of these systems are summarized below.

1. The direct detection scheme is simple, but the trade-off for simplicity is mediocresensitivity and the lack of a built-in mechanism for channel selectivity. Withdirect detection, channel selectivity is achieved with additional components suchas wavelength lters. Even when such lters are used, channel selectivity isgenerally poorer than what can be achieved with heterodyne and homodynedetection.

2. The heterodyne system is equipped with a local oscillator laser and is thereforemore complicated than direct detection, but it enjoys more than a 20-dBimprovement in receiver sensitivity as well as more than 10 3 times the wavelengthselectivity.

3. The homodyne system is similar to the heterodyne system but with zerointermediate frequency (IF). With zero IF, the frequency bandwidth per channelis smaller, and the receiver gain is 3 dB higher, compared to a heterodyne system.The price to be paid is that the homodyne system requires a local oscillator laserthat can track the phase of the signal wave, and this requirement is very severe.

4. Intradyne detection is a mixture of heterodyne and homodyne detection systems.

The stability requirement of the local oscillator is not as severe as that of thehomodyne detection.5. The stimulated effect uses stimulated Brillouin scattering and the system

can be interpreted as detection with built-in phase tracking. The narrownessof the frequency bandwidth and difculty in applying ASK modulation aredisadvantages of this system.

PROBLEMS

12.1 (a) What is the theoretical limit ( D 1) for the output current from a PINphotodiode when the power of the incident light is 43 dBm and thewavelength is D 0.84 m?


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REFERENCES 831

(b) What value was assigned to the quantum efciency to obtain the rule of thumb equation i D 0.5 A/W for expressing the output current i from a PINphotodiode?

12.2 With the polarization diversied circuit shown in Fig. 12.18, prove that as long

as the ASK format is used, the phase jitter incurred in both the transmittingand local oscillator lasers, as well as in the ber during transmission, can beremoved.

12.3 Prove that the delay-and-detect circuit cannot function when the bit rate B is

B D4

2 N 1f

where f is the frequency shift between the two frequencies of the double-frequencyscheme mentioned in Section 12.9.2.

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