Lecture 2 General concepts Digital modulation in general Optical modulation Direct modulation External modulation Modulation formats Differential detection Coherent detection Fiber Optical Communication Lecture 2, Slide 1
Encoding of optical signals We can write the electrical field corresponding to a monochromatic optical wave as e is a unit vector in the direction of E E z, t) eˆ A cos( k z ω t A 0 is the (real) amplitude k 0 is the wave number ω 0 is the angular frequency φ is the phase This is equal to It is often written simply Data can be encoded using Polarization, e E Amplitude, A 0 (Power is proportional to A 02 ) (Angular) frequency, ω 0 Phase, φ z, t) eˆ Re[ A e i(k 0z 0 ( Or by a combination of these 0 ω t) Fiber Optical Communication Lecture 2, Slide 2 ] ( 0 0 0 ) E( z, t) eˆ A e 0 0 0 i(k zω t)
Modulation Using analog modulation, we talk about Amplitude modulation (AM) Frequency modulation (FM) Phase modulation (PM) Using digital modulation, the names are Amplitude-shift keying (ASK) Frequency-shift keying (FSK) Phase-shift keying (PSK) Simplest is ASK modulation in two levels This is also called on-off keying (OOK) Traditionally the most common format (for optical communication systems) Applying modulation to a monochromatic wave broadens the spectrum to a width comparable to the bit rate (symbol rate) Roughly: A 10 Gbit/s OOK signal can pass through a 10 GHz filter Fiber Optical Communication Lecture 2, Slide 3
Analog and digital signals (1.2.1) A physical signal is interpreted as being analog or digital A digital signal will be interpreted as one of the members from a finite set Digital modulation can be Pulse-position modulation (PPM) Pulse-duration modulation Pulse-code modulation (PCM) PCM is most common Required bit rate is B ( 2 f )log 2( M ) Δf is bandwidth of the analog signal M is number of quantization levels We see that B >> Δf What is gained from digital modulation? Fiber Optical Communication Lecture 2, Slide 4
Advantages over analog: Handles noise better Robust to distortion Can be regenerated Can use error correction (FEC) Disadvantages: Requires higher bandwidth Requires more electronics Digital optical modulation Difficult to implement with analog components Fiber Optical Communication Lecture 2, Slide 5
Our task: Carry a sequence of digital information over a channel (fiber + amplifiers) using an analog optical waveform Signal is often written as a k is the kth symbol p(t) is the pulse shape T is the duration of the symbol Traditional classification of optical pulse shapes Nonreturn-to-zero (NRZ) Return-to-zero (RZ) (Modern systems sometimes use digital pulse shaping) Possible modulation formats On-off Keying (OOK)... Signal modulation...and more modern ones, see following slides u( t) ak p( t kt ) Note: can have complex values (ASK + PSK = QAM) k Fiber Optical Communication Lecture 2, Slide 6
Optical modulation The modulation of data onto an optical carrier can be done in two ways Using direct modulation, the light source is modulated by the electrical signal This is simple and requires less hardware Hard to modulate amplitude without changing other parameters, like phase Cannot do PSK Using external modulation, a specifically made modulator is used Light source is not disturbed Modulators can have very high performance Laser electrical data electrical data Laser or LED modulator optical output optical output External modulation has better performance and is more flexible Unfortunately, it is also more expensive Fiber Optical Communication Lecture 2, Slide 7
External modulators are used for high performance There are two main types of external modulators A Mach-Zehnder modulator (MZM) Is made from Lithium niobate (LiNbO 3 ) Has large bandwidth Has higher V mod than EAM Has high extinction ratio (ER) An electro-absorption modulator (EAM) Is made from semiconductor material (InP) Has restricted bandwidth Has smaller V mod and ER External modulators Can be integrated with a laser Right: EAM + DFB (laser) Fiber Optical Communication Lecture 2, Slide 8
Nonreturn-to-zero modulation (1.2.3) Using nonreturn-to-zero modulation, the amplitude stays high between two consecutive ones The book illustrates with square pulses In reality, the pulse shape is given by the electrical drive signals/system response Shape is more smooth, can have overshoot etc. The square pulse has a spectrum sin( f ) FT[ E]( f ) TBsinc( TB f ),sinc( f ) f The power spectral density is plotted in the figure A δ-function at DC First nulls at f = ±B A realistic signal has a bandwidth B Lowpass filter is B/2 (0.6 0.7 B) non-return-to-zero (NRZ)-signal return-to-zero (RZ)-signal 0 1 0 1 1 1 0 Fiber Optical Communication Lecture 2, Slide 9 pulse duration T time time bit period (bit-rate, B = 1/T f/b
Return-to-zero modulation Using return-to-zero modulation, the signal consists of pulses that are 0 1 0 1 1 1 0 more narrow than the bit slot The book illustrates with square pulses The ratio τ/t = τ/t B is called duty cycle In reality, a pulse carver is used or the pulses are generated by a pulse source The RZ spectrum is typically broader than the NRZ spectrum The RZ (OOK) spectrum contains a δ-function at f = B This is extracted (using a bandpass filter) to do clock recovery Clock recovery is much harder for NRZ non-return-to-zero (NRZ)-signal return-to-zero (RZ)-signal Pulse duration pulse duration /T = 0.5 T time time bit period (bit-rate, B = 1/T) Fiber Optical Communication Lecture 2, Slide 10 f/b
Eye diagrams for NRZ and RZ The eye diagram is a superposition of all bits on top of each other A way to provide visual feedback to monitor the performance An ideal OOK NRZ eye is seen in figure The bit slot is between the X-shaped curve intersections The upper and lower levels have no amplitude fluctuations All bits are in perfect synchronization Examples of measured eyes at 40 Gbit/s are seen in the figures NRZ eye is similar to the ideal one but there is noise Notice that transitions are smooth RZ eyes show the pulse shape Power of lower level is not exactly zero Fiber Optical Communication Lecture 2, Slide 11
Constellation diagrams (1.2.3, 10.1.1) A constellation diagram shows the symbols in the complex plane Using traditional OOK The amplitude is zero or a constant value The phase is unknown Drifting with time due to limited monochromaticity = finite linewidth Drifting faster for an LED than for a laser Using PSK, the data is encoded in the phase Binary PSK (BPSK) is seen in the figure There are two alternatives Phase can be tracked using hardware or software We can use relative phase between two consecutive symbols to carry data In this case: differential BPSK Q (Im) Q (Im) I (Re) I (Re) Fiber Optical Communication Lecture 2, Slide 12
Non-binary modulation formats The last ten years or so, non-binary modulation formats have become used in optical communication systems Can carry more than one bit per symbol Amplitude modulation in several levels is called pulse amplitude modulation (PAM) Proakis: Bandpass digital PAM is also called ASK Figure shows 4-PAM, carries two bits per symbol Phase is not important Symbols could have been written as circles Phase modulation in several levels is called phase-shift keying (PSK) Figure shows 4-PSK = quaternary PSK (QPSK) Carries two bits per symbol Symbol rate = Number of symbols transmitted/second Bit rate = Symbol rate [baud] number of bits per symbol Q (Im) Q (Im) I (Re) I (Re) Fiber Optical Communication Lecture 2, Slide 13
Quadrature amplitude modulation (QAM) Simultaneous modulation of the amplitude and the phase is called quadrature amplitude modulation (QAM) Figures show rectangular 16-QAM and 64-QAM Carries 4 and 6 bits per symbol In general: Modulation in M symbols carries log 2 (M) bits per symbol Have been used in wireless systems a long time Difficult to use when symbol rates typically > 10 Gbaud Has not been used for a long time in optical systems For a given bit rate, these formats Have lower bandwidth requirements for the electronics Have higher spectral efficiency (more narrow spectrum) Can be difficult to implement High linearity requirements, typically requires DSP Are more susceptible to noise, require higher SNR Q (Im) Q (Im) I (Re) I (Re) Fiber Optical Communication Lecture 2, Slide 14
Modulator structures Lithium niobate modulators can be made in different ways A phase modulator changes the field according to The voltage V π changes the phase π Typically V π 5 V E out /E in is often called transfer function (although not in frequency domain) A Mach-Zehnder modulator (MZM) is an interferometer E E out in T 1 V1 ( t) V ( t) V exp i exp i 1 2 V V P P out Setting the voltage bias to V b = V π /2......T changes from 1 to 0 as... in E E out E V t i ) out ( exp E in V 2 2V 1( t) V cos 2V...V 1 is changed from V π /4 to V π /4 in 2 waveguide Electrical contact, applied voltage V(t) voltage V 1 (t) voltage V 2 (t) = V 1 (t) + V b Fiber Optical Communication Lecture 2, Slide 15 b b
RZ data generation RZ data is typically generated by turning NRZ into RZ First, NRZ is generated using phase and/or intensity modulators Then, RZ pulses are cut out from the optical signal A pulse carver can be made using a MZM driven by a sinusoidal clock Clock is synchronous with the data By selecting the driving conditions, different pulse shapes are generated The RZ 50% pulse shape Select V b = V π /2 and V 1 = V π /4 cos(2πbt) 2 2 T( t) cos cos ( Bt) 2 The full width at half maximum (FWHM) is T B /2 = 50% T B The clock frequency is B Bias point is at T = 1/2 T t/t B Fiber Optical Communication Lecture 2, Slide 16
RZ data generation The RZ 33% pulse shape Select V b = 0 and V 1 = V π /2 cos(πbt) 2 T( t) cos cos( Bt) 2 T The FWHM is 33% T B The clock frequency is B/2 Bias point is at T = 1 The RZ 67% pulse shape Select V b = V π and V 1 = V π /2 sin(πbt) 2 T( t) cos sin( Bt) 1 2 T t/t B The FWHM is 67% T B The clock frequency is B/2 Bias point is at T = 0 The RZ 67% has a more narrow spectrum than RZ 50% t/t B Fiber Optical Communication Lecture 2, Slide 17
Figure shows measured spectra at 42.7 Gbit/s OOK or DBPSK is used in all cases Spectra change for QAM Comments: NRZ is most narrow CS = carrier suppressed, phase shifting every second bit, no DC DB = duobinary, reduces spectral width by modifying the phases AMI = alternate mark inversion, Gives some reduction of nonlin. AP-RZ = alternate-phase RZ, reduces nonlin. by phase shifting DPSK = differential binary PSK Spectrum examples Fiber Optical Communication Lecture 2, Slide 18
Spectral efficiency The spectral efficiency (SE) is the throughput (bit rate) divided by the occupied spectral width The SE is increased by using a multilevel modulation format Often the word capacity is (mis-)used to denote system bit rate Example: At the same bit rate, the spectrum of a DQPSK signal is more narrow than that for a DBPSK signal As already seen, NRZ gives a more narrow spectrum than RZ Fiber Optical Communication Lecture 2, Slide 19
Differential detection When using differential detection, information is encoded in the phase change from symbol to symbol The phase changes are converted to intensity changes in the receiver Delay-line interferometers are frequently used for this Simplest example is differential binary PSK (DBPSK a.k.a. DPSK) This format will have a higher SNR for a given transmitted power Fiber Optical Communication Lecture 2, Slide 20
Balanced detection of DBPSK Only one photodetector is needed to recover the signal This is called single-ended detection By using two identical detectors, sensitivity can be improved up to 3 db The amplitude is doubled by the current subtraction This is called balanced detection Think of the junctions as couplers See next slide Constructive port i a T B i a i b i b Destructive port Delay interferometer (DI) Fiber Optical Communication Lecture 2, Slide 21
The 3-dB coupler A 3-dB coupler is a key component for understanding modulators/receivers Two waveguides are coupled Half the power is transferred The transferred field is π /2 out of phase The fields E 1 and E 2 are arbitrary input fields The output fields are then E1 ie2 ie1 E2 E3, E4 2 2 If E 2 = 0, then the output powers are P 3 = P 4 = P 1 /2 If both E 1 0 and E 2 0, then there will be interference The physical device is often a Y-junction E 1 (t) E 2 (t) E 3 (t) E 4 (t) Fiber Optical Communication Lecture 2, Slide 22
Coherent detection Traditional receivers detect optical power phase information is lost Coherent detection can recover the phase data Uses a local oscillator (LO) laser in the receiver The simplest possible solution is seen in figure Uses free-space optics, mirror is partially reflecting The entering optical field is E det ( t) Asig ( t)exp( isig ( t) i0t) ALO exp( ilo( t) ilot) The detected current is proportional to E det 2 2 2 idet ( t) Asig ( t) ALO 2Asig ( t) ALO cos ( sig( t) LO ( t)) ( 0 LO The term A LO is just a constant The term A sig 2 can be neglected if A sig 2 << A LO 2 This is the case in practice i det ( t) Asig ( t) ALO cos ( sig( t) LO ( t)) ( 0 LO ) t) ) t) Fiber Optical Communication Lecture 2, Slide 23
Coherent detection If the signal and LO frequencies are equal and if φ LO = 0, we get idet ( t) Asig ( t)cos sig( t) Receiver is sensitive to both amplitude and phase The trouble is the assumptions made above The signal and LO lasers are not phase locked to each other The problem can be handled using hardware or software Hardware: Use a phase-locked loop (PLL) Drawback: Hard to construct, will need highly coherent lasers Software: Track the phase and frequency in digital signal processing (DSP) Drawback: Hard to do at high symbol rates Nevertheless, people are doing just that Fiber Optical Communication Lecture 2, Slide 24