Lecture 7 Fiber Optical Communication Lecture 7, Slide 1

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1 Dispersion management Lecture 7 Dispersion compensating fibers (DCF) Fiber Bragg gratings (FBG) Dispersion-equalizing filters Optical phase conjugation (OPC) Electronic dispersion compensation (EDC) Fiber Optical Communication Lecture 7, Slide 1

2 The dispersion problem and solutions (8.1) Using optical amplification, dispersion (not loss) is the major limitation In general, dispersion is important at bit rates > 5 Gbit/s Even if the source is chirp-free and the fiber is single-mode With a narrow source spectrum and without third-order dispersion, we have 4B 2 L 1 Dispersion must be compensated for Then noise and nonlinearities become the major limitations Compensation can be in Optical domain: DCF, FBG, filters, OPC, and (previously) solitons Electrical domain: Pre- or post-compensation, often using DSP The aim Aim of dispersion compensation is to cancel the phase factor A 1 2 z, t A 0, ~ i 2 i 3 exp[ 2 z 3 z i t] d 2 6 Fiber Optical Communication Lecture 7, Slide 2

3 Compensation in the optical domain In general, an optical device with field transfer function H( ) H( ) exp will modify the electric field to A( L, t) 1 2 The dispersion is perfectly canceled if φ 0 only changes the absolute phase Is of no consequence φ 1 introduces a delay i ( ) H( ) exp i ( ) i A ~ 2 (0, ) H( )exp 2 L 2 H 2 2, 3 3 ( ) 1, L L Important to keep small to avoid latency The dispersion of the fiber acts as an all-pass filter i 3 3 L i t d 6 Dispersion compensation can be placed anywhere if nonlinearities are small Fiber Optical Communication Lecture 7, Slide 3

4 Dispersion-compensating fibers (8.2.1) A dispersion-compensating fiber (DCF) Has normal dispersion, D < 0 Can compensate GVD perfectly Has a tailored dispersion relation that allows TOD compensation Curvature is almost opposite of SMF value some residual TOD Denoting the two transfer functions by H f1 (SMF) and H f2 (DCF), we get A 1 ( L, t) A ~ (0, ) H f 1( L1, ) H f 2 ( L2, )exp( i t) 2 The conditions for compensation after SMF + DCF are L L, L L 0 First condition is most important Second condition is important for a broad-band (WDM) signal When nonlinearities are important, DCF position is important Otherwise, DCF can be put anywhere d Fiber Optical Communication Lecture 7, Slide 4

5 Dispersion maps (8.2.2) DCFs can be placed in different ways Figure: Different dispersion maps Precompensation Postcompensation Periodic compensation Perform equally well in a linear system In practice, periodic compensation is often used Each piece of fiber is compensated Including nonlinearities, performance can be very different Dispersion map design is an important tool to combat nonlinearities in OOK systems Fiber Optical Communication Lecture 7, Slide 5

6 DCF design (8.2.3) Can be made with strong normal dispersion D ps/(nm km) A DCF of length 4 km can compensate for 50 km of SMF Loss is relatively high, db/km Additional amplification is needed noise is increased Figures show example DCF radial profile and the D value A figure-of-merit is dispersion per loss M ps/(nm db) The fiber core is small the nonlinear coefficient is relatively large Typically, γ = 5 W -1 km -1 to compare with γ < 2 W -1 km -1 for SMF Fiber Optical Communication Lecture 7, Slide 6

7 Fiber Bragg gratings (FBG) (8.3) In an FBG, the refractive index varies periodically Made by holographic UV exposure In a chirped grating, the period of n changes with z The Bragg wavelength (which is reflected) varies along the fiber Λ is the distance between two peaks for n Different frequency components experience different delay The grating dispersion is T R = grating round trip time L g = grating length λ = difference in λ B at the two grating ends D g B 2n T R L g 2n c Example: λ = 0.2 nm, D g = 500 ps/(nm cm), L g = 10 cm, compensates for 300 km of SMF There is, for a given length, a trade-off between bandwidth and dispersion Fiber Optical Communication Lecture 7, Slide 7

8 Chirped fiber Bragg gratings Figure shows measured reflectivity and time delay for a 10 cm long linearly chirped grating Dispersion is 5000 ps/nm, equivalent to 300 km SMF Optical bandwidth is 0.12 nm, sufficient for 10 Gbit/s if source is chirp free These devices operate in reflection Loss is mainly due to coupling Can be improved by using a circulator Linearly chirped gratings compensate for β 2 Nonlinearly chirped gratings can, in principle, compensate for higher order fiber dispersion (β 3, β 4 ) Fiber Optical Communication Lecture 7, Slide 8

9 Channels at high bit rates (8.6) For high bit rates, > 40 Gbit/s, TOD/PMD become important Figure shows 2.1 ps pulses after propagation without and with β 3 compensation DCFs are designed to compensate for β 3 Optical filters and chirped gratings can be designed to compensate for β 3 In WDM systems, each channel can be compensated individually: Filters with periodic characteristics can be used Cascaded chirped FBGs optimized for a specific wavelength can be used PMD is problematic since the transfer function is unknown Optical PMD compensators must do monitoring of the signal to get feedback In a coherent receiver, PMD compensation is done by an adaptive equalizer implemented in DSP Fiber Optical Communication Lecture 7, Slide 9

10 Dispersion compensation at the receiver (8.7.3) Can dispersion compensation be done in the receiver? In principle: It depends on the detection method In practice: It also depends on whether you can make the DSP chip or the corresponding analog implementation We have been talking mostly about direct-detection (DD) receivers Electric current proportional to the optical power Phase information is lost Dispersion changes the phase of the spectrum Dispersion compensation cannot be done after DD Using the information available, some compensation can be done Trying to maximize the eye opening in an adaptive equalizer In DSP, the maximum likelihood sequence estimator (MLSE) can be used Uses the Viterbi algorithm Compensates dispersion and PMD by investigating a sequence of bits Algorithm has high complexity, compensates a limited amount of dispersion Fiber Optical Communication Lecture 7, Slide 10

11 Dispersion compensation in a coherent receiver A coherent receiver performs a linear mapping from the optical field to the electrical signal Input: Optical signal from the fiber + light from a local oscillator (LO) laser Output: Two currents proportional to the real and imaginary part of the light The coherent receiver makes is possible to Encode data into the phase Improve the signal quality using DSP The DSP typically used perform Electronic dispersion compensation (EDC) Tracking of polarization and compensation of PMD Tracking of the signal LO phase evolution The drawback is that Developing an application-specific integrated circuit (ASIC) is very complicated and costly An ASIC consumes significant power, EDC consumes a large part of the ASIC Fiber Optical Communication Lecture 7, Slide 11

12 Dispersion compensation in a coherent receiver When the field and the amount of accumulated dispersion is known, electrical dispersion compensation (EDC) is straight-forward Can be done in time or frequency domain In frequency domain: FFT, shift the phase, IFFT Very similar to solution of the Schrödinger equation Performed on a limited amount of data Edges are not correctly compensated, must be handled In time domain: Perform FIR filtering corresponding to GVD Continuous time impulse response is 2 2 it h( t) exp id a 2da Must be discretized at sampling rate, truncated, and delayed to make causal For long systems, the FIR filter is long (many hundred taps) In principle, arbitrary amounts of dispersion can be compensated for Fiber Optical Communication Lecture 7, Slide 12

13 The Nortel system In 2007, Nortel announced a commercial coherent system 40 Gbit/s using QPSK and polarization multiplexing Performs EDC, since Kim Roberts says DCFs add Loss (DCF losses must be compensated for) Nonlinearity (DCF is nonlinear) Cost (DCF modules cost money) Work (Must match fiber lengths) Performs adaptive equalization Separates polarizations Compensates PMD and residual dispersion Probably uses the constant-modulus algorithm Made coherent systems a strong contender to traditional systems Fiber Optical Communication Lecture 7, Slide 13

14 Advanced lightwave systems Lecture A QPSK modulator Differential detection Coherent detection Sensitivity degradation mechanisms Digital signal processing in coherent receivers Dispersion compensation (static equalization) Polarization demultiplexing (adaptive equalization) Phase synchronization Note: The lecture book is somewhat lacking in this chapter Fiber Optical Communication Lecture 7, Slide 14

15 Alternatives to OOK With direct detection, intensity changes influence the received signal Scheme is called intensity modulation with direct detection (IM/DD) IM/DD can do PAM, but not PSK The throughput can be increased By modulating amplitude and phase By sending data in both polarizations This is called dual polarization (DP), polarization-multiplexed (PM), or polarization-division multiplexed (PDM) transmission The Nortel system uses PM-QPSK at 10 Gbaud One channel per polarization, two bits per symbol in each polarization In total, 40 Gbit/s per channel A four-fold increase compared to OOK Also many advantages from DSP Transmitters and receivers for these formats are more difficult to implement Fiber Optical Communication Lecture 7, Slide 15

16 Alternatives to IM/DD There are two main alternatives to IM/DD Using differential detection, consecutive symbols interfere in the receiver The book calls this delay demodulation Using coherent detection, a local oscillator (LO) is used as a phase reference Both these schemes can increase the spectral efficiency Differential detection typically uses M-PSK Coherent detection is more general and can do QAM Using coherent detection, there is a linear mapping from the optical to the electrical domain The received signal can be processed in DSP Compensation of CD Separation of polarizations Compensation of PMD and ISI A coherent receiver is robust to PMD Fiber Optical Communication Lecture 7, Slide 16

17 The 3-dB coupler (again) 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 Harder to track fields through and get correct output power Modeling the system using couplers is simpler E 1 (t) E 2 (t) E 3 (t) E 4 (t) Fiber Optical Communication Lecture 7, Slide 17

18 A QPSK modulator An IQ modulator (IQM) is typically used to generate a QPSK signal The input CW light is split Intensity modulation is performed by using two MZMs By phase shifting π/2 and recombining, a QPSK is obtained Can be easily checked using the model for the coupler PM-QPSK signal: Use 2 IQMs and a polarization beam combiner 8-PSK signal: Can use an IQM followed by a π/2 phase modulator signal input MZM MZM π/2 Fiber Optical Communication Lecture 7, Slide 18

19 Differential detection (10.2.3) Differential detection is done using a delay line interferometer (DLI) A detector for DBPSK is seen below Input signal is split and one arm contains a T S delay Recombining the different signals, the sum and difference of two consecutive symbols is obtained Balanced detection = difference of currents proportional to optical powers Current is proportional to cos(δφ), where Δφ is the phase difference For BPSK Δφ = ±π signal input T S balanced detection + Fiber Optical Communication Lecture 7, Slide 19

20 Differential detection Differential detection is suited for M-PSK A D is typically added to format name, example DQPSK For M > 2, more than one DLI is needed A phase shift is introduced in the lower arm to get correct interference For single-polarization transmission, the DLI works very well For dual-polarization transmission, two DLIs + polarization tracking in hardware is needed Hardware need is more than doubled With differential detection, DSP compensation of CD and PMD is difficult Needs to be compensated for in hardware Differential detection has a SNR penalty compared to coherent detection Beating the pulses with each other reduces the SNR Differential detection is simpler than coherent detection but is outperformed in the longest systems Fiber Optical Communication Lecture 7, Slide 20

21 Coherent detection ( ) The book talks about three ways of implementing coherent detection Homodyne detection The LO laser is phase locked to the signal laser, IF = 0 IF = intermediate frequency = LO/signal frequency difference Synchronous heterodyne demodulation IF 1 GHz, converted to baseband by recovery of IF microwave carrier Asynchronous heterodyne demodulation IF 1 GHz, converted to baseband by envelope detector In practice today, none of these schemes is used, instead Intradyne detection IF 0, but LO laser is not locked to signal laser There is a frequency and phase difference These are typically tracked in DSP Fiber Optical Communication Lecture 7, Slide 21

22 A coherent receiver Typical implementation is to use a 90 hybrid The four outputs are proportional to E signal + k E LO, where k = +1, i, 1, i Check with coupler model! After the 90 hybrid follows the detectors Can be balanced or single-ended The end result is two currents Proportional to the real and imaginary parts of the signal Receiver typically implements polarization-diversity Both polarizations are detected Two 90 hybrids as in figure are needed Signal is input to both hybrids, orthogonal LOs are input Channels are separated in DSP signal input LO input π/2 Fiber Optical Communication Lecture 7, Slide 22

23 Coherent detection Coherent detection is suited for general modulation A coherent receiver has a polarization dependence The LO has a given polarization It is necessary to detect both polarizations Dual-polarization transmission is the natural choice in this case With coherent detection, DSP is typically used in the receiver Tracking of polarization and phase Compensation for CD, PMD, and ISI A coherent receiver has many benefits, but requires complex DSP Fiber Optical Communication Lecture 7, Slide 23

24 Receiver performance Details of the performance of advanced receivers are outside the course In general: Differential detection is harder to investigate than IM/DD Coherent detection is easier to investigate than IM/DD The reason is the linear mapping of the field in a coherent receiver Current is proportional to (signal + noise) Typical situation: The receiver SNR is limited by optical amplifier noise Systems are often long and have many amplifiers Note: A coherent receiver has a gain that avoids the thermal limitation The current is proportional to the LO laser amplitude Fiber Optical Communication Lecture 7, Slide 24

25 Sensitivity degradation mechanisms (10.4) LO laser intensity noise A current proportional to LO laser amplitude is detected If LO laser has relative intensity noise (RIN), SNR is degraded Using balanced detection, DC term is canceled out Solves the problem Signal and LO laser phase noise Detection is phase sensitive, phase drifts degrade performance Phase stability is quantified by the coherence time Inversely proportional to the laser linewidth The phase drift is modeled as a Wiener process Integrated white noise Mean is zero, variance is given by Δν is the sum of Δν signal and Δν LO The phase drift is tracked using DSP Phase drift is a serious limitation, in particular for QAM Fiber Optical Communication Lecture 7, Slide 25

26 Sensitivity degradation mechanisms (10.4) Signal polarization fluctuations The signal output polarization is unknown and drifts with time The LO has a given polarization that does not change Useful signal is only obtained sometimes Polarization-diversity is typically used Does not solve problem, but allows a DSP solution The solution to this problem is to use an adaptive equalizer Will also compensate for PMD and ISI For a properly designed system, the main degradation mechanisms are: Optical amplifier noise Nonlinear Kerr effects Fiber Optical Communication Lecture 7, Slide 26

27 Digital signal processing for a coherent receiver In a typical implementation, the DSP for a PM-QPSK receiver contains the following steps Corrections for receiver optical hardware errors Example: Differing responsivities, angle error in 90 hybrid Compensation of time skew between channels Compensation for chromatic dispersion Can be viewed as a fixed (non-adaptive) equalizer Clock recovery and downsampling/filtering Polarization demultiplexing and adaptive equalization Frequency offset (IF) compensation Phase synchronization Decisions and data recovery Fiber Optical Communication Lecture 7, Slide 27

28 DSP compensation of dispersion Electronic dispersion compensation (EDC) is simple in principle but The amount of dispersion to compensate for must be known For large amounts of accumulated dispersion, the implementation requires significant computational resources Will typically need half of the DSP ASIC EDC can be carried out in time or frequency domain In frequency: EDC similar to solving the linear Schrödinger equation In time: An FIR filter corresponding to the continuous impulse response 2 2 it h( t) exp id a 2da The complexity of frequency and time implementations scales differently with accumulated dispersion Small accumulated dispersion: Use FIR implementation Large accumulated dispersion: Use frequency domain implementation Fiber Optical Communication Lecture 7, Slide 28