Lecture 4 Optical transmitters Photon processes in light matter interaction Lasers Lasing conditions The rate equations CW operation Modulation response Noise Light emitting diodes (LED) Power Modulation response Bandwidth Fiber Optical Communication Lecture 4, Slide 1
LEDs and lasers Light-emitting diode (LED): Based on spontaneous emission Incoherent light Linewidth Δν 10 THz (Δλ = 10 100 nm) Slow response time Much larger linewidth than data rate dispersive limitations Laser: Based on stimulated emission Highly coherent light Linewidth Δν = 0.1 10 MHz Fast response time Usually much smaller linewidth than data rate Fiber Optical Communication Lecture 4, Slide
Photon processes in light matter interaction (3.1.1) Spontaneous emission Absorption Stimulated emission The emitted photon has energy hν E g E g is the bandgap energy Non-radiative recombination Reduces the number of electron-hole pairs (a) Material defects (b) Auger recombination Energy given to another electron (as kinetic energy) Fiber Optical Communication Lecture 4, Slide 3
Semiconductor lasers (3.1.3) Semiconductor lasers use stimulated emission: Coherent light (narrow spectrum, less pulse broadening in fibers) High output power (> 10 mw) Reduced beam divergence, high coupling efficiency (30 70%) High modulation bandwidth Principle: (up to 5 gain GHz) medium in a resonator (Fabry-Perot c Principle: A gain medium with feedback (Fabry- Perot cavity) Optical gain requires population inversion Cannot occur in thermal equilibrium coherent light The gain has a nearly linear dependence on N above N t N is the injected carrier density N t is the transparency density value partially reflecting mirrors (usually cleaved semiconductor facets) R 1 pump R (current) gain medium L power gain: G = exp(gz), where g = gain coefficent Fiber Optical Communication Lecture 4, Slide 4 coherent light
In a heterostructure junction The heterostructure junction Stimulated emission occurs where the bandgap is lower Gain is increased by the increasing carrier density Light is confined to Light the region emission where in a the forward index of biased refraction heterostructure is higher pn-junction Direct bandgap is required AlGaAs, λ = 0.81 0.87 μm InGaAsP λ = 1 1.65 μm Si is not used n-type electrons higher bandgap material thin ( 0.1 m) lower bandgap material p-type conduction band h = hc/ E g valence band higher bandgap material mode profile distance Fiber Optical Communication Lecture 4, Slide 5
The power reflectivity R of an air-semiconductor interface is Usually R 1 = R = R The electric field in the cavity is g is the power gain, α is the power losses Factor of two because this is amplitude, not power After one round-trip, we have E Lasing conditions (3.1.4) The limiting condition for lasing is that and this gives us the laser threshold E z E exp jz t z n 1 R n 1 Fiber Optical Communication Lecture 4, Slide 6 0 g z L E R R exp j z Lt z L 0 1 g Both an amplitude and a phase condition for lasing 1 1 ln L R R 1 E( z L) E( z) L m g
Longitudinal modes and the Fabry-Perot laser (3.1.5) The phase condition can be written ν m are the lasing longitudinal modes Simplest kind of semiconductor laser: A Fabry-Perot laser Uses a Fabry-Perot interferometer Will lase in several modes simultaneously Gives problems with dispersion mc nl Mode frequency spacing is Δν 100 00 GHz for a typical laser m loss longitudinal modes dominant mode (highest gain) gain profile m-x Fiber Optical Communication Lecture 4, Slide 7 m m+x 100-00 GHz for a typical laser A Fabry-Perot laser oscillates in several modes simultaneously
Single-mode lasers (3.) Wavelength-dependent cavity loss single-mode lasing loss profile gain profile longitudinal modes lasing mode Distributed feedback (DFB) laser (most common) Wavelength-selective grating in the cavity Can be temperature tunable (5 nm) External-cavity laser Uses a frequency-selective element outside the cavity Widely tunable (50 nm), narrow linewidth Vertical-cavity surface-emitting laser (VCSEL) Light output orthogonal to substrate easier to produce Very good alternative to an LED Fiber Optical Communication Lecture 4, Slide 8
The rate equations (3.3.1) Describe the static and dynamic behavior of semiconductor lasers The number of photons is P The number of electrons is N Assuming a (transverse and longitudinal) single-mode laser dp P dn I N GP R GP sp dt dt q c p Stimulated emission Spontaneous emission into lasing mode The net rate of stimulated emission is Related to the rate of spontaneous emission n sp is around for semiconductor lasers The photon lifetime is Photon loss rate Electron supply by pumping Spontaneous emission G GN N R n G sp sp p v g Stimulated emission N 0 1 1 1 ln L R R 1 Fiber Optical Communication Lecture 4, Slide 9
CW (steady-state) operation In steady-state, time differentiation yields zero ( d/dt = 0 ) Neglect spontaneous emission for simplicity (R sp = 0) Use the rate equations to get I c For small currents: G p 1, P 0, N q 1 At lasing threshold: G p 1, P 0, N Nth N0, I Ith GN p p Above threshold: G p 1, P I Ith, N Nth const, I I q N th N P th qn c th G th G I th I Fiber Optical Communication Lecture 4, Slide 10
P I curves The output power from one facet, assuming equal facet reflectivity R, is P e 1 v g mir hp 1 v g 1 ln L 1 hp R Two types of degradation with increasing temperature Threshold current increases P I curves bend when injected current is increased The reasons are: Increased non-radiative recombination Increasing internal losses Fiber Optical Communication Lecture 4, Slide 11
Modulation bandwidth (3.3.) The response to current modulation is obtained from the rate equations Two phenomena must be accounted for The gain has a power-dependence (decreases with optical power) The refractive index is changed due to gain/population changes In general, the rate equations must be solved numerically An analytic solution can be obtained for small-signal modulation Modulation current << I b I th Variables are linearized around the bias point For example, the power is modeled P( t) Pb pm sin( mt m) The transfer function is obtained The power transfer function is called modulation response Measured and calculated modulation response in a DFB laser Fiber Optical Communication Lecture 4, Slide 1
Noise in semiconductor lasers The carrier and photon numbers fluctuate The generation process is quantized The main source of noise is spontaneous emission The phase of the noise is random Perturbs both the phase and the amplitude Gives rise to a finite SNR The spectral width 0 Limited coherence Fiber Optical Communication Lecture 4, Slide 13
Relative intensity noise (RIN) (3.3.3) We define the power fluctuation according to The RIN spectrum is the power spectral density (PSD) of δp normalized to the square of the mean power Obtained from the rate equations with added noise terms Peaked close to the relaxation oscillation frequency This is introduced using the auto-correlation of δp Use Wiener Khinchin s theorem P( t) P( t) P( t) C pp ( ) P( t) P( t ) P( t) RIN( ) The SNR is mean power/rms noise C SNR = [C pp (0)] 1/ Obtained as 1/(integral of PSD) pp Typically 0 30 db ( ) e i d Fiber Optical Communication Lecture 4, Slide 14
The LED output power is Light emitting diodes (LEDs) (3.5) η ext is external quantum efficiency Fraction of photons that escape the device, 1 5% η int is internal quantum efficiency Fraction of carriers that recombine radiatively, 50% I is injected current Benefits: Simple fabrication, low cost, reliable, small temperature dependence Drawbacks: P e η ext Low power, low coupling efficiency to fiber (< 10%), large spectral width, smaller modulation bandwidth η int hν q I Fiber Optical Communication Lecture 4, Slide 15
LED CW operation (3.5.1) Left: Output power is first proportional to the injected current......but the curve bends at higher currents......because of increasing internal losses Internal quantum efficiency also decreases with increasing temperature Right: The emitted spectrum for a 1.3 μm InGaAsP LED The spectrum is wide, 50 60 nm Only suitable for short distance communication Fiber Optical Communication Lecture 4, Slide 16
LED modulation response (3.5.) The rate equation for an LED contains no stimulated emission Assume a sinusoidal modulation The carrier modulation is obtained cib cim N t q q 1 We obtain the 3-dB bandwidth Limited by the carrier lifetime Typical value is 50 150 MHz I dn dt I q N t I I exp j t b m exp j t f 3dB c 1 j 3 c m c m m Fiber Optical Communication Lecture 4, Slide 17
LED structures (3.5.3) Surface emitting Low cost Easy manufacturing Poor coupling to fiber Edge emitting Built-in waveguide Directivity Improved coupling Higher bandwidth (00 MHz) Fiber Optical Communication Lecture 4, Slide 18
Source fiber coupling (3.6.1) The coupling efficiency varies significantly < 1% for butt-coupled surface-emitting LED > 90% for lens-coupled laser to SM fiber Transmitter package often contains photo diode Will monitor the power level......and provide feedback for power control Semiconductor lasers are sensitive to optical feedback Often an optical isolator is used Temperature stabilization may be necessary Can use thermo-electric cooler Cost is often dictated by the package, not the laser itself Fiber Optical Communication Lecture 4, Slide 19
Dense wavelength division multiplexing transmitters Uses the ITU-T wavelength grid with spacing of 100/50/5 GHz Active wavelength locking is needed Tunable lasers are attractive Left: Package with wavelength stabilization Right: Wavelength selectable transmitter using monolithic array of lasers covering 160 nm Fiber Optical Communication Lecture 4, Slide 0
Lecture Optical receivers p i n diodes Avalanche diodes Receiver design Receiver noise Shot noise Thermal noise Signal-to-noise ratio Fiber Optical Communication Lecture 4, Slide 1
Optical receivers The purpose of a traditional receiver for OOK is: Convert the optical signal into an electrical signal Recover the data by: Doing clock recovery Performing decisions on the obtained signal In state-of-the-art coherent receivers, additional functionality is performed in digital signal processing (DSP) Electronic dispersion compensation (EDC) Adaptive equalization Phase synchronization This lecture is about OOK systems Necessary to know about......and still common Fiber Optical Communication Lecture 4, Slide
Photodetectors The most critical component is the photodetector Converts the optical signal to an electrical current We want these components to have: High sensitivity Fast response time Low noise High reliability Size compatible with fibers This means that semiconductor materials are exclusively used Photons are absorbed and generate electron hole (e h) pairs This produces a photo-current. Basic requirement: The detector material bandgap energy (E g ) < the photon energy (hν) Fiber Optical Communication Lecture 4, Slide 3
The photocurrent is proportional to the optical power The constant R d is the responsivity η = the quantum efficiency = the number of e h pairs per incident photon Ideally η = 1 R d R d increases with λ until hν = E g R d 0 when the photon energy becomes too low Si or GaAs can be used for short wavelengths (λ < 900 nm) InGaAs is most common at 1.3 and 1.55 μm Most communication systems use reverse-biased p n junctions (photodiodes) of two main types: p i n photodiodes Avalanche photodiodes (APD) Photodiodes (4.1.1) q h 1.4 [A/W] with in μm I p R d P in Fiber Optical Communication Lecture 4, Slide 4
p i n diodes (4..) absorption of photons e h pair generation carrier drift due to built-in and applied field induced current in the external circuit Electric field Energy levels p i n diode: p n junction with an intrinsic (un-doped) layer Response time is limited by the transit time through the i-region W tr v s Responsivity increases with W a trade-off between responsivity and speed High speed (~50 GHz) diodes with η close to unity are available Fiber Optical Communication Lecture 4, Slide 5
p i n diodes, performance p n diodes are limited by diffusion (absorption outside the depletion region) In a p i n diode, the depletion region is wide (intrinsic, undoped) p i n bandwidth limitations: Parasitic capacitance Reduces the speed of voltage changes Transit time Takes time to collect the carriers The dark current should be low Current without input signal Due to stray light and thermal generation of carriers Fiber Optical Communication Lecture 4, Slide 6
Examples of p i n diodes Schematic picture of a p i n diode Green is anti-reflection coating p i n diodes without and with pigtail Important parameters are: Bandwidth Sensitivity Responsivity Polarization dependence No dependence is preferred Fiber Optical Communication Lecture 4, Slide 7
Receiver design (4.3) The digital receiver consists of three parts: Front end (photo-detector, trans-impedance amplifier) Linear channel (amplifier, low-pass filter) Data recovery (clock recovery, decision circuit) front end linear channel data recovery h photodiode preamplifier amplifier filter decision circuit data voltage supply automatic gain control clock recovery Fiber Optical Communication Lecture 4, Slide 8
Receiver front-ends (4.3.1) Transimpedance front-end Rf + - Pd Cp RL - Vout Pd Cp + Vout Simple Electrically stable Low sensitivity for small R L High bandwidth High sensitivity Potentially unstable Small bandwidth for high R L f 1 R C L p f G R f C p Effective input resistance = R f /G Fiber Optical Communication Lecture 4, Slide 9
The linear channel consists of: Linear channel (4.3.) A high-gain amplifier with automatic gain control Constant average output voltage irrespective of the input (within limits) A low-pass filter with bandwidth chosen to: Reject noise outside signal bandwidth Avoid introducing inter-symbol-interference (ISI) The best situation is when the filter (and not other components) limits the overall bandwidth of the receiver The output voltage spectrum is given by H out (ω) = H T (ω)h p (ω) H p (ω) is the photocurrent spectrum H T (ω) is the total transfer function of the front end and the linear channel Normally, H T (ω) is dominated by the filter transfer function H T (ω) H f (ω) Fiber Optical Communication Lecture 4, Slide 30
Data recovery (4.3.3) The data-recovery section consists of A clock-recovery circuit Extracting a sinusoidal component at f = B to enable proper synchronization of the decision circuit Easily done for an OOK RZ signal with a narrow-band filter The signal contains a delta function at f = B More difficult for NRZ No sinusoidal spectral components are present Can use a full-wave rectifier to convert the NRZ signal to RZ containing a delta function at f = B A decision circuit comparing the input voltage with a threshold at the time obtained from the clock recovery input NRZ data RZ waveform extracted clock Deciding whether a "1" or a "0" was received Fiber Optical Communication Lecture 4, Slide 31
Eye diagrams The eye diagram is a superposition of all bits on top of each other Looks like an eye Gives a visual way to monitor the receiver performance Left: An ideal NRZ eye diagram Right: An eye diagram degraded by noise and timing jitter A measured RZ eye diagram at 640 Gbit/s Fiber Optical Communication Lecture 4, Slide 3
Eye diagram interpretation Fiber Optical Communication Lecture 4, Slide 33
Receiver noise (4.4) The detected photo current in the receiver will contain noise There are two fundamental sources of noise Shot noise due to field and charge quantization Thermal noise due to thermal motion of charges The total current, signal + noise, can be written I( t) R Pin ( t) i ( t) i ( t) d s T In addition, there can also be optical noise in P in Comes from lasers and optical amplifiers Will be treated later in the course Remember I p ( t) R Pin ( t) d Fiber Optical Communication Lecture 4, Slide 34
Shot noise Shot noise arises from the particle nature of the photocurrent Current consists of electrons that can only be described statistically Current is not constant but fluctuates Compare with cars on a highway or hails on a roof The variance of the shot noise photocurrent is s i s ( t) Δf is the effective noise bandwidth of the receiver S s (f) is the shot noise two-sided power spectral density (PSD) If the detector dark current I d cannot be neglected we have s q( I I ) f Originating from stray light or thermally generated e h pairs f 0 S s p ( f ) df d qi p f Fiber Optical Communication Lecture 4, Slide 35
Thermal noise Thermal noise originates from the thermal motion of the electrons The two-sided PSD is hf kbt ST ( f ) R exp( hf / k T) 1 R k B is Boltzmann s constant T is the temperature R L is the load resistance The noise variance is T i T ( t) B L In addition, thermal noise is also generated in electrical amplifiers Introduce the amplifier noise figure F n to obtain L f 0 S T ( f ) df (4k B T / R L ) f T (4k T / R ) F f B L n Fiber Optical Communication Lecture 4, Slide 36
Signal-to-noise ratio (SNR) The different noise sources are uncorrelated We obtain the total noise power according to ( I) s T q( I p I d ) f (4k B T / R L ) F f n The signal-to-noise ratio (SNR) of an electrical signal is defined as average signal power SNR noise power This definition is for an analog signal This is not the usual meaning of SNR in digital communication theory Instead E b /N 0 or E s /N 0 is used there E b is the energy per bit E s is the energy per symbol N 0 is the noise PSD I p Fiber Optical Communication Lecture 4, Slide 37
For a p i n receiver we have Noise in p i n receivers (4.4.) SNR q( R P When thermal noise dominates, we have When shot noise dominates, we have SNR We note: I R ) f Pin 4( k T / R Different scaling with input power in the two limits Thermal noise dominates at low input power Shot noise dominates at high input power d in SNR d R 4k L B Rd Pin qf d Rd Pin TF f n Pin h f 0 B P in P in L ) F f n Fiber Optical Communication Lecture 4, Slide 38