Optical Amplifier Basic Properties And System Modeling: A Simple Tutorial
Rezin E. Pidgeon and Don E. Frymyer Scientific-Atlanta, Inc.
Abstract Erbium-doped fiber amplifiers have received noise in the electrical and optical domain. Next much interest for CATV because of their high is a general discussion of the basic principles of output power, low distortion, and low noise operation and characteristics of an EDFA. The capability. These devices have only recently noise figure is derived and characteristics for become commercially available and probably are CATV are shown. not well understood by those who have not been involved with them from a research or applica tions viewpoint. This paper is intended to present THERMAL NOISE a simple coverage of the principles of operation and characteristics of these amplifiers. Signal Thermal noise is an electrical noise phenomena gain, saturation output power, and noise proper that occurs in a conductor or resistor due to the ties are discussed. Equations for optical amplifier continual random scattering of free electrons with noise figure are developed and typical data for the molecules. This electron scattering of free CATV are given. electrons is responsible for the electrical resis tance of the material. Each flight of an electron between collisions with molecules constitutes a INTRODUCTION short pulse of current. This random motion of charges results in a thermally-induced noise volt The rapid developments in fiber-amplifier tech age across the terminals of the resistor. This nology now enable employment of these devices effect, also called Johnson or Nyquist noise, was for telecommunications and CATV with a sub first observed by J. B. Johnson in 1927, and a stantial advancement in system capabilities. For theoretical treatment was given by H. Nyquist in telecommunications, optical amplifiers can easily 1928. Accordingly, for a thermal noise source compensate for fiber loss in very long repeatered the available power in a 1-Hz bandwidth is given transmission links. Experiments have shown that by it is feasible to transmit at multi-Gbit/s rates in [W/Hz] (1) ultra-long distance amplifier cascades with losses p'dl. = kT of a few thousand dB. For CATV, although the where k is Boltzmann's constant (1.38·10-23 expectations are not so astounding, erbium-doped joule/°K, and Tis the absolute temperature in fiber amplifiers (EDFA's) can be used as power degrees Kelvin. At room temperature, kT = amplifiers to boost the output of the laser source 4.0·10-21 W/Hz (-174 dBm/Hz). In a 75 ohm and enable a large increase in the optical loss system and for a bandwidth of 4 MHz, the ther budget. However, EDFA's are expected to have mal noise voltage is -59.2 dBmV, which is the limited application, if any, as repeaters because of familiar number used in CATV carrier-to-noise the high input signal power required to achieve ratio calculations. At room temperature, the acceptable carrier-to-noise ratios for AM CATV. power density spectrum is theoretically constant up to -3000 Ghz and decreases rapidly for This paper begins with a simple discussion of higher frequencies. At optical frequencies, quan-
86 -1992 NCTA Technical Papers tum noise dominates, as discussed in later sec tons per second: tions.
Light, like radio waves, is a form of electromag PHOTODETECTION PROCESS netic radiation. At optical frequencies, the quan tum-mechanical effects become important, and the The photodetector commonly used in CATV discrete nature of light must be considered. The applications is the PIN photodiode. Incident quantum particle of light is the photon, and the photons are absorbed in the depletion region energy of each photon is hv Goules), where his creating electron hole-pairs. Under the influence Planck's constant (6.624·10·34 joule-sec) and v is of the reverse bias electric field, the electrons and the optical frequency. The power of an optical holes drift in opposite directions creating a signal is thus displacement current in the external circuit. For an ideal photodiode, one electron is emitted for (3) P = Nhv each incident photon. The efficiency of generat where N is the average number of photons emit ing electrons is given by the quantum efficiency ted per second by the optical source. However, of the detector, which is defmed as photons are not emitted at a constant rate, but, in number of electrons emitted (7) fact, the emission times of the photons vary 11 randomly. From Poisson's probability distribu = number of incident photons · tion law, it follows that the variance, or mean Since optical power = (number of pho square deviation in the number of photons emitted tons/sec)-hv, and detector current = (number of per second, is equal to the mean number of pho-
1992 NCTA Technical Papers- 87 electrons/sec)-q, it follows that ERBIUM-DOPED FffiER AMPLIFIERS
I = P( 11 q) (8) Amplification occurs in an erbium-doped fiber de hv amplifier (EDF A) due to the photoluminescent where P is incident optical power (W), and Ide is properties of the rare-earth element erbium detector current (A). Responsivity R of the concentrated in the core of the fiber. The atomic detector is defined as energy levels of erbium allow erbium to absorb energy at any of several wavelengths and release R = 1Jq. (9) energy in the 1550-nm range. In the interaction hv of photons and atoms, the frequency of absorbed Noise is inherent in the output of the photodetec or emitted radiation " is related to the difference tor. The origin of this noise can be treated in in energy E between the higher and the lower two ways. In the quantum treatment, the optical energy states E2 and E1 by the expression field is quantized into photons and each photon E = E - E gives rise to an electron with probability 1J. Due 2 1 (12) to the random occurrence in time of the photons, = hv. a noise current is generated which limits the Discrete energy states correspond to particular minimum detectable signal as discussed in the energy levels of the electrons within the atom previous section. In the semiclassical approach, a relative to the nucleus. A single eiectron transi constant electromagnetic field interacts with atoms tion between two energy levels represents a in the photodiode and generates the photodiode change in energy suitable for the absorption or current. Shot noise is generated in this process. emission of a photon. Each electron-hole pair results in a single pulse of detector current of charge q. The total current is the superposition of these pulses occurring randomly in time. Because of this random ExciTED fluctuation, shot noise results just as Schottky STATE observed it did in vacuum-tube amplifiers. ABSCA>TIGI Photodetector shot noise current is
i! = 2qidc (10) = 2qPR [A 21Hz] where Ide is the de current. EI\ISSION
The minimum detectable optical power is defined for quantum efficiency = 1 as the minimum Fig. 1. Erbium three-level system with excited-state power for which the rms value of shot noise is absorption. equal to the de current. Thus, Erbium has a three level system, the ground level pmin = 2hv (11) (N1), the metastable level (NJ, and a higher level This is the same as given in the previous section. (N3) as shown in Fig. 1. In an EDFA the The question as to whether the limit to sensitivity absorbed energy comes from a pump laser. The is imposed by photodetector-generated shot noise optimum pump wavelengths for EDFA's are or the fluctuations in the incident photon number those for which there is no excited state absorp is academic. The resultant photodiode current is tion (ESA). These wavelengths are 980 nm, the same in either case [1]. 1480 nm, or 1047 nm. ESA creates a fourth
level (N4) by the process of exciting or pumping
88 -1992 NCTA Technical Papers the electrons from N2 to N4• This depletes the X is the excess noise parameter of the EDFA. number of electrons or population at the N2 level p._ is the ASE noise power in both polarization creating a need for increased pump power, which modes emitted by the EDFA. Eqn. 13 gives the will increase the pumping rate allowing the optical noise spectral density (W /Hz) at the output system to maintain the same degree of population of the erbium-doped fiber. This noise field has inversion. Population inversion occurs when the all of the statistical properties of thermal noise; it pumped electrons transition from N1 to N3 and is additive and Gaussian with respect to the then rapidly decay to the N2 level. The amount amplified input field [2]. 1Jsp is the inversion of time they spend at the N2 level is controlled by parameter, and with complete population inver the erbium ion fluorescence lifetime which is sion its value is equal to one. To obtain complete approximately 10 ms. Therefore, for complete population inversion everywhere along the fiber, population inversion to occur, the rate at which the pump power into the fiber must be at least the electrons are transitioning from N1 to N2 and twenty times greater than the pump power then held in the Nz level must exceed the number threshold at which population inversion begins of electrons transitioning from N2 to N1 at any [3]. Qualifying this further, the product of the given time. Ideally, the total number of electrons pumping rate and the fluorescence lifetime of the associated with the erbium atoms available per N2 level must be much greater than one, which length of fiber, must remain in the N2 level, and will occur with sufficient remnant pump power. just as quickly as one decays to the lower N1 level Without complete population inversion, 1Jsp another one must already be at the Nz level. increases due to the decrease in number of
Their decay from N2 to N1 can occur in two electrons in level N2• This causes an increase in ways: the amplifier noise figure as given by the equa (a) by spontaneous emission in which the atoms tion NF = 21Jsp as derived later. return to N1 in an entirely random manner, creating optical noise from - 1530 nm to - 1560 nm, and: EDFA IMPLEMENTATION (b) by stimulated emission in which an incident photon causes the release of a second photon of The amplifier gain medium is the erbium-doped the same energy. Stimulated emission produces fiber, whose length varies from a few meters to coherent amplification or gain. about 100 meters. The length can be optimized By this process the optical input signal and noise for either gain or noise characteristics. Also, the generated by spontaneous emission are amplified. optimum length increases with pump power and At the amplifier output there are two optical decreases with the signal power [4]. The fibers components: the desired amplified input signal used typically have a codopant such as germani and amplified spontaneous emission (ASE), which um, aluminum, ytterbium, or phosphorus to is optical noise. change various fiber characteristics. The fiber is designed to utilize pump power as efficiently as For the uniform inversion model, which means possible, and has a mode-field diameter much that the pumping rate throughout the entire length smaller than that of standard single-mode fiber. of erbium-doped fiber is sufficient to keep N2 This results in relatively high splice loss, typical completely populated, the following equations ly about 1 dB. apply: A general block diagram of an EDFA is shown in Fig. 2. Two pump lasers are shown, although a (13) single pump laser can be used either at the erbium fiber input (co-propagating pump) or at the erbium fiber output (counter-propagating pump). In either configuration, the pump power should be greater than approximately 100 mW to
1992 NCTA Technical Papers- 89 eliminate the effect of absorption allowing an EDFA is shown in Fig. 3. As the input signal complete population inversion and identical ASE increases the gain decreases as the amplifier goes powers in the forward and reverse directions. into saturation or gain compression. When an This is important particularly in a system that EDFA is driven sufficiently hard into saturation utilizes a double pump configuration because if the output power tends toward a limiting value one fails, without sufficient pump power available (P83J which is the maximum output power [6]. to the Er-doped fiber, the EDF A noise and gain Saturated output increases approximately linearly characteristics will change drastically. with pump power. As the EDFA goes deeper into saturation, more and more of the pump light Isolators are used to prevent reflected signals is converted into signal. As booster or power from being re-amplified. The reflections would amplifiers, EDFA's are operated deeply in induce intensity noise and intermodulation saturation in order to deliver high output power. distortion by distorting the shape of the ASE The saturated output power of commercially spectra. At high pump powers, such as with a available amplifiers for use as booster amplifiers double-pump configuration, the reflections can is in the range of about 10 dBm to a little over cause laser oscillation or cause the higher ASE 20 dBm. High differential pump-to-signal powers to self-saturate the amplifier and reduce quantum efficiencies have been obtained. There the pump efficiency [5]. exists a performance tradeoff for an EDFA to have low noise amplification and high pumping The general input-output signal characteristic of efficiency. To obtain both, the use of short pump wavelengths are preferred in order to lower the ASE power and obtain high efficiencies by laOIIIIDr WDM IIIO&atw ..a ..fDr WDM laolatar strongly saturating the amplifier. At the 980-nm pump wavelength, 47-mW saturation power (16.7 dBm) has been obtained with 100 mW of pump power [7].
Due to the temporal properties of the erbium fiber, the signal may experience intermodulation Scientific distortion in a single channel system or saturation Atlanta induced crosstalk in a multiple channel system. These transient effects are produced when Fig. 2. BlockdiagramofEDFA withdoublepump. operating in gain saturation. One effect of signal induced gain saturation is to increase the pump attenuation thus reducing the population inversion
2or------~ toward the output of the EDFA which changes Gain saturation : the gain spectrum and creates noise. The gain I 10 spectra will shift under nonuniform gain satura tion conditions depending on such factors as fiber Output POWer O type, fiber length, pump power, pump wave (dBm) length, and signal wavelength [6]. For CATV application, these transient gain effects are -10 dampened by the long fluorescent lifetime in erbium which sets a lower frequency limit of
-20 ::-~_...~-:-:---'---.1--...J approximately 100kHz by filtering out any high -60 -50 -40 -30 -20 -10 0 frequency modulation of the EDFA's gain. Input power (dBm) Fluctuations in the gain spectra are inversely Fig. 3. Amplifier input-output characteristics using proportional to the pumping rate. Therefore, the a 980-nm pump laser [8]. stronger the pump power, the smaller the fluctua-
90 -1992 NCTA Technical Papers I
tion or the smaller the gain-recovery time SIGNAL AND NOISE CHARACTERISTICS constant which minimizes crosstalk and distor tion. The slow gain response combined with the In direct-detection of an optical signal, the output third-order susceptibility of the erbium fiber also current of the photodetector is directly propor prevents the occurrence of intermodulation tional to optical power. However, optical power distortion in multichannel systems [9]. Other is proportional to the square of the magnitude of techniques useful in eliminating the transient gain the E field and the detector responds to the square effects are by utilizing filters at the erbium fiber of the E field. The detector is in reality a square to equalize the gain spectrum and by utilizing an law detector, and the fact that the output of a all-optical feedback loop to the EDFA [4]. photodetector changes 2 dB per dB change in input power is very familiar. In a system with an The output spectrum of an EDFA is given in Fig. optical amplifier, this square-law characteristic 4 with no input signal, and in Fig. 5 for a high causes additional noise currents to be produced at input signal level (5 dBm). In Fig. 5, the the output of the photodetector: these are called amplifier is operating 20 dB into saturation signal-spontaneous (s-sp) beat noise, and sponta (small signal gain reduced 20 dB). neous-spontaneous (sp-sp) beat noise.
SPECTRUM 10 ... 1Eic:IEI,--di_v_ _AOJR. .... :__ .... :...... :l ...... :; . dB : ...... : ...... l ..... ·
SJGNAL:P1n G
-48-88: ...... ~ ...... j·· .... :... . 2 2 -78: ...... :...... :...... :l...... :...... :..... :...... :. ··············· NOISE: 2hv F Pose lsno + lomp 1.seee 1-~00 1·6000 W1 1-S::Sl- W2 1·600000 RES 0-1.- W2-W1 0·069000.- 10-BnM..-div Fig. 6. Diagram for noise figure calculations.
Fig. 4. EDFA output spectrum with no input signal. Consider an optical amplifier directly connected to a photodetector as illustrated in Fig. 6. Pm. is the input signal power and G is amplifier gain. SPECTRUM 10 : ...10 c:IEI..-cliY...... o:.u.~ ...... L There are two components at the output of the amplifier: amplified signal GPm. and amplified d8 spontaneous emission noise Pa.e· Since the . . . 0·40: ...... : ...... · ...... : .... . photodetector is a square-law detector, heterodyn
-30:·· ing and mixing occur. The optical noise hetero dynes with the signal causing the noise spectrum to be translated to de. This noise is signal -!50-40: ..... ····· ...... : ...... :~ ...... : .. . spontaneous beat noise. In an EDFA, the spontaneous emission is randomly polarized and only the noise that is co-polarized with the signal, lhp_, is heterodyned. Likewise, components of Fig. 5. EDFA output spectrum with 5-dBm input the spontaneous emission mix with each other in signal power. the square-law detection process to produce spontaneous-spontaneous beat-noise currents.
1992 NCTA Technical Papers- 91 I
The signal-spontaneous beat-noise current is [10] the photodetector, the output noise currents consist of two components: shot noise due to the l,·2 sp - 2Pin Gp (11q)2- . (14) amplified input signal, and total noise current due - ""' hv to the optical amplifier. The output signal is Assuming the amplified spontaneous emission 2 noise p,_ is constant over an optical bandwidth 1, out = [GPin..i.F (20) - hv Bo, the spontaneous-spontaneous beat-noise current is [ 10] and the output noise currents are
[P (15) lmo·2 +lamp·2 = 2 q in hvq ] + lamp·2 (21)
where {2 mo is shot noise due to the amplified 2 Amplifier Noise Figure signal and i amp is optical amplifier noise. From the preceding equations, amplifier noise factor is The amplifier noise figure as defined and devel ·2 ·2 oped herein follows that presented in reference F=~lmo+lampP [11] and is the same as in [12]. The noise factor 2hv ( GP. _!L)2 F of an amplifier is defined as m hv ·2 SNR. =2.[1+lamp] (22) F ~ m (16) G ·2 SNRout lmo ·2 1 lamp where SNR;, and SNRout are the signal-to-noise = for G ;!!> 1. ratios at the input and output of the amplifier. The input noise, by definition, is that from an Noise figure is noise factor expressed in dB: ideal source. At optical frequencies, the input NF = 10 log F. (23) noise is quantum noise (2hv), whereas in the 10 electrical domain it is KT. For the optical For most practical CATV applications, signal amplifier, the SNR's are defined as electrical spontaneous beat noise dominates and the noise quantities measured at the output of a ideal factor is then
photodetector (11 = 1). Signal currents are 2 expressed inN, and noise currents are in A 21Hz. 4P. G11sp( G-1 )!L 1 m hP F= ------SNR;, is given with the optical source directly G 2q( GP. .!L) (24) connected to the photodetector. The signal m hv measured at the output of the photodetector is = 211sp( G~ 1) (17) = 211sp for G ~ 1 .
The photodetector output noise is shot noise The last expression is the definition that is commonly used for EDFA noise factor. The 2q[P. .!L] (18) minimum value for 1lsp is one, for which the m hv quantum-limit noise figure is 3 dB. Measured and values approaching 3 dB have been achieved with 980-nm pumping, but the minimum achievable P. SNR =-m. (19) value for 1480-nm pumping is about 4 dB. The m 2hv higher noise figure in the 1480-nm pump band is This result is the same as for SNR;, in the optical due to its proximity to the 1550-nm signal emis domain. With the amplifier connected directly to sion band, which causes the erbium three-level
92 -1992 NCTA Technical Papers system to behave differently [13]. This creates a CATV CARRIER-TO-NOISE RATIO finite thermal population (N3) at the pump level which restricts the fiber from being uniformly For CATV system modeling, the carrier-to-noise inverted. Coupling losses in the amplifier unit ratio (CNR) due to the optical amplifier can be increase the amplifier noise figure. External calculated based on the noise factor given in Eqn. noise figures of 5 to 7 dB appear to be readily 27. In multichannel AM operation, the carrier achievable. currents at the output of the photodetector are given by Measurement of Noise Figure mi 2 de [AZ] (28) According to the definition of noise factor given -2- in the preceding section, F is given by currents at the output of an ideal detector with quantum where m is the modulation index per channel. efficiency 71 = 1. For practical measurements, Thus, from Eqn. 27 and G ,._ 1, the CNR due to particularly when operating at high saturated the optical amplifier is given by output power, loss has to be inserted between the amplifier and detector. For simplicity, assume CNR = SNRin m2 [/Hz] that the amplifier noise ramp consists of signal F 2 (29) spontaneous and spontaneous-spontaneous beat SNRin m2 =-p . ()6 [/4 MHz]. noise currents f.-sp and f ap-sp· The noise currents 8 1 measured at the output of the detector are then These expressions are also valid for amplifier ·2 2 ·2 lamp_measured = 71eff lamp (25) noise from other causes (excluding ASE shot ·2 ·2 l..,o_measured = 1J eff lsno noise) such as interferometric -interference noise. iamp measured includes noise currents from all other sources of noise within the amplifier. Also note where that F as given herein is the external noise factor of the amplifier (except for Eqn. 24 which does Ide hv (26) not take into account input and output coupling 11eff = GPm q. losses). CNR expressed in dB for 4-MHz electrical bandwidth is 1Jeff is the total loss factor from the amplifier (30) output to the detector including the detector quantum efficiency. Ide is the photo diode de CNRdB = 89.9- NF + Pin_dBm + 20log(m). current due to amplified signal power (assumption An equivalent RIN can also be given: is that residual pump power is negligible. The = + NF- noise factor of the amplifier is then given by RINdB -155.9 Pm._dBm. (31) As an example, if Pin 0 dBm, m .04, and ·2 = = F = _!_ + _1_ lamp_meaaured NF = 5 dB, then the CNR is 56.9 dB and the amplifier RIN is -150.9 dB/Hz. As is evident G G 1J eff i!,_measured ·2 here, amplifier input power should be in the 1 lamp_measured = - + SNR. -----,-- (27) range of about 0 dbm or greater to prevent G m Ii, excessive degradation of system CNR. The effect ·2 of amplifier RIN is to reduce the system CNR for = SNR. lamp_measured for G ~ 1. short fiber spans, but the high output power of m Ii, the amplifier results in a higher CNR for long fiber spans than is possible with today's DFB lasers only. This characteristic CNR performance is shown in Fig. 7.
1992 NCTA Technical Papers- 93 REFERENCES
[1] A. Yariv, Quantum Electronics, Wiley, New York, 1989. [2] J.P. Gordon and L.F. Mollenauer, "Effects of Fiber Nonlinearities and Amplifier Spacing on Ultra-Long Distance Transmission, • J. Lightwave Technol., Vol. 9, February 1991, pp. 170-173. [3] E. Desurvire, J.L. Zyskind, and C.R. Giles, "Design Optimization for Efficient Erbium-Doped Fiber Amplifiers," J. Lightwave Technol., Vol. 10 15 20 8, November 1990, pp. 1730-1741. UNI[ ATIINIIAIION (
94 -1992 NCTA Technical Papers