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JOURNAL OF LIGHTWAVE TECHNOLOGY. VOL. 7. NO. 7. JULY 1989 1071
Lightwave Systems With Optical Amplifiers N. A. OLSSON
Abstract-Recent advances have brought semiconductor amplifiers to the stage where lightwave systems employing amplifiers in some as- pects clearly out-perform traditional systems. For example, the longest nonregenerated fiber transmission experiments use optical amplifier repeaters, and at very high data-rates (4 Gbit/s), receivers with op- tical pre-amplifiers are substantially more sensitive than their coherent and APD counterparts.
In this paper, fiber optic communication systems employing semi- conductor laser amplifiers are investigated theoretically and experi- mentally. The noise and bit-error-rate characteristics of lightwave sys- tems with optical amplifiers are calculated and the dependence of system performance on amplifier characteristics such as optical band- width, noise figure, gain, etc., is shown. Experimental results are pre- sented on both a 4 Gbit/s optical pre-amplifier as well as coherent and direct detection systems with four in-line amplifiers.
INTRODUCTION HE TRADITIONAL way of compensating for optical T loss in lightwave communication systems has been the
rather cumbersome procedure of regeneration. Regener- ation includes photon-electron conversion, electrical am- plification, retiming, pulse shaping and finally electron- photon conversion. In many applications, direct optical amplification of the light signal would be advantageous. Optical amplifiers can be used in any system that is loss limited; i.e., dispersion effects are not a limiting factor. This is the case for most systems operating near the dis- persion minimum at 1.3 pm, and for coherent lightwave systems. Local area networks, where the main losses are from branching and taps, are also loss limited and can benefit from simple optical amplifiers.
Semiconductor laser amplifiers have been studied for a number of years. Significant work at 0.8-pm wavelength was done in the early 80’s -. Recently major prog- ress has been made in long wavelength devices. Optical amplifiers with high gain, low gain ripple, low noise, and high saturation output power have been reported -. Optical amplifier system applications have also been re- ported, both applications for preamplifiers - and in-line amplifiers [lo]-[ 141.
As optical amplifiers have advanced to the stage that actual system use might be possible in the near future, it is important to know the system consequences, its advan- tages and limitations.‘ In this paper we present a theoret- ical as well as experimental investigation of optical am- plifier lightwave systems. Noise levels, bit-error-rate characteristics (BER), receiver sensitivities, and power
Manuscript received August 20, 1988; revised December 14, 1988. The author is with AT&T Bell Laboratories, Murray Hill, NJ 07974 IEEE Log Number 8927 15 1.
penalties are calculated functions of the relevant optical amplifier parameters.
THEORY DIRECT DETECTION The amplifier noise model presented below is based on
the work by Mukai  and Simon  which we have extended and combined with the receiver models and BER calculations of Smith et al. [ 161. The various symbols are defined in Table I and a schematic is shown in Fig. 1. The analysis presented here applies to traveling wave ampli- fiers (TWA) which are the technologically most important type of amplifier. However, extension of the analysis to resonant or Fabry-Perot amplifiers (FPA) is rather straight- forward by modifying the optical bandwidths for the beat noise components and by including the excess noise factor from the mirror reflectivities as described in .
The spontaneous emission power at the output from a optical amplifier is given by (see Table I for definitions of the symbols):
P,, = Nsp(G - l ) h ~ B , .
For an ideal amplifier, Nsp = 1. For semiconductor laser amplifiers, however, Nsp ranges from 1.4 to more than 4 depending both on the pumping rate and the operating wavelength , . In the following we will write the optical powers as their photo current equivalent, i.e., as the photo current that would be generated by detecting the optical power with a detector with unity quantum effi- ciency.
The photo current equivalent of the spontaneous emis- sion power is:
is, = P S p e / h v = Nsp(G - l)eB,. (2)
After square law detection in the receiver, the received signal power is given by:
s = (G~sqinqout~)’. (3)
The noise terms are:
Nshot = 2BeeqoutL(GIsq,n + I s p )
0733-8724/89/0700-1071$01.00 0 1989 IEEE
1072 JOURNAL OF LIGHTWAVE TECHNOLOGY. VOL. 7. NO. 7. JULY 1989
Psens, B e
Fig. 1. Schematic of amplifier model. See Table 1 for definitions of the terms.
TABLE I DEFINITIONS O F MATHEMATICAL SYMBOLS
B. Electrical bandwidth B. Optical bandwidth e Electronic charge G Optical gain hv Photon energy
4 PCE of local oscillator power FCE of spontaneous emission power PCE of amplifier input power PCE of amplifier input power for "mark" PCE of amplifier input power for "space" Optical loss betwcen amplifier and receiver
I , ( ] ) I,(O) L M Number of channels q, Amplifier input coupling efficiency
Amplifier output coupling efficiency N,o-,p Local oscillator-spontaneous beat noise
N , Nv Spontaneous emission factor N,b, Shot noise N,-,p Signal-spontaneous beat noise Nrp-,p Spontaneous-spontaneous beat noise Nu, Receiver thermal noise Ntd Total noise power
P, Average amplifier input power P- Amplifier saturation output power P,, Receiver sensitivity P,p Spontaneous emission power r Extinction ratio S
Maximum number of cascadable amplifiers
Electrical signal power at receiver Electrical signal power for "mark" Electrical signal power for "space"
Electrical signal power for coherent detection
PCE = Photo Current Equivalent
The expression for N.y-sp and Nsp-sp in ( 5 ) and (6) are derived in Appendix A.
For an amplitude modulated signal of average power Pin, 50-percent duty cycle and an extinction ratio of r, the photo current equivalents of the input powers for a mark
1 ) ) and a space (Zs(0)) are:
I,(I) = ePin2r/(hv(r + I ) ) z.~(o) = ePl,2/(hv(r + 1)).
(10) The BER is given by :
where Q is given by:
S ( 11, S(0) and Ntot( l ) , N,,,(O) are the signal and total noise for a mark and space, respectively. A BER of lop9 requires Q = 6. Equations (1)-(12) form the basis from which the performance of the amplifier systems are eval- uated.
Of particular interest for preamplifier applications is the receiver sensitivity dependence on the amplifier gain, noise figure, and optical bandwidth. The application of optical preamplifiers is at very high data rates where av- alanche photo detectors are limited by their gain-band- width product . Therefore, we have analyzed a - 5- Gbit/s receiver with 2.5-GHz electrical bandwidth. First we calculate the achievable receiver sensitivity versus amplifier gain. The results are shown in Fig. 2. To make the calculations realistic, we have used measured values for the receiver and amplifier parameters. The value cho- sen for the thermal noise current corresponds to a base receiver sensitivity of -25 dBm. At low amplifier gains, the receiver is limited by the thermal noise and conse- quently the receiver sensitivity improves 1 dB for every decibel of gain. For higher gains, the signal-spontaneous and spontaneous-spontaneous beat noise becomes domi- nant, and the best achievable receiver sensitivity depends on the optical bandwidth of the amplifier. The ultimate limit is achieved when B, = 2B, and is in this case equal - -39.4 dBm. This corresponds to 181 photondbit and is close to the expected value of 41 N \ p / r l n . The power penalty versus optical bandwidth with the gain as param- eter is shown in Fig. 3. The penalty is defined as the de- crease in receiver sensitivity as compared to B , = 2B, for each given gain. As expected, the penalty is larger for higher gains when the receiver is closer to the ultimate limit. The receiver sensitivity dependence on the sponta- neous emission coefficient N,, is shown in Fig. 4 for an optical bandwidth of 10 A and for amplifier gains of 15, 20, and 35 dB. For low amplifier gains, the sensitivity dependence on N is quite weak because we are far from the ultimate sensitivity and the receiver is still dominated by thermal noise. At high gain, in the signal-spontaneous beat noise limit, however, the sensitivity is inversely pro- portional to N S p . A 3-dB increase in NSp gives a 3-dB re- duction in sensitivity. Like APD receivers, optical pre- amplifier receivers have signal dependent noise. There- fore, the sensitivity degradation from a nonperfect ex- tinction ratio is worse than in a traditional p-i-n receiver. The effect of the extinction ratio is shown in Fig. 5 as the sensitivity penalty at amplifier gains of 15 dB and 35 dB and an optical bandwidth of 5 A. The extinction ratio is here defined as the ratio of the optical power in the " 1 " state to that in the "0" state. The higher the gain, the more dominant is the signal-spontaneous beat noise (N, - s p ) term and consequently the higher is the extinc- tion ratio penalty. An extinction ratio of 2 0 : 1 or better will in all circumstances give a penalty of 1 dB or le