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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 [1]-[2]. 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 [3]-[7]. Optical amplifier system applications have also been re- ported, both applications for preamplifiers [7]-[9] 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 [2] and Simon [15] 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 [2]. 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 [3], [6]. 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, = PSpe/hv = Nsp(G - l)eB,. (2) After square law detection in the receiver, the received signal power is given by: s = (G~sqinqout~)’. (3) (4) The noise terms are: Nshot = 2BeeqoutL(GIsq,n + Isp) 0733-8724/89/0700-1071$01.00 0 1989 IEEE

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Page 1: Lightwave systems with optical amplifiers - Lightwave ...wcours.gel.ulaval.ca/2017/h/GEL4200/default/6travaux/GEL7014/dev… · Lightwave Systems With Optical Amplifiers N. A. OLSSON

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 [1]-[2]. 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 [3]-[7]. Optical amplifier system applications have also been re- ported, both applications for preamplifiers [7]-[9] 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 [2] and Simon [15] 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 [2].

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 [3], [6]. 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)

(4)

The noise terms are:

Nshot = 2BeeqoutL(GIsq,n + I s p )

0733-8724/89/0700-1071$01.00 0 1989 IEEE

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1072 JOURNAL OF LIGHTWAVE TECHNOLOGY. VOL. 7. NO. 7. JULY 1989

OPTICAL RECEIVER

Psens, B e

AMPLIFIER

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

1,

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

S(1)

S(0)

Smk

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)).

(9)

(10) The BER is given by [16]:

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.

RESULTS Preamplijier

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 [17]. 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 less.

Overall, using very reasonable and achievable values for the amplifier and system parameters ( G = 25 dB, qln

.?

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OLSSON: LIGHTWAVE SYSTEMS WITH OPTICAL AMPLIFIERS 1073

- 40

I

E m D I

-30 > c Lo z Lo

-

B e = 2 5 0 0 MHz

- 2 0 I ! I , I 1 10 20 3 0 40

AMPLIFIER GAIN ( d B )

Fig. 2 . Optical preamplifier sensitivity versus amplifier gain. Calculated forB, = 2500 MHz, N,, = 1.4, q," = 0.31, qout = 0.26, and X = 1.55 Irm.

5 , I

I Be=2500MHz G = 3 5 d B I

1 IO 100 1000

OPTICAL BANDWIDTH (1, Fig. 3. Optical preamplifier sensitivity penalty versus optical bandwidth

Same amplifier parameters as Fig. 2.

-25 I I

-40 ' ' ' ' ! ' ' ' ' ' 1 5 10

SPONTANEOUS EMISSION FACTOR, NSp

Fig. 4. Optical preamplifier sensitivity versus spontaneous emission factor N,p. Same amplifier parameters as Fig. 2.

\ \ G = 3 5 d B I

1 '0 100

EXCTlNCTlON RATIO

Fig. 5. Optical preamplifier sensitivity penalty versus extinction ratio. Same amplifier parameters as in Fig. 2.

= 0.31, Bo = 10 A, Nsp = 1.4, r = 20), the achievable sensitivity for a 2.5-GHz receiver is about -35.2 dBm. This is still 9 dB from the ultimate limit but is about 4 dB better than the best reported APD results. As have been pointed out earlier, optical preamplifier receivers are a vi- able alternative to APD receivers but mainly at high data rates [ 171. The above analysis should give some guidance in the relative importance of the various system and am- plifier parameters.

IN-LINE AMPLIFIER Direct Detection

One of the more promising applications of optical am- plifiers is the in-line amplifier, where the amplifier com- pensates for losses in the system. The losses may be due to fiber losses in a long haul system, tap and splitting losses in a local area network, or coupling and switch losses in an optical switch. For this application, the main concerns are how the system performance is affected by gain, optical bandwidth and the input power of the am- plifier. Also of interest is the ultimate number of amplifier stages that can be cascaded while maintaining reasonable system performance. Several of these issues have been addressed previously [2]. However, prior work has been concerned only with optical signal-to-noise ratios which give an indication of upper limits on the system perfor- mance but do not provide information about major system parameters such as power penalties and noise induced er- ror floors. In this section we will give a detailed analysis of the performance of lightwave systems utilizing optical in-line amplifiers.

First we will address the question: what power penal- ties are incurred at the receiver when a single in-line am- plifier is inserted somewhere in the fiber line? For this case, the most important parameter is the optical input power to the amplifier. The calculation is made as fol- lows. For each given input power to the amplifier, the loss between the amplifier and receiver is varied such as to produce a signal power at the receiver that gives an BER of lop9. No approximations are made and all of the noise terms in equations (4)-(7) are used to evaluate the BER. This receiver sensitivity is then compared to the baseline receiver sensitivity (no amplifiers) and the power penalty is taken as the sensitivity difference. This calculation is shown in Fig. 6 and Fig. 7. In Fig. 6 for electrical band- widths of 2500, 500, and 50 MHz, all for an optical band- width of 50 A. The corresponding base-line sensitivities are; -25, -32, and -42 dBm respectively. Fig. 7 is a calculation of the actual receiver sensitivity for a electri- cal bandwidth of 2500 MHz and for optical bandwidths of 300, 30, and 3 A, respectively. Note that for this cal- culation we have used vi" = l so the amplifier input power refers to the power actually coupled into the amplifier. To give some guidance of what power penalty is acceptable for a system, we show in Fig. 8 a family of BER versus received power curves with the amplifier input power as parameter. The amplifier input powers have been chosen such that the BER receiver power penalties are - 0,

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1074

E ~ -47

m

e 2 t -54

v -49 -

z v)

-53

5 DIRECT DETECTION

COHERENT DETECTION Be=500MHz

-

-

-

-

B,=50A I

- 25 -35 -45 -55

AMPLIFIER INPUT POWER ( d f h )

JOURNAL OF LIGHTWAVE TECHNOLOGY. VOL. 7. NO. 7. JULY 1989

-45 I

-55 I 1 I I I 1 - 20 -30 -40

AMPLIFIER INPUT POWER (dBrn)

Fig. 6. Power penalty for in-line amplifier system. Calculated for G = 25 dB, B,, = SO A, N , , = 1.4, 7," = 1, and infinite extinction ratio.

Fig. 9. ASK heterodyne receiver sensitivity versus in-line amplifier input power. G = 25 dB, PI, = 0 dBm, Nsp = 1.4, 7," = I , B, = 500 MHz, and Bo = 100 A.

5 , I

DIRECT DETECTION Be = 2500 MHz

- 25 - 30 -35 - 40 - 45

AMPLIFIER INPUT POWER (dBm)

Fig. 7. Power penalty for in-line amplifier system versus amplifier input power with optical bandwidth as parameter. G = 25 dB, 7," = 1 , N,, = 1.4, B, = 2500 MHz, and infinite extinction ratio.

$ 10-9 LT I

U

a W

; qo-i4

10-19 - 26 -21 - 16

RECEIVED POWER (dBm)

Fig. 8. BER curves for direct detection in-line amplifier system with am- plifier input powers of -25, -32.89, -34.64, -36.05, -36.66, -37, and -37.45 dBm, giving BER power penalties of -0, O S , 1 , 2, 3 , and 4 dB, and an BER error floor, respectively.

0.5, 1 , 2, 3, and 4 dB, and an error floor at lop9 BER. We see from Fig. 8 that for lop9 BER penalties less than 1 dB, no error-floor exist, at least not for BER > However, in the case of a 2-dB penalty at BER, an error-floor exists at - BER. Fig. 8 indicates that an lop9 BER penalty of 1 dB or so may be acceptable from a system performance point of view. However, the actual requirements will vary from application to application de- pending on the required error statistics.

COHERENT DETECTION To modify (1)-( 12) to correspond to a coherent detec-

tion system is straight forward. For an amplitude shift keying (ASK) system, which we will use as our model coherent system, the signal term (3) is replaced by

where Zlo is the photocurrent equivalent of the local oscil- lator power PI,:

40 = P , o e / ( W . (14)

To the total noise power in (S), we must add the local oscillator shot noise: 2ZloBee, and the local oscillator- spontaneous beat noise:

IIo-sp = 41I0L(G - 1)Nspe~outBe.

With these modifications, we can calculate the receiver sensitivity versus amplifier input power analogous to Fig. 7 for the direct detection case. The result is shown in Fig. 9 for a 500-MHz electrical bandwidth and a local oscil- lator power of 9 dBm. The receiver thermal noise corre- sponds to a direct detection sensitivity of -32 dBm. The coherent baseline receiver sensitivity is - 52.8 dBm or 4 1 photondbit ( 1 Gbit/s). A 2-dB power penalty is incurred for an amplifier input power of -44.5 dBm. Contrary to the direct detection case, for coherent detection the power penalty is independent of the optical bandwidth. This is because the dominant noise term is the local oscillator- spontaneous beat noise which is independent of optical bandwidth. In Fig. 10 we show the calculated BER curves for the coherent detection system. We have chosen the amplifier input powers such that the penalties at lop9 BER are -0, 1, 2, 3, 4, and 5 dBm. In this case, even for a

penalty of 2 dBm, no error floor exist for BER > The difference between the direct detection and co-

herent detection stems from the quadratic dependence of the electrical signal on optical power for direct detection and linear dependence in the case of coherent detection.

It is clear from the above analysis that a single amplifier can be inserted in both direct detection and coherent de- tection systems with no or very small penalty provided the amplifier input power is sufficiently large.

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OLSSON: LIGHTWAVE SYSTEMS WITH OPTICAL AMPLIFIERS 1075

-55 -50 -45 -40

RECEIVED POWER ( d B m )

Fig. 10. BER curves for ASK coherent detection system with in-line am- plifier. Plotted for amplifier input powers of -30, -42, -44.4, -45.7, -46.5, and -47.1 dBm, giving BER penalties of -0, 1, 2, 3, 4 , and 5 dB, respectively.

AMPLIFIER CHAIN Next we will analyze a system with multiple in-line am-

plifiers. We will assume that the gain of each amplifier exactly equals the loss in between two amplifiers. With this assumption, the cumulative effect of the amplifier noise is obtained by replacing N,, in equations (2)-(12) by N Ns,, where N is the number of amplifiers. First we calculate the power penalty at the receiver as function of Nand with the amplifier input power as a parameter. Sim- ilarly to the calculation for Fig. 6; for each input power and optical bandwidth, we vary the loss after the last am- plifier as to produce a signal power at the receiver that gives a BER of lop9. Fig. 11 show the calculated results for a system with 500-MHz electrical bandwidth and an optical bandwidth of 3 A . For amplifier input powers of -30, -20, and -10 dBm, the maximum (1-dB penalty) number of amplifiers are 28, 280, and 2800, respectively. This example with very narrow optical bandwidth and low data rate ( - 1 Gbit/s) gives the upper limit on the num- ber of amplifiers. If we increase the data rate to - 5 Gbit/s (Be = 2500 MHz) and the optical bandwidth to 300 A, which is approximately the unfiltered bandwidth of a 1.3- pm amplifier, the maximum number are 3, 30, and 300 for input powers of -30, -20, and -10 dBm, respec- tively, as shown in Fig. 12.

COHERENT DETECTION The penalty versus number of amplifiers for a coherent

detection system is shown in Figs. 13 and 14. Fig. 13 for a 500-MHz electrical bandwidth, and Fig. 14 for 50-MHz electrical bandwidth. As in the direct detection case, the maximum number of amplifiers that can be used before a given power penalty is reached, is directly proportional to the amplifier input power and very large number of am- plifiers can be cascaded without excessive power penal- ties. For example, with an 'electrical bandwidth of 50 MHz, and an amplifier input power of -30 dBm, 250 amplifiers can be used with a penalty of about 2 dB. In

DIRECT DETECTION Be=520 MHz B 0 = 3 A

1000 10000 10 100 NUMBER OF AMPLIFIERS

Fig. 11. Direct detection receiver sensitivity versus number of in-line am- plifiers. Plotted for amplifier input powers of -30, -20, and - 10 dBm. B, = 500 MHz, 7," = 1, N,, = 1.4, G = 25 dB, E,, = 3 A, r = 100, and X = 1.32 pm.

-16 DIRECT OETECTION

Be = 2500 MHz; Bo= 3006

1 10 100 1000

NUMBER OF AMPLIFIERS

Fig. 12. Direct detection receiver sensitivity versus number of in-line am- plifiers. Plotted for amplifier input powers of -30, -20, and - 10 dBm. E, = 2500 MHz, 7,. = 1, N,, = 1.4, G = 25 dB, E,, = 300 A, r = 100, and X = 1.32 pm.

'" L COHERENT DETECTION I -30 dBm

10 too 1000 -53

NUMBER OF AMPLIFIERS

Fig. 13. Coherent ASK detection receiver sensitivity versus number of in- line amplifiers. Plotted for amplifier input powers of -40 dBm, -30 dBm, and -20 dBm. G = 25 dB, E , = 300 A, N,, = 1.4, 7," = 1, and E, = 500 MHz.

all the above calculations, we assumed an amplifier gain of 25 dB per stage. The results, however, as shown in Figs. 11-14 are independent of the amplifier gain as long as one makes no distinction between G and G - 1.

A rough estimate of the maximum number of amplifiers can be made from the condition that amplifiers can be added as long as the amplifier noise is less than the dom- inant noise term of the receiver. For a direct detection receiver, the dominant noise term is the thermal noise and the amplifier added noise comes from the spontaneous- spontaneous beat noise for large optical bandwidths and from the signal-spontaneous beat noise for narrow optical bandwidths. In the first case the requirement becomes

Nth > (NmaxNsp GeLfBe2Bo (15)

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1076 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 7 . NO. 7, JULY 1989

-54 , I

t COHERENT DETECTION 1 B, = 50 MHz

10 100 1000 1oooo NUMBER OF AMPLIFIERS

Fig. 14. Same as Fig. 13 except B, = 50 MHz.

where L is the loss between the last amplifier and the re- ceiver. By using

where P,,,, is the sensitivity of the receiver, (15) can be written:

( 1 7 ) Pin

17N,&v a where we have used the fact that the signal to noise ratio at BER is - 144. For Be = 2500 MHz, Bo = 300 A, P i n = - 2 0 dBm, and Nsp = 1 . 4 , (17) gives N,,, = 33 in good agreement with the exact calculation of Fig.

Nmax =

TABLE I1 MAXIMUM NUMBER OF CASCADABLE AMPLIFIER

SYSTEM

-30

1 GBit/s DIRECT

5 GBit/s DIRECT - 30

SATURATION LIMIT G=35 dB 70 I I

where Psa, is the saturation output power. Typically, P,,, = +7 dBm, hence the maximum input power to a 25-dB gain amplifier is - 18 dBm. In an amplifier chain were the spontaneous emission adds from stage to stage, the total accumulated spontaneous emission will eventually be suf- ficiently strong to saturate the amplifiers. If we require that the amplified spontaneous emission from the last am- plifier should be less than the saturation output power, the maximum number of amplifiers is limited by:

12. When a narrow optical filter is used, the main ampli- fier added noise is the signal-spontaneous beat noise. In this case the condition on N,,, can be written:

For P,,, = 7 dBm, Bo = 300 A, Nsp = 1 . 4 , and G = 25 dB, (22 ) gives Nm,x = 20 which is far restrictive than that calculated from noise considerations in Fin. 12. -

Nmax < Pin / ( 576BehvNso ) ( 1 8 ) Thus, the main impetus for restricting the optical band- width in an amplifier chain system is not for noise reduc- tion but rather for preventing the accumulated sponta- neous emission from saturating the amplifiers. In Table 11. we have summarized the above discussion and show

a Nmax = 40 for Be = 2500 MHz' = -20 between these two dBm' and N s P = l e 4 ' The

cases occurs when

Bo = Pin/(2"snhu) (19) the maximum number of amplifiers that can be cascaded for different systems. The results are shown for 3 different optical bandwidths and 2 input powers to the amplifiers. For the direct detection systems, we allowed a 1-dB sys- tem penalty, and for the coherent systems a 2-dB penalty.

giving Bo = 45 A for N =50 and P I , = - 2 0 dBm. For coherent detection, finally, the dominant receiver noise is the local oscillator shotnoise and the amplifier added noise is the local oscillator-spontaneous beat noise. In this case the restriction on Nmax is:

Nmax < Pin/(2PsensNsp) ( 2 0 ) which for an input power power of -20 dBm and a sen- sitivity of - 5 2 . 8 dBm gives a N,,, of the order 600.

It is clear from the above analysis that very large num- bers of amplifiers can be cascaded without prohibitive noise penalties. In most cases, in real systems, the limi- tations will not come from amplifier noise but from other considerations. In long-haul systems, for example, dis- persion will accumulate and eventually give rise to the need for a regenerator. In this case, the maximum number of amplifiers will be determined by the spectral purity of the transmitter laser and the dispersion of the fiber.

As we have seen in the preceding analysis, the number of amplifiers is directly proportional to the amplifier input power. The input power, however, can not be made ar- bitrarily large. When the amplifier output power becomes large, the gain saturates. This restrains the amplifier input power to:

Pout = Gpin Psat ( 2 1 )

ULTIMATE CAPACITY OF MULTICHANNEL MULTIAMPLIFIER SYSTEM

Here we will make a rough estimate of the ultimate ca- pacity of a system with multiple amplifiers and multiple channels. As a measure of the capacity we will use the product: N,,,GMB,, i.e., the product of the number of amplifiers multiplied by the gain for each amplifier times the number of channels times the bandwidth of each chan- nel. We will assume that the channel spacing is 10 times the bandwidth of each channel. This rather conservative requirement will minimize crosstalk penalties. Thus using ( 2 2 ) with Bo = 10 MB, from the spontaneous emission overloading restriction we obtain:

NmaxB,MG < P, , , / ( lOhvN, , ) - 2 . 8 ( 2 3 )

If we use the noise limitations on a coherent system in ( 2 0 ) and require that MPin G < P,,, , and that the sensitiv- ity is 60 photondbit (PsenS = 6 0 h v B , / 2 ) , we get

NmaxB,MG < P s a t / ( 6 0 h v B S p ) - 0.5 * ( 2 4 )

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OLSSON: LIGHTWAVE SYSTEMS WITH OPTICAL AMPLIFIERS 1077

For the signal-spontaneous beat noise limited case, we get from (18)

Finally, using (17) for a direct detection system in the spontaneous-spontaneous beat noise limit and using P, ,GM = Psa t , and Bo = 10 B, we get:

(26) The gain-bandwidth product (GBP) of the amplifier chain is given by:

N,,,,,B,MG < Ps,,/(54hvNSp) - 0.5 *

GBP = MBeGNnl". (27) Taking the restrictions (23)-(26) into account, the GBP

is maximum for G = 2.71 ( = e ) [18]. This is an imprac- tically low gain and a multiamplifier system is likely to be suboptimum with respect to the GBP. In Fig. 15 we show the ultimate GBP that can be achieved, plotted ver- sus the gain for each amplifier stage. As can be seen in Fig. 15, the achievable GBP is very large. For a single channel system with 1-GHz bandwidth, the maximum GBP is - 1OSooo Hz for an amplifier gain of 2.72. With a more realistic gain of 25 dB, the GBP is still an impres- sive lo4'' Hz. The main conclusion from this hand wav- ing exercise is that the capacity is directly proportional to P s a t / N s p , which is the true figure of merit for an optical amplifier.

EXPERIMENTAL Device Characteristics

The key device parameters for a traveling wave ampli- fier are: the facet reflectivity, the spontaneous emission factor, and the saturation output power. Below we will give experimental data on these parameters on amplifiers made in our laboratory. Although data is presented only for a 1.5-pm amplifier, virtually identical results have been obtained for 1.3-pm devices.

The amplifiers were fabricated from channel substrate buried heterostructure lasers having cavity lengths of 500 pm. The long cavity length, about twice that of a laser, reduces the wavelength shift of the gain peak after AR coating and increases the maximum gain that can be achieved. The AR coatings were applied by thermal evap- oration of S i0 in an oxygen atmosphere. The partial pres- sure of the oxygen was adjusted to give the optimum in- dex of refraction of the coatings 1191. The film thickness was controlled by in situ monitoring of the light output from the laser being coated [20]. Before AR coating, the devices had typical threshold currents of 17 mA. The spontaneous emission spectrum (TE) at 1 00-mA drive current is shown in Fig. 16. At 1.51-pm wavelength, the peak gain is 29.8 dB. As can be seen in Fig. 16, the re- flectivity, as judged from the Fabry-Perot ripple in the spontaneous emission, has a minimum around 1.54 pm where the ripple vanishes. The actual facet reflectivity was obtained by measuring the resonant and antiresonant gain across the gain curve. From this measurement the geo-

0 10 20 30 AMPLIFIER GAIN

Fig. 15. Gain bandwidth product of in-line amplifier system. Plotted ver- sus optical gain per stage.

WAVELENGTH (,urn)

Fig. 16. TE spontaneous emission spectrum at 100-mA drive current. The peak gain at 1.51 pm is 29.8 dB.

metric mean of the two facet reflectivities R = JR, R2 can be obtained as:

Gmax - Gmin 4Gmax Gmin

R =

where G,,, and Gmi, are the resonant and antiresonant gain, respectively. The result is shown in Fig. 17. At the reflectivity minimum at 1.54 pm, the gain ripple is less than the experimental uncertainty 0.2 dB and the reflec- tivity is less than 3 IOp5 . This is about one order of magnitude less than the best previously published results for the average reflectivity [5]. The spectral region over which the reflectivity is less than 1 * is about 300 A.

Next, the saturation output power was obtained from a measurement of the gain versus amplifier output power. At 1.52-pm wavelength and a gain of 31 dB, the 3-dB saturation output power is +6.5 dBm in the close agree- ment with previously published results [3], 151.

The spontaneous emission coefficient depends on the relative position of the operating wavelength with respect to the gain peak [6]. Here, the spontaneous emission fac- tor was measured using a heterodyne method in which the amplifier output is heterodyned with a local oscillator 1211. The result of this measurement is shown in Fig. 18 show- ing the measured Nsp as function of wavelength at a drive current of 80 mA. At this current, the peak gain at 1.52 pm was 28 dB. The spontaneous emission factor de- creases with increasing wavelength and reaches a mini- mum value of 1.4 at a wavelength 300 A shorter than the gain peak. At 1.51 pm, Nsp is almost 2 times higher or 2.5. This measurement show that, for noise considera- tions, the longer wavelength side of the amplifier spec-

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1078 JOURNAL OF LIGHTWAVE TECHNOLOGY. VOL. 7, NO. 7. JULY 1989

a 1 1 , 1 1 1 1 1 1

1 5 152 1 5 4 1 5 6

WAVELENGTH (pm I

Fig. 17. Measured average facet reflectivity for amplifier in Fig. 16.

FRONT END OUTPUl 9‘” FIBER

Fig. 19. Experimental setup for optical preamplifier receiver. Optical iso- lators are inserted both before the amplifier and in between the amplifier and the grating filter.

L I ’ ’ I I 1 4 9 151 1 5 3 1 5 5

WAVELENGTH ( p m )

Fig. 18. Wavelength dependence of spontaneous emission factor for an 1.55-pm amplifier (same device as Figs. 16 and 17).

trum is preferable. This is especially important in pre- amplifier applications, were the achievable receiver sen- sitivity is directly proportional to N s p .

SYSTEM APPLICATIONS The two main applications for optical amplifiers in ligh-

twave communication systems are as in-line amplifiers and as receiver pre-amplifiers. In in-line applications, the am- plifier operates as a simple repeater providing gain to in- crease the allowable loss between the transmitter and re- ceiver. When operating as a preamplifier, the optical am- plifier boosts the optical signal immediately before the photo detector thereby increasing the receiver sensitivity.

4-Gbitls Optical Preamplzjier At 1.5-pm wavelength, optical preamplifiers have been

demonstrated both at 500 Mbit/s 181, 2 Gbit/s 171, and up to 4 Gbit/s 1221. Noise measurements have also been made on a 10-GHz receiver [9]. Optical preamplifiers are at advantage mainly at very high data-rates where the gain bandwidth product of APD detectors is a limiting factor. Therefore, the preamplifier was evaluated at the fairly high data-rate of 4 Gbit/s to demonstrate its potential ad- vantage over APD receivers.

The experimental setup is shown in Fig. 19. The am- plifier chip had the reflectivity and noise characteristics as shown in Figs. 17 and 18. Optical isolators were inserted both before and after the amplifier for more stable oper- ation and a grating provided optical filtering. The input an output coupling efficiencies were 0.31 and 0.26, re- spectively. The net fiber-to-fiber gain was 14.2 dB at the 1.55-pm operating wavelength and the optical filter band-

1E-10

1E-11

1E-12 - 37 -35 -33 -31

RECEIVED POWER ( dBm )

Fig. 20. BER curve for optical preamplifier receiver at 4 Gbit/s using a 2’’ - 1 NRZ pseudorandom word. “Received power” is the average optical power in the input fiber.

width was 10 A. The source laser was a DFB laser di- rectly modulated with a 215 - 1 NRZ bit stream at 4 Gbit/s. The receiver had a p-i-n detector and a high impedance ( 5 kQ) front end and the sensitivity without the optical pre-amplifier was -25 dBm at 4 Gbit/s [23].

The BER characteristics for the receiver with the opti- cal pre-amplifier is shown in Fig. 20. The received power in Fig. 20 refers to the power in the input fiber to the pre- amplifier. With the optical preamplifier, the receiver sen- sitivity is -34.3 dBm which is about a factor of two bet- ter than the best published APD receiver results at the same data-rate [24]. It is also interesting to note that the best (and only) published coherent receiver sensitivity at 4 Gbit/s is -31.3 dBm, again substantially worse than the sensitivity of the optical preamplifier receiver pre- sented here [25].

The optical preamplifier was operated at a wavelength 400 A longer than the gain maximum. As discussed above, this is advantageous because of the substantially lower noise figure at longer wavelengths. For this particular am- plifier, the noise figure was about 3 dB lower at the op- erating point at 1.55 pm than at the 1.5 1-pm gain maxi- mum.

Using the known device and system parameters, the calculated receiver sensitivity is -35.2 dBm (see Fig. 2). The discrepancy between theory and experiments is be- lieved to be due to intersymbol interference (ISI) from both the modulation characteristics of the laser and from

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OLSSON: LIGHTWAVE SYSTEMS WITH OPTICAL AMPLIFIERS 1079 I

~~

Fig. 21. Experimental setup for long-haul transmission experiment using four in-line amplifiers. SCBR = silicon chip Bragg reflector transmitter laser. I S 0 = optical isolator, PC = polarization controller, ECL = ex- ternal cavity laser, AMP = electrical amplifier, DBX = double balanced mixer, and LPF = low pass filter.

the nonperfect frequency response of the receiver elec- tronics. IS1 effects, which are increasingly important at higher data-rates, have not been accounted for in the the- ory.

In-Line Amplijiers with Coherent Detection As an example of an in-line amplifier application, we

will describe a recent coherent long haul system experi- ment [ 131. In this experiment, four optical amplifiers were used and spaced about 65 km in the transmission path. The detailed experimental setup is shown in Fig. 21. The system operated at 400 Mbit/s and used coherent detec- tion with a frequency shift keying modulation format. Op- tical isolators were inserted in between all amplifiers. These isolators eliminate cross-interaction between the amplifiers and improve the stability of the system. Both the isolators and the optical amplifiers are sensitive to the input polarization of the light; and the polarization was adjusted before each amplifier stage by means of manual fiber polarization controllers.

The amplifiers used in this experiment were of the near traveling wave type with facet reflectivities of the order 5

lop3. The total gain of the four amplifiers was 500 000 000 or 87 dB. However, because of coupling losses, the net useful gain as 50 000 or 47 dB. Despite the heavy coupling losses, the amplifiers provided enough net gain to compensate for the loss in 200 km of fiber, extending the total transmission distance to 372 km, the longest nonregenerated transmission distance for any fiber communication system. The power budget for this system experiment is given in Table 111. Fig. 22 shows the vari- ation of the optical signal power along the fiber path. In between the amplifiers, the signal power drops exponen- tially with distance (linear in decibels) with a slope given by the fiber loss. At each amplifier site, the power is boosted an amount equal to the net gain of the amplifier. A baseline system performance was established by mea- suring the BER characteristics with only a short length of fiber and no optical amplifiers. This meaurement is shown in Fig. 23 as curve A , and gives a receiver sensitivity of -50.0 dBm. With the full length of fiber (372 km) and with the four amplifiers, the receiver sensitivity is -48.5 dBm as shown by curve in Fig. 23. Hence, the penalty is

100 200 300 4 0 0

DISTANCE (km)

Fig. 22. Optical signal level along the 372-km fiber length in the trans- mission experiment shown in Fig. 2 1 .

1 E - I l l I I I I

RECEIVED POWER (dBm)

- 5 4 -52 -50 - 4 8 - 4 6 -

Fig. 23. BER characteristics for 372 km, four in-line amplifier transmis- sion experiment. Curve A is the baseline curve without optical amplifiers and with a short section of fiber; curve B , for the full system.

TABLE Ill POWER BUDGET FOR 372 K M , 4 AMPLIFIER TRANSMISSION EXPERIMENT

Launched Power -2.6 dBm Fiber Loss 83.9 dB Amplifier Gain 87.6 dB

Insertion and Isolator Losses 44.0 dB

LO Inscnion Loss 4.7 dB Receiver Scnsilivity -50.0 dBm Penalty 1.5 dB Margin 0.9 dB

only 1.5 dB and the BER decreases monotonically with increased power without any evidence of an error floor.

Although we used coherent detection in this experi- ment, direct detection can also be used. For example, the same four amplifiers described above were successfully used in a 313-km 1-Gbit/s direct detection system [14].

CONCLUSIONS We are now at the point where systems with optical

amplifiers clearly out-perform traditional systems in terms

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1080 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 7. NO. I. JULY 1989 \

of transmission distance and allowable line loss. For ex- ample, previously, the longest transmission distance for direct detection around 1 Gbit/s was 171 km, substan- E ( t ) = cos (wC,t> + C

the total electric field at the output of the amplifier is M

tially shorter than the 313 km discussed above. And, as k = - M

we have seen, at high data-rates, receivers with optical pre-amplifiers are considerably more sensitive than both coherent and APD receivers. Although the outlook for op- tical amplifiers seems bright, it is not without problems. One of the major tasks in the near future is to design and fabricate an optical amplifier that is polarization indepen- dent. Today's amplifiers have several decibels difference in gain for TE and TM polarized light. Both the facet re- flectivity and internal gain is polarization dependent. Progress has been made in addressing these problems, but no truly polarization independent amplifier has been re- ported yet. A second potential problem is associated with possible crosstalk in amplifiers. A major advantage of an optical amplifier is that it is a multichannel device; i.e., an amplifier can simultaneously and independently am- plify several channels in the same device. However, the simultaneous presence of several channels gives rise to the possibility of crosstalk between the channels. Of par- ticular concern is crosstalk caused by gain saturation [26]- [28] and four-wave mixing [29]-[31]. These effects will not prevent multichannel operation; however, they may put additional restraints on the channel spacing and max- imum output power from the amplifiers. Additional re- search is required to clarify these concerns.

COS ( ( U o + 2ak6v)t + Q k ) . (A4)

The photocurrent i ( t ) generated by a unity quantum ef- ficiency photodetector is proporational to the intensity:

i ( t > = E 2 ( t ) 5 (A51 hv

where the bar indicates time averaging over optical fre- quencies. Hence

M e 4e i ( t ) = GP~, + - C JGp,N,Gv

hv k = - M

. [ k = 5 -M cos ( ( w o + 2ak6v) + + k )

The three terms in (A6) represent, signal, signal-spon- taneous beat noise, and spontaneous-spontaneous beat noise, respectively.

Signal-Spontaneous Beat Noise Examining the signal-spontaneous beat noise term first:

M

APPENDIX A DERIVATION OF THE SIGNAL-SPONTANEOUS AND

THE OUTPUT OF A N OPTICAL AMPLIFIER

i spSp(r ) = 4" hU k = c - M JGP,N,GV SPONTANEOUS-SPONTANEOUS BEAT NOISE TERMS AT * COS (wJ) COS ( ( U o + 2rk6v)t -k + k )

M 2e = - JGp,N,Gv C COS (2ak6vt + + k ) This derivation of the amplifier noise is based on a talk hv k = - M

given by P. S . Henry, who pointed out some inconsis- tencies in the literature and derived the correct results.

For simplicity 7 we assume an optical amplifier with unity CouPling efficiency, uniform gain G, Over an optical bandwidth B o , and an input Power of P i n at optical fie- quency w, centered in the optical passband Bo.

The spontaneous emission power in the optical band- width B, is given by:

where terms - cos (2w,t) which average to zero have been neglected. For each frequency, 2ak6v, in (A7), the sum has two components but with a random phase. Therefore, the power spectrum of iS-,,(r) is uniform in the fre- quency interval 0 - Bo/2 and has a density of:

P,, = Ns,(G - l)hvB,.

(A81 Writing the electric field ESP, representing the sponta- neous emission as a sum of cosine terms:

4e2 hv

= - P,,N,,(G - 1)G.

Spontaneous-Spontaneous Beat Noise From (A6) we have

cos (U, + 2ak6v)t + +Pk) M

cos ((U(, + 2ak6v)t + + k ) (A2)

where +k is a random phase for each component of spon- taneous emission. With M

= 2Nok [ c cos ( P k ) cos ( P I ) ] hv k = - M J = - M Bo 26v 649)

N,,(G - 1)hv = Noand- = M (A3)

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OLSSON: LIGHTWAVE SYSTEMS WITH OPTICAL AMPLIFIERS 1081

Fig. 24. Electrical noise power spectrum of spontaneous-spontaneous (tri- angular), signal-spontaneous (rectangular) beat noise, and dc sponta- neous emission power.

Equation (A9) can be written:

The terms - cos ( Pk + P ) have frequencies - 2w, and average to zero. Rewriting (A1 1 ) gives:

2M 2M

hV k = - O ; = O c c i s p - s p ( 4 = -

N , 6ve

. COS ( ( k - j ) 2 ~ 6 v t + 9, - +;). ( A 1 2 ) The dc term is obtained for k = j and there are 2M such

terms:

e hv Zti = - N06v2M = N s p ( G - l)eB, ( A 1 3 )

Organizing the terms in ( A 1 2 ) according to their fre- quencies we get:

frequency # terms

- ( 2 M - 1)6v 1

- 16v 2M - 1

- 16v 2M - 1 16v 2M - 1

16v 2M - 1

( 2 M - 1 ) 6 v 1 . The terms with same absolute frequency but of opposite

sign add in uhase. Therefore. the Dower sDectrum of the

spontaneous-spontaneous beat noise extends from 0 to B,, with a trianguiar shape and a power density near dc of

2 22N’6ve2 (fi - - 1 ) = 2 N t p ( G - 1 ) e2B,. hv2 2 N s p - s p =

In Fig. 24 we summarize the results of ( A 8 ) , ( A 1 3 ) , and (A14) and show the electrical power spectrum of the beat noise.

ACKNOWLEDGMENT It is the author’s pleasure to thank P. S. Henry for sev-

eral illuminating discussions of optical amplifier noise, and especially for the material in Appendix A .

REFERENCES [ l ] Y. Yamamoto, “Characteristics of AlGaAs Fabry-Perot cavity type

laser amplifiers,” IEEE J . Quantum Electron.. vol. QE-16, no. IO ,

121 T. Mukai, Y. Yamamoto, and T. Kimura, “ S I N and error rate per- formance in AlGaAs semiconductor laser preamplifier and linear re- peater systems,” IEEE Trans. Microwave Theory Tech., vol. MIT- 30, no. 10, pp. 1548-1554, 1982.

[3] T . Saitoh and T. Mukai, “1.5-pm GaInAs traveling-wave semicon- ductor laser amplifier,” IEEE J . Quantum Electron., vol. QE-23, no.

[4] G. Eisentein and R. M. Jopson, “Measurements of the gain spectrum of near traveling-wave and Fabry-Perot semiconductor optical am- plifiers at 1.5 prn,” Int. J . Electron., vol. 60, no. I , pp. 113-121, 1986.

[5] J. C . Simon, “GaInAsP semiconductor laser amplifiers for single mode fiber communications,” J . Lightwave Technol. , vol. LT-5, no.

161 M. G. Oberg and N. A. Olsson, “Wavelength dependence of the noise figure of a traveling wave InGaAsP/InP laser amplifier,” Electron. Let t . , vol. 24, pp. 99-100, 1988.

[7] M. J . O’Mahony, I. W. Marshall, H. J . Westlake, and W. G. Stal- lard, “Wide-band l .5-pm optical receiver using traveling wave laser amplifier,” Electron. Lett . , pp. 1238-1240, 1986.

[8] N. A. Olsson and P. Garbinski, “High-sensitivity direct detection receiver with a 1.5-pm optical preamplifier.” Electron, Let t . , vol. 23, pp. 11 14-1 115, 1986.

191 I. W. Marshall and M. J. O’Mahony, “ IO-GHz optical receiver using a traveling wave semiconductor laser amplifier,” Electron. Lett., vol.

[ lo] I. W. Marshall, M. J. O’Mahony, and P. Constantine, “Optical sys- tem with two packaged 1.5 pm optical amplifiers,” Electron. Lett., vol. 22, no. 5 , pp. 253-254, 1986.

[ I I] M. J. O’Mahony, I . W. Marshall, H. J. Westlake, W. J. Devlin. and J. C. Regnault, “A 200-km 1.5-pm optical transmission experiment using a semiconductor laser amplifier repeater,” presented at OFC’86. Atlanta GA, 1986, pap. WE5.

[I21 N. A. Olsson, “ASK receiver sensitivity measurements with two in- line optical amplifiers,” Electron. Let t . , vol. 21, pp. 1086-1087, 1985.

[ 131 N. A. Olsson, M. G. Oberg, L. A. Koszi, and G. J . Przybylek. “400- Mbit/s coherent transmission experiment using in-line optical ampli- fiers,” Electron. Let t . , vol. 24, pp. 36-37, 1988.

[I41 M. G. Oberg, N. A. Olsson, L. A. Koszi. a n d G . J . Przybylek. “313- km transmission experiment at I Gbit/s using optical amplifiers and a low chirp laser,” Elecrron. Lett., vol. 23, pp. 38-39. 1988.

[ 151 J. C. Simon, “Semiconductor laser amplifier for single-mode optical fiber communications,” J . Optical Commun., vol. 4. no. 2 , pp. 51- 62, 1983.

[16] R. G. Smith and S. Personick, “Semiconductor devices for optical communication,” in Topics in Applied Physics, vol. 39. New York: Springer-Verlag, 1982.

[17] D. M. Fye, “Practical limitations on optical amplifier performance,” J . Lightwave Technol., vol. LT-2, no. 4 , pp. 403-406, 1984.

[IS] P. S . Henry, “A lightwave primer,” lEEE J . Quantum Electron.. vol. OE-21. no. 12. DD. 1862-1879. 1985.

pp. 1047-1052, 1980.

6 , pp. 1010-1020, 1987.

9, pp. 1286-1295, 1987.

24, pp. 1052-1053, 1987.

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Orleans, LA, 1988, post deadline pap. [26] G. Grosskopf, R. Ludwig, and H. G. Weber, “Crosstalk in optical

amplifiers for two channel transmission,” Electron. Lett . , vol. 22,

[27] G. Eisenstein, K. L. Hall, R. M. Jopson, G. Raybon, and M. S . Whalen, “Two color gain saturation in an InGaAsP near travelling wave amplifier,” presented at OFC/IOOC’87, 1987, pap. THC4.

1281 M. G. Oberg and N. A. Olsson, “Crosstalk between intensity mod- ulated wavelength division multiplexed signal in a semiconductor laser amplifier,” IEEE J . Quantum Electron., vol. QE-24, pp. 52-59, 1988.

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T . Saitoh, T . Mukai, and 0. Mikami, “Theoretical analysis and fab- rication of antireflection coatings on laser diode facets,” J . Lightwave Techno/., vol. LT-3, pp. 288-293, 1985. N. A. Olsson, Ph.D. thesis, Cornell University, Ithaca, NY, 1982. N. A. Olsson, “Heterodyne gain and noise measurements of a 1.5- pm resonant semiconductor laser amplifier,” IEEE J. Quantum Elec- tron., vol. QE-22, pp. 671-676, 1986. N . A. Olsson, M. G. Oberg, L. D. Tzeng, and T. Cella, “Ultra-low reflectivity I .5-fim semiconductor laser pre-amplifier,” Electron. Lett., vol. 24, pp. 569-570, 1988. L. D. Tzeng and R. E. Frahm, “A wide bandwidth low-noise p-i-n- FET receiver for high bit-rate optical pre-amplifier applications,” Electron Lett . , vol. 24, pp. 1132-1 134, 1988. B. L. Kaspar, private communication. K. Iwashita and N . Takachio, “4 Gbit/s CPFSK transmission exper- iment through 155 km single mode fiber,” presented at OFC’88. New

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 7. NO. 7, JULY 1989

[29] T. E. Darcie, R. M. Jopson, and R. W. Tkach, “Intermodulation distorsion in optical amplifiers from carrier density modulation,” Electron. Lett . , vol. 23, pp. 1392-1394, 1987.

[30] G. P. Agrawal, “Four wave mixing and phase conjugation in semi- conductor laser media,” Opt. Lett . , vol. 12, pp. 260-262, 1987.

1311 R. M. Jopson, T . E. Darcie, K. T . Gayliard, R. T. Ku, R. E. Tench, N. A. Olsson, and T. C. Rice, “Measurement of carrier density me- diated intermodulation distorsion in an optical amplifier,” Electron. Lett . , vol. 23, pp. 1394-1395, 1987.

* N. Anders Olsson was born in Solleftea, Sweden, on April 13, 1952. He received the “Civilingen- jorsexamen” degree in engineering physics from Chalmers University of Technology, Gothenburg, Sweden, in 1975, and the M.Eng. and Ph.D. de- gree in electrical engineering from Cornell Uni- versity, Ithaca, NY, in 1979 and 1982, respec- tively.

Between 1975 and 1977 he was with Schlum- berger Oveseas SA, Singapore, as Field Engineer assigned to the Far East Asian region. After six

months as a Post-Doctoral Research Associate at Cornell University, he joined Bell Laboratories in 1982. His research interests include semicon- ductor lasers for optical communication, especially single-frequency sources and optical amplifiers.