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Effects of stray reflections on the performance of semiconductor laser amplifiers as in-line optical repeaters
Effects of stray reflections on the performance of semiconductor laser amplifiers as in-line optical repeaters C. Y. J. CHU,
H. GHAFOURI-SHIRAZ
The effects of stray reflections from the ends of optical fibres on the gain and spontaneous emission of a semiconductor laser amplifier have been analysed. The transfer matrix method (TMM) has been applied to give efficient solutions to the problem. The theoretical results show that these stray reflections can seriously deteriorate the performance of a single amplifier and can degrade the overall performance of a system incorporating a cascaded chain of’amplifiers as in-line repeaters. KEYWORDS:
stray reflections,
optical fibres, laser amplifiers
Introduction Semiconductor laser amplifiers (SLAs) have been considered as promising devices to be used as non-regenerative in-line repeaters for long-haul optical communication links to combat attenuation losses accumulated along the optical fibres’. To improve the performance of the SLA, it is necessary to reduce its end-facet reflectivities by using anti-reflection (AR) coatings’. This suppresses the Fabry-Perot (FP) cavity resonances along the amplifier gain spectrum and enhances the bandwidth of the amplifier that is required for implementing the multichannel coherent transmission systems3. SLAs with AR coated facets, known as travelling-wave amplifiers (TWAs), have already been successfully fabricated4 to operate in the wavelength region of around 1.5 pm where optical fibres have low attenuation losses. The wide acceptance of SLAs in practical systems as in-line repeaters has been hindered by the need for coupling between the input and output facets of the device with optical fibres (Fig. l(a)). Moreover, the differences between the refractive index at the fibre-air interface and the air-facet interface will create reflections at these interfaces. The reflection coefficient at the fibre-air interface is relatively small (around 4%-see Ref. 5) compared with that for an uncoated air-facet interface. However, as mentioned above, The authors are in the School of Electronic and Electrical Engineering, The University of Birmingham, Edgbaston, Birmingham 815 2TT, UK. Received 6 January 1994.
0030-3992/94/06/0403-05 Optics & Laser Technology Vol26 No 6 1994
SLAs are usually coated with AR coatings to minimize the reflections of the air-facet interface so that their performances can be improved. In this case, the stray reflections from the fibre-ajr interface will become important’. The stray reflejctions have been experimentally demonstrated to be significant in affecting the performance of fibre-amplifiers in an intensity-modulated (IM) spstem6. Although it is expected that the performance of SLAs will be affected by these stray reflections, to the authors’ knowledge there has not been any systematic study reported in the literature regarding this problem. In this paper, we report a theoretical analysis on the effects of stray reflections from the ends of optical fibres on the performance of SLAs. In the next section, the effects on the gain of the amplifier will be analysed. In the third section, similar analysis on the spontaneous emissions from the amplifier will be reported. Finally, the implications of these results on the system performance and design will be discussed. Effects
on amplifier
gain
Let us consider a single-stage SLA which is used within an optical fibre link as a repeater. The physical configuration for this application is shown in Fig. l(a), where the input and the output of the SLA are coupled to the optical fibres as illustrated. As discussed earlier, there are reflections at each of the facets of the SLA, and stray reflections of around 4% at the ends of optical fibres. We assume that the SLA has a buried heterostructure (BH) and hence is index guiding. This @ 1994 Butterworth-Heinemann Ltd 403
Effects of stray reflections on semiconductor laser amplifiers: C. Y.J. Chu and H. Ghafouri-Shiraz
SemiconductorLaser Amplifier
PI”
R,
R,
(a>
j
4
I
z=-L,
z=o reffl
z=o
R2
R4
!
I
z=L W
addition to absorption losses, the coupling loss between the fibre and each facet of the amplifier. Therefore, to analyse the performance of SLA subject to the effects to stray reflections, one can simply analyse the structure shown in Fig. l(c). To derive the gain and saturation characteristics of the amplifier, one has to solve the following equations which describe the interaction between the photons in the amplifier and the carriers injected by the bias current at steady state’
P
Au’
z=L-tL, y
reff2 z=L
cc>
allows us to represent the SLA as a one-dimensional device having a length L, and facet reflection coefficients of R, and R, (see Fig. l(b)). Here, for the sake of simplicity, we have represented the two ends of the optical fibres as two plane mirrors with reflection coefficients R3 and R4, respectively. The distances between the ends of the fibres from each facet of the amplifier are L, and L,, respectively. It can be seen from Fig. l(b) that each fibre end forms a Fabry-Perot (FP) cavity with the facet of the SLA. We can replace each FP cavity by an equivalent mirror of effective reflectivity ren, and rcff2respectively, as illustrated in Fig. l(c). The quantities reftl and r.rf2 can be derived as’
I
J1+ $Gd-ylL3) 1 + &C evt--hL3) JK + JGwt-y2Ld
r eff*
= 1 +
(la)
(lb)
a,(z)lS,(z)
CW
In the above equations, J is the injection current density provided by the bias current, d is the thickness of the active region, I is the optical confinement factor, N, is the group effective index of the amplifier, S,(z) is the photon density at a distance z for the mth optical mode, g,,,(z) is the material gain coefficient, p is the fraction of the spontaneous emission coupled to the signal mode’, ~1,is the loss coefficient of the active region, and c is the speed of light in free space. The term R(z) is the total carrier recombination rate, including both radiative recombinations due to spontaneous emissions R,,(z), and other non-radiative recombinations like Auger processes”. In terms of carrier density n(z), R(z) and R,,(z) are given by R(z) = &n(z) + Bn2(z) + Cn3(z)
(34
(W all =
4n - no)
(3c)
where A,,, B and C are recombination coefficients due to non-radiative recombinations with impurities and defects, radiative recombinations due to spontaneous emissions, and Auger non-radiative recombinations, respectively, and rsp is the lifetime of carriers due to spontaneous emissions. The photon density S,(z) of the mth mode has to be solved by considering the travelling-fields, F:(z), inside the amplifier*, that is
aFPi(z) ~ = ksF,f(z)P + j/LFf(z) where
y1 =
W. + al3
(14
72
W,
WI
9 = +
cL24
where k, = 2n/l is the free space wave-number with rZ being the wavelength of the light source. In (l), ai3 is the total loss between the mirror at z = -L, and the amplifier facet at z = 0, and az4 is the total loss between the mirror at z = L + L4 and the amplifier facet at z = L. Both of these parameters include, in
404
$ C Csdz)-
aZ
$Giexd--y2L4)
where
=
PR,,(z)+
B
Fig. 1 (a) Semiconductor laser amplifier used as an in-line optical repeater. (b) Configuration used to analyse the effects of stray reflections from fibre ends on the performance of a SLA. (c) The equivalent amplifier structure used in the analysis
rcff =
=
rkk - a,) + (1 - I%,
(4W
The superscripts + in (4b) represent forward and backward travelling waves, respectively, pZ is the propagation constant of the mth optical mode, and a, is the loss coefficient in the cladding. We have dropped the functional dependence of the g,, a, and a, on z for simplicity, assuming such dependence to be implicit. Equations (4) can be solved by imposing the boundary Optics & Laser Technology Vol 26 No 6 1994
Effects of stray reflections on semiconductor laser amplifiers: C. Y.J. Chu and H. Ghafoori-Shiraz
conditions given by (la) and (lb). The photon density S,(z) can then be expressed as .--s
(z)
=
cI~:(w + Im4121N,
m
ChW
(5)
with h = h/2z being the Planck constant. By substituting (5) into (2), we can compute the carrier density n(z), and hence the amplifier output power P,,, from the photon density n(z) at z = L, that is 11 ._
P, = S,(L)choWd/N,
(6) _ k= 1.5pm,L=SOOpm WV=1.5 pm, d= 0.2 pm CL= 25 cm-‘, r = 0.5 x,=x,=o.l%,Ng=3.5
i.L
where Wand d are the width and the thickness of the cavity. The gain of the amplifier G then can be calculated by
t G = P~Pi,
(7) -40
In (7) P, is the input optical power to the amplifier, which can be found from the photon density at z = 0 in (6). We have recently applied the transfer matrix method (TMM)” to solve (2a) and (2b) for an ordinary Fabry-Perot amplifier. This technique is more efficient in terms of computation because it avoids excessive iterations, whilst still taking into account of the variation of photon density along z unlike the other approximation method 12. The analysis can be further simplified when only one signal mode is considered (i.e. m = l), as in the present case. Furthermore, for analysing the SLA which is biased well below its lasing threshold, the coupling of spontaneous emissions to the signal mode can also be neglected12, and the speed of computation can be further increased under this condition by approximating /3 = 0. We have applied the TMM technique to solve (2) for the present case (Fig. l(c)), with the boundary conditions imposed by (la) and (lb). Using (6) and (7), one can calculate the variation of the amplifier gain G against the output optical power P,,,. This is shown in Fig. 2, where the parameters used in the analysis are shown in the inset with L3 = L, = 10 mm, which is the typical distance between the SLA facets and the ends of optical fibres for butt coupling. In calculations, we have assumed that both the absorption and coupling loss between the fibre and the facet is negligible (i.e. al3 = c124= 0). Two pumping levels of y = 0.63 and 0.72 are used in the calculations, where y = i/i,,, (i is the magnitude of the bias current and it,, is the threshold current of the laser structure when the stray reflections are ignored; that is, the threshold current for a solitary amplifier l2 . For comparison, the results with the same set of parameters but neglecting stray reflections (i.e. R, = R, = 0) are also shown as dashed curves in Fig. 2. For y = 0.63, it can be seen that the gain for the case of a solitary SLA (with R, = R, = 0) and that where stray reflections from optical fibre ends are Optics & Laser Technology Vol26 No 6 1994
-30
-20
-10
0
Output Optical Power (in dElm) Fig. 2 Variation of amplifier gain with output optical power for (i) R3 = R., = 0 (dashed curve) and (ii) R3 = R4 = 4% (solid curve). The distances L and &, are fixed at 10 mm
considered, are quite close; when P,,,, is less than -25 dBm. However, as the output optical power increases, the reflections from the fibre ends push the amplifier gain up, instead of reducing it, as in the solitary case (dashed curve). In fact, a peak can be seen in the curves when R, and R, are not zero. This arises because at the region around these peaks, the amplifier gain is approaching that of the lasing threshold. A similar peak is observed for the case of y = 0.72. However, it can be seen that, in this case, the unsaturated gain is lower than that in the solitary case. This is because, as we shall see later, the amplifier is already oscillating at this pumping level. It is well known that optical gain will be clamped once the laser starts to oscillate. Hence, as g is increased from 0.63 to 0.72, the gain of the laser amplifier is suppressed instead of increasing, as is the case for R, = R, = 0. To investigate the effects of increasing the pumping level on the gain performance of the SLA subject to stray reflections from fibres, we have calculated the variation of amplifier gain G with output power P,,, for the same SLA analysed in Fig. 2, but with y = 0.63, 0.72, 0.81, 0.9 and 0.99 respectively (see Fig. 3). It can be seen that all the curves exhibit the peaks described above, and the unsaturated gain reduces as y increases towards 0.99. This is contrary to the normal observation of an increase ‘n unsaturated gain as y increases in a solitary SLA 6*12.This gain compression with increasing pumping level in the SLA subject to stray reflections from fibres justifies our conclusion above that under the influence of stray reflections, the amplifier actually reaches a, lasing threshold at a much lower pumping level than that in the solitary case. As the pumping level increases beyond this new lasing threshold, the gain of the amplifier will be suppressed.
405
Effects of stray reflections
on semiconductor
laser amplifiers:
C. Y.J. Chu and H. Ghafoori-Shiraz
to analyse the problem’. Both approaches give the same result, that is
_ I_= 1,5pqL=5OOpm w= 1.5 pm, d= 0.2 pm a=25cm-‘,r =O.S - R,=R,=0.1%,Ng=3.5
X
GClr,~12 ev(gL) + 1lCl - exp(-d4 (1 - IrelIz)
(8)
where P, is the amount of spontaneous emission power generated from the SLA, Ao is the detection bandwidth, nsp is the population inversion parameter, q is the quantum efficiency of the amplifier’, g is the modal gain coefficient of the amplifier, and G is the gain of the amplifier, which can be found from the analysis discussed in the previous section.
-40
-30
-20
Output Optical
-10
We have calculated the quantity Po/(Aoho) against the pumping rate y using (5) as shown in Fig. 4. Results for both R, = R, = 0 (dash-dot curve) and R, = R, = 4% (solid curve) are shown. The output optical power is fixed to -40 dBm (i.e. the amplifier is unsaturated), and L, = L, = 10 mm. Other parameters of the SLA used for the analysis are shown in the inset of Fig. 4. Again we have neglected the absorption and coupling loss between the fibre and the laser facet. It can be seen that a sharp peak is observed for the case when the stray reflections from the ends of the optical fibres are taken into account. This corresponds to the new lasing threshold, and the pumping level is reduced from unity in the case of the solitary amplifier to about 0.62. The amount of spontaneous emission reduced rapidly once y was increased beyond this critical value. This can be explained by the fact that the amplifier gain G will reduce with increasing y once it reaches the threshold, as observed in the theoretical results in Figs 2 and 3 described in the previous section. Before the lasing threshold is reached, it can be seen that the amount of spontaneous emission is enhanced compared with that for the solitary case. Thus, if the SLA is operated in this region, the noise power emitted from the SLA due to spontaneous emissions will be enhanced under the influence of stray reflections from the ends of optical fibres. This also explains why the amplifier starts to oscillate at a much lower level of y.
0
Power (in dSm)
Fig. 3 The same as Fig. 2 for R3 = R4 = 4% and various pumping levels
Effects
on spontaneous
emissions
The spontaneous emissions from a SLA subject to the effects of stray reflections from fibre ends can be analysed using TMM, by considering the fluctuations on the fields at each point z along the SLA induced by spontaneous emissions. An analytical expression can be derived by the TMM analysis if the variation of the carrier density n with z is negligible, which is usually the case when the amplifier gain is not saturated”. Alternatively, a Green function approach can be used
L 50 5 _ ~=ls~Lm,L=5OO~m 3 -0 6 n c
W=1.5p.l&d=0.2pm
40
. -
a=25cm-*,r =O.S R, =R,=0.1%,Ng=3.5
5 a D
I i I i I ; I
Conclusions
JO -
0
Pumping
0.5 rate i&
Fig. 4 Calculated Po/(Awhw) against pumping level y = i/it,, for both R3 = R4 = 0 and R3 = R4 = 4%
406
1
We have analysed the gain and spontaneous emission power of a SLA by considering the effects of stray reflections from the ends of optical fibres using TMM. It has been shown that such reflections can push the amplifier towards oscillation at a lower value of pumping level. Before this new threshold is reached, the unsaturated gain of the amplifier is not seriously affected, although the gain characteristics deviate significantly from those in a solitary SLA, as the output optical power increases. In addition, the spontaneous emission noise generated by the amplifier is larger under the influence of stray reflections from optical fibres than in the case for a solitary amplifier. Such compression in unsaturated gain and enhanced spontaneous emission noise will degrade the signal-to-noise ratio of the signals travelling across the amplifier, and the overall performance of the system, with a cascaded chain of SLAs as in-line repeaters, will Optics & Laser Technology Vol 26 No 6 1994
Effects of stray reflections
on semiconductor
deteriorate significantly. Furthermore, in such a configuration, the enhanced spontaneous emission power generated from a SLA can be amplified by subsequent stages of amplifiers, which will saturate the entire amplifier chain at a relatively low transmitted power. In more extreme cases, undesired oscillation can result in the entire communication system6. The results shown in Figs 2 to 4 can be used by system designers to calculate the degradation in performance of the system with a cascaded chain of amplifiers due to the stray reflections from fibres. References M.J. Semiconductor laser optical amplifiers for use in future fibre systems, J Lightwave Technol, 6 (1988) 531-544 Eisenstein, G. Semiconductor optical amplifiers, IEEE Circuirs and Devices Mug July (1989) 25-30 O’Mahony,
Dietrich, E., Enning, B., Grosskopf, G., Kuller, L., Ludwig, R., Molt, R., Patzak, E., Weber, H. G. Semiconductor laser optical
amplifiers for multichannel coherence optical transmission, J Lightwave Technol, 7 (1989) 1941-1955
laser amplifiers:
C. Y.J. Chu and H. Ghafouri-Shiraz
4 Snitob, S., Mukai, T. 1.5 pm InGaAsP travelhng-wave semiconductor laser amplifier, IEEE J. Quantum Electron, 23 (1987) 101&1020 5 Ueno, Y., Shimizu, N. Optical fibre fault location method, Appl Opt, 15 (1976) 1385-1388 6 Gimktt, J.L., Igbal, M.Z., Curtis, L., Cbeung, N.K., Righetti, A., Fontana, F., Grasso, G. Impact of multiple reflection noise in
8 Gbit/s lightwave system with optical fibre amplifiers, Electron Lerr 20 (1989) 1393-1394 7 Ghafouri- Shiraz, H., Chu, C.Y.J. Chirp reduction in three-cavity semiconductor laser diodes, Opt Laser Technol, 24 (1992) 73-76 8 Marcuse, D. Computer model of an injection laser amplifier, IEEE J Quantum Electron, 19 (1983) 63-73 9 Henry, C.H. Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers, J Lightwaoe Technol, 4 (1986) 288-297 10 Olshansky, R., Su, C.B., Manning, J., Powazink, W. Measurements of radiative and non-radiative recombination rates in InGaAsP and AlGaHs light sources, IEEE J Quantum Electron 20 (1984) 838-854 11 Bjork, G., Nilsson,0. A new exact and efficient numerical matrix theory of complicated laser structures: properties of asymmetric phase-shifted DFB lasers, J Lighfwave Technol, 1 (1987) 140-146 12 Adams, M.J., Collins, J.V., Henning, I.D. Analysis of semiconductor laser optical amplifiers, IEEE Proc, Parr J, 132 (1985) 58-63
Optics & Laser Technology
Optics & Laser Technology Vol26 No 6 1994
407
H. GHAFOURI-SHIRAZ
The effects of stray reflections from the ends of optical fibres on the gain and spontaneous emission of a semiconductor laser amplifier have been analysed. The transfer matrix method (TMM) has been applied to give efficient solutions to the problem. The theoretical results show that these stray reflections can seriously deteriorate the performance of a single amplifier and can degrade the overall performance of a system incorporating a cascaded chain of’amplifiers as in-line repeaters. KEYWORDS:
stray reflections,
optical fibres, laser amplifiers
Introduction Semiconductor laser amplifiers (SLAs) have been considered as promising devices to be used as non-regenerative in-line repeaters for long-haul optical communication links to combat attenuation losses accumulated along the optical fibres’. To improve the performance of the SLA, it is necessary to reduce its end-facet reflectivities by using anti-reflection (AR) coatings’. This suppresses the Fabry-Perot (FP) cavity resonances along the amplifier gain spectrum and enhances the bandwidth of the amplifier that is required for implementing the multichannel coherent transmission systems3. SLAs with AR coated facets, known as travelling-wave amplifiers (TWAs), have already been successfully fabricated4 to operate in the wavelength region of around 1.5 pm where optical fibres have low attenuation losses. The wide acceptance of SLAs in practical systems as in-line repeaters has been hindered by the need for coupling between the input and output facets of the device with optical fibres (Fig. l(a)). Moreover, the differences between the refractive index at the fibre-air interface and the air-facet interface will create reflections at these interfaces. The reflection coefficient at the fibre-air interface is relatively small (around 4%-see Ref. 5) compared with that for an uncoated air-facet interface. However, as mentioned above, The authors are in the School of Electronic and Electrical Engineering, The University of Birmingham, Edgbaston, Birmingham 815 2TT, UK. Received 6 January 1994.
0030-3992/94/06/0403-05 Optics & Laser Technology Vol26 No 6 1994
SLAs are usually coated with AR coatings to minimize the reflections of the air-facet interface so that their performances can be improved. In this case, the stray reflections from the fibre-ajr interface will become important’. The stray reflejctions have been experimentally demonstrated to be significant in affecting the performance of fibre-amplifiers in an intensity-modulated (IM) spstem6. Although it is expected that the performance of SLAs will be affected by these stray reflections, to the authors’ knowledge there has not been any systematic study reported in the literature regarding this problem. In this paper, we report a theoretical analysis on the effects of stray reflections from the ends of optical fibres on the performance of SLAs. In the next section, the effects on the gain of the amplifier will be analysed. In the third section, similar analysis on the spontaneous emissions from the amplifier will be reported. Finally, the implications of these results on the system performance and design will be discussed. Effects
on amplifier
gain
Let us consider a single-stage SLA which is used within an optical fibre link as a repeater. The physical configuration for this application is shown in Fig. l(a), where the input and the output of the SLA are coupled to the optical fibres as illustrated. As discussed earlier, there are reflections at each of the facets of the SLA, and stray reflections of around 4% at the ends of optical fibres. We assume that the SLA has a buried heterostructure (BH) and hence is index guiding. This @ 1994 Butterworth-Heinemann Ltd 403
Effects of stray reflections on semiconductor laser amplifiers: C. Y.J. Chu and H. Ghafouri-Shiraz
SemiconductorLaser Amplifier
PI”
R,
R,
(a>
j
4
I
z=-L,
z=o reffl
z=o
R2
R4
!
I
z=L W
addition to absorption losses, the coupling loss between the fibre and each facet of the amplifier. Therefore, to analyse the performance of SLA subject to the effects to stray reflections, one can simply analyse the structure shown in Fig. l(c). To derive the gain and saturation characteristics of the amplifier, one has to solve the following equations which describe the interaction between the photons in the amplifier and the carriers injected by the bias current at steady state’
P
Au’
z=L-tL, y
reff2 z=L
cc>
allows us to represent the SLA as a one-dimensional device having a length L, and facet reflection coefficients of R, and R, (see Fig. l(b)). Here, for the sake of simplicity, we have represented the two ends of the optical fibres as two plane mirrors with reflection coefficients R3 and R4, respectively. The distances between the ends of the fibres from each facet of the amplifier are L, and L,, respectively. It can be seen from Fig. l(b) that each fibre end forms a Fabry-Perot (FP) cavity with the facet of the SLA. We can replace each FP cavity by an equivalent mirror of effective reflectivity ren, and rcff2respectively, as illustrated in Fig. l(c). The quantities reftl and r.rf2 can be derived as’
I
J1+ $Gd-ylL3) 1 + &C evt--hL3) JK + JGwt-y2Ld
r eff*
= 1 +
(la)
(lb)
a,(z)lS,(z)
CW
In the above equations, J is the injection current density provided by the bias current, d is the thickness of the active region, I is the optical confinement factor, N, is the group effective index of the amplifier, S,(z) is the photon density at a distance z for the mth optical mode, g,,,(z) is the material gain coefficient, p is the fraction of the spontaneous emission coupled to the signal mode’, ~1,is the loss coefficient of the active region, and c is the speed of light in free space. The term R(z) is the total carrier recombination rate, including both radiative recombinations due to spontaneous emissions R,,(z), and other non-radiative recombinations like Auger processes”. In terms of carrier density n(z), R(z) and R,,(z) are given by R(z) = &n(z) + Bn2(z) + Cn3(z)
(34
(W all =
4n - no)
(3c)
where A,,, B and C are recombination coefficients due to non-radiative recombinations with impurities and defects, radiative recombinations due to spontaneous emissions, and Auger non-radiative recombinations, respectively, and rsp is the lifetime of carriers due to spontaneous emissions. The photon density S,(z) of the mth mode has to be solved by considering the travelling-fields, F:(z), inside the amplifier*, that is
aFPi(z) ~ = ksF,f(z)P + j/LFf(z) where
y1 =
W. + al3
(14
72
W,
WI
9 = +
cL24
where k, = 2n/l is the free space wave-number with rZ being the wavelength of the light source. In (l), ai3 is the total loss between the mirror at z = -L, and the amplifier facet at z = 0, and az4 is the total loss between the mirror at z = L + L4 and the amplifier facet at z = L. Both of these parameters include, in
404
$ C Csdz)-
aZ
$Giexd--y2L4)
where
=
PR,,(z)+
B
Fig. 1 (a) Semiconductor laser amplifier used as an in-line optical repeater. (b) Configuration used to analyse the effects of stray reflections from fibre ends on the performance of a SLA. (c) The equivalent amplifier structure used in the analysis
rcff =
=
rkk - a,) + (1 - I%,
(4W
The superscripts + in (4b) represent forward and backward travelling waves, respectively, pZ is the propagation constant of the mth optical mode, and a, is the loss coefficient in the cladding. We have dropped the functional dependence of the g,, a, and a, on z for simplicity, assuming such dependence to be implicit. Equations (4) can be solved by imposing the boundary Optics & Laser Technology Vol 26 No 6 1994
Effects of stray reflections on semiconductor laser amplifiers: C. Y.J. Chu and H. Ghafoori-Shiraz
conditions given by (la) and (lb). The photon density S,(z) can then be expressed as .--s
(z)
=
cI~:(w + Im4121N,
m
ChW
(5)
with h = h/2z being the Planck constant. By substituting (5) into (2), we can compute the carrier density n(z), and hence the amplifier output power P,,, from the photon density n(z) at z = L, that is 11 ._
P, = S,(L)choWd/N,
(6) _ k= 1.5pm,L=SOOpm WV=1.5 pm, d= 0.2 pm CL= 25 cm-‘, r = 0.5 x,=x,=o.l%,Ng=3.5
i.L
where Wand d are the width and the thickness of the cavity. The gain of the amplifier G then can be calculated by
t G = P~Pi,
(7) -40
In (7) P, is the input optical power to the amplifier, which can be found from the photon density at z = 0 in (6). We have recently applied the transfer matrix method (TMM)” to solve (2a) and (2b) for an ordinary Fabry-Perot amplifier. This technique is more efficient in terms of computation because it avoids excessive iterations, whilst still taking into account of the variation of photon density along z unlike the other approximation method 12. The analysis can be further simplified when only one signal mode is considered (i.e. m = l), as in the present case. Furthermore, for analysing the SLA which is biased well below its lasing threshold, the coupling of spontaneous emissions to the signal mode can also be neglected12, and the speed of computation can be further increased under this condition by approximating /3 = 0. We have applied the TMM technique to solve (2) for the present case (Fig. l(c)), with the boundary conditions imposed by (la) and (lb). Using (6) and (7), one can calculate the variation of the amplifier gain G against the output optical power P,,,. This is shown in Fig. 2, where the parameters used in the analysis are shown in the inset with L3 = L, = 10 mm, which is the typical distance between the SLA facets and the ends of optical fibres for butt coupling. In calculations, we have assumed that both the absorption and coupling loss between the fibre and the facet is negligible (i.e. al3 = c124= 0). Two pumping levels of y = 0.63 and 0.72 are used in the calculations, where y = i/i,,, (i is the magnitude of the bias current and it,, is the threshold current of the laser structure when the stray reflections are ignored; that is, the threshold current for a solitary amplifier l2 . For comparison, the results with the same set of parameters but neglecting stray reflections (i.e. R, = R, = 0) are also shown as dashed curves in Fig. 2. For y = 0.63, it can be seen that the gain for the case of a solitary SLA (with R, = R, = 0) and that where stray reflections from optical fibre ends are Optics & Laser Technology Vol26 No 6 1994
-30
-20
-10
0
Output Optical Power (in dElm) Fig. 2 Variation of amplifier gain with output optical power for (i) R3 = R., = 0 (dashed curve) and (ii) R3 = R4 = 4% (solid curve). The distances L and &, are fixed at 10 mm
considered, are quite close; when P,,,, is less than -25 dBm. However, as the output optical power increases, the reflections from the fibre ends push the amplifier gain up, instead of reducing it, as in the solitary case (dashed curve). In fact, a peak can be seen in the curves when R, and R, are not zero. This arises because at the region around these peaks, the amplifier gain is approaching that of the lasing threshold. A similar peak is observed for the case of y = 0.72. However, it can be seen that, in this case, the unsaturated gain is lower than that in the solitary case. This is because, as we shall see later, the amplifier is already oscillating at this pumping level. It is well known that optical gain will be clamped once the laser starts to oscillate. Hence, as g is increased from 0.63 to 0.72, the gain of the laser amplifier is suppressed instead of increasing, as is the case for R, = R, = 0. To investigate the effects of increasing the pumping level on the gain performance of the SLA subject to stray reflections from fibres, we have calculated the variation of amplifier gain G with output power P,,, for the same SLA analysed in Fig. 2, but with y = 0.63, 0.72, 0.81, 0.9 and 0.99 respectively (see Fig. 3). It can be seen that all the curves exhibit the peaks described above, and the unsaturated gain reduces as y increases towards 0.99. This is contrary to the normal observation of an increase ‘n unsaturated gain as y increases in a solitary SLA 6*12.This gain compression with increasing pumping level in the SLA subject to stray reflections from fibres justifies our conclusion above that under the influence of stray reflections, the amplifier actually reaches a, lasing threshold at a much lower pumping level than that in the solitary case. As the pumping level increases beyond this new lasing threshold, the gain of the amplifier will be suppressed.
405
Effects of stray reflections
on semiconductor
laser amplifiers:
C. Y.J. Chu and H. Ghafoori-Shiraz
to analyse the problem’. Both approaches give the same result, that is
_ I_= 1,5pqL=5OOpm w= 1.5 pm, d= 0.2 pm a=25cm-‘,r =O.S - R,=R,=0.1%,Ng=3.5
X
GClr,~12 ev(gL) + 1lCl - exp(-d4 (1 - IrelIz)
(8)
where P, is the amount of spontaneous emission power generated from the SLA, Ao is the detection bandwidth, nsp is the population inversion parameter, q is the quantum efficiency of the amplifier’, g is the modal gain coefficient of the amplifier, and G is the gain of the amplifier, which can be found from the analysis discussed in the previous section.
-40
-30
-20
Output Optical
-10
We have calculated the quantity Po/(Aoho) against the pumping rate y using (5) as shown in Fig. 4. Results for both R, = R, = 0 (dash-dot curve) and R, = R, = 4% (solid curve) are shown. The output optical power is fixed to -40 dBm (i.e. the amplifier is unsaturated), and L, = L, = 10 mm. Other parameters of the SLA used for the analysis are shown in the inset of Fig. 4. Again we have neglected the absorption and coupling loss between the fibre and the laser facet. It can be seen that a sharp peak is observed for the case when the stray reflections from the ends of the optical fibres are taken into account. This corresponds to the new lasing threshold, and the pumping level is reduced from unity in the case of the solitary amplifier to about 0.62. The amount of spontaneous emission reduced rapidly once y was increased beyond this critical value. This can be explained by the fact that the amplifier gain G will reduce with increasing y once it reaches the threshold, as observed in the theoretical results in Figs 2 and 3 described in the previous section. Before the lasing threshold is reached, it can be seen that the amount of spontaneous emission is enhanced compared with that for the solitary case. Thus, if the SLA is operated in this region, the noise power emitted from the SLA due to spontaneous emissions will be enhanced under the influence of stray reflections from the ends of optical fibres. This also explains why the amplifier starts to oscillate at a much lower level of y.
0
Power (in dSm)
Fig. 3 The same as Fig. 2 for R3 = R4 = 4% and various pumping levels
Effects
on spontaneous
emissions
The spontaneous emissions from a SLA subject to the effects of stray reflections from fibre ends can be analysed using TMM, by considering the fluctuations on the fields at each point z along the SLA induced by spontaneous emissions. An analytical expression can be derived by the TMM analysis if the variation of the carrier density n with z is negligible, which is usually the case when the amplifier gain is not saturated”. Alternatively, a Green function approach can be used
L 50 5 _ ~=ls~Lm,L=5OO~m 3 -0 6 n c
W=1.5p.l&d=0.2pm
40
. -
a=25cm-*,r =O.S R, =R,=0.1%,Ng=3.5
5 a D
I i I i I ; I
Conclusions
JO -
0
Pumping
0.5 rate i&
Fig. 4 Calculated Po/(Awhw) against pumping level y = i/it,, for both R3 = R4 = 0 and R3 = R4 = 4%
406
1
We have analysed the gain and spontaneous emission power of a SLA by considering the effects of stray reflections from the ends of optical fibres using TMM. It has been shown that such reflections can push the amplifier towards oscillation at a lower value of pumping level. Before this new threshold is reached, the unsaturated gain of the amplifier is not seriously affected, although the gain characteristics deviate significantly from those in a solitary SLA, as the output optical power increases. In addition, the spontaneous emission noise generated by the amplifier is larger under the influence of stray reflections from optical fibres than in the case for a solitary amplifier. Such compression in unsaturated gain and enhanced spontaneous emission noise will degrade the signal-to-noise ratio of the signals travelling across the amplifier, and the overall performance of the system, with a cascaded chain of SLAs as in-line repeaters, will Optics & Laser Technology Vol 26 No 6 1994
Effects of stray reflections
on semiconductor
deteriorate significantly. Furthermore, in such a configuration, the enhanced spontaneous emission power generated from a SLA can be amplified by subsequent stages of amplifiers, which will saturate the entire amplifier chain at a relatively low transmitted power. In more extreme cases, undesired oscillation can result in the entire communication system6. The results shown in Figs 2 to 4 can be used by system designers to calculate the degradation in performance of the system with a cascaded chain of amplifiers due to the stray reflections from fibres. References M.J. Semiconductor laser optical amplifiers for use in future fibre systems, J Lightwave Technol, 6 (1988) 531-544 Eisenstein, G. Semiconductor optical amplifiers, IEEE Circuirs and Devices Mug July (1989) 25-30 O’Mahony,
Dietrich, E., Enning, B., Grosskopf, G., Kuller, L., Ludwig, R., Molt, R., Patzak, E., Weber, H. G. Semiconductor laser optical
amplifiers for multichannel coherence optical transmission, J Lightwave Technol, 7 (1989) 1941-1955
laser amplifiers:
C. Y.J. Chu and H. Ghafouri-Shiraz
4 Snitob, S., Mukai, T. 1.5 pm InGaAsP travelhng-wave semiconductor laser amplifier, IEEE J. Quantum Electron, 23 (1987) 101&1020 5 Ueno, Y., Shimizu, N. Optical fibre fault location method, Appl Opt, 15 (1976) 1385-1388 6 Gimktt, J.L., Igbal, M.Z., Curtis, L., Cbeung, N.K., Righetti, A., Fontana, F., Grasso, G. Impact of multiple reflection noise in
8 Gbit/s lightwave system with optical fibre amplifiers, Electron Lerr 20 (1989) 1393-1394 7 Ghafouri- Shiraz, H., Chu, C.Y.J. Chirp reduction in three-cavity semiconductor laser diodes, Opt Laser Technol, 24 (1992) 73-76 8 Marcuse, D. Computer model of an injection laser amplifier, IEEE J Quantum Electron, 19 (1983) 63-73 9 Henry, C.H. Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers, J Lightwaoe Technol, 4 (1986) 288-297 10 Olshansky, R., Su, C.B., Manning, J., Powazink, W. Measurements of radiative and non-radiative recombination rates in InGaAsP and AlGaHs light sources, IEEE J Quantum Electron 20 (1984) 838-854 11 Bjork, G., Nilsson,0. A new exact and efficient numerical matrix theory of complicated laser structures: properties of asymmetric phase-shifted DFB lasers, J Lighfwave Technol, 1 (1987) 140-146 12 Adams, M.J., Collins, J.V., Henning, I.D. Analysis of semiconductor laser optical amplifiers, IEEE Proc, Parr J, 132 (1985) 58-63
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