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Theory of a fibre ring laser mode-locked by cross-phase modulation
1.5January 1995
OPTICS CWMUNICATIONS ELSETIER
Optics Communications 114 (1995) 119-124
Theory of a fibre ring laser mode-locked by cross-phase modulation J-Y. Li a, G.H.C. New a, K. Smith b, M. @bra b ’ Laser Optics
and Spectroscopy Group, Department of Physics, Imperial College, London SW7 2BZ. UK
b BT Laboratories, Martlesham Heath, Ipswich IP5 7RE, UK
Received 6 July 1994
Abstract We have developed a computer model of a novel fibre ring laser, optically mode-locked by cross phase modulation. We have analysed the modulation process in detail, showing that, in the context of the earlier experiment, the nonlinear birefringence induced by cross-phase modulation gives rise to a loss modulation component. Numerical results suggest that this feature is essential if efficient mode-locking is to occur. The importance of attenuation and group delay dispersion in the modulator fibre has been demonstrated.
1. Introduction Recently, Greer and Smith [ 1 ] at BT Laboratories described a novel optically mode-locked erbium fibre ring laser designed to serve as one of the key components of an all-optical digital signal regenerator [ 21. In its ultimate application, the laser is actively modelocked by a pseudo-random data stream [ 21, but the initial demonstration was performed using a continuous stream of optical pulses from another laser to provide the periodic modulation of the laser cavity. These pulses copropagated with the ring laser pulses in a long length (8.8 km) of it&a-cavity fibre, interacting with them through the nonlinear process of cross-phase modulation (XPM). The modulation frequency was tuned to a very high multiple of the natural cavity frequency to achieve multiple FM mode-locking. In this paper, we describe a computer model of the mode-locking process. We show that the effect of XPM, in conjunction with polarisation-sensitive elements in the cavity, is to cause loss modulation as well 0030-4018/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved
XSDIOO30-4018(94)00558-3
as phase modulation. We present evidence to suggest that efficient mode-locking would not occur in the absence of this loss modulation component.
2. Computer
model
For our computer model, we adopted the same general philosophy used in several earlier mode-locked laser simulations [3]. A large complex array representing the intra-cavity field was repeatedly subjected to a sequence of operations including gain, loss, modulation, and spectral filtering; a random source term simulated spontaneous emission and potential mismatch between the modulation period and the natural frequency of the cavity was also allowed for. The processes of gain, loss and spontaneous emission are represented by the equation [ 41
Vi=Vi exp[ (G-r)/21
+Si,
(1)
where the Vi are the values of the electric field defined on a local time mesh at equally-spaced intervals of t,,
120
J-Y. Li et al. /Optics
Communications
Si is a stochastic source term, and G and rare the gain and loss coefficients. The high (millisecond) relaxation time (T,,) of Er3+ means that the gain depletion caused by the passage of each mode-locked pulse is negligible, and the pulse shape is therefore not affected in any significant way. The value of G is determined by the equation [ 71
(2)
,
where Go is the small signal gain coefficient, u is the stimulated emission cross section, and fiw is the photon energy; it is convenient to define a normalised pumping parameter P = Go/T so that P = 1 corresponds to laser threshold. The action of the spectral filter is governed by the equation [ 41 v:‘= (1 -R)V;+RV;_,
)
(3)
114 (1995) 119-124
Fig. 1. Schematic diagram of the modulator.
A schematic diagram of the fibre modulator element is shown in Fig. 1. The x-axis is defined as the polarisation direction of the modulation pulses (E,) which, through XPM, induce phase changes of & and c$? ( = C/Q/~) [6] on the laser pulses (Ec) entering the fibre linearly-polarised at p to the x-axis. Polarisation controllers (the “bat-ears” in the laboratory device) rotate the polarisation of the pulses leaving the modulator by an angle 0. Since the signal in this region of the cavity is observed to be linearly-polarised, the presence of a polariser oriented at 8 to the n-axis can legit-
where R = exp( - t,ltr) and &is the filter memory time. Modulation and cavity length mismatch are included in the equation Vy+8=mVi,
(4)
where m is the modulation factor discussed below, and 6 represents a lateral shift of the entire field array, associated with a temporal mismatch t& in the past, we have normally set 6 = 0 or f 1; here we have used linear interpolation to accommodate non-integer values of s.
3. Modulation element: theory The central feature of the problem is the action of the modulator and particularly (as we demonstrate below) that the nonlinear birefringence induced by XPM, in conjunction with polarisation-sensitive components in the ring, imposes loss as well as phase modulation. Identification of the polarisation-defining elements is not necessary (although we suggest the Faraday isolator [5] as a likely candidate), because the laser is observed to oscillate in a consistent polarisation and the orthogonal component has a demonstrably higher loss. The insertion of a polariser aligned along the preferred direction would not affect the performance of the system and its presence can therefore be assumed in the subsequent analysis.
Fig. 2. Contour plots derived from Eqs. (5)-(7) showing (a) Iml and (b) qf~( = arg[ m) ) as functions of 0 (the angle of the polariser in Fig. 1) and A (the induced phase change).
J-Y. Li et al. /Optics
Communications
114 (1995) 119-124
121
and *=tan-’
sin( f$J + sin( &,j tan( 0) tan( e+ 0)
cos( I&) +cos( &,) tan(e) tan( e+ 0)
’
(7)
Fig. 3. The effective modulation profile in the presence of group delay and attenuation. The location of the pulse under stable modelocked conditions is indicated.
imately be assumed. Bearing in mind that at the end of its circuit, the signal reenters the modulator, we can equate 8 and p without loss of generality. With these definitions, it can be shown that the net (time-dependent) transmission factor of the laser pulse is given 9 by m= Imlexp(il(/) =exp(i+z)cos0cos(8+R)exp(i+Y) Xsin0sin(8+.0),
(5)
where the loss and phase modulation characteristics, written separately, are Im]2=cos2LZ-~sin(28)sin(28+2L?) X 11 -cos(A-~~“V>l,
(6)
Careful study of Eqs. (6) and (7) indicates that desirable characteristics for a mode-locked laser are achieved when Ll= - 2t?, since this yields an optimal increase of I m I with modulating pulses intensity. This feature is clearly illustrated in Fig. 2 in which contours oflmt and $ are displayed as functions of B and (p, in this special case; here & = 34 = 2 yA,*pLI, and y, Aeff, L and I,,, are respectively the XPM coefficient [ 61, the effective fibre core area, the fibre length and the intensity of the modulation pulse; the intensity of the laser pulse itself is assumed to be too small to affect the refractive index of the modulator. Two other factors also have to be taken into account. Although the wavelengths of the co-propagating modulation and laser pulses are close to the dispersion minimum, they are nevertheless slightly different, and the accumulated group delay difference over the 8.8 km is about 50-80 ps. In addition, both pulses suffer attenuation and the decrease in the depth of modulation towards the end of the fibre is significant. The effective value of Iml when these effects are allowed for is displayed in Fig. 3. The way in which the shape of this profile is influenced by dispersion and attenuation, and the consequences this has for the performance of the laser are discussed in the next section.
3e+12
Local
Fig. 4. Typical simulation
tune
(PSI
with the loss modulation
component
of m neutralised by setting Im I =
I.
122
J-Y. Li et al. /Optics
Lvcal
time
Communications
I14 (1995) 119-124
(ps)
Fig. 5. Typical simulation including the loss modulation component of m.
4. Results of the computer model The parameter values used in the computer simulations were: cavity round-trip time T,,,=500 ps, t, = T,,,/2048, detuning factor 6= - 1.4t,, filter memory time tf= 2t,, pumping strength P = 3.5, loss r= 0.2, relaxation time T,, = 1 ms, emission cross section cr = 0.4 pm2, fibre length L = 8.8 km, and Aeff = 50 pm’, duration of the modulating pulse = 20 ps, group delay difference (di2) = - 16 ps/km, attenuation constant a=0.05 km-‘, 8= 1.8 (a= -3.6). To investigate the role of loss modulation in the development of mode-locking, simulations were performed with and without the loss modulation element in Eq. (5). In Fig. 4, where the loss modulation contribution was neutralised by setting Im I = 1, stable mode-locking does not occur, whereas in Fig. 5 where all parts of Eq. (5) were operational, stable short pulse operation is seen to be rapidly achieved. No special care was required in selecting other parameter values, and this behaviour appeared to be quite general. The key conclusion is that the loss modulation component in Eq. (5) is essential if efficient mode-locking is to be achieved. The mode-locked pulse of Fig. 5 is located at the apex of the modulation profile as indicated in Fig. 3; this is in accordance with conventional mode-locking theory [ 81 which suggests that the pulse is formed where the cavity losses are a minimum and that increasing the curvature of the modulation profile reduces the
pulsewidth. The role played by the group time delay difference d12 and the attenuation constant (Ycan now be understood. Increasing d12, which can be achieved experimentally by adjusting the wavelengths of the modulation and laser signals, widens the modulation profile but makes it shallower; decreasing d12 has the opposite effect. Perhaps surprisingly, it is possible for the modulation profile to be too deep and narrow, as this tends to quench the mode-locked pulse; on the other hand, a broad flat-topped profile is certainly not optimal for ultrashort pulse generation. In the latter case, however, the performance is enhanced by a non-zero value of (Ybecause this slants the top of the profile, creating a well-defined location for the laser pulse, as in Fig. 3. Figs. 6 and 7 highlight the importance of (Yand d12 in determining the operating characteristics of the laser. With d,, at its default value of - 16 p&m, Fig. 6 illustrates the dependence of the pulse peak intensity and pulsewidth on a; optimal performance is clearly realised when (Yis around 0.05 km- ‘. Fig. 7 shows the analogous dependence on d12 with (Yheld fixed; the figure demonstrates that when Id12 I is less than about 10 ps/km for 20 ps modulation pulses, the depth of modulation becomes too high, and the 10 ps laser pulses are quenched. 5. Modulation element: experiment As an experimental check on the theoretical predictions, we studied the behaviour of the fibre modulator
J-Y. Li et al. /Optics
123
Communications 114 (1995) 119-124
independent adjustment of the polarisation of the two waves. At the output of the fibre, the two wavelengths were separated by WDM2 and the CW 1.553 pm signal passed through the polarisation controller PC3 and the polariser P to the high-speed (25 ps) photodiode detector D. With the modulating pulses absent, PC 1 and PC3 were adjusted for 50% transmission of the CW beam. The effect of the modulating pulses on the detected CW signal is shown in Fig. 8b for four different settings (a) Intensity
3e+1’
I
1.9e+ll 0.00
,
0.02
I
,
0.04
I
,
I 0.08
0.06
:
0.10
km-’
Ze+ll
le+ll
7
Oe+oo
-20
1
i
I
t
-15
-5
-10
0
psflan (b) Pulsewidtb
(PWHM,
ps)
15s 10 0.00
I 0.02
/
I
I
0.04
I 0.06
I
I 0.08
1
_ 0 10
km-’
Fig. 6. The pulse peak intensity and FWHM as functions of the attenuation for group time delay of - 16 ps/km.
in more detail. The experimental arrangement is depicted in Fig. 8a. A stream of N 20 ps pulses at 1.538 pm (derived from an amplified gain-switched DFFS laser, as in [ 1] ) was combined with a narrow linewidth CW laser signal at 1.553 pm in the wavelength-division multiplexer WDMl, and launched together into the same 8.8 km length of modulator fibre used in the original laser experiment; the polarisation controllers PC 1 and PC2 on the input channels to WDM 1 allowed
O-20
-10
-5
0
Psb Fig. 7. The pulse peak intensity and FWHM as functions of the group time delay for an attenuation of 0.05 km- ‘.
124
J-Y. Li et al. /Optics Communications 114 (1995) 119-124
light clearly demonstrated but, as predicted by the model, the direction of polarisation rotation is clearly a function of the modulating pulse polarisation. The optical power levels used in these experiments were equivalent to those in the laser experiment.
Amplified Gain-Switched
6. Conclusion (1SUnm)
CWECL (1553nm)
(a)
Time(2OpJdiv)
04 Fig. 8. (a) Experimental configuration for the XPM polarisation measurements and (b) the output CW signal recorded on the highspeed detector D for four different settings of PC2, with PC1 and PC3 adjusted for 50% transmission through P in the absence of the modulating pulses.
of PC2 controlling their initial polarisation. Not only is the modification of the polarisation state of the CW
We have modelled the optically mode-locked laser of Greer and Smith [ 11, paying particular attention to the modulation mechanism. We have shown that the conjunction of nonlinear birefringence induced by cross-phase modulation with polarisation-sensitive components in the laser cavity gives rise to a loss modulation component that plays an essential part in the efficient mode-locking of the device. The beneficial effects of attenuation and dispersion in the modulator have been demonstrated and experimental results that support the theoretical model have been presented. References [ 1] E.J. Greer and K. Smith, Electron. Lett. 28 (1992) 1741. [2] J.K. Lucek and K. Smith, Optics Lett. 18 (1993) 1226. [3] J.M. Catherall, G.H.C. New and P.M. Radmom, Optics I&. 7 (1982) 319. [4] J.M. Catherall andG.H.C. New, IEEE J. QuantumElectron. QE22 (1986) 1593. [ 51 A.E. Siegman, Lasers (University Science Books, 1976) p. 535. [ 61 G.P. Agrawal, Nonlinear Fibre Optics (Academic, New York, 1989). [ 71 P.W. Milonni and J.H. Eberly, Lasers (Wiley, New York, 1991) . [8] G.H.C. New, Rep. Prog. Phys.46 (1983) 877.
OPTICS CWMUNICATIONS ELSETIER
Optics Communications 114 (1995) 119-124
Theory of a fibre ring laser mode-locked by cross-phase modulation J-Y. Li a, G.H.C. New a, K. Smith b, M. @bra b ’ Laser Optics
and Spectroscopy Group, Department of Physics, Imperial College, London SW7 2BZ. UK
b BT Laboratories, Martlesham Heath, Ipswich IP5 7RE, UK
Received 6 July 1994
Abstract We have developed a computer model of a novel fibre ring laser, optically mode-locked by cross phase modulation. We have analysed the modulation process in detail, showing that, in the context of the earlier experiment, the nonlinear birefringence induced by cross-phase modulation gives rise to a loss modulation component. Numerical results suggest that this feature is essential if efficient mode-locking is to occur. The importance of attenuation and group delay dispersion in the modulator fibre has been demonstrated.
1. Introduction Recently, Greer and Smith [ 1 ] at BT Laboratories described a novel optically mode-locked erbium fibre ring laser designed to serve as one of the key components of an all-optical digital signal regenerator [ 21. In its ultimate application, the laser is actively modelocked by a pseudo-random data stream [ 21, but the initial demonstration was performed using a continuous stream of optical pulses from another laser to provide the periodic modulation of the laser cavity. These pulses copropagated with the ring laser pulses in a long length (8.8 km) of it&a-cavity fibre, interacting with them through the nonlinear process of cross-phase modulation (XPM). The modulation frequency was tuned to a very high multiple of the natural cavity frequency to achieve multiple FM mode-locking. In this paper, we describe a computer model of the mode-locking process. We show that the effect of XPM, in conjunction with polarisation-sensitive elements in the cavity, is to cause loss modulation as well 0030-4018/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved
XSDIOO30-4018(94)00558-3
as phase modulation. We present evidence to suggest that efficient mode-locking would not occur in the absence of this loss modulation component.
2. Computer
model
For our computer model, we adopted the same general philosophy used in several earlier mode-locked laser simulations [3]. A large complex array representing the intra-cavity field was repeatedly subjected to a sequence of operations including gain, loss, modulation, and spectral filtering; a random source term simulated spontaneous emission and potential mismatch between the modulation period and the natural frequency of the cavity was also allowed for. The processes of gain, loss and spontaneous emission are represented by the equation [ 41
Vi=Vi exp[ (G-r)/21
+Si,
(1)
where the Vi are the values of the electric field defined on a local time mesh at equally-spaced intervals of t,,
120
J-Y. Li et al. /Optics
Communications
Si is a stochastic source term, and G and rare the gain and loss coefficients. The high (millisecond) relaxation time (T,,) of Er3+ means that the gain depletion caused by the passage of each mode-locked pulse is negligible, and the pulse shape is therefore not affected in any significant way. The value of G is determined by the equation [ 71
(2)
,
where Go is the small signal gain coefficient, u is the stimulated emission cross section, and fiw is the photon energy; it is convenient to define a normalised pumping parameter P = Go/T so that P = 1 corresponds to laser threshold. The action of the spectral filter is governed by the equation [ 41 v:‘= (1 -R)V;+RV;_,
)
(3)
114 (1995) 119-124
Fig. 1. Schematic diagram of the modulator.
A schematic diagram of the fibre modulator element is shown in Fig. 1. The x-axis is defined as the polarisation direction of the modulation pulses (E,) which, through XPM, induce phase changes of & and c$? ( = C/Q/~) [6] on the laser pulses (Ec) entering the fibre linearly-polarised at p to the x-axis. Polarisation controllers (the “bat-ears” in the laboratory device) rotate the polarisation of the pulses leaving the modulator by an angle 0. Since the signal in this region of the cavity is observed to be linearly-polarised, the presence of a polariser oriented at 8 to the n-axis can legit-
where R = exp( - t,ltr) and &is the filter memory time. Modulation and cavity length mismatch are included in the equation Vy+8=mVi,
(4)
where m is the modulation factor discussed below, and 6 represents a lateral shift of the entire field array, associated with a temporal mismatch t& in the past, we have normally set 6 = 0 or f 1; here we have used linear interpolation to accommodate non-integer values of s.
3. Modulation element: theory The central feature of the problem is the action of the modulator and particularly (as we demonstrate below) that the nonlinear birefringence induced by XPM, in conjunction with polarisation-sensitive components in the ring, imposes loss as well as phase modulation. Identification of the polarisation-defining elements is not necessary (although we suggest the Faraday isolator [5] as a likely candidate), because the laser is observed to oscillate in a consistent polarisation and the orthogonal component has a demonstrably higher loss. The insertion of a polariser aligned along the preferred direction would not affect the performance of the system and its presence can therefore be assumed in the subsequent analysis.
Fig. 2. Contour plots derived from Eqs. (5)-(7) showing (a) Iml and (b) qf~( = arg[ m) ) as functions of 0 (the angle of the polariser in Fig. 1) and A (the induced phase change).
J-Y. Li et al. /Optics
Communications
114 (1995) 119-124
121
and *=tan-’
sin( f$J + sin( &,j tan( 0) tan( e+ 0)
cos( I&) +cos( &,) tan(e) tan( e+ 0)
’
(7)
Fig. 3. The effective modulation profile in the presence of group delay and attenuation. The location of the pulse under stable modelocked conditions is indicated.
imately be assumed. Bearing in mind that at the end of its circuit, the signal reenters the modulator, we can equate 8 and p without loss of generality. With these definitions, it can be shown that the net (time-dependent) transmission factor of the laser pulse is given 9 by m= Imlexp(il(/) =exp(i+z)cos0cos(8+R)exp(i+Y) Xsin0sin(8+.0),
(5)
where the loss and phase modulation characteristics, written separately, are Im]2=cos2LZ-~sin(28)sin(28+2L?) X 11 -cos(A-~~“V>l,
(6)
Careful study of Eqs. (6) and (7) indicates that desirable characteristics for a mode-locked laser are achieved when Ll= - 2t?, since this yields an optimal increase of I m I with modulating pulses intensity. This feature is clearly illustrated in Fig. 2 in which contours oflmt and $ are displayed as functions of B and (p, in this special case; here & = 34 = 2 yA,*pLI, and y, Aeff, L and I,,, are respectively the XPM coefficient [ 61, the effective fibre core area, the fibre length and the intensity of the modulation pulse; the intensity of the laser pulse itself is assumed to be too small to affect the refractive index of the modulator. Two other factors also have to be taken into account. Although the wavelengths of the co-propagating modulation and laser pulses are close to the dispersion minimum, they are nevertheless slightly different, and the accumulated group delay difference over the 8.8 km is about 50-80 ps. In addition, both pulses suffer attenuation and the decrease in the depth of modulation towards the end of the fibre is significant. The effective value of Iml when these effects are allowed for is displayed in Fig. 3. The way in which the shape of this profile is influenced by dispersion and attenuation, and the consequences this has for the performance of the laser are discussed in the next section.
3e+12
Local
Fig. 4. Typical simulation
tune
(PSI
with the loss modulation
component
of m neutralised by setting Im I =
I.
122
J-Y. Li et al. /Optics
Lvcal
time
Communications
I14 (1995) 119-124
(ps)
Fig. 5. Typical simulation including the loss modulation component of m.
4. Results of the computer model The parameter values used in the computer simulations were: cavity round-trip time T,,,=500 ps, t, = T,,,/2048, detuning factor 6= - 1.4t,, filter memory time tf= 2t,, pumping strength P = 3.5, loss r= 0.2, relaxation time T,, = 1 ms, emission cross section cr = 0.4 pm2, fibre length L = 8.8 km, and Aeff = 50 pm’, duration of the modulating pulse = 20 ps, group delay difference (di2) = - 16 ps/km, attenuation constant a=0.05 km-‘, 8= 1.8 (a= -3.6). To investigate the role of loss modulation in the development of mode-locking, simulations were performed with and without the loss modulation element in Eq. (5). In Fig. 4, where the loss modulation contribution was neutralised by setting Im I = 1, stable mode-locking does not occur, whereas in Fig. 5 where all parts of Eq. (5) were operational, stable short pulse operation is seen to be rapidly achieved. No special care was required in selecting other parameter values, and this behaviour appeared to be quite general. The key conclusion is that the loss modulation component in Eq. (5) is essential if efficient mode-locking is to be achieved. The mode-locked pulse of Fig. 5 is located at the apex of the modulation profile as indicated in Fig. 3; this is in accordance with conventional mode-locking theory [ 81 which suggests that the pulse is formed where the cavity losses are a minimum and that increasing the curvature of the modulation profile reduces the
pulsewidth. The role played by the group time delay difference d12 and the attenuation constant (Ycan now be understood. Increasing d12, which can be achieved experimentally by adjusting the wavelengths of the modulation and laser signals, widens the modulation profile but makes it shallower; decreasing d12 has the opposite effect. Perhaps surprisingly, it is possible for the modulation profile to be too deep and narrow, as this tends to quench the mode-locked pulse; on the other hand, a broad flat-topped profile is certainly not optimal for ultrashort pulse generation. In the latter case, however, the performance is enhanced by a non-zero value of (Ybecause this slants the top of the profile, creating a well-defined location for the laser pulse, as in Fig. 3. Figs. 6 and 7 highlight the importance of (Yand d12 in determining the operating characteristics of the laser. With d,, at its default value of - 16 p&m, Fig. 6 illustrates the dependence of the pulse peak intensity and pulsewidth on a; optimal performance is clearly realised when (Yis around 0.05 km- ‘. Fig. 7 shows the analogous dependence on d12 with (Yheld fixed; the figure demonstrates that when Id12 I is less than about 10 ps/km for 20 ps modulation pulses, the depth of modulation becomes too high, and the 10 ps laser pulses are quenched. 5. Modulation element: experiment As an experimental check on the theoretical predictions, we studied the behaviour of the fibre modulator
J-Y. Li et al. /Optics
123
Communications 114 (1995) 119-124
independent adjustment of the polarisation of the two waves. At the output of the fibre, the two wavelengths were separated by WDM2 and the CW 1.553 pm signal passed through the polarisation controller PC3 and the polariser P to the high-speed (25 ps) photodiode detector D. With the modulating pulses absent, PC 1 and PC3 were adjusted for 50% transmission of the CW beam. The effect of the modulating pulses on the detected CW signal is shown in Fig. 8b for four different settings (a) Intensity
3e+1’
I
1.9e+ll 0.00
,
0.02
I
,
0.04
I
,
I 0.08
0.06
:
0.10
km-’
Ze+ll
le+ll
7
Oe+oo
-20
1
i
I
t
-15
-5
-10
0
psflan (b) Pulsewidtb
(PWHM,
ps)
15s 10 0.00
I 0.02
/
I
I
0.04
I 0.06
I
I 0.08
1
_ 0 10
km-’
Fig. 6. The pulse peak intensity and FWHM as functions of the attenuation for group time delay of - 16 ps/km.
in more detail. The experimental arrangement is depicted in Fig. 8a. A stream of N 20 ps pulses at 1.538 pm (derived from an amplified gain-switched DFFS laser, as in [ 1] ) was combined with a narrow linewidth CW laser signal at 1.553 pm in the wavelength-division multiplexer WDMl, and launched together into the same 8.8 km length of modulator fibre used in the original laser experiment; the polarisation controllers PC 1 and PC2 on the input channels to WDM 1 allowed
O-20
-10
-5
0
Psb Fig. 7. The pulse peak intensity and FWHM as functions of the group time delay for an attenuation of 0.05 km- ‘.
124
J-Y. Li et al. /Optics Communications 114 (1995) 119-124
light clearly demonstrated but, as predicted by the model, the direction of polarisation rotation is clearly a function of the modulating pulse polarisation. The optical power levels used in these experiments were equivalent to those in the laser experiment.
Amplified Gain-Switched
6. Conclusion (1SUnm)
CWECL (1553nm)
(a)
Time(2OpJdiv)
04 Fig. 8. (a) Experimental configuration for the XPM polarisation measurements and (b) the output CW signal recorded on the highspeed detector D for four different settings of PC2, with PC1 and PC3 adjusted for 50% transmission through P in the absence of the modulating pulses.
of PC2 controlling their initial polarisation. Not only is the modification of the polarisation state of the CW
We have modelled the optically mode-locked laser of Greer and Smith [ 11, paying particular attention to the modulation mechanism. We have shown that the conjunction of nonlinear birefringence induced by cross-phase modulation with polarisation-sensitive components in the laser cavity gives rise to a loss modulation component that plays an essential part in the efficient mode-locking of the device. The beneficial effects of attenuation and dispersion in the modulator have been demonstrated and experimental results that support the theoretical model have been presented. References [ 1] E.J. Greer and K. Smith, Electron. Lett. 28 (1992) 1741. [2] J.K. Lucek and K. Smith, Optics Lett. 18 (1993) 1226. [3] J.M. Catherall, G.H.C. New and P.M. Radmom, Optics I&. 7 (1982) 319. [4] J.M. Catherall andG.H.C. New, IEEE J. QuantumElectron. QE22 (1986) 1593. [ 51 A.E. Siegman, Lasers (University Science Books, 1976) p. 535. [ 61 G.P. Agrawal, Nonlinear Fibre Optics (Academic, New York, 1989). [ 71 P.W. Milonni and J.H. Eberly, Lasers (Wiley, New York, 1991) . [8] G.H.C. New, Rep. Prog. Phys.46 (1983) 877.