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Polarization-mode dynamics in strained 1.3 μm InGaAsPInP lasers under picosecond current modulation
15 July 1995
OPTICS COMMUNICATIONS ELSEWIER
Optics Communications
118 (1995)
323-328
Polarization-mode dynamics in strained 1.3 pm InGaAsP/InP lasers under picosecond current modulation A. Klehr, R. Miiller, P. Enders, M. Vo13,T. Elsaesser Max-Born-lnstitutfiir Nichtlineare Optik und Kurueitspektroskopie. Rudower Chaussee 6, D-12489 Berlin, Germany Received 12 December
1994; revised version received 8 March 1995
Abstract The dynamic behaviour of the TE and TM polarized output from ridge-waveguide InGaAsP/InP lasers which are electrically pumped with 300 ps pulses is studied experimentally and theoretically. For the first time, different polarization characteristics depending on the amplitude of the current pulse and the level of the dc bias are reported. While strong mode competition resulting in TE or TM mode emissionin separate current intervals is found in the cw regime, simultaneous lasing of both modes, transients between TE and TM in the ps range as well as common GHz relaxation oscillations of TE and TM emission are observed under pulsed excitation. TE and TM pulses shorter than 40 ps are measured. The laser dynamics is modelled through space-dependent rate equations. Numerical results suggest, that the fast polarization switching is due to a lateral shift of the TE and TM modes against each other.
1. Introduction The physical properties and the operation parameters of semiconductor lasers are strongly modified by introducing mechanical strain into the active region. For instance, biaxial tensile stress in the active layer of InGaAsP/InP lasers as a result of lattice mismatch between subs&rate and epitaxial layers enhances the optical gain for TM polarized emission and leads to laser operation in both the TM and the TE mode [ 1,2]. Combined TE and TM emission as well as switching between the two polarization states are induced by a variation of temperature [ 31, by the onset of stimulated emission of higher-order lateral TM modes [4] or by waveguiding effects [ 5,6]. Direct polarization switching in a solitary laser diode was first observed by Chen and Liu who applied current pulses of nanosecond duration to a buried-heterostructure InGaAsP/InP laser at low temperature and observed TM spikes of 200 ps 0030-4018/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIOO30-4018(95)00214-6
width [ 3,7 1. Experiments with ridge-waveguide (RW) InGaAsP/InP lasers at room temperature have demonstrated simultaneous relaxation oscillations of the TE and TM mode in the 4 GHz range [ 81. At 900 MHz sinusoidal current modulation, TE-TM switching times of the order of 50 ps were reported [9]. Very recently, the switching behaviour was studied in detail up to modulation frequencies of 500 MHz [ lo]. The fast dynamics of polarization switching gives direct insight into the fundamental nonlinear interaction between differently polarized laser modes. Until now, there is only limited information on the dynamic properties in the GHz range. Furthermore, the short switching times and the orthogonal polarizations of the TE and TM output open promising possibilities for the generation of well-defined optical transients on the picosecond time scale which can be controlled by the electrical input to the device. In this Letter, we present new experimental and theoretical results on the polar-
324
A. Klehr et al. /Optics
Communications
ization behavior of strained InGaAsP/InP lasers. Driving the device with 300 ps current pulses allows the first direct measurement of the TE and TM lasing dynamics in the GHz range under the conditions of single-pulse excitation. Depending on the amplitude of the current pulse and the level of the dc bias, a variety of picosecond sequences of TE and TM polarized pulses are realized. A theoretical model based on spacedependent rate equations is developed, where the gain parameters are obtained from S-band k-p calculations. This model accounts for different lateral profiles of the ‘I’Eand TM mode intensities.
2. Laser structure and experimental setup A cross section of the InGaAsP/InP RW lasers investigated is sketched in Fig. 1. The detailed description of the layer structure is found in Ref. [ lo]. Laser radiation is generated in the 0.15 pm thick quatemary InGaAsP active layer below the ridge. The longitudinal axis (z) is the direction of light propagation. The electric field vectors of the TE and TM waves are oscillating in the lateral (n) and transverse (y) direction, respectively. The cross section of the ridge consists of a trapezoidal bottom part with a basis length of about w = 4.5 pm and a 3.5 pm wide rectangular upper part. The lattice mismatch between the active layer and the substrate results in a tensile stress of 5 X lo* to 1 X lo9 dynlcm’. Square current pulses of 300 ps duration at a repetition frequency of 82 MHz (syncroscan frequency of the streak camera C1587) were produced with a pulse generator HP 8 133 A, amplified to a maximum amplitude of about 340 mA and applied to the laser diode through a 18 GHz bias tee. In the amplifier, the current pulse was transformed into a nearly trapezoidal pulse
118 (1995) 323-328
with a top width of 200 ps and a bottom width of about 350 ps. The amplitude of the current pulse in the laser diode was estimated from the voltage drop across a 3 R high-frequency chip resistor using a microwave probe. The optical output of the laser was splitted by a Glan-Thompson prism into TE and TM polarized components. Subsequently, each of the two beams was focused to the slit of the streak camera (time resolution 10 ps). The average light power of the TE and TM beam was measured with broad-area Ge-photodiodes. Due to the time interval of about 12 ns between two successive current pulses (corresponding to the repetition rate of 82 MHz), which is long, when compared with the recovery time of the active medium of about 2.5 ns, effective single-pulse excitation is realized.
3. Experimental
results
Fig. 2 shows a typical static light power-current characteristics with ‘I&TM switching. There are two well separated current intervals of TE and TM mode lasing. Lasing starts in the ‘IF mode at a threshold current of Ithe= 45 mA and changes to TM at Z,, = 60 mA. Figs. 3 and 4 display results on the dynamic laser output generated by a current input of a dc bias current Zbplus 300 ps pulses of amplitude Zr,= 180 mA and Zp= 340 mA, respectively. In Fig. 3a, the average emission power of the TE and the TM mode is plotted as a function of the dc bias Z,,.For Zr= 180 mA, a minimum I ;i
12 -
TE
,I
_______TM
,’
I I’
I
/’ I’ I’
E
5
I’
:
g4-
ridge G-/W--_, yt
Z
/
L
X
a&e layer
Fig. 1. Schematic cross section of the ridge-waveguidelasers investigated.
injection current [mA] Fig. 2. MeasuredstationaryTE and TM outputpower per facet as a function of the dc injection current.I, is the T’Ethresholdcurrent, I., the currentfor the TE + TM transition.
A. Klehr et al. /Opfics
dc bias current
Communications 118 (1995) 323-328
I, [mA]
325
where a successive onset of TE and Th4 emission is found (cf. Fig. 2), separated by an injection current difference of Z, - Zth,N mA. For higher dc bias, Ii, = 40 mA (Fig. 3d), simultaneous TE and TM emission is observed at early times, while subsequent strong mode competition leads to a short intense TE pulse of 56 ps duration (fwhm) , which is followed by a much broader TM pulse. In Fig. 4a, the average power of the TE and TM mode is plotted versus I,, for a larger amplitude of the 300 ps current pulses, ZP= 340 mA. In contrast to smaller modulation amplitudes (Fig. 3), the average TM output power exceeds the average TE power at all bias currents lb. Correspondingly, the time resolved
I, = 340 mA ,,a .’
I,=40mAi
dc bias current I, [mA]
ice
time [ns] 200’
(b)
Fig. 3. Measured transient behaviour of a laser pumped with 300 ps current pulses of amplitude I, = 180 mA (repetition rate 82 MHz) for different dc bias currents I,. (a) Average TE and TM output power versus It,. The inset presents a detailed view of the T@ and TM curves in the vicinity of I,,, = 21 mA being the bias cunent for the onset of TE king at the actual modulation curmnt. (b) Polariration resolved output power versus time measured with a streak camera at Ib= 2 1 mA. Lasing occurs only in the TE mode. (c) Same as (b), but I,= 22 mA. Both TE and TM lasing is observed. (d) Same as (b) , but Ib = 40 mA. Mode competition gives rise to successive TE and TM pulses.
dc-bias current of Zbmin = 21 mA is necessary to achieve Te laser emission, see the steep increase of the TE power in the inset of Fig. 3a. Close to Zbmin a significant increase of the Th4 power is observed, too, i.e., TM lasing starts in the same current regime, but with It, The time-resolved measurement at slightly above Zbmin. Ii, = Zbmin indicates the emission of a single TE pulse of a temporal width of approximately 100 ps, see Fig. 3b. At It, = 22 mA, both modes are excited, see Fig. 3c. These results are in contrast to the steady-state case,
I,= 70 mA
;-.__....
I-.- ..___... I
0.6
-.
._
__
0.8
1.0
time [ns] Fig. 4. Same as Fig. 3, but I,=340 mA. (a) Average TJ8 and TM mode power versus dc bias current showing dominance of TM emission. (b) TM and TE pulses of widths less than 40 ps at Ib = 0. (c) TM and TE pulses at I,= 10 mA. TM starts relaxation oscillations. (d) Well developed with relaxation oscillations of TE and TM at I,, = 70 mA.
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A. Klehr et al. /Optics Communications 118 (1995) 323-328
data in Fig. 4b show first a TM pulse of - 30 ps width followed by a weaker TE pulse of - 38 ps duration. The time delay between the two peaks iz 50 ps. Applying a small bias current of Zb= 10 mA, the TM mode start to exhibit relaxation oscillations, see Fig. 4c. For even higher dc-currents, both TM and TE emission undergo well developed relaxation oscillations with modulation frequency in the gigahertz range, see Fig. 4d. Very recently, 8 GHz relaxation oscillations of the TE and TM mode were observed over the exciting current pulse of 3 ns duration. Successive TJZ and TM peaks of these oscillations were shifted against each other by about 22 ps [ 111.
4. Theoretical results The time evolution of the TE and TM output power was studied theoretically for the case of 300 ps pulse excitation at vanishing bias current, I,, = 0. Our numerical calculations are based on a simplified version of the model by Chinone et al. [ 121 extended to a twomode laser with strained active layer. The rate equation system used takes into account different TE and TM mode profiles 1‘k”, ( * and 1Pm 12 which depend on the lateral coordinate n (cf. Fig. 1), but not on time. Thus, the local photon densities in the two modes are expressed through s,(x, t) = Q,(t) 1!Pe(x- 8,) I 2 and
a+,) and the carrier concentration at transparency nt,e(m) were calculated as functions of the biaxial stress in the active layer using an B-band k-p model. Details of this band model will be presented elsewhere. For the numerical examples given below, a relative lattice mismatch between the active layer and the substrate of Aal a = - 1 X 10 -’ was assumed corresponding to a biaxial tensile stress of the order of 1 X lo9 dyn/cm’. G, and G,,, are normalized modal gain functions which are connected with the local gain, +G,=
+m
G &IK.12k I *, -cc
4=
I
lW2k
(4)
--m
where I” is the transverse optical confinement factor. An analogous relation holds for G,,,. The parameter K, (K,) denotes the cavity losses: K._(,) = L -’ ln( l/ &cm)) + ‘$(,) where L is the laser length, R,(,, the facet reflectivity and Ki,,(,) the internal loss. rSr,is the spontaneous recombination time of carriers. B, and B, are normalized rates of spontaneously emitted photons,
Be(m)
=
r e(m)
-
*e(m)
-CCC
J%x, TV
(5)
-rn
p, ( p,) denotes the fraction of B,( B,) being emitted into the TE (TM) mode. pp is the pump rate corresponding to the injection current. Because a short time interval of 300 ps is considered, carrier diffusion can be neglected. The mode profiles were approximated by Gaussians, I ?Pee(,,,) I2 = exp[ - 4 In 2(x/w,,,, I 2]. The output power per laser facet is [ 121
s,(x, r) =Q,~~)I~,,,(~-%,I)2, where Q,andQ,,, describe their time dependence. 8, and S,,, are shifts of the profiles relative to the center of the ridge (x = 0). The following equations have been adopted to evaluate the time evolution of Q,, Q,,, and the local carrier conP e(m) centration n = n (x, t) ,
dQc -=u dt
g.e[G-
~1Qe+ We,
dQm -==u,.,[G,-~,lQ,+P,B,, dt dn z =pp-
If_
(1) (2)
-~g,e~eQeI~~12-~g.m~mQmI~~12.
%P
(3) Here, ug,+,) denotes the group velocity for the TE (TM) mode. g, =g,(x, t) and g,,,=g,(x, t) are the local gain functions given by g, = u,(n - n,,) and g, = a,( n - n,,) . The differential gain coefficient
where EC,,,) denotes the photon energy and d, is the thickness of the active layer. The numerical values used for computation are listed in Table 1. Fig. 5 displays curves of calculated TE and TM output power versus time assuming 300 ps current pulses of rectangular shape with pump rates of pp = 1.2 X 102* cmP3 s-’ (a, b) and pp= 1.6~ 102* cmP3 s-l (c). Outside the ridge ( Ix] > w/2), pp = 0 is assumed. For the curves of Fig. 5a, both the TE and TM profiles are centered at X= 0 (8, = S,,, = 0), whereas shifts of
A. Klehr et al. /Optics
Communications 118 (1995) 323-328
321
Table I Parameter values used for numerical calculations Parameter
Value
(1, %l nt,, n,., L’g.e. QYrn R, R, Ke
2.38 X 1O-‘6 cm2 2.87 X lo-l6 cm* 1.47X lOI* cmm3 1.39X 10’scm-3 6.67 X lo9 cm s-r 0.39 0.26 57 cm- ’ 17 cm-’ 10 cm-’ 2.5x10-9s 1 x 10-x 0.42 0.39 200X tom4 cm 0.15X lO+cm 5 X 1O-4 cm 1.53x lo-l9 ws
%I %~. %l % A. Pnl r, J-“, L
d, W L &,
Se = 1.1 p_rnand 6, = 0 are chosen in Figs. 5b, c. The curves in Figs. 5b, c agree qualitatively with those in Figs. 4b, c. It should be stressed, that without lateral shift of the TE mode, no time separation between the TM and the TE pulse was obtained. Thus, the observed polarization switching in the ps-range can be attributed to a small shift of the lateral profiles of the TE and TM mode against each other. Measurements of the static near fields at currents I < Ii, and I > I,, (Fig. 2) support the idea of a lateral shift, in revealing a difference of about 1 pm between the peaks of the TE and TM fundamental lateral modes.
The high biaxial tensile stress in the active layer of the lasers investigated leads to a threshold carrier density for TM polarized laser emission that is only slightly higher than that for the TE emission (see inset of Fig. 3a). The small separation of the lasing thresholds allows the control of the polarization state of the laser output by the injection current. Due to strong mode competition, the static light emission is characterized by either TE or TM mode lasing. Under pulsed operation, however, mode coexistence can be observed. Here, the carrier population is well above both TE and
.._.....
TE TM
200
go
~_~
J3
(b)
L 400
-(
64ps[-
$
ii
z
jj
;: ;: I:
200
5 a 2
0. -!55psl(c) 400
200
:: :: /j
:: :: ;j ::
4 0.: time [ns] Fig. 5. Calculated TE and TM output power as a function of time assuming a single 300 ps current pulse applied at I = 0 for different lateral shifts of the TE mode profile and pump rates. (a) No lateral shift, i.e., both polarization modes exhibit the same lateral protile (w,=w,=2~m)centeredatx=O,cf.Fig. 1;~=1.2X1028cm-3 s- ‘. (b) Different profile widths: w, = 1.8 pm, w, = 2.0 pm, and lateralshift6,=1.1 pmoftheTEmode;&,=O,~= 1.2X 10Zscm-3 s-‘. In contrast to (a), TM and TE light emissions are now well separated in time. (c) Same as (b), but p,= 1.6X lo** cm-s SK’. The higher pump rate causes relaxation-like oscillations.
threshold. This is similar to the well-known phenomenon of simultaneous oscillations of several longitudinal modes during the transient regime at step excitation [ 131. It should be stressed, that the lateral waveguiding by the ridge factors the TM mode [ 51. This effect is enhanced by the higher carrier concentration under the ridge at short pulse excitation, because there is almost no lateral carrier diffusion. For high pump pulse amplitudes, this effect can even lead to a predominantly TM polarized emission. As a novel effect, our theoretical results suggest, that the onset of TM and subsequent switching to TE emission is connected with a shift of their lateral profiles against each other. This means, they interact with some-
TM
5. Discussion
-
400
328
A. Klehr et al. /Optics
Communications
what different parts of the carrier distribution, such that TE emission can start, although the decreasing TM emission indicates carrier depletion (cf. Fig. 4b). This gives rise to fast polarization switching. In conclusion, the dynamics of the TE- and TMpolarizedoutputfromaridge-waveguideInGaAsP/InP laser was investigated under 300 ps current pulse modulation at a repetition rate of 82 MHz. At low modulation amplitude, lasing starts in the TE mode, similar to cw operation. For high modulation amplitudes, the TM mode reaches
threshold
first. Differently
polarized
pulses of a width of less than 40 ps and a time delay of 50 ps between their peaks were measured.
References [l] S. Adams and D.T. Cassidy, J. Appl. Phys. 64 (1988) 6631.
118 (1995) 323-328
[2] T.C. Chong and C.G. Fonstad, IEEE J. Quantum Electron. 25
(1989) 171. [3] Y.C. Chen and J.M. Liu, Appl. Phys. Lett. 45 (1984) 604. [4] N.K. Dutta and D.C. Krafi, J. Appl. Phys. 56 ( 1984) 65. [5] M.C. Amann and B. Stegmiiller, I. Appl. Phys. 63 (1988) 1824. [ 61 R. Maciejko, A. Golebiowski, A. Champagne and J.M. Glinksi, DEEEJ. Quantum Electron. 29 ( 1993) 5 1. [7] Y.C. Chen and J.M. Liu, Appl. Phys. Lett. 46 (1985) 16. 181 A. Klehr. B. Rheinl%nderand 0. Ziemann. lnt. J. Ontoelectron. _ . 5 (199oj 513. [9] A. Klehr, A. B&Wolff, R. Miiller, M. Vol3, J. Sacher, W. ElsLser and E.O. Giibel, Electron.Lett. 27 ( 1991) 1680. [ lo] A. Klehr, R. Miiller, M. VoS and A. B&Wolff, Appl. Phys. Lett. 64 (1994) 830. [ 1l] A.Klehr, R. Miiller and M. Voa, 8 GHz polarization selfmodulation in strained 1.3 pm InGaAsP/InP ridge waveguide lasers, CLEO’95, Tech. Digest CWF13 (in press). [ 121 N. Chinone, K. Aiki and R. Ito, J. QuantumElectron. 14 (1978) 625. [ 131 D. Marcuse and T.P. Lee, IEEE J. Quantum Electron. 19 (1983) 1397.
OPTICS COMMUNICATIONS ELSEWIER
Optics Communications
118 (1995)
323-328
Polarization-mode dynamics in strained 1.3 pm InGaAsP/InP lasers under picosecond current modulation A. Klehr, R. Miiller, P. Enders, M. Vo13,T. Elsaesser Max-Born-lnstitutfiir Nichtlineare Optik und Kurueitspektroskopie. Rudower Chaussee 6, D-12489 Berlin, Germany Received 12 December
1994; revised version received 8 March 1995
Abstract The dynamic behaviour of the TE and TM polarized output from ridge-waveguide InGaAsP/InP lasers which are electrically pumped with 300 ps pulses is studied experimentally and theoretically. For the first time, different polarization characteristics depending on the amplitude of the current pulse and the level of the dc bias are reported. While strong mode competition resulting in TE or TM mode emissionin separate current intervals is found in the cw regime, simultaneous lasing of both modes, transients between TE and TM in the ps range as well as common GHz relaxation oscillations of TE and TM emission are observed under pulsed excitation. TE and TM pulses shorter than 40 ps are measured. The laser dynamics is modelled through space-dependent rate equations. Numerical results suggest, that the fast polarization switching is due to a lateral shift of the TE and TM modes against each other.
1. Introduction The physical properties and the operation parameters of semiconductor lasers are strongly modified by introducing mechanical strain into the active region. For instance, biaxial tensile stress in the active layer of InGaAsP/InP lasers as a result of lattice mismatch between subs&rate and epitaxial layers enhances the optical gain for TM polarized emission and leads to laser operation in both the TM and the TE mode [ 1,2]. Combined TE and TM emission as well as switching between the two polarization states are induced by a variation of temperature [ 31, by the onset of stimulated emission of higher-order lateral TM modes [4] or by waveguiding effects [ 5,6]. Direct polarization switching in a solitary laser diode was first observed by Chen and Liu who applied current pulses of nanosecond duration to a buried-heterostructure InGaAsP/InP laser at low temperature and observed TM spikes of 200 ps 0030-4018/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIOO30-4018(95)00214-6
width [ 3,7 1. Experiments with ridge-waveguide (RW) InGaAsP/InP lasers at room temperature have demonstrated simultaneous relaxation oscillations of the TE and TM mode in the 4 GHz range [ 81. At 900 MHz sinusoidal current modulation, TE-TM switching times of the order of 50 ps were reported [9]. Very recently, the switching behaviour was studied in detail up to modulation frequencies of 500 MHz [ lo]. The fast dynamics of polarization switching gives direct insight into the fundamental nonlinear interaction between differently polarized laser modes. Until now, there is only limited information on the dynamic properties in the GHz range. Furthermore, the short switching times and the orthogonal polarizations of the TE and TM output open promising possibilities for the generation of well-defined optical transients on the picosecond time scale which can be controlled by the electrical input to the device. In this Letter, we present new experimental and theoretical results on the polar-
324
A. Klehr et al. /Optics
Communications
ization behavior of strained InGaAsP/InP lasers. Driving the device with 300 ps current pulses allows the first direct measurement of the TE and TM lasing dynamics in the GHz range under the conditions of single-pulse excitation. Depending on the amplitude of the current pulse and the level of the dc bias, a variety of picosecond sequences of TE and TM polarized pulses are realized. A theoretical model based on spacedependent rate equations is developed, where the gain parameters are obtained from S-band k-p calculations. This model accounts for different lateral profiles of the ‘I’Eand TM mode intensities.
2. Laser structure and experimental setup A cross section of the InGaAsP/InP RW lasers investigated is sketched in Fig. 1. The detailed description of the layer structure is found in Ref. [ lo]. Laser radiation is generated in the 0.15 pm thick quatemary InGaAsP active layer below the ridge. The longitudinal axis (z) is the direction of light propagation. The electric field vectors of the TE and TM waves are oscillating in the lateral (n) and transverse (y) direction, respectively. The cross section of the ridge consists of a trapezoidal bottom part with a basis length of about w = 4.5 pm and a 3.5 pm wide rectangular upper part. The lattice mismatch between the active layer and the substrate results in a tensile stress of 5 X lo* to 1 X lo9 dynlcm’. Square current pulses of 300 ps duration at a repetition frequency of 82 MHz (syncroscan frequency of the streak camera C1587) were produced with a pulse generator HP 8 133 A, amplified to a maximum amplitude of about 340 mA and applied to the laser diode through a 18 GHz bias tee. In the amplifier, the current pulse was transformed into a nearly trapezoidal pulse
118 (1995) 323-328
with a top width of 200 ps and a bottom width of about 350 ps. The amplitude of the current pulse in the laser diode was estimated from the voltage drop across a 3 R high-frequency chip resistor using a microwave probe. The optical output of the laser was splitted by a Glan-Thompson prism into TE and TM polarized components. Subsequently, each of the two beams was focused to the slit of the streak camera (time resolution 10 ps). The average light power of the TE and TM beam was measured with broad-area Ge-photodiodes. Due to the time interval of about 12 ns between two successive current pulses (corresponding to the repetition rate of 82 MHz), which is long, when compared with the recovery time of the active medium of about 2.5 ns, effective single-pulse excitation is realized.
3. Experimental
results
Fig. 2 shows a typical static light power-current characteristics with ‘I&TM switching. There are two well separated current intervals of TE and TM mode lasing. Lasing starts in the ‘IF mode at a threshold current of Ithe= 45 mA and changes to TM at Z,, = 60 mA. Figs. 3 and 4 display results on the dynamic laser output generated by a current input of a dc bias current Zbplus 300 ps pulses of amplitude Zr,= 180 mA and Zp= 340 mA, respectively. In Fig. 3a, the average emission power of the TE and the TM mode is plotted as a function of the dc bias Z,,.For Zr= 180 mA, a minimum I ;i
12 -
TE
,I
_______TM
,’
I I’
I
/’ I’ I’
E
5
I’
:
g4-
ridge G-/W--_, yt
Z
/
L
X
a&e layer
Fig. 1. Schematic cross section of the ridge-waveguidelasers investigated.
injection current [mA] Fig. 2. MeasuredstationaryTE and TM outputpower per facet as a function of the dc injection current.I, is the T’Ethresholdcurrent, I., the currentfor the TE + TM transition.
A. Klehr et al. /Opfics
dc bias current
Communications 118 (1995) 323-328
I, [mA]
325
where a successive onset of TE and Th4 emission is found (cf. Fig. 2), separated by an injection current difference of Z, - Zth,N mA. For higher dc bias, Ii, = 40 mA (Fig. 3d), simultaneous TE and TM emission is observed at early times, while subsequent strong mode competition leads to a short intense TE pulse of 56 ps duration (fwhm) , which is followed by a much broader TM pulse. In Fig. 4a, the average power of the TE and TM mode is plotted versus I,, for a larger amplitude of the 300 ps current pulses, ZP= 340 mA. In contrast to smaller modulation amplitudes (Fig. 3), the average TM output power exceeds the average TE power at all bias currents lb. Correspondingly, the time resolved
I, = 340 mA ,,a .’
I,=40mAi
dc bias current I, [mA]
ice
time [ns] 200’
(b)
Fig. 3. Measured transient behaviour of a laser pumped with 300 ps current pulses of amplitude I, = 180 mA (repetition rate 82 MHz) for different dc bias currents I,. (a) Average TE and TM output power versus It,. The inset presents a detailed view of the T@ and TM curves in the vicinity of I,,, = 21 mA being the bias cunent for the onset of TE king at the actual modulation curmnt. (b) Polariration resolved output power versus time measured with a streak camera at Ib= 2 1 mA. Lasing occurs only in the TE mode. (c) Same as (b), but I,= 22 mA. Both TE and TM lasing is observed. (d) Same as (b) , but Ib = 40 mA. Mode competition gives rise to successive TE and TM pulses.
dc-bias current of Zbmin = 21 mA is necessary to achieve Te laser emission, see the steep increase of the TE power in the inset of Fig. 3a. Close to Zbmin a significant increase of the Th4 power is observed, too, i.e., TM lasing starts in the same current regime, but with It, The time-resolved measurement at slightly above Zbmin. Ii, = Zbmin indicates the emission of a single TE pulse of a temporal width of approximately 100 ps, see Fig. 3b. At It, = 22 mA, both modes are excited, see Fig. 3c. These results are in contrast to the steady-state case,
I,= 70 mA
;-.__....
I-.- ..___... I
0.6
-.
._
__
0.8
1.0
time [ns] Fig. 4. Same as Fig. 3, but I,=340 mA. (a) Average TJ8 and TM mode power versus dc bias current showing dominance of TM emission. (b) TM and TE pulses of widths less than 40 ps at Ib = 0. (c) TM and TE pulses at I,= 10 mA. TM starts relaxation oscillations. (d) Well developed with relaxation oscillations of TE and TM at I,, = 70 mA.
326
A. Klehr et al. /Optics Communications 118 (1995) 323-328
data in Fig. 4b show first a TM pulse of - 30 ps width followed by a weaker TE pulse of - 38 ps duration. The time delay between the two peaks iz 50 ps. Applying a small bias current of Zb= 10 mA, the TM mode start to exhibit relaxation oscillations, see Fig. 4c. For even higher dc-currents, both TM and TE emission undergo well developed relaxation oscillations with modulation frequency in the gigahertz range, see Fig. 4d. Very recently, 8 GHz relaxation oscillations of the TE and TM mode were observed over the exciting current pulse of 3 ns duration. Successive TJZ and TM peaks of these oscillations were shifted against each other by about 22 ps [ 111.
4. Theoretical results The time evolution of the TE and TM output power was studied theoretically for the case of 300 ps pulse excitation at vanishing bias current, I,, = 0. Our numerical calculations are based on a simplified version of the model by Chinone et al. [ 121 extended to a twomode laser with strained active layer. The rate equation system used takes into account different TE and TM mode profiles 1‘k”, ( * and 1Pm 12 which depend on the lateral coordinate n (cf. Fig. 1), but not on time. Thus, the local photon densities in the two modes are expressed through s,(x, t) = Q,(t) 1!Pe(x- 8,) I 2 and
a+,) and the carrier concentration at transparency nt,e(m) were calculated as functions of the biaxial stress in the active layer using an B-band k-p model. Details of this band model will be presented elsewhere. For the numerical examples given below, a relative lattice mismatch between the active layer and the substrate of Aal a = - 1 X 10 -’ was assumed corresponding to a biaxial tensile stress of the order of 1 X lo9 dyn/cm’. G, and G,,, are normalized modal gain functions which are connected with the local gain, +G,=
+m
G &IK.12k I *, -cc
4=
I
lW2k
(4)
--m
where I” is the transverse optical confinement factor. An analogous relation holds for G,,,. The parameter K, (K,) denotes the cavity losses: K._(,) = L -’ ln( l/ &cm)) + ‘$(,) where L is the laser length, R,(,, the facet reflectivity and Ki,,(,) the internal loss. rSr,is the spontaneous recombination time of carriers. B, and B, are normalized rates of spontaneously emitted photons,
Be(m)
=
r e(m)
-
*e(m)
-CCC
J%x, TV
(5)
-rn
p, ( p,) denotes the fraction of B,( B,) being emitted into the TE (TM) mode. pp is the pump rate corresponding to the injection current. Because a short time interval of 300 ps is considered, carrier diffusion can be neglected. The mode profiles were approximated by Gaussians, I ?Pee(,,,) I2 = exp[ - 4 In 2(x/w,,,, I 2]. The output power per laser facet is [ 121
s,(x, r) =Q,~~)I~,,,(~-%,I)2, where Q,andQ,,, describe their time dependence. 8, and S,,, are shifts of the profiles relative to the center of the ridge (x = 0). The following equations have been adopted to evaluate the time evolution of Q,, Q,,, and the local carrier conP e(m) centration n = n (x, t) ,
dQc -=u dt
g.e[G-
~1Qe+ We,
dQm -==u,.,[G,-~,lQ,+P,B,, dt dn z =pp-
If_
(1) (2)
-~g,e~eQeI~~12-~g.m~mQmI~~12.
%P
(3) Here, ug,+,) denotes the group velocity for the TE (TM) mode. g, =g,(x, t) and g,,,=g,(x, t) are the local gain functions given by g, = u,(n - n,,) and g, = a,( n - n,,) . The differential gain coefficient
where EC,,,) denotes the photon energy and d, is the thickness of the active layer. The numerical values used for computation are listed in Table 1. Fig. 5 displays curves of calculated TE and TM output power versus time assuming 300 ps current pulses of rectangular shape with pump rates of pp = 1.2 X 102* cmP3 s-’ (a, b) and pp= 1.6~ 102* cmP3 s-l (c). Outside the ridge ( Ix] > w/2), pp = 0 is assumed. For the curves of Fig. 5a, both the TE and TM profiles are centered at X= 0 (8, = S,,, = 0), whereas shifts of
A. Klehr et al. /Optics
Communications 118 (1995) 323-328
321
Table I Parameter values used for numerical calculations Parameter
Value
(1, %l nt,, n,., L’g.e. QYrn R, R, Ke
2.38 X 1O-‘6 cm2 2.87 X lo-l6 cm* 1.47X lOI* cmm3 1.39X 10’scm-3 6.67 X lo9 cm s-r 0.39 0.26 57 cm- ’ 17 cm-’ 10 cm-’ 2.5x10-9s 1 x 10-x 0.42 0.39 200X tom4 cm 0.15X lO+cm 5 X 1O-4 cm 1.53x lo-l9 ws
%I %~. %l % A. Pnl r, J-“, L
d, W L &,
Se = 1.1 p_rnand 6, = 0 are chosen in Figs. 5b, c. The curves in Figs. 5b, c agree qualitatively with those in Figs. 4b, c. It should be stressed, that without lateral shift of the TE mode, no time separation between the TM and the TE pulse was obtained. Thus, the observed polarization switching in the ps-range can be attributed to a small shift of the lateral profiles of the TE and TM mode against each other. Measurements of the static near fields at currents I < Ii, and I > I,, (Fig. 2) support the idea of a lateral shift, in revealing a difference of about 1 pm between the peaks of the TE and TM fundamental lateral modes.
The high biaxial tensile stress in the active layer of the lasers investigated leads to a threshold carrier density for TM polarized laser emission that is only slightly higher than that for the TE emission (see inset of Fig. 3a). The small separation of the lasing thresholds allows the control of the polarization state of the laser output by the injection current. Due to strong mode competition, the static light emission is characterized by either TE or TM mode lasing. Under pulsed operation, however, mode coexistence can be observed. Here, the carrier population is well above both TE and
.._.....
TE TM
200
go
~_~
J3
(b)
L 400
-(
64ps[-
$
ii
z
jj
;: ;: I:
200
5 a 2
0. -!55psl(c) 400
200
:: :: /j
:: :: ;j ::
4 0.: time [ns] Fig. 5. Calculated TE and TM output power as a function of time assuming a single 300 ps current pulse applied at I = 0 for different lateral shifts of the TE mode profile and pump rates. (a) No lateral shift, i.e., both polarization modes exhibit the same lateral protile (w,=w,=2~m)centeredatx=O,cf.Fig. 1;~=1.2X1028cm-3 s- ‘. (b) Different profile widths: w, = 1.8 pm, w, = 2.0 pm, and lateralshift6,=1.1 pmoftheTEmode;&,=O,~= 1.2X 10Zscm-3 s-‘. In contrast to (a), TM and TE light emissions are now well separated in time. (c) Same as (b), but p,= 1.6X lo** cm-s SK’. The higher pump rate causes relaxation-like oscillations.
threshold. This is similar to the well-known phenomenon of simultaneous oscillations of several longitudinal modes during the transient regime at step excitation [ 131. It should be stressed, that the lateral waveguiding by the ridge factors the TM mode [ 51. This effect is enhanced by the higher carrier concentration under the ridge at short pulse excitation, because there is almost no lateral carrier diffusion. For high pump pulse amplitudes, this effect can even lead to a predominantly TM polarized emission. As a novel effect, our theoretical results suggest, that the onset of TM and subsequent switching to TE emission is connected with a shift of their lateral profiles against each other. This means, they interact with some-
TM
5. Discussion
-
400
328
A. Klehr et al. /Optics
Communications
what different parts of the carrier distribution, such that TE emission can start, although the decreasing TM emission indicates carrier depletion (cf. Fig. 4b). This gives rise to fast polarization switching. In conclusion, the dynamics of the TE- and TMpolarizedoutputfromaridge-waveguideInGaAsP/InP laser was investigated under 300 ps current pulse modulation at a repetition rate of 82 MHz. At low modulation amplitude, lasing starts in the TE mode, similar to cw operation. For high modulation amplitudes, the TM mode reaches
threshold
first. Differently
polarized
pulses of a width of less than 40 ps and a time delay of 50 ps between their peaks were measured.
References [l] S. Adams and D.T. Cassidy, J. Appl. Phys. 64 (1988) 6631.
118 (1995) 323-328
[2] T.C. Chong and C.G. Fonstad, IEEE J. Quantum Electron. 25
(1989) 171. [3] Y.C. Chen and J.M. Liu, Appl. Phys. Lett. 45 (1984) 604. [4] N.K. Dutta and D.C. Krafi, J. Appl. Phys. 56 ( 1984) 65. [5] M.C. Amann and B. Stegmiiller, I. Appl. Phys. 63 (1988) 1824. [ 61 R. Maciejko, A. Golebiowski, A. Champagne and J.M. Glinksi, DEEEJ. Quantum Electron. 29 ( 1993) 5 1. [7] Y.C. Chen and J.M. Liu, Appl. Phys. Lett. 46 (1985) 16. 181 A. Klehr. B. Rheinl%nderand 0. Ziemann. lnt. J. Ontoelectron. _ . 5 (199oj 513. [9] A. Klehr, A. B&Wolff, R. Miiller, M. Vol3, J. Sacher, W. ElsLser and E.O. Giibel, Electron.Lett. 27 ( 1991) 1680. [ lo] A. Klehr, R. Miiller, M. VoS and A. B&Wolff, Appl. Phys. Lett. 64 (1994) 830. [ 1l] A.Klehr, R. Miiller and M. Voa, 8 GHz polarization selfmodulation in strained 1.3 pm InGaAsP/InP ridge waveguide lasers, CLEO’95, Tech. Digest CWF13 (in press). [ 121 N. Chinone, K. Aiki and R. Ito, J. QuantumElectron. 14 (1978) 625. [ 131 D. Marcuse and T.P. Lee, IEEE J. Quantum Electron. 19 (1983) 1397.