Carrier scenarios in optically injected quantum-dot semiconductor lasers

Carrier scenarios in optically injected quantum-dot semiconductor lasers

Optics Communications 308 (2013) 243–247 Contents lists available at ScienceDirect Optics Communications journal homepage: www.elsevier.com/locate/o...

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Optics Communications 308 (2013) 243–247

Contents lists available at ScienceDirect

Optics Communications journal homepage: www.elsevier.com/locate/optcom

Carrier scenarios in optically injected quantum-dot semiconductor lasers Basim Abdullattif Ghalib a, Sabri J. Al-Obaidi b, Amin H. Al-Khursan c,n a

Laser Physics Department, Science College for Women, Babylon University, Hilla, Iraq Physics Department, Science College, Al-Mustansiriyah University, Baghdad, Iraq c Nassiriya Nanotechnology Research Laboratory (NNRL), Science College, Thi-Qar University, Nassiriya, Iraq b

art ic l e i nf o

a b s t r a c t

Article history: Received 25 August 2012 Received in revised form 11 July 2013 Accepted 11 July 2013 Available online 25 July 2013

A model for optical injection locking in quantum dot (QD) lasers is stated where the electron and hole dynamics are treated separately and their scenarios in the ground state (GS), excited state (ES) in the QDs and in the wetting layer (WL) are examined. A decline in the GS electron occupation probability, and then, a left returned spiral behavior is shown in their phase space projections at high injection ratio. The GS occupation probabilities for electrons and holes are reduced drastically with increasing injection ratio. The injection map is also plotted. & 2013 Elsevier B.V. All rights reserved.

Keywords: Quantum dot Optical injection Carrier scenarios Ground state Excited state Wetting layer

1. Introduction There is a wide variety of optical communication applications requires a large modulation bandwidth, while others need narrow band filter centers at resonance frequency. Although the direct modulation is used to increase the bandwidth but, the injection locking is shown to do best for the above mentioned requirements [1]. It is well known that under optical injection, semiconductor lasers exhibit a rich variety of nonlinearities. In this case, the system dynamics was characterized by two frequencies: the frequency of the optically injected signal and that of the slave laser itself. Then their difference (detuning) controls the slave laser without affecting the master one. This phenomenon of locking oscillators is known since 1665 [2]. In addition to applications depend on bandwidth controlling, there are many other applications depend on the nonlinearity of the laser system. For example, excitability can be observed in the behavior of a stable dynamical system that exhibits pulses when perturbed above threshold [3] by an extra degrees of freedom such as optical injection. Chaos can be seen in the behavior of these nonlinear systems. The synchronization of chaos between nonlinear semiconductor laser systems is used for secure data transmissions and communications applications [4].

n

Corresponding author. Tel.: +964 7813809600. E-mail address: [email protected] (A.H. Al-Khursan).

0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.07.034

Quantum dot (QD) semiconductor lasers are an excellent candidates for high speed data and telecommunication applications due to the carrier confinement in three dimensions. They exhibit some distinctive features like low threshold current and low sensitivity to feedback due to strongly damped relaxation oscillations thus, they shows a stable operation for a wide range of feedback, but the root to chaos is clearly observed. These external perturbations can lead to improve the modulation bandwidth of these QD lasers [3,5–8]. A limited number of works deal with optical injection in QD lasers. Now one of them deals with carrier dynamics in their states [9]. The study of the dynamics in different QD states is important to know the physical parameters controlling them. Injection-locking is a very useful tool for stabilizing the laser, however injection-locked semiconductor lasers show a rich variety of dynamics. For optical injection-locking, two lasers are used with almost the same oscillation frequencies, see Fig. 1, and the frequency detuning between them must usually be within several GHz. Light emitted from the master laser is injected into the slave laser. When the injection locking conditions are satisfied the frequency of the slave laser is locked to that of the master laser. There are two important parameters in injection-locking: frequency detuning, Δω, which is the frequency difference between the master and the free-running slave lasers, and injection ratio, rinj, which is the ratio between the injected power from the master laser and the lasing power of the free-running slave laser. This work studies of injection locking dynamics in QD lasers. Section 2

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Master Laser

Slave Laser

Table 1 Parameters used in the calculations.

Isolator Fig. 1. Optical injection system used in QD optically injected semiconductor laser.

states the rate equations model used for QD laser dynamics. Section 3 includes the calculated results of optical injection locking. Section 4 includes the conclusions from this work.

2. Theoretical model

Parameter

Symbol Value

Unit

Recombination lifetime of electrons in GS

τ er;G

1

ns

Recombination lifetime of holes in GS

τ hr;G

1

ns

Recombination lifetime of electrons in ES

τ er;E

1

ns

Recombination lifetime of holes in ES

τ hr;G

1

ns

Recombination lifetime of electrons in WL Recombination lifetime of holes in WL

τ er;w

1 1

ns ns

0.6 0.3

ns ns

1

ns

Carrier capture time of electrons in WL Carrier capture time of holes in WL

τ hr;w τ ec;w

Carrier escape time of electrons from ES to WL

τ hc;w τ ee;ES

Carrier escape time of holes from ES to WL

τ he;ES

Carrier relaxation time of electrons from GS to ES τ ee;GS

In the QD laser, we considers a separate system for electrons and holes in the QD ground state (GS) and exited state (ES). The structure studied is the self-organized QDs InAs/InGaAs/GaAs material system which is grown experimentally by Kim et al. [10]. Most of the parameters are taken from this structure. The parameters used are stated in Table 1. A schematic diagram of the QD model used here is shown in Fig. 2. Our model recognizes between lifetimes according to the carrier type (electron or hole). First the carriers are injected into the wetting layer with rate I/q and relax into the dot. The carriers are captured in the ES with rates 1=τec;w ; 1=τhc;w , for electrons (e) and holes (h), and from ES to GS with rates 1=τec;E ; 1=τhc;E . The carriers escape back from the GS to the ES with rates 1=τee;G ; 1=τhe;G or from the ES back to the WL with rates 1=τee;E ; 1=τhe;E . The recombination rates of carriers from the WL and the QD confined states are τer;w ; τhr;w ; τer;E ; τhr;E ; τer;G ; τhr;G , respectively. The system rate equations of the injection locking QD semiconductor lasers is given by

τ he;GS

1

ns

0.4

ns

1

ns

Carrier relaxation time of electrons from ES to GS τ ec;E

6

ps

Carrier relaxation time of holes from ES to GS

τ hc;E

3

ps

Linewidth enhancement factor Optical confinement factor

α Γ

2

Density of QDs

NQ

5  1014

cm  2

Laser length

L

2  103

cm

Effective thickness of the active Layer

Lw

0:2  106 cm

Carrier relaxation time of holes from GS to ES

7  103

kinj dEs Es 1 þ Es ð1 þ iαÞΓg G υg ðρeG þ ρhG 1Þ þ Em eðiΔωtÞ þ Rsp ¼ dt 2τs 2 τin ð1Þ dρeG ρe 1 ¼  eG  Γg G υg ðρeG dt τr;G N Q ρe ð1ρe Þ ρe ð1ρe Þ þρhG 1Þ Es j2 þ E e G  G e E τc;E τe;G dρeE ρe ρe ð1ρe Þ ρe ð1ρe Þ ρe Ne ð1ρeE Þ ¼  eE  E e G þ G e E  eE þ we dt τr;E τe;E τc;E τe;G τc;w N Q dρhG ρh 1 ¼  hG  Γg G υg ðρeG dt τr;G N Q ρh ð1ρh Þ ρh ð1ρh Þ h þρG 1Þ Es j2 þ E h G  G h E τc;E τe;G

ð2Þ

ð3Þ

ð4Þ

dρhE ρh ρh ð1ρh Þ ρh ð1ρe Þ ρh Nh ð1ρeE Þ ¼  hE  E h G þ G h E  hE þ wh dt τc;w N Q τc;E τe;G τr;E τe;E

ð5Þ

ρe NQ N e ð1ρe Þ N e dN ew J ¼ c1 þ Ee  w e E  e w dt q τe;E τr;w τc;w

ð6Þ

N h ð1ρh Þ N h  w h E  hw τc;w τr;w

ð7Þ

dN hw dt

¼

J c2 þ q

ρhE NQ τhe;E

where ES and Em are the complex electric fields of the slave and master lasers, respectively. For the slave laser with QD active region the other parameters are: Γ is optical confinement factor, g G , is the gain in the GS, νg is the group velocity, kinj ¼ ðð1r 20 =r 0 Þr inj Þ is the injection coefficient with r 0 is the reflectivity of the slave laser and r inj is the percentage of the injected master to

Fig. 2. Energy diagram of the active layer of the QD laser.

the slave lasers, Δω ¼ ðωm ωs Þ is the detuning between the master and slave lasers, α is the linewidth enhancement factor, ρeG ; ρhG ; ρeE ; ρhE are occupation probability in GS and ES for electrons (e) and holes (h), respectively. Rsp is the spontaneous emission rate in GS, τs is the photon lifetime, New and N hw are the electron and hole carrier densities in the wetting layer, NQ is the QD density. Jc1 and Jc2 are the current densities of electrons and holes, respectively. Eqs. (1)–(7) are solved numerically to describe the dynamics of the carriers in WL in and the QD GS and ES for electrons and holes.

3. Calculations and discussion Fig. 3(a) shows the output photon density for the slave laser at different optical injection ratios. The photon density is increased with increasing injection ratio. Fig. 3(b) shows a zoom of the output at rinj ¼ 2% where the locking is observed. Fig. 3(c) and (d) shows that in addition to reducing photon density at low injection, no locking is obtained with lower injection (rinj ¼0.1%). Although the injection-locking is less studied in QD lasers, but a constant time series at low current is confirmed experimentally for QDs [9]. It is also with the main conclusion drown from [12]. To discuss this, one can see Fig. 4(a) where time series of the

B.A. Ghalib et al. / Optics Communications 308 (2013) 243–247

Photon Density Es (m-2)

6

x 1018

Occupation probability of electrons in GS

Photon Density 0.9

5

0.8

4

0.7 0.6

3

0.5 2 0.4 1 0

0.3 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.2

1 -8

0.1

x 10

time (s)

0 x 1018 Photon Density Es (m-2)

245

0

0.1

0.2

0.3

0.4

Photon Density

0.5

0.7

0.6

0.8

0.9

5

Occupation probability of electrons in ES

0.9

4

1 x 10-9

Time (sec)

0.8 3

0.7

2

0.6 0.5

1

0.4 0 1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

0.3

-9

0.2

x 10

time (s)

Photon Density Es (m-2)

0.1 12

x 1015

0

Photon Density

0

0.1

0.2

0.3

0.4

0.5

0.7

0.6

0.8

0.9

Time (sec)

10 8

1 x 10-8

Occupation probability of holes in ES

6

0.95

4 2

0.9

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

time (s)

1 -8 x 10

0.85

Photon Density Es (m-2)

0.8 15

x 10

13

Photon Density

0.75 1

2

3

4

5

6

7

8

9

Time (sec)

10

10 -10 x 10

Occupation probability of holes in ES

5

1

0 0

0.1

0.2

0.3

0.4

0.5 time (s)

0.6

0.7

0.8

0.9

1

0.8

x 10-8

Fig. 3. (a) Time variation of photon density in GS at three values of rinj, (b): zoom of rinj ¼ 2%, (c) rinj ¼ 0.9%, rinj ¼ 0.1%. Note that Jc1 ¼ 2.5 Jth, α¼ 2 and S ¼ 0.1ES.

0.6

0.4

electron occupation probability ðρeG Þ are plotted at these injections. While ρeG is high for low injection, it reduces drastically at high injection ratio. While electrons are built up due to relaxation from other states to GS in the slave laser, it begins to depleted after the injected field from the master laser arrive to the slave laser. A sharp decrease in ρeG began after  2.5 ps and  1.6 ps for the injection ratios 0.9% and 2%, respectively. This decrease can be reasoned to the electromagnetic induced transparency (EIT) results from destructive quantum interference between the two laser beams [11]. EIT results ‘here’ from the coherent coupling between the QD system in the slave laser and the injected master laser field (the pump field). Accordingly, this interference between two absorption paths results in a transparency spectral window at the resonance frequency. Thus, the reduction in ρeG can explains the high photon density where most of the carriers are used into inversion. Fig. 4(b)–(d) shows occupation probabilities for electrons in ES ðρeE Þ, holes in GS ðρhG Þ and holes in ES ðρhE Þ, respectively, ρeE is also reduced at high injection ratio, while both ρhG and ρhE are also reduced and a drastic increase is also shown at high injection

0.2

0 0

0.1

0.2

0.3

0.4

0.5

Time (sec)

0.6

0.7

0.8

0.9

1 x 10-8

Fig. 4. Time variation of occupation probability of (a) electrons in GS, (b) electrons in ES, and holes in (c) GS and (d) ES. All at three values of Rinj when Jc1 ¼ 2.5 Jth, α¼ 2, and S ¼0.1ES.

but their reduction is small compared with the electron occupations due to their low contribution to the photon density. The result of Fig. 4(a) contains that one can fix the detuning and obtain EIT by changing the injection ratio. In Fig. 5(a) and (b), the time series of WL carrier density for both electrons ðNew Þ and holes ðNhw Þ is shown. Here the picture is a replica of what we see in Fig. 4. High carrier density is obtained at high injection. This is with the conclusion that the WL works as a common reservoir. Accordingly, the main contribution comes from electrons, and a lesser to holes,

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B.A. Ghalib et al. / Optics Communications 308 (2013) 243–247

7

x 10

16

Occupation probability of holes and electrons in GS

Electrons in wetting layer rinj = 2% rinj = 0.9% rinj = 0.1%

6 5 e

Nw 4 3 2 1 0

7

0

x 10

0.1

0.2

0.3

0.4

0.5 0.6 Time (sec)

0.7

0.8

0.9

1 x 10

-8

Occupation probability holes in ES vs.Occupation probability electrons in ES

Holes in wetting layer

16

rinj = 2% rinj = 0.9% rinj = 0.1%

6 5 h Nw 4

3 2 1 0

0

0.1

0.2

0.3

0.4

0.5

Time (sec)

0.6

0.7

0.8

0.9

1 x 10

Fig. 6. Phase portraits of occupation probability of: (a) GS electrons vs. GS holes and (b) ES electrons vs. ES holes. All at three values of Rinj when Jc1 ¼ 2.5 Jth, α¼ 2 and S¼ 0.1ES.

-8

Fig. 5. Time variation of carrier density of: (a) electrons in wetting layer at and (b) holes in wetting layer. All at three values of Rinj when Jc1 ¼2.5 Jth, α¼ 2 and S¼ 0.1ES.

7

x 1016

Electrons and holes in wetting layer

6 5

in GS. The phase space projections onto ðρeG ρhG Þ planes and ðρeE ρhE Þ planes are shown in Fig. 6(a) and (b), respectively. In Fig. 6(a), first, a linear increment in GS carrier probabilities is shown, then for high injection ratios, a decline is shown for ρeG ≥0:5. This value of probability is expected to be the threshold occupation probability. Thus, a decline is appeared with the begin of inversion. At r inj ¼ 2% the decline begins, somewhat, earlier than r inj ¼ 0:9%, but both begin a left-returned spiral behavior near the end of the trajectory. The appearance of wave fronts and spiral waves can be represented as a result of excitability [3]. The spiral and decline are not shown at low injection rate. In Fig. 6(b) a second root of linear relations is appeared and a right-going spirals is shown in the ðρeE ρhE Þ plane. In both figures, the spiral is wider at r inj ¼ 0:9% as shown in the insets. One must also refers that the spiral behavior occurs at higher hole probabilities ðρhG ; ρhE Þ and low electron probabilities ðρeG ; ρeE Þ. This also refers to the high contribution of electron probabilities and especially ρeG in the inversion. Fig. 7 shows the relation between electron and hole densities in the WL. It shows a good synchronization between electrons and holes in WL. This can be explained that the relaxations between QD states is faster than the field injection between the two lasers. So the synchronization is shown in WL while it is not shown in QD GS and ES after the injection of master field presents at slave laser and this is why QD GS and ES probabilities, shown in Fig. 6, have low synchronization than Fig. 7. The spiral behavior is shown in Fig. 7 at all injection ratios. Fig. 8 shows the photon density vs. ρeG , Fig. 8(a), and ρhG , Fig. 8(b), the inset shows a high periodic behavior. From the above figures one can relate their behavior to that seen by Otto et al. [6]. But one must refers that the periodic behavior occurs at low electron probability ρeG , Fig. 8(a), and high hole probability ρhG , Fig. 8(b), which refers to the high electron contribution in the inversion which reduces its probability while the probability is still high for low injection ratios which is not accomplished high photon oscillations as shown in the underlying curve in Fig. 8(a). Fig. 9 shows the effect of detuning on the

e

Nw

4 3 2 1 0

0

1

2

3

4

Nwh

5

6

7 x 1016

Fig. 7. Carrier density of WL electrons vs. WL holes at three values of Rinj when Jc1 ¼2.5 Jth, α ¼2 and S¼ 0.1ES.

photon density where they become smaller and shifted at time with detuning change, but at all these detunings the locking is observed. This behavior is confirmed experimentally for semiconductor lasers [13]. Fig. 10 shows the relation between the photon density and detuning with the injection current as a parameter. It is known as an injection map. As we refer in Fig. 4(a) above, the hole burning behavior is shown at high current and EIT is used to explain it. But one must refer to another behavior seen in Fig. 10, that the photon density is reduced first when the injection current density increases from 0.001 jth to 0.003 jth, then it increases with further increment in the current density. This can be explained with the help of Fig. 4, where a drastic reduction in the occupation probability reduces the overall photon density, but when the current density is increased, the overall carrier density, and then photon density, is increased.

4. Conclusions The optical injection locking in QD lasers is studied where electron and hole dynamics are treated separately. Locking is obtained at some high injection ratio. The results show that one can fix the detuning

B.A. Ghalib et al. / Optics Communications 308 (2013) 243–247

x 1018

and obtain EIT by either changing the current density or the injection ratio. High synchronization between electrons and holes in WL, and a low one in the QD GS due to the main contribution and faster relaxation in the later. If one achieves a good synchronization between QD lasers, then it is adequate to develop its use in synchronization applications in the optical communications which is the work we argued by our group.

Occupation probability of electrons in GS vs.Photon Density

6 rinj = 0.1% rinj = 0.9% rinj = 2%

Photon Density(m-2)

5 4 3 2

References

1 0 0

0.1

0.2

0.3

0.4

e

0.5

0.6

0.7

0.8

0.9

G

Photon Density(m-2)

6

x 1018

Occupation probability of holes in GS vs.Photon Density rinj = 0.1% rinj = 0.9% rinj = 2%

5 4 3 2 1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

h G

Fig. 8. Photon density vs. occupation probability of: (a) electrons in GS and (b) holes in GS at three values of rinj when Jc1 ¼ 2.5 Jth, α ¼2 and S ¼0.1ES. The inset in (a) shows a zoom of rinj ¼ 2%.

2.5

Photon Density

x 1018

detuning = 10

Photon Density Es (m-2)

detuning = 8

2

detuning = 6

1.5

1

0.5

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (sec)

0.9

1 x 10-9

Fig. 9. Time variation of photon density in GS at three values of detuning when Jc1 ¼ 2.5 Jth, rinj ¼ 1.7%, α ¼2 and S¼ 0.1ES.

8.5

Photon Density vs.Detuning

x 1015 jc1=0.007jth jc1=0.005jth

8

jc1=0.003jth jc1=0.001jth

Photon Density(m-2)

247

7.5

7

6.5

6

5.5

-1

-0.8

-0.6

-0.4

-0.2

0

Detuning

0.2

0.4

0.6

0.8

1

x 1011

Fig. 10. Photon density vs. Detuning at four values of jc1 when rinj ¼0.9%.

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