OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 2277–2289
« Show journal navigation

Travelling wave analysis on high-speed performance of Q-modulated distributed feedback laser

Jiankun Zhi, Hongli Zhu, Dekun Liu, Lei Wang, and Jian-Jun He  »View Author Affiliations


Optics Express, Vol. 20, Issue 3, pp. 2277-2289 (2012)
http://dx.doi.org/10.1364/OE.20.002277


View Full Text Article

Acrobat PDF (894 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The structure of a Q-modulated distributed feedback laser is designed and simulated. A large reflectivity modulation of the rear reflector is achieved by using an anti-resonant cavity formed by two deep trenches with the one between the modulator and phase section filled by a high index dielectric material. The travelling wave model is presented to analyze the high speed performance of the laser. Due to the effect of the wave propagation in the structure, the modulation extinction ratio decreases with increasing cavity length. It is shown that 40Gb/s RZ signal modulation can be achieved with an extinction ratio of 7dB and 10dB, respectively, for a cavity length of 500μm and 300μm.

© 2012 OSA

1. Introduction

While the advanced modulation formats such as the differential quadrature phase shift keying (DQPSK) are being developed for ultra-long-haul optical transmission, the traditional on-off keying (OOK) will remain the predominant solution for shorter distance communications due to the simplicity, small size and low cost of the transceivers. Recently we proposed a semiconductor laser structure incorporating a monolithically integrated electro-absorptive Q-modulation mechanism that has potential advantages of high-speed, low-chirp, high extinction ratio and high power efficiency [10

10. J.-J. He, “Proposal for Q-Modulated Semiconductor Laser,” IEEE Photon. Technol. Lett. 19(5), 285–287 (2007). [CrossRef]

]. Rate equation analysis has shown that the Q-modulated laser (QML) can achieve 40Gb/s return-to-zero (RZ) modulation with excellent signal quality [11

11. D. Liu, L. Wang, and J.-J. He, “Rate Equation Analysis of High Speed Q-Modulated Semiconductor Laser,” J. Lightwave Technol. 28, 3128–3135 (2010).

]. While its bandwidth is much higher than that of directly modulated laser (DML), an additional advantage is that its wavelength chirp due to carrier density perturbation decreases with increasing bit rate, in opposite to the case of DML and EML. Besides, the QML does not emit light when the signal is at the OFF state, as opposed to the case of EML where the light is emitted and then absorbed. This increases significantly the power efficiency of QML as compared to EML since in the latter case the power is absorbed wastefully 50% of the time for non-return-to-zero (NRZ) signal or 75% of the time for RZ signal, even in the case of ideal waveforms.

The rate equation model does not consider any particular structure of the laser cavity. It only uses a simple parameter, the photon lifetime, to characterize the laser cavity. It can be considered as a “zero-dimension” (in spatial domain) model of the laser. As a result, it can only show the general behavior and mechanism of Q-modulation, but cannot provide any insight on the effect of structural parameters such as the cavity length and phase. Nor can it be used as a simulation tool for structural design because it only shows the modulation behavior when the photon life time is modulated, but does not concern how the photon lifetime modulation is achieved. In particular, the rate equation analysis does not take into account the wave propagation in the laser structure. It provides a good approximation of the laser behavior when the cavity round-trip propagation time is much smaller than the bit duration. However, for 40 Gb/s and beyond, the round-trip propagation time is no longer negligible for typical cavity lengths. In this paper, we analyze the high-speed performance of Q-modulated distributed feedback (DFB) laser using the travelling wave method that can take into account the wave propagation in the cavity. The effect of the cavity length on the modulation performance of the laser is revealed for the first time.

2. Theoretical model

The structure of the Q-modulated DFB laser is schematically shown in Fig. 1
Fig. 1 Schematic of the Q-modulated laser
. It consists of a gain section, a phase section, and a Q-modulator section at the rear end of the laser. The modulator section is placed between two deep etched trenches which constitute an anti-resonant Fabry–Pérot cavity acting as a rear reflector. The gain section incorporates a DFB grating for providing feedback to the laser cavity. The phase section is adjusted by current injection so that the reflection by the rear Q-modulator interferes constructively with the distributed feedback mechanism. Although the grating is not necessary in the modulator and phase sections, it is incorporated throughout the structure for fabrication simplicity so that a uniform grating can be patterned using holographic method. Contrary to the direct modulated laser, the QML keeps the pump current constant in the gain section. By varying the absorption coefficient of the modulator waveguide through a current injection or reverse-biased electro-absorption effect, the reflectivity of the rear reflector is modulated, resulting in the modulation of the Q-factor (or the photon lifetime) of the laser cavity, and consequently the lasing threshold and output power.

The modulator section is typically very short, in the order of 10-20μm, which is over an order of magnitude smaller than the gain section. Therefore, in this paper, for simplicity, we neglect the wave propagation in the modulator section and use the transfer matrix method (TMM) [12

12. See, for example, L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

] to simulate the reflectivity of the rear reflector. When a modulation signal is applied on the modulator section, the effective reflectivity reff of the rear reflector can be considered to change instantaneously. Also, the effect of the phase adjustment by the phase section can be considered by adding a phase in the effective reflectivity reff of the rear reflector, while the length of the phase section can be included in the overall DFB cavity length for the dynamic simulation using the traveling wave method [13

13. X. Li, Optoelectronic Devices - Design, Modeling and Simulation (Cambridge University Press, 2009).

].

The optical field in the DFB laser cavity can be written in the following form
E(z,t)=[F(z,t)eiβ0z+R(z,t)eiβ0z]eiw0t
(1)
where F(z,t)and R(z,t) represent, respectively, the forward and backward waves propagating along the longitudinal direction z with an effective propagation constant β0 and angular frequency ω0. The time-dependent coupled wave equations in the waveguide can be written as
1vgF(z,t)t+F(z,t)z=(12g12α0iδbiω0cΔn)F(z,t)+iκR(z,t)+sf
(2)
1vgR(z,t)tR(z,t)z=(12g12α0iδbiω0cΔn)R(z,t)+iκF(z,t)+sr
(3)
where vg is the group velocity,κ is the coupling coefficient, α0 is the waveguide loss, and g is the gain expressed by

g(z,t)=Γαg[N(z,t)Nt]1+εP(z,t)
(4)

Here Γis the confinement factor of the mode field in the gain medium, αg=dgdN is the differential gain, N(z,t)is the carrier density at position z and time t, Ntis carrier density at transparency,ε is the gain compression coefficient, andP(z,t) is the photon density. δbis the deviation from the Bragg condition given by
δb=ω0cneffπΛ
(5)
with Λthe pitch of the grating, and neff the effective refractive index. The effective refractive index change Δndue to the carrier density variation is given by
Δn=λ04πΓααg[N(z,t)-Nt]
(6)
where αis the linewidth enhancement factor. The variation of the carrier density N(z,t) is governed by the following time-dependent carrier rate equation
dN(z,t)dt=JedAN(z,t)BN(z,t)2CN(z,t)3αg[N(z,t)Nt]1+εP(z,t)vgP(z,t)
(7)
where Jis the injected current density, dis the thickness of the active layer, and A, B, C are the nonradiative recombination coefficient, bimolecular recombination coefficient and auger recombination coefficient, respectively. sf and sr are the spontaneous noises coupled into the forward and backward waves, respectively, which are expressed by
sf,r(z,t)sf,r*(z',t)=βKRspδ(tt')δ(zz')/vg
(8)
sf,r(z,t)sf,r(z',t)=0
(9)
where Rsp=BN2/L is the spontaneous emission per unit length, β is the coupling coefficient of spontaneous emission into the lasing mode; and K is the transverse Petermann’s factor [14

14. K. Petermann, “Calculated spontaneous emission factor for double-heterostructure injection lasers with gain-induced waveguiding,” IEEE J. Quantum Electron. 15(7), 566–570 (1979). [CrossRef]

].

The coupled wave Eqs. (2) and (3) can be rewritten in the following matrix format
(1vgt±z)[F(z,t)R(z,t)]=[A11(z,t)A12(z,t)A21(z,t)A22(z,t)][F(z,t)R(z,t)]+[Sf(z,t)Sr(z,t)]
(10)
whereA11(z,t)=A22(z,t)=12g12α0iδbiω0cΔn, andA12(z,t)=A21(z,t)=iκ.

t=kΔt,k=0,1,2,....z=nΔz,n=1,2,3,...
(11)

Then, the left hand side of Eq. (10) is calculated by
F(z,t)t=12(Fn+1,k+1Fn+1,kΔt+Fn,k+1Fn,kΔt)
(12)
F(z,t)z=12(Fn+1,k+1Fn,k+1Δz+Fn+1,kFn,kΔz)
(13)
R(z,t)t=12(Rn+1,k+1Rn+1,kΔt+Rn,k+1Rn,kΔt)
(14)
R(z,t)z=12(Rn+1,k+1Rn,k+1Δz+Rn+1,kRn,kΔz)
(15)
where Fn,kand Rn,k denote the values of F(nΔz,kΔt) andR(nΔz,kΔt), respectively. Similarly, the right hand side of Eq. (10) is given by
[A11(z,t)A12(z,t)A21(z,t)A22(z,t)][F(z,t)R(z,t)]+[Cf(z,t)Cr(z,t)]=14[An+1,k+111An+1,k+112An+1,k+121An+1,k+122][Fn+1,k+1Rn+1,k+1]+14[An+1,k11An+1,k12An+1,k21An+1,k22][Fn+1,kRn+1,k]+14[An,k+111An,k+112An,k+121An,k+122][Fn,k+1Rn,k+1]+14[An,k11An,k12An,k21An,k22][Fn,kRn,k]+14[Cn+1,k+1fCn+1,k+1r]+14[Cn+1,kfCn+1,kr]+14[Cn,k+1fCn,k+1r]+14[Cn,kfCn,kr]
(16)
with the following boundary condition at z=0 and NΔz
R(0,t)=F(0,t)reff
(17)
F(NΔz,t)=R(NΔz,t)r'
(18)
where r’ is the reflectivity of the cleaved facet at the front end and reffis the effective reflectivity of the rear reflector which can be calculated by the TMM method. When a signal is applied on the modulator section, it is assumed thatreffwould change instantaneously along with the signal.

By plugging Eqs. (12)-(16) into Eq. (10) and using the boundary conditions in Eqs. (17)-(18), we can calculate the values of F(z,t) and R(z,t)for all positions z=nΔz and time t=kΔt.

The output power from the front end of the laser can be calculated by

PoutF(t)=dwΓvghcλ(|F(L,t)|2|R(L,t)|2)
(19)

SinceF(z,t)andR(z,t) contain not only the magnitude but also the phase, the frequency chirp Δf of the output signal can be easily obtained by calculating the time derivation of the phase ΦF(z,t) of F(z,t) as follows

Δf=12πΦF(L,t)t
(20)

3. Results and discussions

We consider a Q-modulated DFB laser operating at 1.55μm. The grating pitch is Λ=241.2nm, with the effective index varying from n1=3.215 ton2=3.21. The length of the active region is La=241.2μm(1000 pitches), with the corresponding normalized coupling coefficient κLa=2(n1n2)La(n1+n2)Λ=1.56.

The two etched trenches are designed with a width equal to an odd-integer multiple of quarter wavelength. The modulator section is placed in an anti-resonant cavity which satisfies
4πnλLm+Φ1+Φ2=(2m+1)π
(21)
where n andLmare the effective refractive index and length of the modulator section, respectively, Φ1 and Φ2are the reflection phases of the two deep trenches.

In order to achieve a high reflectivity modulation, the trench between the modulator and the phase section (Trench 1) needs to have a relatively low reflectivity while the trench at the other end of the modulator (Trench 2) needs to have a high reflectivity. This can be achieved by using trenches with widths equal to an odd integer multiple of quarter-wavelength and filling Trench 1 with a high index dielectric material while Trench 2 can be simply an air trench. As an example, Trench 1 is filled with silicon nitride with a refractive index n'=2.0 and the trench width is w1=5λ0/(4n'), while Trench 2 is filled with air with a widthw2=5/4λ0. In this case, the reflection phases of the two deep trenches is Φ1=Φ2=0. The length of the modulator section between the two trenches in our numerical example isLm=25.25λ0/n=12.2μm.

Figure 2
Fig. 2 Magnitude (a) and phase (b) of the effective reflectivity spectrum of the rear reflector when the absorption coefficient of the modulator section is 0 or 2000 cm−1.
shows the reflectivity and phase of the rear reflector. We assume that when a reversed biased voltage signal is applied on the modulator section, its absorption coefficient changes from 0 to 2000 cm−1, corresponding to the ON (1) and OFF (0) states, respectively. We can see that for the center wavelength λ0=1.55μmwhich corresponds to the anti-resonant condition, when the absorption coefficient changes from 0 to 2000 cm−1, the effective reflectivity of the rear reflector changes by the largest amount from 0.85 to 0.2, while the phase change is minimal. This leads to a large threshold modulation (as we will see later, while producing a minimal adiabatic wavelength chirp.

The lower level reflectivity can be further reduced by using a filler with a larger refractive index for Trench 1. Figure 3
Fig. 3 Effective reflectivity of the rear reflector as a function of the absorption coefficient of the modulator waveguide, with the refractive index of the gap filler for Trench 1 as a parameter.
shows the variation of the effective reflectivity of the rear reflector as a function of the absorption coefficient. We can see that when there is no gap filler, corresponding to the refractive index of gap filler = 1, the effective reflectivity changes from 0.95 to 0.68 when the absorption coefficient of the modulator waveguide changes from 0 to 2000cm−1. When a gap filler with a refractive index of 2 is used, the effective reflectivity changes from 0.85 to 0.2. And when the refractive index of gap filler is 2.5, the variation range is further enlarged, becoming from 0.78 to 0.07. Note that the lower level reflectivity can also be reduced by using a trench width (for Trench 1) that deviates away from an odd integer multiple of quarter wavelength or by using a shallowly etched trench, but the reflectivity is more sensitive to the trench width or etching depth, resulting in a more stringent fabrication tolerance. Besides, the lower the reflectivity of Trench 1, the larger the phase variation of the effective reflectivity of the rear reflector due to the refractive index variation associated with the absorption modulation in the Q-modulator, which leads a larger wavelength chirp [10

10. J.-J. He, “Proposal for Q-Modulated Semiconductor Laser,” IEEE Photon. Technol. Lett. 19(5), 285–287 (2007). [CrossRef]

,11

11. D. Liu, L. Wang, and J.-J. He, “Rate Equation Analysis of High Speed Q-Modulated Semiconductor Laser,” J. Lightwave Technol. 28, 3128–3135 (2010).

]. Therefore, it is important to choose suitable gap filler so that Trench 1 has a high reflectivity while producing sufficient reflectivity modulation of the rear reflector. For example, as we will see later, when the length of active region is 1000~3000 pitches, good performance is obtained when the ON state reflectivity is 0.85 and the OFF state reflectivity is 0.2~0.3, which means that a gap filler with refractive index of 2 is appropriate.

In the QML structure, both the DFB grating and the rear reflector contributed to the feedback mechanism of the laser. A phase section is necessary to ensure the constructive interference of the two feedback mechanisms. It plays the role of adjusting the phase of the effective reflectivity of the rear reflector. Figure 4
Fig. 4 Threshold gain (a) and center wavelength (b) versus the phase.
shows the variation of the threshold gain and the resonance wavelength of the laser when the phase changes. As we can see in Fig. 4(a), there is a large threshold gain difference between the ON and OFF states of the modulator (i.e. when its absorption coefficient changes from 0 to 2000 cm−1). When the phase is at the optimal value, which is about 7π/4 in our numerical example, the threshold gain is the lowest for the ON state while the threshold difference between the ON and OFF states is very large (from 20 cm−1 to 95 cm−1). Also, from Fig. 4(b), we can see that a mode-hop can occur at a certain phase. However, by adjusting the phase section, the lasing wavelength at the ON state can be tuned for over 1 nm without significant increase in threshold or mode-hop. While the mode hop can also occur for the OFF state, it occurs at a very high threshold value which is normally above the operating point.

Figure 5
Fig. 5 Transmission gain spectra of the ON and OFF states
shows the transmission gain spectra for the ON and OFF states when the phase is set to 7π/4 and the injected current is near the threshold of the ON state. As we can see, for the ON state (α=0), the transmission gain for the lasing mode is more than 45dB, which is a clear sign of start-oscillation. Yet for the OFF state (α=2000cm1), the transmission gain is negative, which indicates failure to oscillate. Therefore, the mechanism of the Q-modulation works effectively from the static simulation.

For the dynamic analysis, we use the traveling wave model as described in Section 2 with parameters given in Table 1

Table 1. Parameters used in the travelling wave model

table-icon
View This Table
| View All Tables
. Figure 6
Fig. 6 Output waveform (left) and frequency chirp and carrier density (right) of the QML under 40Gb/s RZ signal modulation when the injected current into the gain section is 60mA and the reflectivity of the rear reflector changes from 0.3 to 0.85 (a); and when the injected current is 80mA and the reflectivity of the rear reflector varies from 0.3 to 0.5 (b); from 0.3 to 0.85 (c); and from 0.5 to 0.85 (d).
shows the output waveform (left figure), and the frequency chirp and the average carrier density (right figure) when a 40Gb/s return-to-zero (RZ) signal is applied to the Q-modulator. The corresponding duration of the ON state signal in the “1” bit is 12.5ps. Figure 6(a) shows the case where the injected current into the gain section is 60mA and the reflectivity of the rear reflector changes from 0.3 to 0.85 when the signal changes from the OFF to the ON state. For Fig. 6(b)-6(c), the injected current is 80mA and the reflectivity of the rear reflector changes from 0.3 to 0.5 (b), from 0.3 to 0.85 (c) or from 0.5 to 0.85 (d). The length of the active-region is 241.2μm (1000 pitches), corresponding to a round trip propagation time of 5.8ps. The phase is optimized at about 1.8π. For all the above cases, we can first observe that the carrier density variation is relatively slow. It does not follow the input signal or output waveform because the carrier density change cannot respond to high speed modulation due to limited carrier life time. Unlike the case of directly modulated laser where the carrier density variation is a prerequisite for output power modulation, the carrier density does not need to be modulated for generating output power modulation in QML. In fact, the carrier density variation is only a consequence of photon density modulation, and it decreases with increasing frequency. This is the reason why the QML can produce a lower adiabatic chirp compared to DML [10

10. J.-J. He, “Proposal for Q-Modulated Semiconductor Laser,” IEEE Photon. Technol. Lett. 19(5), 285–287 (2007). [CrossRef]

], especially at high modulation frequency. Note that the frequency chirp calculated by Eq. (20) includes both adiabatic chirp (related to the carrier density variation) and transient chirp (inherently associated with the output signal modulation).

On the detailed modulation characteristics, let us first look at the case where the gain section is injected with a constant current of 80mA.When the reflectivity of the rear reflector is modulated from 0.3 to 0.5 (Fig. 6(b)), the lasing threshold changes from 60 mA to 28 mA. The output power is low and the extinction ratio of the modulation is also low. The slowly varying adiabatic chirp follows the carrier density variation (in opposite direction) and is relatively small. The frequency chirp is dominated by transient chirp which is about 15 GHz. By increasing the ON state reflectivity of the rear reflector to 0.85 (Fig. 6(c)), which corresponds to a threshold current of 7.5 mA, not only the peak power of the ON state is increased, the OFF state power is reduced due to limited carrier recovery time after carrier depletion by stimulated emission at the ON state, as shown in Fig. 6(b). This results in an excellent extinction ratio, even though the 80mA injected current into the active region is higher than the threshold (60mA) of the OFF state. The transient frequency chirp is increased to about 35GHz. Note that if we reduce the injected current to the threshold or below, as shown in Fig. 6(a), although the power level at the OFF state can be further reduced, the peak power at the ON state is much more pattern dependent, which is therefore not desirable. When the OFF state reflectivity is increased to 0.5, the output power at the OFF state increases as expected (Fig. 6(d)), and consequently the extinction ratio is reduced. At the same time, the variation of the peak power at the ON state decreases, resulting in less pattern dependency. The frequency chirp is also reduced.

4. Conclusions

Acknowledgments

The authors thank Profs. Xun Li and Wei-Ping Huang of McMaster University, Hamilton, Canada for help and discussions on the travelling wave modeling. This work was supported by the National High-Tech R&D Program of China (grant No. 2011AA010305), the Natural Science Foundation of Zhejiang Province (grant No. Z1110276) and the Fundamental Research Funds for the Central Universities of China.

References and links

1.

R. M. Spencer, “High speed Direct Modulation of Semiconductor Laser,” Int. J. High Speed Electron. Syst. 8(3), 377–416 (1997). [CrossRef]

2.

K. Takagi, S. Shirai, Y. Tasuoka, C. Watatani, T. Ota, T. Takiguchi, T. Aoyagi, T. Nishimura, and N. Tomita, “120°C 10 Gb/s Uncooled Direct Modulated 1.3 AlGaInAs MQW DFB Laser Diodes,” IEEE Photon. Technol. Lett. 16, 2415–2417 (2004). [CrossRef]

3.

C. W. Chow, C. S. Wong, and H. K. Tsang, “Reduction of Amplitude Transients and BER of Direct Modulation Laser Using Birefringent Fiber Loop,” IEEE Photon. Technol. Lett. 17(3), 693–695 (2005). [CrossRef]

4.

M. Minakata, “Recent Progress of 40 GHz High-speed LiNbO3 Optical Modulator,” Active and Passive Optical Components for WDM Communication,” Proc. SPIE 4532, 16–27 (2001). [CrossRef]

5.

P. Tang, A. L. Meier, D. J. Towner, and B. W. Wessels, “High-speed Travelling-wave BaTiO3 Thin-film Electro-optic Modulators,” Electron. Lett. 41(23), 1296–1297 (2005). [CrossRef]

6.

Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp Characteristics of 10-Gb/s Electroabsorption Modulator Integrated DFB Lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000). [CrossRef]

7.

H. Takeuchi, “Ultra-fast Electroabsorption Modulator Integrated DFB Lasers,” Proc. of IEEE International Conference On Indium Phosphide and Related Materials, 428–431 (2001).

8.

M. Suzuki, Y. Noda, H. Tanaka, S. Akiba, Y. Kushiro, and H. Isshiki, “Monolithic Integration of InGaAsP/InP Distributed Feedback Laser and Electroabsorption Modulator by Vapor Phase Epitaxy,” J. Lightwave Technol. 5(9), 1277–1285 (1987). [CrossRef]

9.

U. Westergren, M. Chaciński, and L. Thylén, “Compact and efficient modulators for 100 Gb/s ETDM for telecom and interconnect applications,” Appl. Phys., A Mater. Sci. Process. 95(4), 1039–1044 (2009). [CrossRef]

10.

J.-J. He, “Proposal for Q-Modulated Semiconductor Laser,” IEEE Photon. Technol. Lett. 19(5), 285–287 (2007). [CrossRef]

11.

D. Liu, L. Wang, and J.-J. He, “Rate Equation Analysis of High Speed Q-Modulated Semiconductor Laser,” J. Lightwave Technol. 28, 3128–3135 (2010).

12.

See, for example, L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

13.

X. Li, Optoelectronic Devices - Design, Modeling and Simulation (Cambridge University Press, 2009).

14.

K. Petermann, “Calculated spontaneous emission factor for double-heterostructure injection lasers with gain-induced waveguiding,” IEEE J. Quantum Electron. 15(7), 566–570 (1979). [CrossRef]

15.

T. Yu, L. Wang, and J.-J. He, “Bloch Wave Formalism of Photon Lifetime in Distributed Feedback Lasers,” J. Opt. Soc. Am. B 26(9), 1780–1788 (2009). [CrossRef]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(250.4110) Optoelectronics : Modulators

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: December 9, 2011
Revised Manuscript: January 3, 2012
Manuscript Accepted: January 8, 2012
Published: January 17, 2012

Citation
Jiankun Zhi, Hongli Zhu, Dekun Liu, Lei Wang, and Jian-Jun He, "Travelling wave analysis on high-speed performance of Q-modulated distributed feedback laser," Opt. Express 20, 2277-2289 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2277


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. M. Spencer, “High speed Direct Modulation of Semiconductor Laser,” Int. J. High Speed Electron. Syst.8(3), 377–416 (1997). [CrossRef]
  2. K. Takagi, S. Shirai, Y. Tasuoka, C. Watatani, T. Ota, T. Takiguchi, T. Aoyagi, T. Nishimura, and N. Tomita, “120°C 10 Gb/s Uncooled Direct Modulated 1.3 AlGaInAs MQW DFB Laser Diodes,” IEEE Photon. Technol. Lett.16, 2415–2417 (2004). [CrossRef]
  3. C. W. Chow, C. S. Wong, and H. K. Tsang, “Reduction of Amplitude Transients and BER of Direct Modulation Laser Using Birefringent Fiber Loop,” IEEE Photon. Technol. Lett.17(3), 693–695 (2005). [CrossRef]
  4. M. Minakata, “Recent Progress of 40 GHz High-speed LiNbO3 Optical Modulator,” Active and Passive Optical Components for WDM Communication,” Proc. SPIE4532, 16–27 (2001). [CrossRef]
  5. P. Tang, A. L. Meier, D. J. Towner, and B. W. Wessels, “High-speed Travelling-wave BaTiO3 Thin-film Electro-optic Modulators,” Electron. Lett.41(23), 1296–1297 (2005). [CrossRef]
  6. Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp Characteristics of 10-Gb/s Electroabsorption Modulator Integrated DFB Lasers,” IEEE J. Quantum Electron.36(8), 900–908 (2000). [CrossRef]
  7. H. Takeuchi, “Ultra-fast Electroabsorption Modulator Integrated DFB Lasers,” Proc. of IEEE International Conference On Indium Phosphide and Related Materials, 428–431 (2001).
  8. M. Suzuki, Y. Noda, H. Tanaka, S. Akiba, Y. Kushiro, and H. Isshiki, “Monolithic Integration of InGaAsP/InP Distributed Feedback Laser and Electroabsorption Modulator by Vapor Phase Epitaxy,” J. Lightwave Technol.5(9), 1277–1285 (1987). [CrossRef]
  9. U. Westergren, M. Chaciński, and L. Thylén, “Compact and efficient modulators for 100 Gb/s ETDM for telecom and interconnect applications,” Appl. Phys., A Mater. Sci. Process.95(4), 1039–1044 (2009). [CrossRef]
  10. J.-J. He, “Proposal for Q-Modulated Semiconductor Laser,” IEEE Photon. Technol. Lett.19(5), 285–287 (2007). [CrossRef]
  11. D. Liu, L. Wang, and J.-J. He, “Rate Equation Analysis of High Speed Q-Modulated Semiconductor Laser,” J. Lightwave Technol.28, 3128–3135 (2010).
  12. See, for example, L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).
  13. X. Li, Optoelectronic Devices - Design, Modeling and Simulation (Cambridge University Press, 2009).
  14. K. Petermann, “Calculated spontaneous emission factor for double-heterostructure injection lasers with gain-induced waveguiding,” IEEE J. Quantum Electron.15(7), 566–570 (1979). [CrossRef]
  15. T. Yu, L. Wang, and J.-J. He, “Bloch Wave Formalism of Photon Lifetime in Distributed Feedback Lasers,” J. Opt. Soc. Am. B26(9), 1780–1788 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited