Impact of Thermal Effects on Simulation Accuracy of
Nonlinear Dynamics in Semiconductor Lasers
Cheng Guan Lim, Member, IEEE, Stavros Iezekiel, Senior Member, IEEE, and
Christopher M. Snowden, Fellow, IEEE
Abstract—Simulations based on a carrier heating model are performed to investigate the behavior of a directly modulated 1.55-µm InGaAsP distributed feedback (DFB) laser diode (LD). Results show that bandgap shrinkage has a significant effect on the simulated nonlinear behavior of LDs. However, the varying na-ture of lattice temperana-ture and excess carrier energy relaxation is important to produce simulated results that agree with measured results.
Index Terms—Chaos, laser stability, nonlinear optics, semicon-ductor lasers.
I. INTRODUCTION
T
HE SEMICONDUCTOR laser diode (LD) is a device known to exhibit a rich variety of nonlinear dynamics, including chaos and self-pulsations. Such highly nonlinear be-havior is normally seen as undesirable, although some applica-tions, such as chaotic communicaapplica-tions, rely on it. In either case, it is vital to be able to predict the nonlinear characteristics of an LD with excellent accuracy. The single-mode rate equations have been used widely [1]–[17] to simulate the large signal behavior of LDs. Over the years, the predictive power of the single-mode rate equations has been improved by the introduc-tion of a phenomenological gain suppression factor [18]–[20]. Subsequently, the effects of current-dependent gain suppres-sion on the accuracy of nonlinear dynamics simulation were studied [21], [22] as gain suppression had been shown to be bias-dependent [23], [24]. This dependence of the gain suppres-sion has been attributed to the variations of lattice temperature, as optical gain is very sensitive to temperature changes. To test this postulation, the single-mode rate-equation model needs to be revised to incorporate temperature effects, which is the aim of this paper. As the effect of carrier heating dominates over lattice heating [25]–[27] for the biasing conditions considered in [21], [22], the effect of carrier heating will be specifically investigated. Hence, a carrier temperature rate equation will be presented and used in conjunction with the carrier and photon rate equations to simulate the nonlinear dynamics of a 1.55-µm distributed-feedback (DFB) LD. Calculated results will be com-Manuscript received July 7, 2004; revised December 29, 2004, and April 26, 2005.C. G. Lim is with the Department of Photonics/Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan, R.O.C. (e-mail: C.G.LIM@ieee.org).
S. Iezekiel is with the School of Electronic and Electrical Engineering, Uni-versity of Leeds, Leeds LS2 9JT, U.K.
C. M. Snowden is with the University of Surrey, Surrey GU2 7XH, U.K. Digital Object Identifier 10.1109/JSTQE.2005.853748
pared to the measured results, and the research findings will be presented. To reduce any complications that might arise from inadequately accounted lattice temperature, the lattice tempera-ture will be extracted based on the measured results.
In Section II, the carrier heating model used in this analysis and simulation considerations are presented. Simulation results are presented and discussed in Section III in three parts. In the first part, the lattice temperature is assumed to be constant for all bias currents. Here, the effects of bandgap shrinkage on simula-tion results will be reported. The second part is concerned with the study of longitudinal optical (LO) phonons by incorporating a LO phonon temperature rate equation. As for the final part, the varying nature of the lattice temperature is accounted for in the simulations.
II. CARRIERHEATINGMODEL ANDSIMULATION CONSIDERATIONS
The first step in formulating a carrier temperature rate equa-tion is to consider the major physical causes of carrier heating in semiconductor lasers, which are described as follows.
1) Due to the energy difference between the cladding and the active layers in semiconductor lasers, injected carriers must release this excess energy in order to relax down to the lasing band. Excess energy is redistributed to carriers in the active layer by carrier-carrier scatterings, thus causing a rise in carrier temperature.
2) Besides stimulating free carriers to recombine, photons can also be absorbed by free carriers (i.e., free-carrier absorption). This process causes the energies of absorbed photons to be transferred to free carriers, increasing their energy and hence their temperature.
3) The Auger recombination process describes the absorption of the energy released from a non-radiative carrier recom-bination by a free carrier, which therefore gains excess energy. Thus the carrier temperature rate equation needs to account for Auger recombination heating especially for long-wavelength LDs.
4) Spontaneous and stimulated emissions are the results of recombination of free carriers with below average energy. Therefore, the carrier reservoir in the active layer is de-prived of its lowest energy carriers, causing the average carrier energy and temperature to change.
5) Finally, heated carriers relax their excess energy to longi-tudinal optical phonons and acoustic phonons.
Taking these processes into account, the carrier temperature rate equation (in its general form) is formulated as
dTe dt = dTinj dt + dTfca dt + dTAuger dt −Te− TL τ − dTspon dt − dTstim dt (1)
where Teand TL are the average carrier temperature and lattice
temperature, respectively; Tinj, Tfca, TAuger, Tspon, and Tstim
are the contributing temperature terms due to the injection cur-rent, free-carrier absorption, Auger recombination, spontaneous and stimulated emissions, respectively; and τ is the carrier
energy relaxation time. In a more specific form, each of the previous terms is modeled as follows. The contribution of the injection current to the average carrier temperature is given by
dTinj dt = ηiI/e N V Einj (2)
where ηiis the internal quantum efficiency, I the injection
cur-rent, e the electronic charge, N the carrier density, V the volume of the active layer, and Einjthe excess energy of an injected
car-rier. Free-carrier absorption heating is modeled as
dTfca dt = vgαfcaSVE N V =vgαfcaSE N (3)
where vg is the group velocity, αfcathe free-carrier absorption
coefficient, S the photon density, and E the energy of emitted photons. Auger recombination is significant in long-wavelength LDs, and its contribution to the carrier temperature is described by dTAuger dt = CN3V N V Eg = CN2Eg (4)
where C is the Auger recombination coefficient and Eg the
bandgap energy. Spontaneous and stimulated emissions remove electrons from the conduction band-edge, thus reducing the pop-ulation of free-electrons with the lowest energy. This affects the average carrier temperature, and their contributions can be cal-culated using the following:
dTspon dt = Te(t)− Te(t−δt) δt = TeN V − BN2V δtE /(N V )− Te δt =Te− BNδtE − Te δt =−BNE (5) dTstim dt = Te(t)− Te(t−δt) δt =[TeN V − vgGSVδtE]/(N V )− Te δt
Fig. 1. Energy band diagram to demonstrate the calculation of the excess energy of an injected carrier.
= Te− (vgGSδtE)/N− Teδt
=−vgGSE
N (6)
where B is the bimolecular recombination coefficient and G the optical gain. Gathering all contributing temperature terms and substituting them into (1) yields the following carrier heating model, which is combined with the single-mode rate equations:
dN dt = ηiI eV − AN − BN 2− CN3− v gGS (7) dS dt = ΓvgGS− S τp + ΓβBN2 (8) dTe dt = ηiI/e N V Einj+ vgαfcaSE N + vgGSE N −Te− TL τ + BNE + CN2Eg (9)
where A is the nonradiative recombination coefficient, Γ the optical confinement factor, τp the photon lifetime, and β the
spontaneous emission factor.
With reference to Fig. 1, the equation for calculating the energy of injected carriers is formulated as
Einj= E + 0.5(Ecladding− E) (10)
where Ecladdingis the energy difference between the conduction
and valence bands of the cladding, and has a value of 1.35 eV for InP cladding [29].
The absorption α(E) and gain G(E) models used are given by (11) [31] and (12) [32], respectively α(E) = e2h|M b|2 4π2 om2ocnE × 2mr ¯ h2 3/2 × (E − Eg)1/2 × [1 − fc(Ec)− fv(Ev)] (11) G(E) = e2h|M b|2 4π2 om2ocnE × 2mr ¯ h2 3/2 × (E − Eg)1/2 × fc(Ec)× fv(Ev) (12)
where h is Planck’s constant, ¯h the reduced Planck’s constant, n the refractive index of the active layer, c the speed of light in
vacuum, o the permittivity of free-space, mothe free-electron
mass, mra mass ratio,|Mb|2the average matrix element for the
with the energy Ec, and fv(Ev) is the occupation probability of
a hole with the energy Ev.
Change in refractive index (δn) of the active layer due to car-rier density change (δnN) and current-induced heating (δnT)
is calculated as follows: δn = δnN + δnT = δN ∂n ∂N + 1 2Λ δT ∂λ ∂T (13) where δN is the change in carrier density, dn/dN the rate of change in refractive index with carrier density, Λ the corrugation periodicity, δT the temperature change and dλ/dT the rate of change in emission wavelength with temperature.
As the refractive index changes, there is a corresponding shift in lasing wavelength δλ = δλN + δλT = (2Λ)δN ∂n ∂N + δT ∂λ ∂T (14) where δλ is the overall wavelength-shift, δλN the
carrier-induced wavelength-shift, and δλT the wavelength shift caused
by current-induced heating.
Besides bandgap shrinkage, the index change due to vari-ations in carrier density and current-induced heating, and subsequent blue-shifting and red-shifting of the operating wave-length, are also taken into account by varying the photon energy. The optical absorption and gain experienced by the shifted op-erating wavelength are calculated using (11) and (12), respec-tively, with the corresponding value of|Mb|2, n, E, Eg, fc(Ec),
and fv(Ev) at each shifted operating wavelength. Finally, the
change in group velocity due to refractive index change is also considered.
All these changes are accounted for in the simulations through the change in all n- and E-related terms in (7)–(14). The mag-nitude of E is obtained from
E = h c λ + δλ + δT dE dT (15) where λ is the lasing wavelength.
III. RESULTS ANDDISCUSSIONS
In this section, the nonlinear dynamics of a directly modulated 1.55-µm DFB LD having the parameters shown in Table I will be studied numerically. In the first part of this analysis, TL was
assumed to be constant, under all biasing conditions, and τwas
assumed to be fixed at the value determined by the bias current and does not vary with modulation conditions.
As can be observed from the femtosecond pump-probe trans-mission measurement performed in [33] for a semiconductor optical device having very similar characteristics with the de-vice in this work, carriers lose their excess energy in three phases (i.e., ultrafast, fast, and slow). By neglecting the long energy re-laxation process, the value of τat threshold was estimated to be
1.333 ps. With this value, TLwas found to be 339 K at threshold
by fitting the calculated L–I curve to measured results. For the first case, TL will be assumed to be at this value for other bias
TABLE I
PARAMETERVALUES OF A1.55 µm InGaAsP DISTRIBUTEDFEEDBACK(DFB) SEMICONDUCTORLASER
currents. From the bifurcation maps shown in Fig. 2, it was noted that the simulated results do not resemble the measured results at all. This is due to neglecting the bandgap shrinkage effect [a phenomenon that has an adverse effect on the gain spectrum (Fig. 3)] as can be seen from the behavioral maps (Fig. 4) ob-tained from simulations that accounted for bandgap shrinkage. In the latter case, the value of TL at threshold was found to
be 447 K, and the simulated behavioral maps are very similar to those simulated using constant gain suppression [21], [22]. However, discrepencies arise when comparing them with the measured results [14].
In the second part of the investigation, simulations were based on a two-level carrier heating model by incoporating a longitu-dinal optical phonon temperature rate equation shown in (16), and changing TL as in (9) to the LO phonon temperature (i.e.,
TLO) dTLO dt = Te− TLO τ − TLO− TL τLO (16) where TLOis the longitudinal optical phonon temperature, and τLOis the longitudinal optical phonon lifetime.
Hall et al. [33] have suggested that heat carrier distribution cools to an equilibrium temperature with a time constant of ap-proximately 1 ps. As mentioned earlier, carriers lose their excess energy in three phases (i.e., ultrafast, fast, and slow phases). The estimated values for τ by considering only the ultrafast decay
phase are 0.733, 0.556, and 0.467 ps in the absorption, trans-parency, and gain regions, respectively. These values give an average value of 0.585 ps. However, if the fast energy decay-ing phase is also taken into account together with the ultrafast energy decaying phase to estimate the value of τ, then the
Fig. 2. Bifurcation regions considering a lattice temperature of 339 K and without taking bandgap shrinkage and carrier-induced index change into ac-count. (a) Idc= 18 mA. (b) Idc= 20 mA. (c) Idc= 22 mA.
are 1.4, 1.422 and 1.111 ps, respectively. These values give a mean value of 1.311 ps for τ. In the simulations that follow,
a value of 0.948 ps (i.e., the average of the above two mean values) is used for τ. Simulated results showed that by taking
TL to be constant at 300 K, the carrier heating effect on the
nonlinear dynamics of laser diode cannot be observed because of the relatively much shorter τ as compared to the
modula-Fig. 3. Calculated gain spectra of the DFB LD at the threshold carrier density (i.e., 2.32× 1024m−3). (a) Bandgap shrinkage was not taken into
considera-tion. (b) Bandgap shrinkage was accounted for.
tion period. In other words, Tewould have relaxed to 300 K on
a time scale that is much shorter than one modulation period; hence, after the carrier energy relaxation phase, there is no sign of gain suppression. This deduces the same conclusion made before that TLdoes not stay constant at 300 K. Instead it varies
with the bias current.
A reverse engineering approach was used, whereby simulated results were fitted to measured results by varying TL and τLO
at each of the selected modulation frequencies for each of the bias currents. Fitting begins by assuming the appropriate extracted value of τLO for the bias current considered, and
varying TL. The optical gain calculated here (approximately
2× 104m−1) is the same as that calculated using the
conven-tional single-mode rate equation model that uses differential gain [32]. With the aid of the calculated gain spectra of this LD [Fig. 3(b)], TL was estimated to be around 450 K. If
no acceptable results were obtained, TL was varied and τLO
was changed accordingly. This process was repeated until the values of TL and τLOthat yield the best-fitted calculated
nonlinear behavior were obtained. For this case, the best choice of TL and τLO at each selected modulation frequency (i.e.,
Fig. 4. Route of bifurcation for the case where TL is 447 K and effects of
bandgap shrinkage and refractive index change due to variation of carrier density are taken into account. (a) Idc= 18 mA. (b) Idc= 20 mA. (c) Idc= 22 mA.
(b), respectively. The values at other modulation frequencies were then obtained by interpolation. The explanation for these irregular characteristics is given in the final part of this analysis. As can be seen from the bifurcation maps shown in Fig. 6, the simulated result at a bias current of 18 mA does bear some resemblance to the measured result. However, the experimentally observed period-tripling, period-quadrupling, higher order bifurcation, and chaos at a bias current of 20 mA were not produced in the simulation. Similarly, simulation did not show the period-quadrupling behavior observed in measure-ment when the bias current was set at 22 mA. These missing
Fig. 5. Estimated variations of (a) lattice temperature, and (b) longitudinal optical phonon lifetime with modulation frequency. Triangle: Idc= 18 mA,
star: Idc= 20 mA, and diamond: Idc= 22 mA.
details are due to the fact that the value of τ was fixed, and a
constraint was set on the lowest value of τLOto compromise for
computational efficiency. In the next part of this investigation, the one-level carrier heating model was revisited taking into account the varying nature of TL, and hence τas well.
As the constraint imposed on τLO, due to reasons of
computa-tional efficiency, was hindering the investigation of the effect of varying TLon simulated behavior of LDs, the one-level carrier
heating model in the final part of this analysis (where there is only one time constant in describing the decaying rate of the excess energy of carriers) was revisited with varying TL and
τ taken into consideration. First of all, the best choice of TL
and τ at each of the selected modulation frequencies over the
frequency range from 2.0 to 4.0 GHz was acquired using the previously described method. The resulting graphs of TL and
τ versus the modulation frequency are shown in Fig. 7(a) and
(b), respectively. With these values of TL and τ, the simulated
bifurcation maps (Fig. 8) showed good agreement with mea-sured results [14]. The observed discrepency at a bias current of 18 mA for modulation currents and frequencies ranging from 18 to 22 mA and 2.6 to 2.8 GHz, respectively, is attributed
Fig. 6. Regions of simulated bifurcation. (a) Idc= 18 mA. (b) Idc= 20 mA.
(c) Idc= 22 mA.
to the fact that the dependence of τ on modulation current
has not been considered exclusively. Even so, simulations still yield remarkable agreement with measured results. The phe-nomena that gave rise to the characteristics of the TL and τ
versus modulation frequency graphs shown in Fig. 7(a) and (b), respectively, are explained as follows. Due to nonlinearity and the parasitic capacitance of LDs, the number of carriers injected into the active layer under large-signal conditions dif-fers from one modulation frequency to another. Therefore, at different modulation currents and frequencies, the carrier en-ergy is different, which results in irregular characteristics of
Fig. 7. Graphs of (a) Lattice temperature. (b) τversus modulation frequency.
The effects of bandgap shrinkage and carrier-induced index change were taken into account in the simulations. Triangle: Idc= 18 mA, star: Idc= 20 mA,
and diamond: Idc= 22 mA.
carrier energy relaxation time as a function of bias current [Fig. 7(b)]. However, for simplicity, the dependence of carrier energy relaxation time on the modulation current has not been exclusively considered here. The dependence of lattice temper-ature on bias current is directly related to that of the carrier energy relaxation time, because the temperature transfer rate from carriers to the lattice is determined by the carrier energy relaxation time. Therefore, the lattice temperature rises as the carrier energy relaxation time decreases, which explains the re-sult shown in Fig. 7(a). However, the generally increasing trend of the lattice temperature as the modulation frequency increases seems questionable. Nevertheless, this can be explained as fol-lows. Clearly, as the modulation frequency increases, a larger portion of the modulation current will bypass the active layer and flow through the shunt capacitance of the LD current block-ing layers to the ground. This means that the average energy of the carriers within the active layer is lower [in agreement with Fig. 7(b)], hence the lattice temperature should also decrease in-stead of rising [Fig. 7(a)]. However, in reality, resistive heating also contributes to the lattice temperature. When the modulation
Fig. 8. Regions of bifurcations. (a) Idc= 18 mA. (b) Idc= 20 mA.
(c) Idc= 22 mA. Calculated using one-level carrier heating model with varying
lattice temperature, bandgap shrinkage effect, and carrier-induced index change.
frequency increases, the conversion efficiency of the laser diode drops, and a larger portion of the modulation current is shunted to the ground. This explains the generally rising lattice temperature as the modulation frequency increases [Fig. 7(a)]. Hence, although the temperature contribution from Joule heating might be relatively much smaller compared to other temperature contribution processes [25], it might have some in-fluence as far as further improvement of simulation accuracy is concerned, especially for the situation where the LD is subjected to large signal high-frequency modulation.
IV. CONCLUSION
For the first time, a carrier heating model has been used to study the nonlinear dynamics of LDs. Simulations performed on a 1.55-µm DFB LD revealed the importance of taking bandgap shrinkage into account. Carrier-induced index change, and hence wavelength drift, was found to have negligible ef-fect on the calculated nonlinear behavior of LDs. Simulations that account for the varying nature of lattice temperature and carrier energy relaxation time supports the current-dependent gain suppression concept proposed in [21], [22]. Further analy-sis suggested that the lattice temperature variation could be due to resistive heating. Hence, it is postulated here that in order to accurately reproduce the measured nonlinear behavior of LDs in simulations, resistive heating might have to be accounted for.
REFERENCES
[1] C. H. Lee, T. H. Yoon, and S. Y. Shin, “Period doubling and chaos in a directly modulated laser diode,” Appl. Phys. Lett., vol. 46, pp. 95–97, Jan. 1985.
[2] K. Y. Lau and A. Yariv, “Ultra-high speed semiconductor lasers,” IEEE J.
Quantum Electron., vol. QE-21, no. 2, pp. 121–138, Feb. 1985.
[3] Y. C. Chen, H. G. Winful, and J. M. Liu, “Subharmonic bifurcations and irregular pulsing behaviour of modulated semiconductor lasers,” Appl.
Phys. Lett., vol. 47, pp. 208–210, Aug. 1985.
[4] M. Tang and S. Wang, “Simulation studies of bifurcation and chaos in semiconductor lasers,” Appl. Phys. Lett., vol. 48, pp. 900–902, Apr. 1986. [5] M. Tang and S. Wang, “Simulation studies of the dynamic behaviour of semiconductor lasers with Auger recombination,” Appl. Phys. Lett., vol. 50, pp. 1861–1863, Jun. 1987.
[6] Y. Hori, H. Serizawa, and H. Sato, “Chaos in a directly modulated semi-conductor laser,” J. Opt. Soc. Amer. B., vol. 5, pp. 1128–1132, May 1988. [7] Y. G. Zhao, “Simulation studies of frequency locking, quasi-periodicity, subharmonic bifurcation, and chaos in modulated semiconductor lasers,”
IEEE J. Quantum Electron., vol. 28, no. 10, pp. 2009–2015, Oct. 1992.
[8] R. S. Tucker and I. P. Kaminow, “High-frequency characteristics of di-rectly modulated InGaAsP ridge waveguide and buried heterostructure lasers,” IEEE J. Lightw. Technol., vol. LT-2, no. 8, pp. 385–393, Aug. 1984.
[9] R. S. Tucker, “High-speed modulation of semiconductor lasers,” IEEE J.
Lightw. Technol., vol. LT-3, no. 12, pp. 1180–1192, Dec. 1985.
[10] N. H. Jensen, P. L. Christiansen, and O. Skovgaard, “On period dou-bling bifurcations in semiconductor lasers,” Proc. Inst. Elect. Eng.—
Optoelectron., vol. 135, pp. 285–288, Aug. 1988.
[11] L. Chusseau, E. Hemery, and J.-M. Lourtioz, “Period doubling in directly modulated InGaAsP semiconductor lasers,” Appl. Phys. Lett., vol. 55, pp. 822–824, Aug. 1989.
[12] T. Y. Yoon, C. H. Lee, and S. Y. Shin, “Perturbation analysis of bistabil-ity and period doubling bifurcations in directly-modulated laser diodes,”
IEEE J. Quantum Electron., vol. 25, no. 9, pp. 1993–2000, Sep. 1989.
[13] E. Hemery, L. Chusseau, and J. M. Lourtioz, “Dynamics behaviours of semiconductor lasers under strong sinusoidal current modulation: model-ing and expermient at 1.3 µm,” IEEE J. Quantum Electron., vol. 26, no. 4, pp. 633–641, Apr. 1990.
[14] H. F. Liu and W. F. Ngai, “Nonlinear dynamics of a directly modulated 1.55 µm InGaAsP distributed feedback semiconductor laser,” IEEE J.
Quantum Electron., vol. 29, no. 6, pp. 1668–1674, Jun. 1993.
[15] S. Bennett, C. M. Snowden, and S. Iezekiel, “Nonlinear dynamics in directly modulated multiple-quantum-well laser diode,” IEEE J. Quantum
Electron., vol. 33, no. 11, pp. 2076–2083, Nov. 1997.
[16] H. Lamela, G. Carpintero, and F. J. Mancebo, “Period tripling and chaos in the dynamic behavior of directly modulated diode lasers,” IEEE J.
Quantum Electron., vol. 34, no. 10, pp. 1797–1801, Oct. 1998.
[17] S. F. Yu, “Nonlinear dynamics of vertical-cavity surface-emitting lasers,”
IEEE J. Quantum Electron., vol. 35, no. 3, pp. 332–341, Mar. 1999.
[18] J. Manning, R. Olshansky, D. M. Fye, and W. Powazinik, “Strong influence of nonlinear gain on spectral and dynamic characteristics of InGaAsP lasers,” Electron. Lett., vol. 21, pp. 496–497, May 1985.
[19] G. P. Agrawal, “Effects of nonlinear gain on single-frequency behaviour of semiconductor lasers,” Electron. Lett., vol. 22, pp. 696–697, Jun. 1986.
[20] G. P. Agrawal, “Effects of gain nonlinearities on period doubling and chaos in directly modulated semiconductor lasers,” Appl. Phys. Lett., vol. 49, pp. 1013–1015, Oct. 1986.
[21] C. G. Lim, S. Iezekiel, and C. M. Snowden, “Is noise a crucial factor in rate equation modelling of nonlinear dynamics in laser diodes?,” Appl.
Phys. Lett., vol. 77, pp. 3493–3495, Nov. 2000.
[22] C. G. Lim, S. Iezekiel, and C. M. Snowden, “Influence of the injection current dependence of gain suppression on the nonlinear dynamics of semiconductor lasers,” Appl. Phys. Lett., vol. 78, pp. 2384–2386, Apr. 2001.
[23] S. Schuster and H. Haug, “Calculation of the gain saturation in CW semi-conductor lasers with Boltzmann kinetics for Coulomb and LO phonon scattering,” Semicond. Sci. Technol., vol. 10, pp. 281–289, Mar. 1995. [24] Z. Toffano and A. Destrez, “New gain compression factor determination
by harmonic analysis in semiconductor lasers,” Electron. Lett., vol. 31, pp. 202–203, Feb. 1995.
[25] R. Ait-Sadi, A. J. Lowery, and B. Tuck, “Two-dimensional tempera-ture modelling of DH laser diodes using the transmission-line modelling (TLM) method,” Proc. Inst. Elect. Eng.—Sci. Meas. Technol., vol. 141, pp. 7–14, Jan. 1994.
[26] M. Szymanski, M. Zbroszczyk, and B. Mroziewicz, “The influence of different heat sources on temperature distributions in broad-area diode lasers,” Proc. Conf. Advanced Optoelectronics and Lasers, Alushta, Crimea, Ukraine, vol. 1, pp. 252–254, Sep. 2003.
[27] L. V. Asryan, N. A. Gun’ko, A. S. Polkovnikov, R. A. Suris, G. G. Zegrya, B. B. Elenkrig, S. Smetona, J. G. Simmons, P. K. Lau, and T. Makino, “High-power and high-temperature operation of InGaAsP/InP multiple quantum well lasers,” Semicond. Sci. Technol., vol. 14, pp. 1069–1075, 1999.
[28] N. K. Dutta and R. J. Nelson, “Gain measurements in 1.3 µm InGaAsP-InP double heterostructure lasers,” IEEE J. Quantum Electron., vol. QE-18, no. 1, pp. 44–48, Jan. 1982.
[29] V. B. Gorfinkel and S. Luryi, “Fundamental limits for linearity of CATV lasers,” IEEE J. Lightw. Technol., vol. 13, no. 2, pp. 252–259, Feb. 1995. [30] L. D. Westbrook, “Measurements of dg/dN and dn/dN and their de-pendence on photon energy in λ = 1.5 µm InGaAsP laser diodes,” Proc.
Inst. Elect. Eng.—Optoelectron., vol. 133, pp. 135–142, Apr. 1986.
[31] G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. New York: Van Nostrand, 1993.
[32] C. G. Lim, “Rate equation modelling of nonlinear dynamics in directly modulated and self-pulsating semiconductor lasers,” Ph.D. dissertation Dept. Electron. Elect. Eng., Inst. Microwave and Photonics, Univ. Leeds, Leeds, U.K., 2001.
[33] K. L. Hall, G. Lenz, E. P. Ippen, U. Koren, and G. Raybon, “Carrier heating and spectral hole burning in strained-layer quantum-well laser ampifiers at 1.5 µm,” Appl. Phys. Lett., vol. 61, pp. 2512–2514, Nov. 1992.
Cheng Guan Lim (S’94–A’97–M’00) was born in
Singapore in 1971. He received the B. Eng. (Hon-ours) degree in electronic and electrical engineer-ing in 1997 and the Ph.D. degree at the Institute of Microwave and Photonics of Department of Elec-tronic and Electrical Engineering from the University of Leeds, Leeds, U.K., in 2001.
From 2001 to 2003, he was a Research Engi-neer at the Yokohama Research and Development Laboratories of The Furukawa Electric Company, Yokohama, Japan, working on the development of semiconductor laser modules for digital and analog telecommunication applica-tions. In 2003, he joined Agilent Technologies, Singapore, as a Senior Engineer focusing on optoelectronic device manufacturing. From 2004 to 2005, he was a Senior Research Scientist at the Institute for Infocomm Research, Singapore, (a member of the Agency for Science, Technology and Research-Singapore, and a National University of Singapore affiliated research institute) dealing with radio-over-fiber technologies. Presently, he is an Assistant Professor at the Department of Photonics/Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu, Taiwan R.O.C. where he is establishing the Computational Optoelectronics and Optical-components Laboratory (COOL). His prime research interest is in semiconductor device physics, in particular high-speed semiconductor devices used in communication systems, modelling and simulation of advanced semiconductor devices. At present, he is especially interested in optical injection technique for performance enhancement in
radio-over-fiber systems; optical generation and modulation of microwave/millimeter-waves based on optical injection phase-locked loop; developing a quick CSO and CTB evaluation scheme for CATV laser diodes; and photonic integrated circuits (PICs). He has one pending U.S. patent, one pending Japanese patent, and published several international refereed journal and conference papers.
Dr. Lim has served as a Steering Committee Member for the Inaugural IEEE International Workshop on Antenna Technology 2005 (Singapore), and as a Technical Program Committee member for the 2005 Symposium on Technol-ogy Fusion of Optoelectronics and Communications-International Conference on Photonics. In 1995, he was awarded the Crab Tree Prize for outstanding academic achievement, the Hewlett-Packard Prize in 1997 for the recognition as the best student in high-frequency engineering, and the F. W. Carter Prize in 2001 for presenting the best Ph.D. thesis.
Stavros Iezekiel (S’88–M’90–SM’00) received the
B.Eng. and Ph.D. degrees in electronic and electri-cal engineering from the University of Leeds, Leeds, U.K., in 1987 and 1991, respectively. His Ph.D. stud-ies concerned the nonlinear dynamics of laser diodes. From 1991 to 1993, he worked in conjunction with M/A-COM Corporate R&D Center on the develop-ment of microwave photonic multichip modules. He is now a Senior Lecturer at the University of Leeds, where he leads the research activity in microwave photonics.
Dr. Iezekiel received the 1999 IEE Measurement Prize for his work on light-wave network analysis. As a member of the UKRI MTT/ED/AP/LEO Joint Chapter AdCom, he has organized a number of IEEE events, and he is also the U.K. Representative for Commision D of URSI.
Christopher M. Snowden (S’82–M’82–SM’91–
F’96) received the B.Sc. (Hons.), M.Sc., and Ph.D. degrees in electronic and electrical engineering from the University of Leeds, Leeds, U.K., in 1977, 1979, and 1982, respectively.
He is Vice-Chancellor and Chief Executive of the University of Surrey, Surrey, U.K. Prior to this, he was Chief Executive Officer of Filtronic ICS. He joined Filtronic plc in 1998 as Director of Technology be-fore being promoted to Joint Chief Executive Officer in 1999. He is a non-executive Director of Intense Ltd., designing and manufacturing photonic products, and CENAMPS Ltd., which is involved in microsystems and nanotechnology. He is a member of the U.K.s National Advisory Committee on Electronic Materials and Devices, and an Advisor on the U.K.s Office of Science and Technology/DTI Foresight Pro-gramme. He is Deputy Chairman of the European Microwave Association. He worked as the Senior Staff Scientist in Corporate Research and Development at M/A-COM Inc. in the USA, from 1989 to 1991. He has been a consultant for several other major international microwave electronics companies in the USA and U.K. He held the personal Chair of Microwave Engineering at the Univer-sity of Leeds from 1992 to 2005 and during the period 1995–98 he was Head of the School of Electronic and Electrical Engineering. He was the Founder and first Director of the Institute of Microwaves and Photonics located in the School. During his time at Leeds, he has supervised 49 successful Ph.D. candidates. He was a Visiting Professor at the University of Durham until 2005.
Prof. Snowden is a Fellow of the Royal Academy of Engineering, a Fel-low of the IEE, and a FelFel-low of the City and Guilds Institute. He was awarded the Royal Academy of Engineering’s Silver Medal in 2004. He is currently a Distinguished Lecturer for the IEEE Electron Devices Soci-ety. He was awarded the 1999 Microwave Prize of the IEEE Microwave Theory and Techniques Society. He has written eight books and over 300 papers. He is a member of the IEEE Compound Semiconductor Device Technology Committee.
