In high-speed laser devices the occurrence of a pho-ton-photon resonance increases the modulation bandwidth sub-stantially. In this paper our attention is focused on the design of DBR lasers in which this effect is exploite

P. Bardella, I. Montrosset

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PORTO Publications Open Repository TOrino

Design and simulation of DBR lasers  
with extended modulation bandwidth  
exploiting photon-photon resonance effects 
Paolo Bardella, Ivo Montrosset 
Dipartimento di Elettronica e Telecomunicazioni 
Politecnico di Torino, Torino, Italy 
ivo.montrosset@polito.it 
 
 
Abstract— In high–speed laser devices the occurrence of a pho-
ton–photon resonance increases the modulation bandwidth sub-
stantially. In this paper our attention is focused on the design of 
DBR lasers in which this effect is exploited. 
Keywords - DBR lasers, photon-photon resonance, detuned 
loading, extended modulation, time–domain simulation 
I.  INTRODUCTION 
In conventional high-speed laser devices the modulation re-
sponse is largely determined by the carrier–photon resonance 
(CPR). However, the occurrence of a photon–photon resonance 
(PPR) can increase the –3dB modulation bandwidth substan-
tially. In this paper our attention is focused on the design of a 
DBR cavity in which the PPR frequency is fixed by the design 
procedure. The PPR has been observed in distributed Bragg 
reflector (DBR) laser diodes [1,2], in coupled-cavity-injection-
grating (CCIG) lasers [3,5], and in passive-feedback lasers 
[6,7], but a thorough explanation to achieve this operation con-
dition also in simple DBR lasers has not been presented [8,9]. 
The design procedure for DBR cavity laser is here identified; 
the small and large signal modulation results presented support 
the correctness and accuracy of the proposed design procedure. 
II. DESIGN PROCEDURE 
In this paper we present a design procedure for a simple 
DBR cavity that allows obtaining with a good accuracy a PPR 
effect at the desired frequency. This is very important in prac-
tical applications because the gap between the traditional CPR 
and the PPR in the small signal intensity modulation (IM) re-
sponse should be filled by the contribution of the two effects in 
order to avoid unwanted reduction of the device modulation 
response (Fig.1). 
 For this reason the CPR response should be as wide as 
possible respect to the PPR frequency; this can obtained e.g. by 
operating the laser in the so called detuned loading condition 
[8]. When the laser is operating in this condition a particular 
attention must be paid to avoid mode competition between the 
lasing mode (at longer wavelength respect to the Bragg peak) 
and the cavity mode on the other side of the stop band. There-
fore the cavity should be designed in such a way that the Free 
Spectral Range of the cavity inside the grating stop band is 
comparable to the separation between the first two minima of 
the grating reflectivity function around the Bragg wavelength.  
Once this condition is fulfilled, and enhanced CPR modula-
tion bandwidth can be obtained without the risk of mode com-
petition, we can then enforce the second condition on the PPR 
frequency, which corresponds to the separation between the 
lasing mode and the side mode (PPR mode): we impose this 
side mode to be on the first side lobe of the reflectivity function 
as shown in the example of the Round Trip gain and phase 
function reported in Fig.2. 
Using the simple resonance equation condition for the de-
tuned lasing mode and the corresponding side mode generating 
the PPR one can relate the following cavity parameters: active 
 
Figure 1.  Example of IM responses. The PPR peak is not sufficient to obtain 
an efficient extension of the modulation bandwidth if a strong gap is present 
between CPR and PPR (black continuous line): the CPR should be wide 
enough to flatten the IM response (red dashed line). 
The work reported in this paper has been carried out within the EU FP7 
project “Development of low-cost technologies for the fabrication of high-
performance telecommunication lasers” (DeLight) under grant agreement n° 
224366. 
 
 
Figure 2.  Round Trip Gain (RTG, blue curve) and phase (red curve) function 
at threshold for a DBR cavity.. The squared red point represents the lasing 
mode; the blue markers indicate cavity modes below threshold. 
 
CPR PPR 
and grating section lengths (LA, LG), grating coupling coeffi-
cient () and PPR frequency. 
The results are reported in the map in Fig. 3, obtained for a 
chosen PPR frequency of 35GHz between the lasing mode 
operating at the maximum detuned loading condition and the 
PPR mode located in the first side mode of the reflectivity 
function: in the plane (LA - LG) we present the values of LG 
satisfying the requested PPR frequency.  
III. SIMULATION RESULTS 
For the device indicated by the marker in Fig. 3, whose 
characteristic parameters are illustrated in Table I, we com-
puted the small and the wide digital signal modulation response 
using our FiniteDifference TravellingWave  program [10]. 
In Fig. 4 a color map of the normalized small signal mod-
ulation response [11] is presented; the modulation frequency is 
reported in the abscissa while in the ordinates the lasing mode 
position respect to the Bragg frequency is varied changing the 
phase φA of the cleaved facet mirror reflectivity at the active 
region side. A similar tuning effect can be obtained changing 
the current injected in the Bragg grating. 
Evidence of PPR around 35GHz is quite clear from this 
modulation map. The dark strip the IM color map in the range 
0°30° corresponds to a self pulsation condition [10]. 
Large signal modulations were calculated for the three val-
ues of terminal phase indicated in Fig 4 using a NRZ PRBS 
signal at different modulation bit rates. The choice was done to 
compare the cases without (case A) and with (case B) PPR 
effect and to see the limitations to the maximum achievable 
large signal modulation introduced by a too pronounced mod-
ulation response peak in the small signal response (case C).  
The corresponding eye diagrams are presented in Fig. 5. As 
shown from the 40Gb/s signal modulation the response with a 
high resonance peak (case C) is strongly reducing the eye 
opening  and the small signal modulation bandwidth represents 
in this case an upper limit for the achievable large signal mod-
ulation.  In the other two cases (A, B) the large signal modula-
tion bandwidth can be extended significantly beyond the –3dB 
modulation band (up to 40Gb/s and 60Gb/s, respectively). 
IV. CONCLUSIONS 
A novel procedure to design DBR lasers with extended 
modulation bandwidth has been presented and validated by 
large signal digital modulation simulations. The results show 
that in some conditions it is possible to extend significantly the 
–3dB modulation bandwidth and also the transmission bit rate. 
REFERENCES 
[1] O. Kjebon et al., Electron. Lett., 33, pp. 488–489,  1997. 
[2] L. Bach et al., IEEE Photon. Technol. Lett., 16, pp. 18–20, 2004. 
[3] W. Kaiser et al., IEEE Photon. Technol. Lett., 16, pp. 1997–1999, 2004. 
[4] F. Gerschütz et al., Opt. Express, 16, pp. 5596–5601, 2008. 
[5] M. Vallone et al., IEEE J. Quantum. Electron., 47, pp. 1269–1276, 2011. 
[6] M. Radziunas et al., IEEE J. Sel. Top. Quantum Electron., 13, pp. 136–
142, 2007. 
[7] U. Troppenz et al., ECOC 2009, 20-24 September, Vienna, 2009. 
[8] U. Feiste, IEEE J. Quantum Electron., 34, pp. 2371–2379, 1998. 
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[10] L.A. Coldren, S.W. Corzine, Diode Lasers and Photonic Integrated 
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[11] P. Bardella, I. Montrosset, IEEE J. Sel. Top. Quantum Electron., 11, pp. 
361–366, 2005. 
 
TABLE I.  PARAMETERS USED IN THE TIMEDOMAIN ANALYSIS 
Parameters description and symbols [11] Values 
Active region length, LA 140µm 
Bragg grating region length, LG 780 µm 
Grating coupling coefficient,  21cm
-1 
Transversal optical confinement factor, Гxy 0.15 
Differential gain, a 10 10-16cm2 
Transparent carrier density, Ntr 10
18cm-3 
Active region intrinsic losses, αi,A 10cm
-1 
Bragg grating region intrinsic losses, αi,G 5cm
-1 
Linewidth enhancement factor, α 3 
Gain compression factor, ε 5 10-17 cm3 
 
  
Figure 5.  (left) 40Gb/s eye diagram computed for case A; extintion ratio 
 (ER) = 6dB. (center) 60Gb/s eye diagram computed for case B; ER = 4.5dB.  
(right) 40Gb/s eye diagram computed for case C.  
 
Figure 4.   Modulation map of the considered device, obtained at the bias 
current of 200mA, as a function of φA. The red continuous line  indicates the  
-3dB modulation response level, while the white dashed, continuous  and 
dotted lines represent the 0dB, +3dB and +5dB modulation response levels re-
spectively; the gray dash-dotted line refers to the output power whose values 
are reported on the axis in the upper border of the figure.The 3 values of the 
φA parameter considered for the large signal analysis are indicated with arrows 
 
Figure 3.  Values of LG (in µm) required to obtain a 35GHz PPR, as a 
function of LA and LG. The circular black marker highlights the structure 
considered in the TimeDomain analysis. 


Diode Lasers and Photonic Integrated Circuits,

TABLE I. PARAMETERS USED IN THE TIMEDOMAIN ANALYSIS Parameters description and symbols [11] Values Active region length, LA 140µm Bragg grating region length, LG 780 µm Grating coupling coefficient,  21cm -1 Transversal optical confinement factor,

Design and simulation of DBR lasers with extended modulation bandwidth exploiting photon-photon resonance effect

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