Abstract: Microdisc lasers (MDLs) are an attractive option for on-chip laser sources, wavelength converters and even all-optical optical memory. We have developed a comprehensive model for the wavelength conversion in MDLs, which is compared with measurements

B J Offrein

C Minkenberg

F Horst

H J S Dorren

J Hofrichter

L Liu

N Chrysos

O Raz

R Kumar

T De Vries

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A fast and comprehensive microdisc laser model applied to
all-optical wavelength conversion
J. Hofrichter1, O. Raz2, F. Horst1, N. Chrysos1, C. Minkenberg1, T. de Vries2, H.J.S. Dorren2, R. Kumar3, 
L. Liu3 and B.J. Offrein1
1: IBM Research GmbH, IBM Research – Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
2: COBRA Research Institute, Eindhoven University of Technology, PO. Box 512, 5600MB Eindhoven, The Netherlands
3:Photonics Research Group, INTEC Department, Ghent University – IMEC, St. Pietersnieuwstraat 41, 9000 Ghent, Belgium
Abstract: Microdisc lasers (MDLs) are an attractive option for on-chip laser sources, wavelength converters and even all-optical 
optical memory. We have developed a comprehensive model for the wavelength conversion in MDLs, which is compared with 
measurements.
©2010 Optical Society of America
OCIS codes: (130.7405) Wavelength conversion devices; (230.7405) Wavelength conversion devices
1. Introduction
Microdisc lasers (MDLs) heterogeneously integrated on silicon wafers [1] as shown in Figs. 1(a) and (b) are an 
interesting candidate for on-chip laser sources [2], all-optical wavelength converters [3,4] and also all-optical 
memories [5,6]. Here, we investigate MDLs to demonstrate all-optical signal processing and switching. Within a 
MDL, several modes are competing. Several longitudinal modes may lase simultaneously, originating from the free 
spectral range (FSR) of the cavity being smaller than the the broad gain spectrum of the MQW gain material. All 
these modes may lase in both the clockwise and the counter-clockwise direction. Typically several lasing peaks are 
present as indicated in Fig. 1(c), where the main lasing mode is located at approx. 1585 nm, and the higher 
wavelength side-mode is present at approx. 1617 nm.
            
Fig. 1 – A MDL on a SOI waveguide, (a) microscope image, (b) cross section, (c) typical lasing spectrum of a MDL
Earlier numerical models of MDLs have concentrated on the dynamics of two counter propagating modes at the 
same wavelength [7,8]. These models cannot simulate the competition between longitudinal modes in gain-
dispersive media. There exists a model to describe the latter, using an estimated parabolic dependency of the gain 
with wavelength [9]. In this work, we have combined these models into a single model, simulating a disc laser 
having several co- and counter propagating modes. In the next section, the model will be described and in section 3, 
simulation results will be compared with measurements [4].
2. The 1D microdisc laser model 
To accurately simulate the behavior of a MDL as a wavelength converter, we implemented a 1D laser rate equation 
model. We expanded the model suggested by Van Campenhout et al. [1] for several modes and included self and cross 
gain suppression with the corresponding factors S and C [7-9]. A parabolic gain curvature was assumed to account 
for the non-uniform gain spectrum [10].  Equation (1) gives the radially dependent gain term where G0 is the 
maximum gain at the central lasing mode 0 and a is the gain curvature parameter. To save computation time and 
speed up the model, the photon densities Scw,ccw,i are modelled as lumped photon densities of the i-th mode with the 
corresponding propagation direction. Because we have a quantum well active material for the given devices, 
logarithmic gain is assumed, where N0 is the threshold carrier density.
2
, 0 0 , , , ,
0
( )
( , , ( ), ) 1 ( ) (1 ) lnCW CCW CW CCW S CW CCW i C CCW CW i
i i
n r
g S S n r r G a S S
N
              (1)
In Eq. (2), the carrier density is locally reduced by stimulated emission into the corresponding mode. Therefore the 
overlap with the modal distribution (r) is being calculated. For whispering gallery cavities, (r) can be 
approximated by a normalized Bessel function of the first kind  0/J r z , where  is the azimuthal order of the 
b ca
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corresponding mode and z0 the first Bessel zero of ( )J z . The modal distribution is normalized such that
2
0
( ) 1
R
r rdr  .
2
2 2 2 3
, , , , 2 2
( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )CW i CW i CCW i CCW i g
i i a
n r I n r n r
g r S g r S v r R An r Bn r Cn r D
t R qt r r r


    
                 
  (2)
Besides stimulated emission into the respective lasing modes, also non-lasing recombination is taken into account by
the coefficients A, B and C for one, two and three particle processes, respectively. The electrical pumping current I
flowing through the disk area R2 generates charge carriers in the active region, whose thickness is ta. Regions with 
depleted carrier concentrations due to stimulated emission in the region of the mode (spatial hole-burning) are 
refilled by diffusion of charge carriers with the diffusion constant D. In contrast to Eqs. (1) and (2) the photon 
densities defined in Eq. (3) are modelled by lumped variables whose spatial distribution is obtained from(r). Each 
photon density experiences a decay time constant p due to e.g. scattering or absorption.
, , , , 2 2 2
, , , ,0 0
int , , , , , , ,
2 ( ) ( ) 2 ( ) ( )
R RCW CCW i CW CCW i
CW CCW i g CW CCW i
p
CCW CW i ext ext CW CCW i CW CCW i
S S
S v g r r r r Bn r r r r
t
k S k S S
 


        

 
  (3)
The build-up of the mode is achieved by stimulated emission with the modal gain gCW,CCW,i in the active region,
whose overlap with the mode is  Also spontaneous emission with the factor B is coupled into the lasing mode with 
the spontaneous emission coupling factor . In addition, scattering due to sidewall roughness causes a coupling of 
the counter-propagating modes which is modelled by kint [11]. The external injection coupling factor kext models the 
coherent external injection [7,8] of light into the respective lasing mode. Table I lists the values of the parameters
used in the model. The model’s radial dependency enables the simulation of spatial hole-burning which limits output 
power, modal recovery and thus the device speed.
3. Simulations and experiments
MDLs can be operated as wavelength converters by injecting light into the non-dominant lasing mode, i.e., the mode 
at approx. 1617 nm in Fig. 1(c) for our case. By gain suppression, the previously dominant central lasing mode i.e. 
the mode at approx. 1586 nm, is suppressed. In order to operate at high bit rates and high repetition rates, we 
accelerated the recovery of the central by seeding low-power continuous-wave light into the central lasing mode 
[3,4]. When monitoring the relative eye opening 
1, 0, 1,max( ) /eye eyeEO P P P  during wavelength conversion, it becomes 
clear that seeding improves the eye opening for both 10 Gb/s and 20 Gb/s, As can be seen from Figs. 3(a) and (b), 
the EO is strongly improved by seeding of continuous-wave light into the central mode.
Fig. 3 – Relative eye opening (EO) in % at (a) 10 Gb/s and (b) 20 Gb/s.
The eye diagram for 50 W signal injection in the absence of seeding is reproduced in Figs. 4(a) and (d) for 10 and 
20 Gb/s. The largest EOs that can be achieved with seeding are shown in Figs. 4(b) and (e) for 10 and 20 Gb/s, 
respectively. The simulated eye diagrams demonstrate excellent agreement with the experimental data in Figs. 4(c) 
Table I. Simulation parameters
Param. R G0 N0 s c kint kext vg 0
Value 3.75 m 1500cm-1 1.5e18cm-3 2e-17 cm3 4e-17 cm3 1.5e8 s-1 8.8e10s-1 8.817e9 cm s-1 1550 nm
Param. A B C D   I a ta
Value 1e-8s-1 2e-10 cm3 s-1 1.63e-28 cm6 s-1 8 cm2 s-1 1e-3 0.267 3 mA 1.3e13 cm-3 18 nm
ba
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and (f). Although the power levels in the waveguide are experimentally inaccessible, the rise and fall times are not 
only equivalent but also symmetric in both cases. From Fig. 4(b) the 10%-to-90% rise time was estimated to be
approx. 55 ps. To further improve the operation speed of the devices, a higher external signal injection may be used. 
It was also found that a lower total intensity in the cavity, i.e. a smaller disc diameter, leads to faster switching time. 
Experimentally [4], the scheme of injection seeded disc lasers wavelength converter was shown to operate error-free 
with a bit-error rate (BER) of below 10-9 for the operation at 10 Gb/s when using seeding. Although the eye for 20 
Gb/s looks degraded, a BER of below 10-3 was achieved which is still below the forward-error correction (FEC) 
limit and thus acceptable for some applications.
Fig. 4 – Wavelength conversion: Simulation at 10 Gb/s with 50 W injection and (a) without seeding, (b) with 2W seeding,  (c) measurement at 
10 Gb/s with seeding. Simulation at 20 Gb/s with 50 W injection and (d) without seeding, (e) with 5W seeding, (f) measurement at 20 Gb/s
with seeding.
4. Conclusion
We have presented a fast and comprehensive model for the simulation of MDLs. The numerical studies on 
wavelength conversion of MLDs provided excellent agreement with measurements at both 10 and 20 Gb/s. It was 
shown that with seeding, wavelength conversion can be performed at 20 Gb/s with an acceptable BER. The model 
holds promise to facilitate the further exploration of various MDL functionalities, and to guide experimental work.
5. Acknowledgment
The authors acknowledge the financial support by the European Union FP7-ICT project “HISTORIC”.
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a b c
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A fast and comprehensive microdisc laser model applied to all-optical wavelength conversion

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A fast and comprehensive microdisc laser model applied to all-optical wavelength conversion

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