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Synchronization and Chaos in a Laser Diode driven by a Resonant Tunneling Diode
B. Romeira, J. M. L. FigueiredoCentro de Electrónica, Optoelectrónica e Telecomunicações,
Universidade do Algarve, Gambelas, 8005-139 Faro, [email protected], [email protected]
T. J. Slight, L. Wang, E. Wasige, C. N. IronsideDepartment of Electronics and Electrical Engineering,
University of Glasgow, Glasgow G12 8LT, United Kingdom
J. M. Quintana, M. J. AvedilloInstituto de Microelectrónica de Sevilla, IMSE-CNM,
Universidad de Sevilla, Sevilla, Spain
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Introduction
� We report on a novel approach to OptoElectronic integrated circuits (OEIC’s) for communications lasers.
� Vertical integration of a resonant tunnelling diode (RTD) and Laser Diode (LD) has been achieved
� Here we report on a hybrid integrated RTD-LD circuit (separate RTD and LD Chips)
� The hybrid circuit was initially built to obtain insight into the fully integrated chip
� Hybrid system has shown a variety of very interesting and potentially very useful operating regimes
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Outline
� Introduction to the RTD
� Theory of the RTD-LD circuit – the Liénard’s Oscillator theory – closely related to Van der Pol oscillator
� Chaos Theory
� Simple Oscillator
� Synchronised modes of operation
� Chaotic modes of operation
� Summary and conclusion
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RTD based Devices Optoelectronic and microwave circuits incorporating RTDs
RTDs features include pronounced nonlinear current-voltage (I-V)characteristic, wide-bandwidth NDR (up to few of THz), very high frequencysignal generation (up to hundreds of GHz), and relative easiness in fabrication.Because of these characteristics, it is expected on RTD based devices newprocessing circuits’ functionalities in optical and microwave domains.
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Emitter
contact (AuGe)NiAu silicalight
Substrate
collector
contact
The fundamental and third harmonic frequencies
were 342 GHz and 1.02 THz, respectively.
AlA
s
n I
nG
aA
s
InG
aA
s
n I
nG
aA
s
AlA
s
RTD
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Resonant Tunnelling DiodesA resonant tunnelling diode (RTD) is a device which uses quantum effects toobtain negative differential resistance (NDR).
Illustration of a typical RTD I-V characteristic and the effect of applied bias.
n InGaAs
n InGaAs
Emittern+ InGaAs
Substrate
AlAs
AlAsInGaAsDouble-Barrier{
n+ InGaAsCollector
~10 nm
DBQW-RTD Structure. The transmission probability for an
InGaAs/AlAs RTD.
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Integrate RTD-LD Chip layout
p-type
contact
n-type
contact
Laser
active
region
RTD
Silica
Insulating
Layer
3µm
wide
laser
ridge
22µm
wide
ridge
Semi-
insulating
substrate
Heavily
p-doped
InGaAs
contact layer
Laser
emission
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Resonant Tunnelling Diode driving a Laser Diode
Representation of the
electrical connections in the
PCB. The wire length was
4.5 mm and had total
inductance of 9 nH.
Schematic of the RTD-LD implemented circuit. Room temperature I-V characteristics.
� Hybrid Optoelectronic Integrated Circuit based on a RTD-LD
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Model and comparison with experiment
� Electrical Model: nonlinear second order differential equation
Experimental and modeled I-V curves
Equivalent Liénard’s oscillator
F(V)C
LR
V(t)
Vin(t)= VDC+VAC sin(2�fint)
Experimental and modeled
electrical self-oscillations.
From Kirchhoff’s rules, the circuit can be described by the
following equations:
Which are equivalent to the Liénard’s second-order
differential equation:
( )[ ]tfVVL
tIVFtVCtIinACDC
π2sin1
)()()()( +=+= ��
)2sin()()()()( tfVVGtVVHtVinAC
π=++ ���
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Model and comparison with experiment
� Optical Model: single mode rate equations
Electron density N(t) and the photon density S(t)
( ))(1
)(
0)(
0
)()()('
tS
tSNtNg
tN
q
tItN
ετϑ +−−−=
( ) ,)()(
)(1
)(
0)(
0)('
τ
β
τε
tN
p
tS
tS
tSNtNgtS +−
+−=
Parameters:
I (t) - current through the laser diode
given by Liénard’s model;
q - electron charge;
ϑ - active region volume;
τ - spontaneous electron lifetime;
τp – photon lifetime
� - spontaneous emission factor;
g0 - gain coefficient;
N0 - minimum electron density
required to obtain a positive gain;
ε- value for the nonlinear gain
compression factor. Photo-detected signal and the model output
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Synchronisation map as a function of the
frequency of the applied signal
(a)Shows the region of
synchronisation (white)
and unsynchronised
regions (blue)
(b)This is the bifurcation
map as a function of the
applied frequency
� Fixed applied signal amplitude of 0.15 V
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Frequency Division as a function of the frequency
of the applied signal� Experimental laser output when RF signals Vin(t)=VACsin(2�fint) are applied:
(a) Experimental spectrum of the laser optical output showing frequency division by 5
when VAC=150 mV and fin=2.5 GHz;
(b) Laser output showing frequency division by 2: VAC=150 mV at 0.9 GHz;
Experimental results are confirmed by the Liénard´s theory
when compared with the theoretical synchonization map
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Synchronisation 2D Map for the RTD-LD – from
the theory of the Liénards oscillator
This colour map show as coloured regions the synchronised areas (each colour
represents harmonically related frequencies) as a function of the amplitude and
frequency of the applied signal to the RTD-LD
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13
Optical spectrum of a quasi-periodic signal
when the DC bias is 1.806 V. The input RF
frequency is 2.2 GHz and power is -2 dBm.
Optical spectrum of a chaotic signal when the
DC bias is 1.809 V. The input RF frequency
is 2.2 GHz and power is -2 dBm.
Figures below present optical chaos results in a RTD-LD circuit that self-oscillates around
2.0 GHz subjected with a 2.2 GHz input frequency. When the bias voltage is increased
from 1.806 V to 1.809 V the optical signal becomes chaotic with a clear broad-band peak
near the input frequency.
Optical Chaos in a Laser Diode Driven by a Resonant Tunneling Diode –Experimental Observation
1.6 1.8 2.0 2.2 2.4-70
-60
-50
-40
-30
-20
-10
0
Op
tica
l O
utp
ut (a
. u
)
Frequency (GHz)
Broad-band peak
RF Signal
1.6 1.8 2.0 2.2 2.4-70
-60
-50
-40
-30
-20
-10
0
Op
tical O
utp
ut (a
. u
.)
Frequency (GHz)
RF Signal
Subharmonic/
ultrasubharmonic
peaks
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Theory confirms - RTD-LD Lyapunov Exponents
Chaotic regions C1 (exponent > 0) whenamplitude AC signal is increased to 1.5 V.
Quasi-periodic signals (exponent = 0) between
synchronized regions (exponent < 0) whenamplitude AC signal is 0.15 V.
Lyapunov Characteristic Exponents (LCEs), which provide a qualitative and quantitative
characterization of the RTD-LD dynamical behavior, are related to the exponentially fast
divergence or convergence of nearby trajectories in the phase space. They are used to
analyze the stability of the Liénard´s dynamical system and to check sensitive dependence
on initial conditions, that is, the presence of chaotic attractors.
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15
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RTD-LD 790 nm Circuit – The Route to Chaos (1)
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16
0.0 0.5 1.0 1.5 2.0
-70
-60
-50
-40
-30
-20
fin/3
RF signal
886 MHz
Optical O
utp
ut (a
. u
.)
Frequency (GHz)
(a) Injection locking (fin/1)
(b) Frequency Division by 3 (fin /3)
(c) Frequency Division by 6 (fin/6)
(d) Chaos
(a) (b)
(c) (d)
RTD-LD 790 nm Circuit – The Route to Chaos (2)
0.0 0.5 1.0 1.5 2.0
-70
-60
-50
-40
-30
-20
RF signal
823 MHz
fin/1
Op
tical O
utp
ut (a
. u
.)
Frequency (GHz)
0.0 0.5 1.0 1.5 2.0
-70
-60
-50
-40
-30
-20
-10
RF signal
930.0 MHz
fin/6
Optica
l O
utp
ut (a
. u
.)
Frequency (GHz)0.0 0.5 1.0 1.5 2.0
-70
-60
-50
-40
-30
-20
-10
Broad Spectrum
RF signal
930.1 MHz
Op
tica
l O
utp
u (
a. u
.)
F requency (GHz)
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17
Conclusions and future work
� The operation of the resonant tunnelling diode –laser diode (RTD-LD) circuit can be described by a Liénard’s oscillator approach.
� The model can be used to predict observed the synchronisation, quasi-periodic and chaos behaviour of electrical and optical output from the RTD-LD circuit
� Applications include clock recovery and encryption using synchronised chaos