2
Synchronization and Chaos in a Laser Diode driven by a Resonant Tunneling Diode B. Romeira, J. M. L. Figueiredo Centro de Electrónica, Optoelectrónica e Telecomunicações, Universidade do Algarve, Gambelas, 8005-139 Faro, Portugal [email protected], [email protected] T. J. Slight, L. Wang, E. Wasige, C. N. Ironside Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8LT, United Kingdom J. M. Quintana, M. J. Avedillo Instituto de Microelectrónica de Sevilla, IMSE-CNM, Universidad de Sevilla, Sevilla, Spain 2 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 3 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 4 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 frequency signal generation (up to hundreds of GHz), and relative easiness in fabrication. Because of these characteristics, it is expected on RTD based devices new processing circuits’ functionalities in optical and microwave domains. Emitter contact (AuGe)NiAu silica light Substrate collector contact The fundamental and third harmonic frequencies were 342 GHz and 1.02 THz, respectively. AlAs n InGaAs InGaAs n InGaAs AlAs RTD 5 Resonant Tunnelling Diodes A resonant tunnelling diode (RTD) is a device which uses quantum effects to obtain negative differential resistance (NDR). Illustration of a typical RTD I-V characteristic and the effect of applied bias. n InGaAs n InGaAs Emitter n+ InGaAs Substrate AlAs AlAs InGaAs Double-Barrier { n+ InGaAs Collector ~10 nm DBQW-RTD Structure. The transmission probability for an InGaAs/AlAs RTD. 6 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 7 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 8 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 L R V(t) V in (t)= V DC +V AC sin(2f in t) 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: ( ) [ ] t f V V L t I V F t V C t I in AC DC π 2 sin 1 ) ( ) ( ) ( ) ( + = + = ) 2 sin( ) ( ) ( ) ( ) ( t f V V G t V V H t V in AC π = + + 9 Model and comparison with experiment Optical Model: single mode rate equations Electron density N(t) and the photon density S(t) ( ) ) ( 1 ) ( 0 ) ( 0 ) ( ) ( ) ( ' t S t S N t N g t N q t I t N ε τ ϑ + - - - = ( ) , ) ( ) ( ) ( 1 ) ( 0 ) ( 0 ) ( ' τ β τ ε t N p t S t S t S N t N g t S + - + - = Parameters: I (t) - current through the laser diode given by Liénard’s model; q - electron charge; ϑ - active region volume; τ - spontaneous electron lifetime; τ p – photon lifetime - spontaneous emission factor; g 0 - gain coefficient; N 0 - minimum electron density required to obtain a positive gain; ε- value for the nonlinear gain compression factor. Photo-detected signal and the model output 10 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 11 Frequency Division as a function of the frequency of the applied signal Experimental laser output when RF signals V in (t)=V AC sin(2f in t) are applied: (a) Experimental spectrum of the laser optical output showing frequency division by 5 when V AC =150 mV and f in =2.5 GHz; (b) Laser output showing frequency division by 2: V AC =150 mV at 0.9 GHz; Experimental results are confirmed by the Liénard´s theory when compared with the theoretical synchonization map 12 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 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 Optical Output (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 Optical Output (a. u.) Frequency (GHz) RF Signal Subharmonic/ ultrasubharmonic peaks 14 Theory confirms - RTD-LD Lyapunov Exponents Chaotic regions C 1 (exponent > 0) when amplitude AC signal is increased to 1.5 V. Quasi-periodic signals (exponent = 0) between synchronized regions (exponent < 0) when amplitude 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. 15 RTD-LD 790 nm Circuit – The Route to Chaos (1) 16 0.0 0.5 1.0 1.5 2.0 -70 -60 -50 -40 -30 -20 f in /3 RF signal 886 MHz Optical Output (a. u.) Frequency (GHz) (a) Injection locking (f in /1) (b) Frequency Division by 3 (f in /3) (c) Frequency Division by 6 (f in /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 f in /1 Optical Output (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 f in /6 Optical Output (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 Optical Outpu (a. u.) Frequency (GHz)

Introduction RTD based Devices Optoelectronic and microwave …w3.ualg.pt/~jlongras/2008-SIOE08ALGGLACNI-BR.pdf · 2017-07-17 · 17 Conclusions and future work The operation of the

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Page 1: Introduction RTD based Devices Optoelectronic and microwave …w3.ualg.pt/~jlongras/2008-SIOE08ALGGLACNI-BR.pdf · 2017-07-17 · 17 Conclusions and future work The operation of the

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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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2

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

���������� ������������ �����

3

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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4

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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5

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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6

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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7

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

���������� ������������ �����

8

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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9

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

���������� ������������ �����

10

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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11

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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12

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

���������� ������������ �����

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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14

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)

Page 2: Introduction RTD based Devices Optoelectronic and microwave …w3.ualg.pt/~jlongras/2008-SIOE08ALGGLACNI-BR.pdf · 2017-07-17 · 17 Conclusions and future work The operation of the

���������� ������������ �����

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