Controlling the dynamics time scale of a diode laser using filtered optical feedback

Controlling the dynamics time scale of a diode laser using filtered

optical feedback.A.P.A. FISCHER,

Laboratoire de Physique des Lasers, Universite Paris XIII, UMR CNRS 7538, FRANCE

G.VEMURI,

Indiana University, Indianapolis, IN, USA

M. YOUSEFI, D. LENSTRA, Vrije Universiteit Amsterdam, THE NETHERLANDS

WORKSHOP Les Houches - September 25, 26, 27st, 2001

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Motivation

• Defining and Designing optical systems for all optical signal processing. (Fast all optical device (ns time scale) for optical telecommunication) (DWDM).

• Investigating stability of DL locked on a selective element • Ability of locked laser to switch from one locked frequency to another one

(switching time)• Dynamics and chaos for diode laser with filtered optical feedback • Frequency selective element introduce a non linearity in frequency that leads

to new dynamics in frequency.• Is FOF a way of controlling the chaos “complexity”, in restricting the

“freedom” of the system ? • Only combination of experimental and theoretical results (simulations) can

distinguish noise from chaos.

C.O.F F.O.F

Conventional Optical Feedback Filtered Optical Feedback


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Description of the system• Schematic • Filter : frequency to power conversion

– Gain– Phase

• Diode laser : tunable frequency generator – Current I– optical injection

• Optical Feedback loop :– An external cavity loop– A ring cavity


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Filter• Fabry-Perot

interferometer

Transmitivity in power is an Airy function

• Equation of the filter for the simulation• Lorentzian filter : • 2 : FWHM m : resonance frequency• Amplitude & Phase

• Michelson interferometer

• birefringent slab in between polarizers

P P

012

1. cos.


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• On the flank of the filter a “linear” frequency-power conversion is operated.

• It is a frequency selective element

• It can be seen as a non linear element

Filter features


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Filter properties for a Fabry-Pérot interferometer

• The inverse of the resolution (=c/2ef) of the Fabry-Perot filter define a delay =1/ .

• Dynamics faster than are smoothed and averaged• The Fabry-Perot acts as a RC= filter. The cavity

(M1,M2) need to be “fulfilled” with multiple reflections.


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Semiconductor Diode Laser• Simulation parameters

– FIELD

– INVERSION

– Frequency tunability

– Slowly varying envelope approach : external cavity round trip time– n : normalized carrier inversion to threshold– P=|E|2 : photon number

– P0=(J-Jthr)/0 photon number under solitqry laser operation

: linewidth enhancement factor : differential gain coefficient– T1 : carrier lifetime, =(1+T1P0)/T1 0 : photon decay rate– J and J thr : pump current and threshold value

• Experimental characteristics– Fabry-Pérot type DL– Single mode 5mW output =780nm– solitary laser spectrum

– Tunabitlity :– 1 mA ---> 0,750 GHz


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Optical Feedback• Experiment

– EXTERNAL CAVITY :

– RING EXTERNALTY CAVITY

• Simulation parameters– FIELD

– INVERSION

– Frequency tunability

– FILTER

– Slowly varying envelope approach / : external cavity round trip time / n : normalized carrier inversion to threshold / P=|E|2 : photon number / P0=(J-Jthr)/0 photon number under solitqry laser operation / : linewidth enhancement factor / : differential gain coefficient / T1 : carrier lifetime, =(1+T1P0)/T1 / 0 : photon decay rate / J and J thr : pump current and threshold value / : feedback rate


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Analytical steady state solutions• Frequency shift s induced by the FOF :

• It is a transcendental equation

with related to the filter profile

is the extra phase added by the filter


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Graphical solutions - Steady state 0 (free running solution ) ----> = 0 + (new frequency due to FOF)

• Ceff=0

No feedback

0 100 200 300 400 500 600 700 800 900 10000

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• No filter

COF

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• No filter

COF

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Lorentzian

filter

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Lorentzian

filter

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Lorentzian

filter


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Lorentzian

filter

300 350 400 450 500 550 600 650 700300

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Lorentzian

filter

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Lorentzian

filter

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Lorentzian

filter

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Lorentzian

filter

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filter


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Lorentzian

filter


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Hysteresis• Principle of hysteresis in frequency


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Hysteresis in case of multiple filters

• Experiment• Sketch


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Temporal aspects of the steady state P

ow

er tra

nsm

itted thro

ugh

the

filter


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Temporal aspects of the steady state P

ow

er tra

nsm

itted thro

ugh

the

filter


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Dynamical aspects


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Dynamical aspects - “complexity”


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Dynamical aspects - Experiment• Fabry-Pérot filter d=0.027m, f=6,FWHM=926MHz


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Dynamical aspects - Experiment• Time series show periodic frequency variations• Period is related to the external cavity length

• Large filter (FWHM =1,47GHz) (e=1,7cm, finesse=6)

– External cavity oscillations.(52 MHz - 19ns - L1=2,85m)

Period of the frequency dynamics as a function of the external cavity length

05

1015202530

0 2 4 6Length of the external cavity (m)

pe

rio

d o

f th

e f

req

ue

ncy

va

riat

ion

s (

ns

)• Period of the frequency

variations is proportional to the external cavity length.


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Dynamics of the periodic frequency variations

• How to explain a self frequency modulation in a diode laser ?


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Dynamics • FOF creates “islands” of different

behaviours• Some ‘island” with periodical Frequency

variations• “Islands” with undamping of the

relaxation oscillations (RO)• Is that possible to suppress completely

the RO ? (with a narrow filter)


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Relaxation oscillations filtering ?• Narrow filter • (30MHz)

• Large filter• 3,5 GHz

• 230MHz

•Free running (~50MHz) (No

feedback)

•Line width narrowing ~10MH (Feedback ~-40dB)

•Periodical Frequency Variations (~ -35dB) (FM with low modulation index)

•Undamping of the RO (~ -30dB)

•Coherence collapse (-20dB)

• COF• inifinite


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Influence of the strengh of the non-linearity

• Fabry-Pérot filter FWHM= 230MHz

• Fabry-Pérot filterFWHM=520 MHz

•How does the filter width influences the dynamical behaviour ?


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Comparison of the spectra


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Comparison of the different spectra

• Controlled dynamics and chaos- Trade-off


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Diode lasers basicsRelaxation Oscillations

• Energy exchange between the inversion and the field in the laser.• Frequencies are typical a few GHz - related to the carrier lifetime

~0,2ns• Photon lifetime ~5 ps• Damping rates : 10 9 s-1

Documents

Controlling the dynamics time scale of a diode laser using filtered optical feedback