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

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

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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

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

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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

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

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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.

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

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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

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

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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

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

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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

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

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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

100

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1000

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

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

• No filter

COF

0 100 200 300 400 500 600 700 800 900 10000

100

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800

900

1000

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

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

• No filter

COF

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000

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

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

Lorentzian

filter

0 100 200 300 400 500 600 700 800 900 10000

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400

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900

1000

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

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

Lorentzian

filter

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

900

1000

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

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

Lorentzian

filter

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

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

Lorentzian

filter

300 350 400 450 500 550 600 650 700300

350

400

450

500

550

600

650

700

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

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

Lorentzian

filter

300 350 400 450 500 550 600 650 700300

350

400

450

500

550

600

650

700

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

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

Lorentzian

filter

300 350 400 450 500 550 600 650 700300

350

400

450

500

550

600

650

700

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

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

Lorentzian

filter

300 350 400 450 500 550 600 650 700300

350

400

450

500

550

600

650

700

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

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

Lorentzian

filter

300 350 400 450 500 550 600 650 700300

350

400

450

500

550

600

650

700

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

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300 350 400 450 500 550 600 650 700300

350

400

450

500

550

600

650

700

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

Lorentzian

filter

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

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300 350 400 450 500 550 600 650 700300

350

400

450

500

550

600

650

700

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

Lorentzian

filter

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

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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

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

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Dynamical aspects

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Dynamical aspects - “complexity”

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

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

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

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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.

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

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Dynamics of the periodic frequency variations

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

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

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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)

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

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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

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

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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 ?

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

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Comparison of the spectra

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Comparison of the different spectra

• Controlled dynamics and chaos- Trade-off

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

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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