Laser diodes with phase conjugate feedback

Risø National Laboratory
Laser diodes with phase conjugate feedback
Paul M. Petersen
Risø National Laboratory, Denmark
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Generation of phase conjugate waves
A 4
A 1
Nonlinear
medium χ (3)
A 2
A 3
The classic configuration for four-wave mixing
The interaction between the three waves A 1 , A 2 and A 3 inside
the nonlinear medium leads to the generation of a phase conjugate
beam A 3 propagating exactly counteropposed to A 4
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Phase aberration correcting properties of
phase conjugate waves
original distorted corrected
• Corrects for phase aberrations inside the laser cavity
• Output beam of laser cavity close to the diffraction limit
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Phase conjugate mirrors
normal mirror phase conjugate mirror
The autoretracing property of phase conjugate mirrors
is important for the basic understanding of how these
mirrors work in laser cavities
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
High-power laser diode arrays
proton implantation
metallization
GaAs (p-type)
GaAlAs (p-type)
GaAlAs
GaAlAs (n-type)
GaAs (n-type)
gain
High output power (>50 W)
Long lifetimes (>30.000 h)
Very poor spatial and temporal coherence
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Optical phase conjugation using
photorefractive materials
BaTiO 3
crystals
Self-pumped phase conjugation
using photorefractive materials
•Self-organizing process leads to optical phase conjugation
•No external pump beams are needed
•High reflectivities (> 90 %) even at low optical power levels
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Improvement of the coherence properties
of laser diode arrays
Method: phase conjugate feedback
-effective coupling of the laser elements
-self starting feedback configuration
-at high output power instabilities take place
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Phase conjugate feedback
Løbel et al., Optics Lett. 23, 825 (1998)
Frequency selective phase conjugate feedback
eliminates instabilities
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)
.

Risø National Laboratory
Single-mode operation
Intensity [arb.]
FWHM=0.02 nm
(10 GHz)
PC-Feedback
Freely run.
0.63
nm
0.63
nm
810 811 812 813 814 815 816 817
Wavelength [nm]
100 µm
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Asymmetric phase conjugate feedback
Single-lobe configuration
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Far-field
output
Diffraction
limited output
with singlelobe
config.
Intensity [arb. units]
0
0
0
1.4 times the
diffraction limit
-5 -4 -3 -2 -1 0 1 2 3 4 5
Radiation angle [deg]
Single-lobe
Twin-lobe
Runs freely
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Etalon setup
Coherence degree γ
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
Array runs freely (2I th )
Feedback applied (2I th )
Feedback applied (3I th )
Output sent
to Michelson
interferometer
Coherence
length is
increased
several orders
of magnitude
0,1 1 10 100
Path difference [mm]
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)
.

Risø National Laboratory
Grating configuration
Phase conjugate
feedback only applied
to one of two far-field
lobes.
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Singlemode
(a)
Single-mode
operation
BW < 0.03 nm
Wavelength
is tunable
over 20 nm !
Intensity [arbitrary units]
807 808 809 810 811 812 813 814
Wavelength [nm]
(b)
(c)
(d)
(e)
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Optical phase conjugation using
semiconductor lasers
P. Kürz, R. Nagar, and T. Mukai, Appl.
Phys. Lett. 68, pp.1180-1182, 1996
•Highly efficient phase conjugation is obtained (R>>100 %)
•May be used for frequency stabilization of semiconductor
lasers in external feedback configurations
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Four-wave mixing operation in high power diodes
0
L
The nonlinear polarization is given by P=
ε χ( N)
E
nc
where χ( N) =− ( β+i)g(N) , g(N)=a(N-N
0)
ω
Z
R=R 1 Z=0
R=0
Gain and refractive
index gratings
A 1
A 3
Semiconductor
amplifier
A 2
Electrode
0
Z=L
dA1
* *
=−α0A1− γ( AA
1 4
+ A2A3) A4
(1A)
dz
*
dA2
* * * *
=+ α0A2 − γ( AA
1 4
+ A2A3) A3
(1B)
dz
dA3
* *
=+ α0A3+ γ( AA
1 4
+ A2A3) A2
(1C)
dz
*
dA4
* * * *
=− α0A4 + γ( AA
1 4
+ A2A3) A1
(1D)
dz
(1 − iβ
) g0
α0
=− is the effective gain
2(1 + P )
P
0
=
E
0
P
s
2
0
0
is the average intercavity pump intensity
2C
γ=-i α0
is the coupling factor
1+
P
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
DFWM in diodes using total internal reflection
0
Gain and refractive
index gratings
A 1
High reflective
coating
Z=0
Semiconductor
amplifier
Electrode
L
Z
A 3
A 2
Z=L
Antireflection
coating
Spatial- and temporal
filtering
Output
beam
M
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Generation of carriers is governed by the rate Equation:
dN I N 2
= − + D ∇ N − g ( N ) E
0
dt qV τ
s
(1)
where N(x,y,z) is the excited carrier population,
s
is the carrier recombination time,I is the injected current
D the ambipolar diffusivity, E 0 is the total optical field
g(N)=a(N-N 0 ) is the gain.
Assuming that:
N = N +∆nexp( i∆ky)
(2)
We find that the third order susceptibility is given by:
χ
FWM
⎛
⎞
⎜
⎟
χ
FWM ,max
1
=
⎜
⎟
2 2
E ⎜ IkD
0
s
τ ⎟
s 2
1+ 1+
2 θ
I ⎜ I
s
s
E ⎟
⎝ +
0 ⎠
2
(3)
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
The nonlinear susceptibility χ (3)
χ (3)
The third order nonlinear susceptibility versus the angle [in units of 1/( k(D
a
R
)-½)]
The nonlinear susceptibility is reduced to half the maximum at an angle
corresponding to:
2
E0
1+
1 Is
θ½
=
k Dτ
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)
s

Risø National Laboratory
The mode suppression factor
0
Z=0
Semiconductor
amplifier
Electrode
L
Z
Z=L
The output beam is a result of diffraction in the induced gratings inside
the semiconductor amplifier. The diffraction angle ’ inside the
semiconductor is given by: sin θ’ = λ/(Λn). For small angles the phase
difference between a wave diffracted at the front facet and the back facet
of the amplifier is given by:
δ = 2πnL/λ -2πnLcos θ’/λ = 2πn(1-cosθ’)/λ
Since 1-cosθ’= 2sin 2 (θ’/2) and n sin’ = sin we obtain:
4π
L
δ = Sin
λn
2
θ
2
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
The mode suppression factor
8
The mode suppression factor δ
6
4
2
1 2 3 4 5
The mode suppression factor δ of the induce
grating versus the angle between the interfering
laser beams in the four-wave interaction (L=1 mm,
n=3.4, •=810 nm)
In practice the factor must be somewhat larger 2 π to have effectively
suppression of different axial modes in the broad area amplifier.
The critical angle for which mode suppression occurs depends on the length of
the amplifier and is determined by :
θ =
crit
nλ
2Arcsin( )
2L
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Fundamental condition for laser action
In general, the laser system needs mode suppression from the
gratings and a large nonlinear susceptibility. This condition leads to
the condition that the angle must be chosen according to:
E0
1+
⎛ nλ
⎞ 1 Is
2arcsin
⎜
θ
2L ⎟ < <
⎝ ⎠ k Dτ
s
2
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Risø National Laboratory
Nonlinear gratings and mode suppression
(Numerical example)
Mode suppression
Inserting L=1 mm, n=3.4, •=810 nm for GaAlAs we
obtain crit
= 4.2
Nonlinear gratings
For GaAlAs the parameters are D a
=13cm 2 /s and R
=1
ns and consequently we obtain at 810 nm ½
= 6.5
Mode suppression and strong gratings are obtained
when 4.2 < < 6.5°
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)

Dynfrac amic tivein dexg gain andre rating -s
A1
Sem icond uctor
E lectro
amp lifier
A3 A2
O utpu t
b eam
Risø National Laboratory
Monolithic dynamic grating laser
Permanent grating
A 1
Dynamic gain and refractive
index gratings
Semiconductor
amplifier
A 3
A 2
Electrode
Output
beam
Paul Michael Petersen, Laser Diodes with External Feedback (tutorial)