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Emil Voiculescu 1
Improving the beam quality by concurrently modifying the index and
the doping profile in LMA fibers
Emil Voiculescu
Technical University of Cluj, RO
Emil Voiculescu 2
Introduction
• We carried out a comprehensive study on the influence of the index profile over
the distribution of the optical power among various modes. A systematical
approach consisted in exploring most of the possible graded-index profiles, to
facilitate the fundamental mode by concurrently rejecting the higher modes, to
generate a so-called ‘quality beam’.
• Most common doping profiles have been considered first, then various other
kind of doping have been tested, in order to optimize the beam shape, i.e. to
increasing the higher-order mode attenuation.
• The LAD 3.2 has been used, and we are grateful to our colleague Dr Mircea
Hotoleanu, principal writer of the software, and Mr Ettiene Friedrich for having
helped in getting promptly the license from Liekki.
Emil Voiculescu 3
Graded index profile: standard notation of principal quantities
n – the refractive index
n1 – n2 − profile heightΔ = ( n1 – n2 ) / n1 ≤ 1 %
NA = √n12 – n2
2
Δ = NA2/2n12
n2 = nSiO2 = 1.4573 – index of pure silica
n1 = √NA2+n22 = 1.45898
Emil Voiculescu 4
Large core fiber (40 μm diameter) Example of index profile for single mode operation
1,45721,45741,45761,45781,458
1,45821,45841,45861,45881,459
1,4592
0 0,000005 0,00001 0,000015 0,00002 0,000025
Core radius (m)
Ref
ract
ion
in
dex
To reject higher-order modes one needs a depression in the index characteristic around 9μm of radius and below one third of the index height n1 – n2.
Emil Voiculescu 5
Output optical power as a function of the fiber length
Second mode M2 drastically attenuated by the depressed index profile used
To reach maximum level, 6.5m of length will do
Emil Voiculescu 6
Doping profile used with the previous simulation : parabolic, most common
0,00E+00
2,00E+25
4,00E+25
6,00E+25
8,00E+25
1,00E+26
1,20E+26
1,40E+26
1,60E+26
1,80E+26
0 0,000005 0,00001 0,000015 0,00002 0,000025
Core radius [m]
Do
pan
t co
nce
ntr
atio
n
Doping characteristic as given by the fiber manufacturer (implicitly set by the simulator)
Emil Voiculescu 7
Large core (40 μm diameter) ytterbium-doped fiber
Larger gain, tentatively modified doping profile to assist in higher-order modes rejection
Emil Voiculescu 8
Doping profiles used
0,00E+00
2,00E+25
4,00E+25
6,00E+25
8,00E+25
1,00E+26
1,20E+26
1,40E+26
1,60E+26
1,80E+26
0,00E+00 5,00E-06 1,00E-05 1,50E-05 2,00E-05 2,50E-05
Core radius [m]
Do
pan
t co
nce
ntr
atio
n
Emil Voiculescu 9
Doping profiles used
To obtain almost total suppression of higher-order modes as in the power plot,we still need to maintain the depression in the index profile
1,45721,45741,45761,45781,458
1,45821,45841,45861,45881,459
1,4592
0 0,000005 0,00001 0,000015 0,00002 0,000025
Core radius [m]
Ref
ract
ion
in
dex
Emil Voiculescu 10
Another common doping profile : linear (triangular), same 40 μm core diameter
0,00E+00
2,00E+25
4,00E+25
6,00E+25
8,00E+25
1,00E+26
1,20E+26
1,40E+26
1,60E+26
1,80E+26
0 0,000005 0,00001 0,000015 0,00002 0,000025
Core radius [m]
Do
pan
t co
nce
ntr
atio
n
Emil Voiculescu 11
Gain characteristic slightly lower, single mode operation maintained
Emil Voiculescu 12
Facts
• as narrowing the core diameter is out of question (which, however, is the only way to go from multimode to the single mode operation with lower power), then
• a pseudo-, or virtual-narrowing is necessary.
This consists in creating a depression in the index profile around
the middle of the core-radius, i.e. narrowing the high-index
region as much as the single-mode operation requires.
Emil Voiculescu 13
Is that so?
Yes, it is. If we indulge in placing the index depression point fartherfrom the fiber axis, or/and the index depression is less deeper, several higher-order modes might appear. Assume a step in the core-index profile, with a corner at 9 μm and a variation of 10-3 of the index :
1,45721,45741,45761,45781,458
1,45821,45841,45861,45881,459
1,4592
0 0,000005 0,00001 0,000015 0,00002 0,000025
Core radius [m]
Ref
ract
ion
in
dex
Emil Voiculescu 14
A step in the core-index profile, with a corner at 9 μm and a variation of 10-3 of the index
Second and third mode are more powerful than the fundamental mode, which is unacceptable
This time a parabolic doping profile – the one set by the manufacturer has been used.
Emil Voiculescu 15
Improving the behavior
However, one might improve that behavior by changing the doping profile as in the following diagram :
0,00E+00
2,00E+25
4,00E+25
6,00E+25
8,00E+25
1,00E+26
1,20E+26
1,40E+26
1,60E+26
1,80E+26
0 0,000005 0,00001 0,000015 0,00002 0,000025
Core radius [m]
Do
pan
t co
nce
ntr
atio
n
As the index step is 9 μm far from the fiber axis, the step in the doping profile has been intentionally set closer to the axis : 5 μm. This counts as a thinner-core fiber.
Emil Voiculescu 16
Simulation results
All modes attenuated beginning with 6.7 dB for M2. Obviously, optimization required.
Emil Voiculescu 17
Facts
• If virtual thinner-core fibers are to be emulated, then the worst-case happens for the thickest core : 40 μm for Liekki LMA fibers;
• If one try to bypass the step in the doping profile, or to push it farther from the fiber axis, or to move outside the steps in both characte-ristics – index and dopant profiles, then the limits are clear. The following example is explicit. First
Let’s take a graded doping profile, a linear one :
0,00E+00
2,00E+25
4,00E+25
6,00E+25
8,00E+25
1,00E+26
1,20E+26
1,40E+26
1,60E+26
1,80E+26
0 0,000005 0,00001 0,000015 0,00002 0,000025
Core radius [m]
Do
pan
t C
on
ven
trat
ion
Do
pa
nt
co
nc
en
tra
tio
n
Emil Voiculescu 18
Facts
Then, a step depression in the core-index at the usual 9 μm distance from the axis...
1,45721,45741,45761,45781,458
1,45821,45841,45861,45881,459
1,4592
0 0,000005 0,00001 0,000015 0,00002 0,000025
Core radius [m]
Ref
ract
ion
co
nce
ntr
atio
nR
efra
ctio
n i
nd
ex
Emil Voiculescu 19
What happens?
Modes M3 and M2 are comparable with the useful M1 mode.
Emil Voiculescu 20
Conclusion
• One has to make a trade-off among both profile distortions; technological constraints apply.
• It seems that the depression in the index profile has to be in all circumstances close to a / 2, a being the core radius.
• The doping profile has to be modulated mostly the same way, however it is less effective in distributing the power among modes, it rather influences the total amount of generated power.
Emil Voiculescu 21
Is this behavior the same in thinner-core fibers ?
Yes, it is. Let’s take the following example : a 30 μm-thick core Ytterbium-doped fiber provided with a linear graded index (depression point at 9 μm from the axis, easier to be bypassed ).
1,45721,45741,45761,45781,458
1,45821,45841,45861,45881,459
1,4592
0 2E-06 4E-06 6E-06 8E-06 1E-05 1E-05 1E-05 2E-05
Core radius [m]
Ref
ract
ion
in
dex
Emil Voiculescu 22
Is this behavior the same in thinner-core fibers ?
We want to attenuate higher-order modes, so we deliberately introduce a step depression in the doping profile :
0,00E+00
2,00E+25
4,00E+25
6,00E+25
8,00E+25
1,00E+26
1,20E+26
1,40E+26
1,60E+26
1,80E+26
0 2E-06 4E-06 6E-06 8E-06 1E-05 1E-05 1E-05 2E-05
Core radius [m]
Do
pan
t co
nce
ntr
atio
n
Emil Voiculescu 23
Simulation results
An attenuation of 8.5 dB of mode M2 follows, which might be further improved.
Emil Voiculescu 24
Simulation results
It is even better for 20 μm core fibers.
Take this graded-index fiber :
1,45721,45741,45761,45781,458
1,45821,45841,45861,45881,459
1,4592
0 0,000002 0,000004 0,000006 0,000008 0,00001 0,000012
Core radius [m]
Ref
ract
ion
in
dex
Emil Voiculescu 25
Simulation results
And let us use the implicit parabolic doping :
0,00E+00
2,00E+25
4,00E+25
6,00E+25
8,00E+25
1,00E+26
1,20E+26
1,40E+26
1,60E+26
1,80E+26
0 0,000002 0,000004 0,000006 0,000008 0,00001 0,000012
Core radius [m]
Do
pan
t co
nce
ntr
atio
n
Emil Voiculescu 26
Simulation results
This pure single-mode operation results:
Emil Voiculescu 27
Simulation results
If we try to ignore the depression point in the index profile, for instance by choosing a parabolic graded index in the core (very common) :
1,45721,45741,45761,45781,458
1,45821,45841,45861,45881,459
1,4592
0 0,000002 0,000004 0,000006 0,000008 0,00001 0,000012
Core radius [m]
Ref
ract
ion
in
dex
Emil Voiculescu 28
Simulation results
Then, even if we modify the doping profile to assist with higher order modes rejection / attenuation :
0,00E+00
2,00E+25
4,00E+25
6,00E+25
8,00E+25
1,00E+26
1,20E+26
1,40E+26
1,60E+26
1,80E+26
0 0,000002 0,000004 0,000006 0,000008 0,00001 0,000012
Core radius
Do
pan
t co
nce
ntr
atio
n
Emil Voiculescu 29
Simulation results
We might get issues !
Emil Voiculescu 30
Conclusions
Anyway,
1. Mode M2 is over 6 time attenuated, and it could be attenuated more severely if the refraction index profile would be made up to fulfill the beam-aspect requirement.
2. It is a lot more easier to solve the single mode operation for the thinner-core fiber ( YDF DC 20 /400) than for the 30μm-core fiber and 40 μm-core fiber.
Emil Voiculescu 31
Conclusions
Allowed area to place the index characteristic in (the gray region) for single-mode operation - applies for 20μm-thick core LMA fibers.
Point D defines by its coordinates [r,n] the necessary depression in the index profile : D [ 5μm; 1,4582]
Emil Voiculescu 32
Conclusions
Depression point position obtained for the 30μm-thick core LMA fibers to get sufficient attenuation of the higher order modes
The index profile has to fit in the shaded area
Emil Voiculescu 33
Conclusions
Allowed area to place the index characteristic in (the gray region) for single-mode operation - applies for 40μm-thick core LMA fibers.
The index profile has to fit in the shaded area
Emil Voiculescu 34
Final thoughts and perspective work
• Main concern: as operation is forcibly moved to the single-mode, the virtual
narrowing of the physical core raises the problem of the energy distribution in
the core, i.e. the energy density. This has to be studied next.
• Another obvious perspective will consist in verifying the assertions made in
this paper by practical experimenting. One has to find to what extent the
results we got can be implemented in the manufacturing process. And what
would be the actual outcome.
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