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.