1. 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

2. 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.

3. Emil Voiculescu 3 Graded index profile: standard notation of principal quantities n – the refractive index n 1 – n 2 − profile height Δ = ( n1 – n2 ) / n1 ≤ 1 % NA = √ n 1 2 – n 2 2 Δ = NA 2 /2n 1 2 n 2 = n SiO 2 = 1.4573 – index of pure silica n 1 = √ NA 2 +n 2 2 = 1.45898

4. Emil Voiculescu 4 Large core fiber (40 μm diameter) Example of index profile for single mode operation 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 n 1 – n 2.

5. Emil Voiculescu 5 Output optical power as a function of the fiber length Second mode M 2 drastically attenuated by the depressed index profile used To reach maximum level, 6.5m of length will do

6. Emil Voiculescu 6 Doping profile used with the previous simulation : parabolic, most common Doping characteristic as given by the fiber manufacturer (implicitly set by the simulator)

7. Emil Voiculescu 7 Large core (40 μm diameter) ytterbium-doped fiber Larger gain, tentatively modified doping profile to assist in higher-order modes rejection

8. Emil Voiculescu 8 Doping profiles used

9. 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

10. Emil Voiculescu 10 Another common doping profile : linear (triangular), same 40 μm core diameter

11. Emil Voiculescu 11 Gain characteristic slightly lower, single mode operation maintained

12. 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.

13. Emil Voiculescu 13 Is that so? Yes, it is. If we indulge in placing the index depression point farther from 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 :

14. 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.

15. Emil Voiculescu 15 Improving the behavior However, one might improve that behavior by changing the doping profile as in the following diagram : 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.

16. Emil Voiculescu 16 Simulation results All modes attenuated beginning with 6.7 dB for M 2. Obviously, optimization required.

17. 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 : Dopant concentration

18. Emil Voiculescu 18 Facts Then, a step depression in the core-index at the usual 9 μm distance from the axis... Refraction index

19. Emil Voiculescu 19 What happens? Modes M 3 and M 2 are comparable with the useful M 1 mode.

20. 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.

21. 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 ).

22. 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 :

23. Emil Voiculescu 23 Simulation results An attenuation of 8.5 dB of mode M 2 follows, which might be further improved.

24. Emil Voiculescu 24 Simulation results It is even better for 20 μm core fibers. Take this graded-index fiber :

25. Emil Voiculescu 25 Simulation results And let us use the implicit parabolic doping :

26. Emil Voiculescu 26 Simulation results This pure single-mode operation results:

27. 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) :

28. Emil Voiculescu 28 Simulation results Then, even if we modify the doping profile to assist with higher order modes rejection / attenuation :

29. Emil Voiculescu 29 Simulation results We might get issues !

30. Emil Voiculescu 30 Conclusions Anyway, 1. Mode M 2 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.

31. 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]

32. 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

33. 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

34. 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.