1. Cascaded multi-dithering technique for high power beam combination setup Hee Kyung Ahn Korea Research Institute of Standards and Science (KRISS)

2. Introduction

3. Motivation High power, high beam quality lasers play a crucial role in industrial fields, military weapons, and scientific research. Coherent beam combination (CBC) CBC is a method to obtain high power and high quality beam by coherently adding low power beams. Active phase control Thermal effects and nonlinear effects limits the output power up to several tens of kW. 3/23

4. Locking of Optical Coherence by Single-detector Electronic-frequency Tagging (LOCSET) The maximum number of beam elements to be combined is limited to 100~200. PM MO... AMP MO: Master Oscillator PM: Phase Modulator AMP: Amplifier PD: Photodetector ω2ω2 ω1ω1... PM... LOCSET Electronics... ω3ω3 ωNωN Central robe of far field image PD Modulation Demodulation 4/23

5. Cascaded Multi-Dithering (CMD) technique -The series of modulating frequencies applied in LOCSET can be repeatedly used. -Up to 10,000 beams can be combined through 2 dimensional CMD, resulting in achieving ultra-high power and high beam quality lasers. Cascaded Multi-Dithering (CMD) technique 5/23

6. Theoretical background

7. ω1ω1 ωiωi ωNωN 1 LOCSET feedback PDPD LOCSET Schematic diagram Electric field of the i th modulated beam: Photocurrent i PD : i th error signal S i : i PD i th error signal S i is only proportional to the i th phase φ i. Feedback  Phase locking Modulating term i th phase 7/25 7/23

8. CMD Schematic diagram MxN beam combination 8/25 ΩMΩM Ω1Ω1 ΩkΩk PDPD PDPD 1 st line phase locking2 nd line phase locking PDPD ω1ω1 ωiωi ωNωN LOCSET feedback PDPD i PD Electronics ω1ω1 ωiωi ωNωN ω1ω1 ωiωi ωNωN k M 1 LOCSET feedback 8/23

9. 1 st line phase locking - LOCSET ω1ω1 ωiωi ωNωN Ω1Ω1 1 ω1ω1 ωiωi ωNωN ΩkΩk k PDPD PDPD 1 st line phase locking Formula: the same as those of LOCSET i th error signal S i : i th error signal S i is proportional only to the i th phase error φ i. 9/25 9/23

10. 2 nd line phase locking– CMD Electric field of i th of the 1 st line and k th of the 2 nd line modulated beam: k th error signal S k : k th error signal S k is proportional to the k th phase error Φ k. 1 st modulating term 2 nd modulating term k th phase 10/25 ΩMΩM Ω1Ω1 1 LOCSET feedback ΩkΩk M PDPD PDPD PDPD PDPD 2 nd line phase locking ω1ω1 ωiωi ωNωN i PD k 10/23

11. Limitation of CMD Constraints on CMD technique -The modulating frequencies in the 1 st line ω 1 to ω N and the modulating frequencies in the 2 nd line Ω 1 to Ω M should be chosen among the 100~200 limited frequencies in order to be discriminated one another in demodulation. -Ex) N frequencies in the 1 st line, (200-N) frequencies in the 2 nd line. Total number of beam elements to be combined: N*(200-N) -Up to 10,000 beams can be combined through 2 dimensional CMD, resulting in achieving ultra-high power lasers. Influence of beat and sum frequencies arising from modulating frequencies in series ΩkΩk ω1ω1 ωiωi ωNωN k 11/23

12. Simulation

13. ω 1 = 199.9 MHz ω 2 = 197.9 MHz ω 3 = 195.9 MHz ω 100 = 1.9 MHz β = 0.1π ω L = 1.94×10 14 M = 1.8×10 5 dt = 1/(6×10 9 ) t = [dt, Mdt] f s = 1/dt =6×10 9 Δω=2 MHz E 1 (i,1) = cos(2πω L t(i,1)+βsin(2πω 1 t(i,1)) + φ 1 ); E 2 (i,1) = cos(2πω L t(i,1)+βsin(2πω 2 t(i,1)) + φ 2 ); E 100 (i,1) = cos(2πω L t(i,1)+βsin(2πω 100 t(i,1)) + φ 100 );... Phase φ i,g is given random number df = 1/(Mdt)=0.3×10 5 freq = [0, 6×10 9 ] with 0.3×10 5 interval (180001) … Interval f in FFT : 0.03MHz error caused by beat and sum noises Simulation condition LOCSET for 100 beam combination 13/23

14. φ i,g ↔ φ i,c... (φ i,g -φ i,c )/ φ i,g... (= error) Simulating 100 times and averaging, = 1.09(±0.53)% of error The error is small enough to be neglected. Simulation results LOCSET for 100 beam combination 14/23

15. ω 1 = 199.9 MHz ω 2 = 197.9 MHz ω 3 = 195.9 MHz ω 50 = 101.9 MHz df = 1/(Mdt)=0.3×10 5 freq = [0, 6×10 9 ] with 0.3×10 5 interval (180001) … Interval f in FFT : 0.03MHz Ω 1 = 99.9 MHz Ω 2 = 97.9 MHz Ω 3 = 95.9 MHz Ω 50 = 1.9 MHz Δω=2 MHz … β = 0.1π γ = 0.1π ω L = 1.94×10 14 M = 1.8×10 5 dt = 1/(6×10 9 ) t = [dt, Mdt] f s = 1/dt =6×10 9 Δω=2 MHz Simulation condition CMD for 50×50 beam combination 15/23

16. error caused by beat and sum noises E 1 (i,1) = cos(2πω L t(i,1)+βsin(2πω 1 t(i,1)) + γsin(2πΩ 1 t(i,1)) + Φ 1 ) E 2 (i,1) = cos(2πω L t(i,1)+ βsin(2πω 2 t(i,1)) + γsin(2πΩ 1 t(i,1)) + Φ 1 ) E 50 (i,1) = cos(2πω L t(i,1)+ βsin(2πω 50 t(i,1)) + γsin(2πΩ 1 t(i,1)) + Φ 1 ) E 51 (i,1) = cos(2πω L t(i,1)+ βsin(2πω 1 t(i,1)) + γsin(2πΩ 2 t(i,1)) + Φ 2 ) E 2500 (i,1) = cos(2πω L t(i,1)+ βsin(2πω 50 t(i,1)) + γsin(2πΩ 50 t(i,1)) + Φ 50 )... Phase Φ k,g is given random number... 1 st array Simulation condition CMD for 50×50 beam combination 16/23

17. Φ k,g ↔ Φ k,c... (Φ k,g - Φ k,c )/ Φ k,g... (= error) Simulating 100 times and averaging, = 1.56(±0.52)% of error The error is small enough to be neglected, and a similar order of magnitude to that of LOCSET. H.K. Ahn and H.J. Kong, “The analysis of the feasibility the cascaded multi-dithering technique for coherent beam combining of a large number of beam elements ”, Appl. Opt. 55(15), p. 4101 (2016). Simulation results CMD for 50×50 beam combination 17/23

18. Experimental results

19. 19/23 16 beam combination through CMD Experimental setup

20. -16 beams was successfully combined with λ/31 of root mean square (RMS) phase error through CMD technique. 16 beam combination through CMD Results of 16 fiber beam combination 20/25 Open Loop Closed Loop H. K. Ahn, H. J. Kong, “Cascaded multi-dithering theory for coherent beam combining of multiplexed beam elements” Opt. Express 23(9), p. 12407 (2015). 20/23

21. Future perspectives

22. Multi-dimensional CMD technique ω1ω1 ω2ω2 ωNωN PD...... LOCSET feedback Ω1Ω1 1 ω1ω1 ω2ω2 ωNωN PD...... ΩMΩM M...... ω1ω1 ω2ω2 ωNωN...... Ω1Ω1 ω1ω1 ω2ω2 ωNωN...... ΩMΩM M............ 1 1 l...... Ψ1Ψ1 ΨlΨl...... Ultra high power beam! Low damage threshold of phase modulator cannot endure high-power amplified beam as the power of the combined beams get higher passing through stages. 22/23

23. ω1ω1 ω2ω2 ωNωN PD...... LOCSET feedback Ω1Ω1 1 PD ΩMΩM M...... Ω1Ω1 ΩMΩM M............ 1 1 l...... Ψ1Ψ1 ΨlΨl...... Multi-dimensional CMD technique ω1ω1 ω2ω2 ωNωN...... ω1ω1 ω2ω2 ωNωN...... ω1ω1 ω2ω2 ωNωN...... PD The problem can be easily overcome by amplifying beam elements after modulating the combined beam elements in series …! Amplifiers 23/23

24. Thank you for your attention!