Naval Research Labratry Washingtn, DC 0375-530 NRL/MR/6790--11-9371 Beam Cmbining and Atmspheric Prpagatin f High Pwer Lasers Phillip Sprangle Jseph Peñan Beam Physics Branch Plasma Physics Divisin Bahman Hafizi Icarus Research, Inc. Bethesda, Maryland Nvember 9, 011 Apprved fr public release; distributin is unlimited.
Frm Apprved REPORT DOCUMENTATION PAGE OMB N. 0704-0188 Public reprting burden fr this cllectin f infrmatin is estimated t average 1 hur per respnse, including the time fr reviewing instructins, searching existing data surces, gathering and maintaining the data needed, and cmpleting and reviewing this cllectin f infrmatin. Send cmments regarding this burden estimate r any ther aspect f this cllectin f infrmatin, including suggestins fr reducing this burden t Department f Defense, Washingtn Headquarters Services, Directrate fr Infrmatin Operatins and Reprts (0704-0188), 115 Jeffersn Davis Highway, Suite 104, Arlingtn, VA 0-430. Respndents shuld be aware that ntwithstanding any ther prvisin f law, n persn shall be subject t any penalty fr failing t cmply with a cllectin f infrmatin if it des nt display a currently valid OMB cntrl number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY). REPORT TYPE 3. DATES COVERED (Frm - T) 09-11-011 Interim May 011 September 011 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Beam Cmbining and Atmspheric Prpagatin f High Pwer Lasers 6. AUTHOR(S) Phillip Sprangle, Jseph Peñan, and Bahman Hafizi,* 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 67-9996-01 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Research Labratry 4555 Overlk Avenue, SW Washingtn, DC 0375-530 8. PERFORMING ORGANIZATION REPORT NUMBER NRL/MR/6790--11-9371 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) Office f Naval Research 875 Nrth Randlph Street, Suite 145 Arlingtn, VA 03-1995 10. SPONSOR / MONITOR S ACRONYM(S) ONR 11. SPONSOR / MONITOR S REPORT NUMBER(S) 1. DISTRIBUTION / AVAILABILITY STATEMENT Apprved fr public release; distributin is unlimited. 13. SUPPLEMENTARY NOTES *Icarus Research, Inc., P.O. Bx 30780, Bethesda, MD 0814-0780 14. ABSTRACT Slid state lasers are ne f the candidates fr efficient and cmpact directed energy systems. T achieve the necessary pwer levels many laser beams must be cmbined t frm a single fcused beam. We discuss cherent and incherent cmbining f multi-kw, high quality lasers and the effects f atmspheric turbulence and aersls n the prpagatin f the cmbined beams. We analyze the beam centrid wander and spreading cntributins t the spt size and btain the pwer n target fr a range f turbulence levels. We find that there is virtually n difference in the pwer n target between cherently cmbined and incherently cmbined beams. We als find that fr km-range prpagatin in mderate turbulence, there is a maximum intensity that can be prpagated t the target which is independent f initial beam size and beam quality. In additin, due t turbulence, it is nt necessary t have extremely high quality beams, i.e., M < 3 is sufficient. Fr lw levels f turbulence, tip-tilt crrectins can be used t reduce the beam centrid wander cntributin t the spt size. The HELCAP laser prpagatin cde is used t cmpare the prpagatin efficiency f cherently and incherently cmbined beams fr varius levels f turbulence and prpagatin ranges. 15. SUBJECT TERMS High pwer lasers Laser cmbining 16. SECURITY CLASSIFICATION OF: a. REPORT Turbulence b. ABSTRACT c. THIS PAGE Unclassified Unclassified Unclassified 17. LIMITATION OF ABSTRACT i 18. NUMBER OF PAGES UU 15 19a. NAME OF RESPONSIBLE PERSON Phillip Sprangle 19b. TELEPHONE NUMBER (include area cde) (0) 767-3493 Standard Frm 98 (Rev. 8-98) Prescribed by ANSI Std. Z39.18
Beam Cmbining and Atmspheric Prpagatin f High Pwer Lasers Phillip Sprangle, Jseph Peñan and Bahman Hafizi 1 Plasma Physics Divisin Naval Research Labratry Abstract Slid state lasers are ne f the candidates fr efficient and cmpact directed energy systems. T achieve the necessary pwer levels many laser beams must be cmbined t frm a single fcused beam. We discuss cherent and incherent cmbining f multi-kw, high quality lasers and the effects f atmspheric turbulence and aersls n the prpagatin f the cmbined beams. We analyze the beam centrid wander and spreading cntributins t the spt size and btain the pwer n target fr a range f turbulence levels. We find that there is virtually n difference in the pwer n target between cherently cmbined and incherently cmbined beams. We als find that fr km-range prpagatin in mderate turbulence, there is a maximum intensity that can be prpagated t the target which is independent f initial beam size and beam quality. In additin, due t turbulence, it is nt necessary t have extremely high quality beams, i.e., M < 3 is sufficient. Fr lw levels f turbulence, tip-tilt crrectins can be used t reduce the beam centrid wander cntributin t the spt size. The HELCAP laser prpagatin cde is used t cmpare the prpagatin efficiency f cherently and incherently cmbined beams fr varius levels f turbulence and prpagatin ranges. 1. Icarus Research, Inc., Bethesda MD Manuscript apprved Octber 18, 011 1
I. Intrductin Advances in slid state lasers, i.e., slab and fiber lasers, have made them candidates fr directed energy applicatins [1, ]. T achieve the necessary pwer levels needed fr these applicatins, it is necessary t cmbine a large number f lasers and prpagate the beam many kilmeters in a turbulent atmsphere. In the fllwing we discuss laser prpagatin in a maritime envirnment and cmpare the prpagatin characteristics f cherently and incherently cmbined beams, see Fig. 1. Based n ur analysis and simulatins we find that fr typical levels f turbulence 15 / 3 ( > 5 10 m ) and multi-km prpagatin ranges, there is virtually n difference, n target, between cherently and incherently cmbined laser beams. In strng turbulence, beam centrid wander and spreading are nt distinct, i.e., the beam breaks up int multiple beamlets. Therefre, emplying tip-tilt crrectin is less effective in strng turbulence than in weak turbulence. We find that when adaptive ptics are nt effective there is n advantage in having excellent quality laser beams; a beam quality f M < 3 is sufficient. There is a maximum intensity that can be placed n a target which is independent f the initial beam spt size (aperture) and laser beam quality M. II. Atmspheric Prpagatin (Spt Size, Intensity, Extinctin) Prpagatin thrugh atmspheric turbulence results in spreading f the laser beam radius and wandering f the laser beam centrid which lead t fluctuatins f the intensity n target. a) Laser Beam Radius The time averaged laser spt size R(L) at range L is given by R 4 ( L) = ( λ L / π R ) ( M +. 9( R / r ) ) + θ jitter L + R ( 1 L / L f ), (1) where R is the initial spt size, λ is the laser wavelength, M is the intrinsic laser beam L f quality, is the fcal length, is the transverse cherence length assciated with turbulence and θ is the mechanical jitter angle f the beam. Equatin (1) is valid fr the parameters jitter r cnsidered here [3,4]. The strength f the turbulence is characterized by the structure parameter 15 13 3 [4,5]. Typically is in the range f 10 / 10 m at grund level [4, 5]. Fr a
cnstant value f C n the transverse cherence length used 3 / 5. Hwever, as far as laser beam prpagatin is cncerned the effective strength f turbulence is nt determined by C alne, but als depends n the range f prpagatin and the wavelength. The n relevant cmbinatin is the Rytv variance, defined by σ = 10.5 R λ L 7 / 6 11/ 6. Fr weak turbulence ( σ << 1), beam wander and spreading are distinct and tip-tilt cmpensatin can be R used t crrect fr beam centrid wander. On the ther hand, fr strng turbulence ( σ > 1) the beam breaks up int multiple beams and beam wander and spreading are nt distinct, hence, tiptilt cmpensatin is less effective. The Rytv variance is a measure f the intensity scintillatin level n axi s at the targ ( ) et, i.e., σ R here is r = I I / I fr weak turbulence. = 0. 184( λ / L) R The laser spt size due t diffractin and turbulence, R = ( R + RW ) 1/ S, cnsists f a cntributin due t spreading and a cntributin due t centrid wander as shwn in Fig. R S. The beam centrid wander is given by R W R W 5/ 3 = 1. 7( λ L / π R ) ( R / r ), () and the spt size spreading is given by R = R. S R W b) Laser Intensity The peak laser intensity n axis, at the target, is where PT I peak M 6. 8 PT / r ) + = 4 +. 9( R ( π R θ jitter R / λ) λ L exp( γ L), (3) is the ttal transmitted laser pwer and γ = α + β is the atmspheric extinctin (absrptin and scattering) cefficient. In a maritime envirnment, aersl scattering dminates mlecular extinctin. Typical values fr aersl absrptin and scattering are α 1 10 A 3 km 1 and 1 β.1km, respectively, fr a laser wavelength f 1μm [6]. When turbulence is A 0 sufficiently strng, i.e., r 1.7 R / M, the intensity n target reaches a maximum and Eq. (3) reduces t < I max =.17 P ( r / λ L) exp( γ L). (4) T where mechanical jitter has been neglected. It is imprtant t nte that this maximum intensity is independent f the initial spt size and beam quality. Increasing the aperture size r imprving 3
beam quality will nt increase the intensity n target. Nte als that fr typical parameters this maximum intensity is btained fr mdest initial laser spt sizes f R 10cm. c) Prpagatin Efficiency The prpagatin efficiency is defined as the rati f the pwer n target t the ttal transmitted pwer and fr a Gaussian laser beam is given by η prp = ( 1 exp( R / R ))exp( γ L), (5) target where R target is the radius f the target. III. Beam Cmbining In this sectin we give a brief verview f the tw laser beam cmbining cnfiguratins. a) Cherent Cmbining Cherent beam cmbining [7] relies n cnstructive interference f many lasers t prduce high intensities n target, Fig. 1(a). It achieves this by effectively making the aperture size larger which, in vacuum, results in the peak intensity n target t be N, where I is the peak intensity f a single beam at the target and N is the number f cmbined beams. The diffractin length f the cmbined laser array is ~ N times lnger than that f the individual beams. Hwever, as Eq. (4) indicates, even fr relatively mderate turbulence, the peak intensity is essentially independent f aperture size s that the benefit f cherent cmbining is lst. In additin, cherent cmbining can be difficult t achieve. It requires phase lcking and plarizatin matching f the lasers, narrw linewidths ( δ λ / λ < 10 5 ) and gd ptical beam quality. The prpagatin efficiency fr cherent cmbining can als be limited by the filling factr f the laser array. A filling factr less than unity results in sme f the laser energy residing in side lbes utside f the central lbe. b) Incherent Cmbining Fr incherent cmbining [8] each beam is fcused and directed t the target by individually cntrlled steering mirrrs, Fig. 1(b). Incherent beam cmbining des nt require phase lcking, plarizatin matching r narrw linewidths. It shuld therefre result in a simpler and mre rbust system cmpared t the cherently cmbined cnfiguratin. The diffractin length is determined by the diffractin length f the individual beams. This is f little I 4
cnsequence in mderate t strng turbulence since the intensity n target becmes independent f the diffractin length, see Eq. (4). IV. Cmparisn f Cherent and Incherent Cmbining In cmparing the tw laser cmbining architectures we keep the size f the beam directr and ttal transmitted pwer the same, Fig. 3. We cmpare the laser spt size, prpagatin efficiency and intensity n target fr the tw cnfiguratins in the presence f varius levels f turbulence. In rder t minimize the number f parameters in the cmparisn, Gaussian beams are used in bth beam cmbining cnfiguratins. We assume that the laser linewidths are sufficiently small t be neglected. In bth cases beams are cmbined, either cherently r incherently. A single Gaussian f initial spt size R is used t mdel the N cherently cmbined beams [Fig.3(a)] while fr the incherently cmbined beams [Fig.3(b)] the initial spt sizes f the N beams is ˆ 1/ R BD / N where N ˆ = ( ( N 1) + 1). Althugh idealized mdels are used in the cmparisn the cnclusin is independent f whether the beams have a Gaussian, rectangular r ther prfile. We find that fr typical target ranges and levels f turbulence the spt size n target is essentially the same fr bth beam cmbining architectures. As an example cnsider the case where all beams in bth architectures are fcused n the target at range L. The spt size n target frm Eq. (1), fr the cherently cmbined and incherently cmbined beams are respectively given by R = π + CC N BD 4 1/ ( λ L / RBD )( M.9( RBD / r ) ), (6a) R = π ˆ + IC 4 1/ ( λ L / RBD ) ( N M.9( RBD / r ) ), (6b) where mechanical jitter has been neglected and the beam quality assciated with bth cnfiguratins are taken be the same and equal t M. In btaining Eq. (6) frm Eq. (1), the initial spt sizes fr the cherently and incherently cmbined beam cnfiguratins were taken t be R = and R R / Nˆ 1/, respectively. The nly difference in Eqs. (6a) and (6b) is in R BD = BD 4 the beam quality terms, i.e., terms prprtinal t M. The spt size n target is the same fr bth cmbining architectures when the level f turbulence is high enugh s that the transverse cherence satisfies ˆ 1/ r < 1.7 RBD /( N M ). (7) 5
This cnditin is easily satisfied fr typical ranges and levels f turbulence. As a specific example, we use the fllwing parameters in the cmparisn; ttal transmitted pwer PT = 100 kw, beam directr spt size R BD = 5cm, target range L = 5km, turbulence 15 / 3 level = 5 10 m ( r =. 7 cm, σ = 3.), target area π = 50cm ( R target = 4cm), R R target ttal extinctin cefficient γ = 0, number f cmbined beams N = 9, initial spt size f cherently cmbined beam R BD = 5 cm, initial spt size f incherently cmbined beams ˆ / 1 R BD / N = 6. 5cm and intrinsic beam quality M = 1. The result f the cmparisn is summarized in Table I. Nte that the maximum intensity frm Eq. (4) is I max = 617 W/cm. Cherently Cmbined Incherently Cmbined Spt size n target, R[cm] 10. 10.4 Centrid wander, RW [cm] 5. 4 6. 7 Prpagatin efficiency, η prp[%] 6 5 Intensity n target, I [W/cm ] 614 583 peak Table I. Shws the cmparisn between the tw cmbining architectures. We nw present a mre detailed cmparisn using the atmspheric laser prpagatin cde HELCAP. HELCAP is a 3-dimensinal, fully time-dependent, nnlinear atmspheric prpagatin cde, the details f which are discussed in Ref. 6. Atmspheric turbulence is mdeled by using phase screens distributed alng the prpagatin path which mdify the phase f the laser beam [6]. The phase perturbatins n each screen are characterized by a Klmgrv spectrum with a strength parameter. Fr the cmparisn the laser wavelength is chsen t be λ = 1μm, the spt size f the beam directr is RBD transmitted pwer is = 5cm, the range is P T L = 5km, the target area is 50cm and the ttal = 100 kw. Figure 3 shws the crss-sectinal area f the laser beams at the surce. Fr the cherent cmbining case the intensity is Gaussian with a 1/ e radius f 6
R / while fr the incherent cmbining case N = 9 laser beams are distributed in a square BD array pattern, with P = 11.1kW in each beam. In Fig. 4 the spt size n target is pltted as a functin f the refractive index structure cnstant C n. The curves are btained frm Eq. (6) and the dts are the results f HELCAP simulatins. The cherent cmbining results are shwn in red and the incherent cmbining results are shwn in blue. Figure 4 shws that virtually the same spt size is btained n the target irrespective f the cmbining architecture. Figure 5 is a plt f the n-axis intensity at the target, frm Eq. (3), versus the refractive index structure cnstant C. In the simulatins, the intensity is averaged ver a small 0.5 cm n area t reduce the variatins due t scintillatin. The cherent cmbining results are shwn in red and the incherent cmbining results are in blue. The peak intensity n target is essentially the 15 / 3 same fr bth cnfiguratins at mderate levels f turbulence r higher, i.e., > 5 10 m. Figure 6 cmpares the transverse prfiles f the laser beams n target. Qualitatively similar patterns are bserved n the target fr (a) cherent cmbining and (b) incherent cmbining cases, with pwer n target f 8 kw and 5 kw, respectively. Figure 7 shws the beam prfiles n target when tip-tilt crrectin is applied t remve beam centrid wander. Fr the incherent cmbining case, tip-tilt crrectin changes the rientatin f the entire array, and nt the relative rientatins f the individual beams. Cmparisn with Fig. 7 shws that tip-tilt crrectin reduces the spt size and nearly dubles the pwer n target. With tip-tilt crrectin the pwer n target is 50 kw fr (a) cherent cmbining and 44 kw fr (b) incherent cmbining. Figure 8 shws the spt size n target as a functin f turbulence level C n fr three values f beam quality, M = 1 (red), M = 3 (green) and M = 5 (blue). The curves are btained frm Eq. (6) and the dts are the results f HELCAP simulatins. Figure 8 indicates that the spt size n target is essentially the same, independent f initial beam quality, when the 15 / 3 turbulence level exceeds C 5 10 m. n 7
V. Cnclusins We have presented a cmparisn f cherent and incherent laser beam cmbining cnfiguratins that are ptential candidates fr efficient and cmpact directed energy applicatins. The pwer levels required fr these applicatins require that beams frm many lasers be cmbined. In the absence f turbulence, cherent cmbining has distinct advantages which include extended prpagatin range and higher intensity n target. Hwever, in the presence f typical levels f atmspheric turbulence these advantages may nt be realized. Fr example, fr typical hrizntal prpagatin, i.e., unifrm, ~ 5 km range, and mderate levels f turbulence, the peak intensity and spt size n target are virtually identical fr the tw cmbining cnfiguratins. We als find that there is a maximum intensity that can be prpagated t the target which is independent f initial beam size and beam quality fr kmranges and mderate turbulence. Hence, it is nt necessary t have extremely high quality beams, i.e., M < 3 is sufficient. Fr weak t mderate turbulence levels, tip-tilt crrectins and adaptive ptics can reduce beam wander and spreading fr bth cherently and incherently cmbined beams. The effects f turbulence can als be significantly reduced fr vertical r slanted prpagatin paths. Simulatin results frm the prpagatin cde HELCAP supprt these findings. Acknwledgments This wrk was supprted by the Office f Naval Research and the Naval Research Labratry. The authrs appreciate useful discussins with Peter Mrrisn and Quentin Saulter. 8
(a) Cherent cmbining P 0 N R BD (b) Incherent cmbining P 0 N R IC Figure 1: Schematic f (a) cherently and (b) incherently cmbined laser beams. y R wander R x R ST Figure : Schematic shwing the effects f turbulence n beam prpagatin, displacement (wander), and spt size is R = R W + R S. R S is the centrid is the increase in spt size (spreading). The lng-term average R w 9
(a) Cherent cmbining (b) Incherent cmbining R BD R IC Figure 3. Crss sectinal view f (a) cherent and (b) incherent cmbining cnfiguratins at the surce. T keep the beam directr dimensins the same the spt size f incherent beams 1/ (square array) is RIC = RBD /( ( N 1) + 1) fr N beams. Spt size n target [cm] Thery Simulatins Cherent Incherent 10-16 10-15 10-14 /3 [m Figure 4: Spt size n target [Eq. (6)] vs. fr cherently cmbined (red curve) and incherently cmbined (blue curve) beams. Red and blue dts dente HELCAP simulatin results fr cherently and incherently cmbined beams, respectively. The beam directr diameter is 50 cm and the range t the target is 5 km fr bth cases. The ttal transmitted pwer is 100 kw. Fr the incherent case, we assume 9 fibers with 11.1 kw per fiber. ] 10
Peak intensity [kw/cm ] Thery Simulatins Cherent Incherent 10-16 10-15 10-14 10-13 /3 [m Figure 5: Peak intensity n target [Eq. (3)] vs., fr cherently cmbined (red) and incherently cmbined (blue) beams fr the same parameters as Fig. 4. ] 11
Intensity [kw/cm ] (a) Cherent cmbining (b) Incherent cmbining Target area = 50 cm Pwer n target = 8 kw Target area = 50 cm Pwer n target = 5 kw Figure 6: Transverse prfiles f average intensity n target fr (a) cherently cmbined beams and (b) incherently cmbined beams. Aersl and mlecular absrptin and scattering have 15 / 3 been neglected. The turbulence level is = 5 10 m. The ttal transmitted pwer is 100 kw. Fr the incherent case, we assume 9 fibers with 11.1 kw per fiber. Fr a target with an area f 50 cm, the pwer n the target is 8 kw and 5 kw fr the cherently and incherently cmbined beams, respectively. Intensity [kw/cm ] (a) Cherent cmbining w/ tip-tilt crrectin (b) Incherent cmbining w/ tip-tilt crrectin Target area = 50 cm Pwer n target = 50 kw Target area = 50 cm Pwer n target = 44 kw Figure 7: Transverse prfiles f average intensity n target fr (a) cherently cmbined beams and (b) incherently cmbined beams with tip-tilt crrectin applied, i.e., n wander, fr the same parameters as Fig. 5. Fr a target with an area f 50 cm, the pwer n the target is 50 kw and 44 kw fr the cherently and incherently cmbined beams, respectively. 1
Spt size n target [cm] M Thery 1 = 3 5 Simulatins 10-16 10-15 10-14 10-13 /3 [m Figure 8: Spt size n target vs. Cn fr initial beam quality factrs M = 1 (red), 3 (green), and 5 (blue). Slid curves dente values frm Eq. (6), pints dente simulatin results. The initial beam spt size is 6.5 cm and the range t the target is 5 km fr bth cases. Results shw that spt size n target is relatively independent f beam quality fr > 10 14 / 3 m. ] 13
References 1. G.D. Gdn, et al., IEEE J. Sele. Tpics Quantum Electrn. 13, 460 (007).. D.J. Richardsn, J. Nilssn and W.A. Clarksn, J. Opt. Sc. Am. B 7, B63 (010). 3. Equatin (1) is valid fr r << R < L and L k L min, where L is the uter scale length and L = min( R, 0. 86 r ). min 4. R.L. Fante, Prc. IEEE 63, 1669 (1975). 5. L.C. Andrews and R.L. Phillips, Laser Beam Prpagatin thrugh Randm Media, SPIE Press, Bellingham, Washingtn, USA (005). 6. P. Sprangle, J. Penan and B. Hafizi, J. Directed Energy, 71 (006). 7. T.Y. Fan, IEEE J. Sel. Tpics Quantum Elect. 11, 567 (005). 8. P. Sprangle, A. Ting, J. Peñan, R. Fischer and B. Hafizi, IEEE J. Quantum Electrn. 45, 138 (009). 14