Abstract

We report experimental results of multiple Stokes generation of a frequency-doubled Nd:YAG laser in H2, D2, and CH4 in a focusing geometry. The energies at four Stokes orders were measured as functions of pump energy and gas pressure. The characteristics of the Stokes radiation generated in these gases are compared for optical production of multiple wavelengths. The competition between Raman components is analyzed in terms of cascade Raman scattering and four-wave mixing. The results indicate the possibility of using these generation processes for atmospheric aerosol measurements by means of multiwavelength lidar systems. Also this study distinguishes between the gases, as regards the tendency to produce several wavelengths (H2, D2) versus the preference to produce mainly first Stokes radiation (CH4).

© 1991 Optical Society of America

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  1. P. Ping, H. Nakane, Y. Sasano, S. Kitamura, “Numerical simulation of the retrieval of aerosol size distribution from multiwavelength laser radar measurements,” Appl. Opt. 28, 5259–5265 (1989).
    [CrossRef]
  2. H. Muller, H. Quenzel, “Information content of multispectral lidar measurements with respect to the aerosol size distribution,” Appl. Opt. 24, 648–654 (1985).
    [CrossRef] [PubMed]
  3. R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984).
  4. Y. Sasano, E. V. Browell, “Light scattering characteristics of various aerosol types derived from multiple wavelength lidar observations,” Appl. Opt. 28, 1670–1679 (1989).
    [CrossRef] [PubMed]
  5. O. Uchino, M. Tokunaga, M. Maeda, Y. Miyazoe, “Differential-absorption-lidar measurement of tropospheric ozone with excimer-Raman hybrid laser,” Opt. Lett. 8, 347–349 (1983).
    [CrossRef] [PubMed]
  6. A. Papayannis, G. Ancellet, J. Pelon, G. Megie, “Multiwavelength lidar for ozone measurements in the troposphere and the lower stratosphere,” Appl. Opt. 29, 467–476 (1990).
    [CrossRef] [PubMed]
  7. J. J. Ottusch, D. A. Rockwell, “Measurement of Raman gain coefficient of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076–2080 (1988).
    [CrossRef]
  8. D. C. Hanna, D. J. Pointer, D. J. Pratt, “Stimulated Raman scattering of picosecond light in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. QE-22, 332–336 (1986).
    [CrossRef]
  9. W. K. Bischel, M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677–682 (1986).
    [CrossRef]
  10. D. A. Russell, W. B. Roh, “High-resolution CARS measurement of Raman linewidths of deuterium,” J. Mol. Spectrosc. 124, 240–242 (1987).
    [CrossRef]
  11. N. Bloembergen, G. Bret, P. Lallemand, A. Pine, P. Simova, “Controlled stimulated Raman amplification and oscillation in hydrogen gas,” IEEE J. Quantum Electron. QE-3, 197–201 (1967).
    [CrossRef]
  12. G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
    [CrossRef]
  13. R. Mahon, T. J. McIlrath, V. P. Myerscough, D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
    [CrossRef]
  14. J. J. Fox, F. G. H. Tate, “Refractivity of all gases and vapors and of elementary substances in the isotropic solid and liquid states,” in International Critical Tables of Numerical Data, Physics, Chemistry and Technology, E. W. Washburn, ed. (McGraw-Hill, New York, 1930), Vol. VII, pp. 1–11.
  15. J. Bartels, H. Borchers, H. Hausen, K.-H. Hellwege, K. L. Schafer, E. Schmidt, Landolt–Bornstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1962), pp. 6.871–6.885.
  16. T. R. Loree, R. C. Sze, D. L. Barker, P. B. Scott, “New lines in the UV: SRS of excimer laser wavelengths,” IEEE J. Quantum Electron. QE-15, 337–342 (1979).
    [CrossRef]
  17. D. Diebel, M. Bristow, R. Zimmerman, “Stokes shifted laser lines in KrF-pumped hydrogen: reduction of beam divergence by addition of helium,” Appl. Opt. 30, 626–628 (1991).
    [CrossRef] [PubMed]
  18. Z. Chu, U. N. Singh, T. D. Wilkerson, “A self-seeded SRS system for the generation of 1.54 μm eye-safe radiation,” Opt. Commun. 75, 173–178 (1990).
    [CrossRef]
  19. D. A. Haner, I. S. McDermid, “Stimulated Raman shifting of the Nd:YAG fourth harmonic (266 nm) in H2, HD and D2,” IEEE J. Quantum Electron. 26, 1292–1298 (1990).
    [CrossRef]
  20. W. B. Grant, E. V. Browell, N. S. Higdon, S. Ismail, “Raman shifting of KrF laser radiation for tropospheric ozone measurements,” Appl. Opt. 30, 2628–2633 (1991).
    [CrossRef] [PubMed]

1991 (2)

1990 (3)

Z. Chu, U. N. Singh, T. D. Wilkerson, “A self-seeded SRS system for the generation of 1.54 μm eye-safe radiation,” Opt. Commun. 75, 173–178 (1990).
[CrossRef]

D. A. Haner, I. S. McDermid, “Stimulated Raman shifting of the Nd:YAG fourth harmonic (266 nm) in H2, HD and D2,” IEEE J. Quantum Electron. 26, 1292–1298 (1990).
[CrossRef]

A. Papayannis, G. Ancellet, J. Pelon, G. Megie, “Multiwavelength lidar for ozone measurements in the troposphere and the lower stratosphere,” Appl. Opt. 29, 467–476 (1990).
[CrossRef] [PubMed]

1989 (2)

1988 (1)

J. J. Ottusch, D. A. Rockwell, “Measurement of Raman gain coefficient of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076–2080 (1988).
[CrossRef]

1987 (1)

D. A. Russell, W. B. Roh, “High-resolution CARS measurement of Raman linewidths of deuterium,” J. Mol. Spectrosc. 124, 240–242 (1987).
[CrossRef]

1986 (2)

D. C. Hanna, D. J. Pointer, D. J. Pratt, “Stimulated Raman scattering of picosecond light in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. QE-22, 332–336 (1986).
[CrossRef]

W. K. Bischel, M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677–682 (1986).
[CrossRef]

1985 (1)

1983 (1)

1979 (2)

R. Mahon, T. J. McIlrath, V. P. Myerscough, D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

T. R. Loree, R. C. Sze, D. L. Barker, P. B. Scott, “New lines in the UV: SRS of excimer laser wavelengths,” IEEE J. Quantum Electron. QE-15, 337–342 (1979).
[CrossRef]

1975 (1)

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
[CrossRef]

1967 (1)

N. Bloembergen, G. Bret, P. Lallemand, A. Pine, P. Simova, “Controlled stimulated Raman amplification and oscillation in hydrogen gas,” IEEE J. Quantum Electron. QE-3, 197–201 (1967).
[CrossRef]

Ancellet, G.

Barker, D. L.

T. R. Loree, R. C. Sze, D. L. Barker, P. B. Scott, “New lines in the UV: SRS of excimer laser wavelengths,” IEEE J. Quantum Electron. QE-15, 337–342 (1979).
[CrossRef]

Bartels, J.

J. Bartels, H. Borchers, H. Hausen, K.-H. Hellwege, K. L. Schafer, E. Schmidt, Landolt–Bornstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1962), pp. 6.871–6.885.

Bischel, W. K.

Bjorklund, G. C.

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
[CrossRef]

Bloembergen, N.

N. Bloembergen, G. Bret, P. Lallemand, A. Pine, P. Simova, “Controlled stimulated Raman amplification and oscillation in hydrogen gas,” IEEE J. Quantum Electron. QE-3, 197–201 (1967).
[CrossRef]

Borchers, H.

J. Bartels, H. Borchers, H. Hausen, K.-H. Hellwege, K. L. Schafer, E. Schmidt, Landolt–Bornstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1962), pp. 6.871–6.885.

Bret, G.

N. Bloembergen, G. Bret, P. Lallemand, A. Pine, P. Simova, “Controlled stimulated Raman amplification and oscillation in hydrogen gas,” IEEE J. Quantum Electron. QE-3, 197–201 (1967).
[CrossRef]

Bristow, M.

Browell, E. V.

Chu, Z.

Z. Chu, U. N. Singh, T. D. Wilkerson, “A self-seeded SRS system for the generation of 1.54 μm eye-safe radiation,” Opt. Commun. 75, 173–178 (1990).
[CrossRef]

Diebel, D.

Dyer, M. J.

Fox, J. J.

J. J. Fox, F. G. H. Tate, “Refractivity of all gases and vapors and of elementary substances in the isotropic solid and liquid states,” in International Critical Tables of Numerical Data, Physics, Chemistry and Technology, E. W. Washburn, ed. (McGraw-Hill, New York, 1930), Vol. VII, pp. 1–11.

Grant, W. B.

Haner, D. A.

D. A. Haner, I. S. McDermid, “Stimulated Raman shifting of the Nd:YAG fourth harmonic (266 nm) in H2, HD and D2,” IEEE J. Quantum Electron. 26, 1292–1298 (1990).
[CrossRef]

Hanna, D. C.

D. C. Hanna, D. J. Pointer, D. J. Pratt, “Stimulated Raman scattering of picosecond light in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. QE-22, 332–336 (1986).
[CrossRef]

Hausen, H.

J. Bartels, H. Borchers, H. Hausen, K.-H. Hellwege, K. L. Schafer, E. Schmidt, Landolt–Bornstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1962), pp. 6.871–6.885.

Hellwege, K.-H.

J. Bartels, H. Borchers, H. Hausen, K.-H. Hellwege, K. L. Schafer, E. Schmidt, Landolt–Bornstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1962), pp. 6.871–6.885.

Higdon, N. S.

Ismail, S.

Kitamura, S.

Koopman, D. W.

R. Mahon, T. J. McIlrath, V. P. Myerscough, D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

Lallemand, P.

N. Bloembergen, G. Bret, P. Lallemand, A. Pine, P. Simova, “Controlled stimulated Raman amplification and oscillation in hydrogen gas,” IEEE J. Quantum Electron. QE-3, 197–201 (1967).
[CrossRef]

Loree, T. R.

T. R. Loree, R. C. Sze, D. L. Barker, P. B. Scott, “New lines in the UV: SRS of excimer laser wavelengths,” IEEE J. Quantum Electron. QE-15, 337–342 (1979).
[CrossRef]

Maeda, M.

Mahon, R.

R. Mahon, T. J. McIlrath, V. P. Myerscough, D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

McDermid, I. S.

D. A. Haner, I. S. McDermid, “Stimulated Raman shifting of the Nd:YAG fourth harmonic (266 nm) in H2, HD and D2,” IEEE J. Quantum Electron. 26, 1292–1298 (1990).
[CrossRef]

McIlrath, T. J.

R. Mahon, T. J. McIlrath, V. P. Myerscough, D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

Measures, R. M.

R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984).

Megie, G.

Miyazoe, Y.

Muller, H.

Myerscough, V. P.

R. Mahon, T. J. McIlrath, V. P. Myerscough, D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

Nakane, H.

Ottusch, J. J.

J. J. Ottusch, D. A. Rockwell, “Measurement of Raman gain coefficient of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076–2080 (1988).
[CrossRef]

Papayannis, A.

Pelon, J.

Pine, A.

N. Bloembergen, G. Bret, P. Lallemand, A. Pine, P. Simova, “Controlled stimulated Raman amplification and oscillation in hydrogen gas,” IEEE J. Quantum Electron. QE-3, 197–201 (1967).
[CrossRef]

Ping, P.

Pointer, D. J.

D. C. Hanna, D. J. Pointer, D. J. Pratt, “Stimulated Raman scattering of picosecond light in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. QE-22, 332–336 (1986).
[CrossRef]

Pratt, D. J.

D. C. Hanna, D. J. Pointer, D. J. Pratt, “Stimulated Raman scattering of picosecond light in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. QE-22, 332–336 (1986).
[CrossRef]

Quenzel, H.

Rockwell, D. A.

J. J. Ottusch, D. A. Rockwell, “Measurement of Raman gain coefficient of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076–2080 (1988).
[CrossRef]

Roh, W. B.

D. A. Russell, W. B. Roh, “High-resolution CARS measurement of Raman linewidths of deuterium,” J. Mol. Spectrosc. 124, 240–242 (1987).
[CrossRef]

Russell, D. A.

D. A. Russell, W. B. Roh, “High-resolution CARS measurement of Raman linewidths of deuterium,” J. Mol. Spectrosc. 124, 240–242 (1987).
[CrossRef]

Sasano, Y.

Schafer, K. L.

J. Bartels, H. Borchers, H. Hausen, K.-H. Hellwege, K. L. Schafer, E. Schmidt, Landolt–Bornstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1962), pp. 6.871–6.885.

Schmidt, E.

J. Bartels, H. Borchers, H. Hausen, K.-H. Hellwege, K. L. Schafer, E. Schmidt, Landolt–Bornstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1962), pp. 6.871–6.885.

Scott, P. B.

T. R. Loree, R. C. Sze, D. L. Barker, P. B. Scott, “New lines in the UV: SRS of excimer laser wavelengths,” IEEE J. Quantum Electron. QE-15, 337–342 (1979).
[CrossRef]

Simova, P.

N. Bloembergen, G. Bret, P. Lallemand, A. Pine, P. Simova, “Controlled stimulated Raman amplification and oscillation in hydrogen gas,” IEEE J. Quantum Electron. QE-3, 197–201 (1967).
[CrossRef]

Singh, U. N.

Z. Chu, U. N. Singh, T. D. Wilkerson, “A self-seeded SRS system for the generation of 1.54 μm eye-safe radiation,” Opt. Commun. 75, 173–178 (1990).
[CrossRef]

Sze, R. C.

T. R. Loree, R. C. Sze, D. L. Barker, P. B. Scott, “New lines in the UV: SRS of excimer laser wavelengths,” IEEE J. Quantum Electron. QE-15, 337–342 (1979).
[CrossRef]

Tate, F. G. H.

J. J. Fox, F. G. H. Tate, “Refractivity of all gases and vapors and of elementary substances in the isotropic solid and liquid states,” in International Critical Tables of Numerical Data, Physics, Chemistry and Technology, E. W. Washburn, ed. (McGraw-Hill, New York, 1930), Vol. VII, pp. 1–11.

Tokunaga, M.

Uchino, O.

Wilkerson, T. D.

Z. Chu, U. N. Singh, T. D. Wilkerson, “A self-seeded SRS system for the generation of 1.54 μm eye-safe radiation,” Opt. Commun. 75, 173–178 (1990).
[CrossRef]

Zimmerman, R.

Appl. Opt. (6)

IEEE J. Quantum Electron. (7)

D. A. Haner, I. S. McDermid, “Stimulated Raman shifting of the Nd:YAG fourth harmonic (266 nm) in H2, HD and D2,” IEEE J. Quantum Electron. 26, 1292–1298 (1990).
[CrossRef]

T. R. Loree, R. C. Sze, D. L. Barker, P. B. Scott, “New lines in the UV: SRS of excimer laser wavelengths,” IEEE J. Quantum Electron. QE-15, 337–342 (1979).
[CrossRef]

N. Bloembergen, G. Bret, P. Lallemand, A. Pine, P. Simova, “Controlled stimulated Raman amplification and oscillation in hydrogen gas,” IEEE J. Quantum Electron. QE-3, 197–201 (1967).
[CrossRef]

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
[CrossRef]

R. Mahon, T. J. McIlrath, V. P. Myerscough, D. W. Koopman, “Third-harmonic generation in argon, krypton, and xenon: bandwidth limitations in the vicinity of Lyman-α,” IEEE J. Quantum Electron. QE-15, 444–451 (1979).
[CrossRef]

J. J. Ottusch, D. A. Rockwell, “Measurement of Raman gain coefficient of hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. 24, 2076–2080 (1988).
[CrossRef]

D. C. Hanna, D. J. Pointer, D. J. Pratt, “Stimulated Raman scattering of picosecond light in hydrogen, deuterium, and methane,” IEEE J. Quantum Electron. QE-22, 332–336 (1986).
[CrossRef]

J. Mol. Spectrosc. (1)

D. A. Russell, W. B. Roh, “High-resolution CARS measurement of Raman linewidths of deuterium,” J. Mol. Spectrosc. 124, 240–242 (1987).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

Z. Chu, U. N. Singh, T. D. Wilkerson, “A self-seeded SRS system for the generation of 1.54 μm eye-safe radiation,” Opt. Commun. 75, 173–178 (1990).
[CrossRef]

Opt. Lett. (1)

Other (3)

R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984).

J. J. Fox, F. G. H. Tate, “Refractivity of all gases and vapors and of elementary substances in the isotropic solid and liquid states,” in International Critical Tables of Numerical Data, Physics, Chemistry and Technology, E. W. Washburn, ed. (McGraw-Hill, New York, 1930), Vol. VII, pp. 1–11.

J. Bartels, H. Borchers, H. Hausen, K.-H. Hellwege, K. L. Schafer, E. Schmidt, Landolt–Bornstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1962), pp. 6.871–6.885.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup for the mutiple Stokes generation.

Fig. 2
Fig. 2

Calculated Raman gain coefficient gR as a function of gas pressure for H2, D2, CH4.

Fig. 3
Fig. 3

Calculated wave-vector mismatch Δk (a), and normalized conversion efficiency of second Stokes generated only by four-wave mixing (b), as a function of gas pressure for H2, D2, and CH4.

Fig. 4
Fig. 4

Energy conversion efficiency of first Stokes (□), second Stokes (▲), third Stokes (△), and first anti-Stokes (○) as a function of pump energy in (a) H2, (b) D2, and (c) CH4 at a pressure of 20 atm and with a 1-m focal-length lens. The residual fraction of pump light (●) is also indicated.

Fig. 5
Fig. 5

Residual fraction of pump (●) and energy conversion efficiency at first Stokes (□), second stokes (▲), and first anti-Stokes (○) in (a) H2, (b) D2, and (c) CH4 as a function of gas pressure for a constant pump energy of 150 mJ and a lens of 1-m focal length.

Fig. 6
Fig. 6

Residual fraction of pump and energy conversion efficiency for the Stokes orders is shown as a function of D2 gas pressure using two focusing geometries and a constant pump energy of 150 mJ. Different cases can be identified as residual pump with fL1 = 50 cm (●); first Stokes with fL1 = 50 cm (■); second Stokes with fL1 = 50 cm (▲); residual pump with fL1 = 100 cm (○); first Stokes with fL1 = 100 cm (□); second Stokes with fL1 = 100 cm (△).

Tables (3)

Tables Icon

Table I Parameters Used for the Calculation of the Raman Gain at a Pressure of 20 atm and Temperature of 25°C

Tables Icon

Table II Calculations of Optimum Pressure and Wave-Vector Mismatch for Second Stokes at a Pressure of 20 atm and Temperature of 25°C

Tables Icon

Table III Calculations of Optimization Pressure and Wave-Vector Mismatch for Anti-Stokes at a Pressure of 20 atm and Temperature of 25°C

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

g R = 2 λ s 2 h c ν s Δ N π c Δ ν ( d σ d Ω ) ,
g R = A p / Δ ν ,
I : ω S 2 = ω S 0 + ω S 1 ω AS 1 ,
II : ω S 2 = 2 ω S 1 ω S 0 .
P = B p 2 exp ( b | Δ k | ) ,
I : Δ k = k S 2 ( k S 0 + k S 1 k AS 1 ) ,
II : Δ k = k S 2 ( 2 k S 1 k S 0 ) ,
n = 10 6 p r 1 + T 273 + 1 ,
r = 10 6 ( n 0 ° C , 1 atm 1 ) ,
( 3 n 0 ° C , 1 atm 2 1 2 n 0 ° C , 1 atm 2 + 2 ) = a 1 a 4 λ 2 + a 2 a 5 λ 2 + a 3 a 6 λ 2 ,
b | Δ k | = C p ,
P = B p 2 exp ( C p ) ,
p * = 2 / C .
I : C = 2 π b 10 6 1 + T 273 ( r S 2 λ S 2 r S 0 λ S 0 r S 1 λ S 1 + r AS 1 λ AS 1 ) ,
II : C = 2 π b 10 6 1 + T 273 ( r S 2 λ S 2 2 r S 1 λ S 1 + r S 0 λ S 0 ) ,
I : p * = 10 6 π b ( 1 + T 273 ) ( r S 2 λ S 2 r S 0 λ S 0 r S 1 λ S 1 + r AS 1 λ AS 1 ) 1 ,
II : p * = 10 6 π b ( 1 + T 273 ) ( r S 2 λ S 2 2 r S 1 λ S 1 + r S 0 λ S 0 ) ,
III : ω AS 1 = ω S 0 + ω S 1 ω S 2 ,
IV : ω AS 1 = 2 ω S 0 ω S 1 .
11.2 p + 1.58 p
3.67 p + 3.58 p

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