Abstract

In application, laser power is modulated prior to harmonic generation to a large part. Consequently modulation characteristics are influenced as a result of the non-linearity of harmonic generation. Within this paper, straight-forward approaches to calculate modulation key parameters (rise time, fall time, bandwidth and contrast ratio) of an acousto-optical modulator prior to harmonic generation stage are presented. The results will be compared to experimental data for third harmonic generation (THG) of a 1064 nm fs-laser which is power-modulated by a TeO2-AOM prior to THG. In the latter case, rise time and fall time are significantly reduced to approximately 66% after THG both in experimental and analytical study.

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References

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  1. N. Savage, “Acousto-optic devices,” Nat. Photonics4(10), 728–729 (2010).
    [CrossRef]
  2. A. W. Warner and D. A. Pinnow, “Miniature acousto-optic modulators for optical communications,” IEEE J. Quantum Electron.9(12), 1155–1157 (1973).
    [CrossRef]
  3. A. J. DeMaria, R. Gagosz, and G. Barnard, “Ultrasonic-refraction shutter for optical master oscillators,” Appl. Phys. (Berl.)34, 453–456 (1963).
  4. D. Maydan, “Fast modulator for extraction of internal laser power,” Appl. Phys. (Berl.)41, 1552–1559 (1970).
  5. J. H. Garcia-López, V. Aboites, A. V. Kir’yanov, M. J. Damzen, and A. Minassian, “High repetition rate Q-switching of high power Nd:YVO4 slab laser,” Opt. Commun.218(1-3), 155–160 (2003).
    [CrossRef]
  6. R. Mazelsky and D. K. Fox, “An introduction to acousto-optic materials,” Mater. Sci. Forum61, 1–6 (1990).
    [CrossRef]
  7. D. Maydan, “Acoustooptical pulse modulators,” IEEE J. Quantum Electron.6(1), 15–24 (1970).
    [CrossRef]
  8. I. C. Chang, “Acoustooptic devices and applications” in Handbook of Optics V, M. Bass, ed. (McGraw-Hill Professional, 2010)
  9. J. M. Khosrofian and B. A. Garetz, “Measurement of a gaussian laser beam diameter through the direct inversion of knife-edge data,” Appl. Opt.22(21), 3406–3410 (1983).
    [CrossRef] [PubMed]
  10. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Series in Pure & Applied Optics, 2007), Chap. 21.
  11. D. Eimerl, “High average power harmonic generation,” IEEE J. Quantum Electron.23(5), 575–592 (1987).
    [CrossRef]
  12. J. A. Armstrong, N. N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127(6), 1918–1939 (1962).
    [CrossRef]
  13. S. P. Velsko, M. Webb, L. Davis, and C. Huang, “Phase-matches harmonic generation in lithium triborate (LBO),” IEEE J. Quantum Electron.27(9), 2182–2192 (1991).
    [CrossRef]

2010 (1)

N. Savage, “Acousto-optic devices,” Nat. Photonics4(10), 728–729 (2010).
[CrossRef]

2003 (1)

J. H. Garcia-López, V. Aboites, A. V. Kir’yanov, M. J. Damzen, and A. Minassian, “High repetition rate Q-switching of high power Nd:YVO4 slab laser,” Opt. Commun.218(1-3), 155–160 (2003).
[CrossRef]

1991 (1)

S. P. Velsko, M. Webb, L. Davis, and C. Huang, “Phase-matches harmonic generation in lithium triborate (LBO),” IEEE J. Quantum Electron.27(9), 2182–2192 (1991).
[CrossRef]

1990 (1)

R. Mazelsky and D. K. Fox, “An introduction to acousto-optic materials,” Mater. Sci. Forum61, 1–6 (1990).
[CrossRef]

1987 (1)

D. Eimerl, “High average power harmonic generation,” IEEE J. Quantum Electron.23(5), 575–592 (1987).
[CrossRef]

1983 (1)

1973 (1)

A. W. Warner and D. A. Pinnow, “Miniature acousto-optic modulators for optical communications,” IEEE J. Quantum Electron.9(12), 1155–1157 (1973).
[CrossRef]

1970 (2)

D. Maydan, “Acoustooptical pulse modulators,” IEEE J. Quantum Electron.6(1), 15–24 (1970).
[CrossRef]

D. Maydan, “Fast modulator for extraction of internal laser power,” Appl. Phys. (Berl.)41, 1552–1559 (1970).

1963 (1)

A. J. DeMaria, R. Gagosz, and G. Barnard, “Ultrasonic-refraction shutter for optical master oscillators,” Appl. Phys. (Berl.)34, 453–456 (1963).

1962 (1)

J. A. Armstrong, N. N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127(6), 1918–1939 (1962).
[CrossRef]

Aboites, V.

J. H. Garcia-López, V. Aboites, A. V. Kir’yanov, M. J. Damzen, and A. Minassian, “High repetition rate Q-switching of high power Nd:YVO4 slab laser,” Opt. Commun.218(1-3), 155–160 (2003).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127(6), 1918–1939 (1962).
[CrossRef]

Barnard, G.

A. J. DeMaria, R. Gagosz, and G. Barnard, “Ultrasonic-refraction shutter for optical master oscillators,” Appl. Phys. (Berl.)34, 453–456 (1963).

Bloembergen, N. N.

J. A. Armstrong, N. N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127(6), 1918–1939 (1962).
[CrossRef]

Damzen, M. J.

J. H. Garcia-López, V. Aboites, A. V. Kir’yanov, M. J. Damzen, and A. Minassian, “High repetition rate Q-switching of high power Nd:YVO4 slab laser,” Opt. Commun.218(1-3), 155–160 (2003).
[CrossRef]

Davis, L.

S. P. Velsko, M. Webb, L. Davis, and C. Huang, “Phase-matches harmonic generation in lithium triborate (LBO),” IEEE J. Quantum Electron.27(9), 2182–2192 (1991).
[CrossRef]

DeMaria, A. J.

A. J. DeMaria, R. Gagosz, and G. Barnard, “Ultrasonic-refraction shutter for optical master oscillators,” Appl. Phys. (Berl.)34, 453–456 (1963).

Ducuing, J.

J. A. Armstrong, N. N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127(6), 1918–1939 (1962).
[CrossRef]

Eimerl, D.

D. Eimerl, “High average power harmonic generation,” IEEE J. Quantum Electron.23(5), 575–592 (1987).
[CrossRef]

Fox, D. K.

R. Mazelsky and D. K. Fox, “An introduction to acousto-optic materials,” Mater. Sci. Forum61, 1–6 (1990).
[CrossRef]

Gagosz, R.

A. J. DeMaria, R. Gagosz, and G. Barnard, “Ultrasonic-refraction shutter for optical master oscillators,” Appl. Phys. (Berl.)34, 453–456 (1963).

Garcia-López, J. H.

J. H. Garcia-López, V. Aboites, A. V. Kir’yanov, M. J. Damzen, and A. Minassian, “High repetition rate Q-switching of high power Nd:YVO4 slab laser,” Opt. Commun.218(1-3), 155–160 (2003).
[CrossRef]

Garetz, B. A.

Huang, C.

S. P. Velsko, M. Webb, L. Davis, and C. Huang, “Phase-matches harmonic generation in lithium triborate (LBO),” IEEE J. Quantum Electron.27(9), 2182–2192 (1991).
[CrossRef]

Khosrofian, J. M.

Kir’yanov, A. V.

J. H. Garcia-López, V. Aboites, A. V. Kir’yanov, M. J. Damzen, and A. Minassian, “High repetition rate Q-switching of high power Nd:YVO4 slab laser,” Opt. Commun.218(1-3), 155–160 (2003).
[CrossRef]

Maydan, D.

D. Maydan, “Acoustooptical pulse modulators,” IEEE J. Quantum Electron.6(1), 15–24 (1970).
[CrossRef]

D. Maydan, “Fast modulator for extraction of internal laser power,” Appl. Phys. (Berl.)41, 1552–1559 (1970).

Mazelsky, R.

R. Mazelsky and D. K. Fox, “An introduction to acousto-optic materials,” Mater. Sci. Forum61, 1–6 (1990).
[CrossRef]

Minassian, A.

J. H. Garcia-López, V. Aboites, A. V. Kir’yanov, M. J. Damzen, and A. Minassian, “High repetition rate Q-switching of high power Nd:YVO4 slab laser,” Opt. Commun.218(1-3), 155–160 (2003).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127(6), 1918–1939 (1962).
[CrossRef]

Pinnow, D. A.

A. W. Warner and D. A. Pinnow, “Miniature acousto-optic modulators for optical communications,” IEEE J. Quantum Electron.9(12), 1155–1157 (1973).
[CrossRef]

Savage, N.

N. Savage, “Acousto-optic devices,” Nat. Photonics4(10), 728–729 (2010).
[CrossRef]

Velsko, S. P.

S. P. Velsko, M. Webb, L. Davis, and C. Huang, “Phase-matches harmonic generation in lithium triborate (LBO),” IEEE J. Quantum Electron.27(9), 2182–2192 (1991).
[CrossRef]

Warner, A. W.

A. W. Warner and D. A. Pinnow, “Miniature acousto-optic modulators for optical communications,” IEEE J. Quantum Electron.9(12), 1155–1157 (1973).
[CrossRef]

Webb, M.

S. P. Velsko, M. Webb, L. Davis, and C. Huang, “Phase-matches harmonic generation in lithium triborate (LBO),” IEEE J. Quantum Electron.27(9), 2182–2192 (1991).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (Berl.) (2)

A. J. DeMaria, R. Gagosz, and G. Barnard, “Ultrasonic-refraction shutter for optical master oscillators,” Appl. Phys. (Berl.)34, 453–456 (1963).

D. Maydan, “Fast modulator for extraction of internal laser power,” Appl. Phys. (Berl.)41, 1552–1559 (1970).

IEEE J. Quantum Electron. (4)

A. W. Warner and D. A. Pinnow, “Miniature acousto-optic modulators for optical communications,” IEEE J. Quantum Electron.9(12), 1155–1157 (1973).
[CrossRef]

D. Maydan, “Acoustooptical pulse modulators,” IEEE J. Quantum Electron.6(1), 15–24 (1970).
[CrossRef]

D. Eimerl, “High average power harmonic generation,” IEEE J. Quantum Electron.23(5), 575–592 (1987).
[CrossRef]

S. P. Velsko, M. Webb, L. Davis, and C. Huang, “Phase-matches harmonic generation in lithium triborate (LBO),” IEEE J. Quantum Electron.27(9), 2182–2192 (1991).
[CrossRef]

Mater. Sci. Forum (1)

R. Mazelsky and D. K. Fox, “An introduction to acousto-optic materials,” Mater. Sci. Forum61, 1–6 (1990).
[CrossRef]

Nat. Photonics (1)

N. Savage, “Acousto-optic devices,” Nat. Photonics4(10), 728–729 (2010).
[CrossRef]

Opt. Commun. (1)

J. H. Garcia-López, V. Aboites, A. V. Kir’yanov, M. J. Damzen, and A. Minassian, “High repetition rate Q-switching of high power Nd:YVO4 slab laser,” Opt. Commun.218(1-3), 155–160 (2003).
[CrossRef]

Phys. Rev. (1)

J. A. Armstrong, N. N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127(6), 1918–1939 (1962).
[CrossRef]

Other (2)

I. C. Chang, “Acoustooptic devices and applications” in Handbook of Optics V, M. Bass, ed. (McGraw-Hill Professional, 2010)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Series in Pure & Applied Optics, 2007), Chap. 21.

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Figures (4)

Fig. 1
Fig. 1

Schematical layout of experimental setup.

Fig. 2
Fig. 2

Average THG power vs. average fundamental power. Polynomial regression equals Eq. (14). Regression of Eq. (9) is for ΘSHG = 2.88 10−7 W-1/2m and ΘTHG = 1.02 10−7 W-1/2m. Regression of Eq. (12) is for Θ*SHG = 0.843 W-1/2 and Θ*THG = 0.251 W-1/2. Max. value of experimental PTHG/PFUN equals 3.4% at PFUN = 1.51 W. Plots of regressions of Eq. (9) and Eq. (12) are exactly on each other.

Fig. 3
Fig. 3

Temporal development of normalized average power prior to and after THG.

Fig. 4
Fig. 4

Rise/fall time trise/fall and bandwidth fm vs. average THG power PTHG. Upper limit of trise/fall and lower limit of fm equal values before THG (152 ns and 3.3 MHz respectively).

Tables (1)

Tables Icon

Table 1 Results forΘSHG, ΘTHG, Θ*SHG and Θ*THG

Equations (14)

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I(x,y)= I 0 exp( 2 r 2 w 0 2 )= I 0 exp( 2( x 2 + y 2 ) w 0 2 )
P(t)= x I( x,y )dy dx= 1 2 P 0 ( 1+erf( 2 Vt w 0 ) )
t rise = t fall =t( P(t)/ P 0 =0.9 )t( P(t)/ P 0 =0.1 )=1.28 w 0 V
f m 0.5 2 ( t rise + t fall ) =0.78 V 2 w 0
I SHG (x,y)= I FUN (x,y)tan h 2 ( Θ SHG I FUN (x,y) )
Θ SHG = L SHG d eff,SHG ε 0 ω 2 Z SHG 3
I THG (x,y)= 3 2 I SHG (x,y) sin 2 ( Θ THG I FUN (x,y) I SHG (x,y) )
Θ THG =2 L THG d eff,THG ε 0 ω 3 Z THG 3
P THG (t)=2 f rep τ w FUN w 0 Vt I THG (x,y)dydx
P SHG (t)=P(t)tan h 2 ( Θ SHG * P(t) )
Θ SHG * = Θ SHG 1 2π w FUN 2 f rep τ
P THG (t)= 3 2 P SHG (t) sin 2 ( Θ THG * P(t) P SHG (t) )
Θ THG * = Θ THG 1 2π w FUN 2 f rep τ
P THG =0.00714 P 4 +0.0164 P 3 +0.0138 P 2

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