Abstract

Three conditions for non-collinear third harmonic generation by a PTR glass volume Bragg grating are demonstrated using infrared ultrashort pulse illumination. Each condition corresponds to a different angle of grating orientation and a separate generation mechanism. We identify the mechanisms as corresponding to sum-frequency generation, Bragg diffraction of 3ω, and a non-resonant Bragg condition involving three ω photons interacting with a nonlinear grating vector. Theoretical modeling is performed using wave vector additions and the results are compared to experimental measurements.

© 2009 Optical Society of America

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References

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  1. O. M. Efimov, L.B. Glebov, and V. I. Smirnov, "High-frequency Bragg gratings in a photothermorefractive glass," Opt. Lett. 25, 1693-1695 (2000).
    [CrossRef]
  2. L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, "New approach to robust optics for HEL systems," Proc. SPIE 4724, 101-109 (2002).
    [CrossRef]
  3. L. B. Glebov, L. N. Glebova, V. I. Smirnov, M. Dubinskii, L. D. Merkle, S. Papernov, and A.W. Schmid, "Laser Damage Resistance of Photo-Thermo-Refractive Glass Bragg Gratings," Proceedings of Solid State and Diode Lasers Technical Review. Albuquerque, Poster-4 (2004).
  4. V. I. Smirnov, S. Juodkazis, V. Dubikovsky, J. Hales, B. Ya. Zel’dovich, H. Misawa, and L. B. Glebov, "Resonant third harmonic generation by femtosecond laser pulses on Bragg grating in photosensitive silicate glass," Conference on Lasers and Electro-Optics CLEO-2002 paper CTuG7 (2002).
  5. S. Juodkazis, E. Gaizauskas, V. Jarutis, J. Reif, S. Matsuo and H. Misawa, "Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating," J. Phys. D: Appl. Phys. 39,50 (2006).
    [CrossRef]
  6. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell. Syst. Tech. J. 48, 2909 (1969).
  7. I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, "Modeling of Gaussian beam diffraction on volume Bragg gratings in PTR glass," Proc. SPIE 5742, 183-194 (2005).
    [CrossRef]
  8. J. X. Cheng and X. S. Xie, "Green’s function formulation for third-harmonic generation microscopy," J. Opt. Soc. Am. B 19, 1604-1610 (2007).
    [CrossRef]

2007 (1)

2006 (1)

S. Juodkazis, E. Gaizauskas, V. Jarutis, J. Reif, S. Matsuo and H. Misawa, "Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating," J. Phys. D: Appl. Phys. 39,50 (2006).
[CrossRef]

2005 (1)

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, "Modeling of Gaussian beam diffraction on volume Bragg gratings in PTR glass," Proc. SPIE 5742, 183-194 (2005).
[CrossRef]

2002 (1)

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, "New approach to robust optics for HEL systems," Proc. SPIE 4724, 101-109 (2002).
[CrossRef]

2000 (1)

1969 (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell. Syst. Tech. J. 48, 2909 (1969).

Cheng, J. X.

Ciapurin, I. V.

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, "Modeling of Gaussian beam diffraction on volume Bragg gratings in PTR glass," Proc. SPIE 5742, 183-194 (2005).
[CrossRef]

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, "New approach to robust optics for HEL systems," Proc. SPIE 4724, 101-109 (2002).
[CrossRef]

Efimov, O. M.

Gaizauskas, E.

S. Juodkazis, E. Gaizauskas, V. Jarutis, J. Reif, S. Matsuo and H. Misawa, "Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating," J. Phys. D: Appl. Phys. 39,50 (2006).
[CrossRef]

Glebov, L. B.

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, "Modeling of Gaussian beam diffraction on volume Bragg gratings in PTR glass," Proc. SPIE 5742, 183-194 (2005).
[CrossRef]

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, "New approach to robust optics for HEL systems," Proc. SPIE 4724, 101-109 (2002).
[CrossRef]

Glebov, L.B.

Jarutis, V.

S. Juodkazis, E. Gaizauskas, V. Jarutis, J. Reif, S. Matsuo and H. Misawa, "Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating," J. Phys. D: Appl. Phys. 39,50 (2006).
[CrossRef]

Juodkazis, S.

S. Juodkazis, E. Gaizauskas, V. Jarutis, J. Reif, S. Matsuo and H. Misawa, "Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating," J. Phys. D: Appl. Phys. 39,50 (2006).
[CrossRef]

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell. Syst. Tech. J. 48, 2909 (1969).

Matsuo, S.

S. Juodkazis, E. Gaizauskas, V. Jarutis, J. Reif, S. Matsuo and H. Misawa, "Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating," J. Phys. D: Appl. Phys. 39,50 (2006).
[CrossRef]

Misawa, H.

S. Juodkazis, E. Gaizauskas, V. Jarutis, J. Reif, S. Matsuo and H. Misawa, "Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating," J. Phys. D: Appl. Phys. 39,50 (2006).
[CrossRef]

Reif, J.

S. Juodkazis, E. Gaizauskas, V. Jarutis, J. Reif, S. Matsuo and H. Misawa, "Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating," J. Phys. D: Appl. Phys. 39,50 (2006).
[CrossRef]

Smirnov, V. I.

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, "Modeling of Gaussian beam diffraction on volume Bragg gratings in PTR glass," Proc. SPIE 5742, 183-194 (2005).
[CrossRef]

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, "New approach to robust optics for HEL systems," Proc. SPIE 4724, 101-109 (2002).
[CrossRef]

O. M. Efimov, L.B. Glebov, and V. I. Smirnov, "High-frequency Bragg gratings in a photothermorefractive glass," Opt. Lett. 25, 1693-1695 (2000).
[CrossRef]

Stickley, C. M.

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, "New approach to robust optics for HEL systems," Proc. SPIE 4724, 101-109 (2002).
[CrossRef]

Xie, X. S.

Bell. Syst. Tech. J. (1)

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell. Syst. Tech. J. 48, 2909 (1969).

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

J. Phys. D: Appl. Phys. (1)

S. Juodkazis, E. Gaizauskas, V. Jarutis, J. Reif, S. Matsuo and H. Misawa, "Optical third harmonic generation during femtosecond pulse diffraction in a Bragg grating," J. Phys. D: Appl. Phys. 39,50 (2006).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, "New approach to robust optics for HEL systems," Proc. SPIE 4724, 101-109 (2002).
[CrossRef]

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, "Modeling of Gaussian beam diffraction on volume Bragg gratings in PTR glass," Proc. SPIE 5742, 183-194 (2005).
[CrossRef]

Other (2)

L. B. Glebov, L. N. Glebova, V. I. Smirnov, M. Dubinskii, L. D. Merkle, S. Papernov, and A.W. Schmid, "Laser Damage Resistance of Photo-Thermo-Refractive Glass Bragg Gratings," Proceedings of Solid State and Diode Lasers Technical Review. Albuquerque, Poster-4 (2004).

V. I. Smirnov, S. Juodkazis, V. Dubikovsky, J. Hales, B. Ya. Zel’dovich, H. Misawa, and L. B. Glebov, "Resonant third harmonic generation by femtosecond laser pulses on Bragg grating in photosensitive silicate glass," Conference on Lasers and Electro-Optics CLEO-2002 paper CTuG7 (2002).

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Figures (6)

Fig. 1.
Fig. 1.

Experimental arrangement for investigating third harmonic generation and diffraction by transmitting Bragg gratings in PTR glass.

Fig. 2.
Fig. 2.

Two-beam THG by a PTR glass TBG irradiated with IR femtosecond pulses: (a) wave vector additions of transmitted and diffracted photons to produce third harmonic (b) photograph from experiment. K - grating vector, ωT - transmitted photon, ωD -diffracted photon. Phase-matching is not satisfied.

Fig. 3.
Fig. 3.

Wave vector conditions for non-collinear THG by a PTR glass TBG: (a) front surface diffracted THG (b) nonlinear grating THG, K NL - nonlinear grating vector (c) photographs of 3ω(2) and 3ω(3) from experiment at 1588 nm.

Fig. 4.
Fig. 4.

Dependence of third harmonic intensity from PTR glass TBG on incident angle for (1) 3ω(i) beam (2) 3ω(ii) beam.

Fig. 5.
Fig. 5.

Dependence of third harmonic intensity on incident angle for the two-beam THG case: (a) 3ω(i) beam (b) 3ω(ii) beam. 1 - theory 2 - experiment.

Fig. 6.
Fig. 6.

Spectrum of femtosecond pulse shows an asymmetric profile.

Tables (3)

Tables Icon

Table 1. Measured angles for non-collinear THG by a TBG in PTR glass (∧ = 4 μm, L = 0.97 mm, n 1 = 607 ppm).a

Tables Icon

Table 2. Cauchy coefficients for PTR glass.

Tables Icon

Table 3. Theoretically derived and experimentally measured angles of grating orientation to obtain non-collinear THG for a PTR glass TBG (∧ = 4 μm, L = 0.97 mm, n 1 = 607 ppm).

Equations (31)

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sin θ = λ 2 n ( λ ) ,
k 3 ω ( i ) = 2 k T ( λ , θ ) + 2 k D ( λ , θ ) ,
k 3 ω ( ii ) = k T ( λ , θ ) + k D ( λ , θ ) ,
k T ( λ , θ ) = k ( λ , θ ) ,
k D ( λ , θ ) = k ( λ , θ ) + K ,
k ( λ , θ ) = 2 π λ n ( λ ) [ sin θ x ̂ + cos θ z ̂ ] ,
K = 2 π x ̂ .
n ( λ ) = A + B λ 2 + C λ 2 + D λ 4 + E λ 6 + F λ 8 ,
k 3 ω = k ( λ / 3 , θ ) = 3 ( 2 π λ ) n ( λ ) .
k 3 ω ( 2 ) = k ( λ / 3 , θ ) + K ,
k 3 ω ( 3 ) = 3 k ( λ , θ ) + K NL .
θ = sin 1 [ n sin θ media ] .
I 3 ω ( i ) = κ I ω T I ω T I ω D ,
I 3 ω ( ii ) = κ I ω D I ω D I ω T ,
I ω D = I 0 η ( θ ) ,
I ω T = 1 I ω D ,
η ( θ ) = sin 2 { v 2 ( θ ) + ξ 2 ( θ ) } 1 + ξ 2 ( θ ) / v 2 ( θ ) ,
v ( θ ) = π n 1 L λ cos θ ,
ξ ( θ ) = z 2 cos θ [ K sin θ K 2 λ 4 π n ( λ ) ] .
χ 3 = χ 3 ( 0 ) + δ χ 3 ( 0 ) exp ( i K NL · r ) ,
E 3 ω exp ( i k 3 ω · r ) P 3 ω d 3 r ,
P 3 ω = χ 3 E 1 E 2 E 3 .
E 1 = E 2 = E 3 = E 0 exp ( i k ω · r ) ,
E 3 v χ 3 ( 0 ) E 0 3 exp [ i ( k 3 ω 3 k ω ) · r ] d 3 r
+ v δχ 3 ( 0 ) E 0 3 exp [ i ( k 3 ω 3 k ω + K NL ) · r ] d 3 r .
( k 3 ω 3 k ω + K NL ) ·r = 0 .
E 1 = E 2 = E 0 exp ( i k T · r ) ,
E 3 = E 0 exp ( i k D · r ) .
E 3 v χ 3 ( 0 ) E 0 3 exp [ i ( k 3 ω 2 k T k D ) · r ] d 3 r
+ v δχ 3 ( 0 ) E 0 3 exp [ i ( k 3 ω 2 k T k D + K NL ) · r ] d 3 r .
( k 3 ω 2 k T + K D ) ·r = 0 .

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