Abstract

We analyze a solution of the heat equation for second harmonic generation (SHG) with a focused Gaussian beam and simulate the temperature rise in SHG materials as a function of the second harmonic power and the focusing conditions. We also propose a quantitative value of the heat removal performance of SHG devices, referred to as the effective heat capacity Cα in phase matched calorimetry. We demonstrate the inverse relation between Cα and the focusing parameter ξ, and propose the universal quantity of the product of Cα and ξ for characterizing the thermal property of SHG devices. Finally, we discuss the strategy to manage thermal dephasing in SHG using the results from simulations.

© 2014 Optical Society of America

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References

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  1. S. V. Tovstonog, S. Kurimura, and K. Kitamura, “High power continuous-wave green light generation by quasiphase matching in Mg stoichiometric lithium tantalate,” Appl. Phys. Lett. 90, 0511115 (2007).
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. G. K. Samanta, S. C. Kumar, K. Devi, and M. Ebrahim-Zadeh, “Multicrystal, continuous-wave, single-pass second-harmonic generation with 56% efficiency,” Opt. Lett. 35(20), 3513–3515 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. P. Zeil, A. Zukauskas, S. Tjörnhammar, C. Canalias, V. Pasiskevicius, and F. Laurell, “High-power continuous-wave frequency-doubling in KTiOAsO4.,” Opt. Express 21(25), 30453–30459 (2013).
    [CrossRef] [PubMed]
  7. N. E. Yu, S. Kurimura, Y. Nomura, and K. Kitamura, “Stable High-Power Green Light Generation with Thermally Conductive Periodically Poled Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 43(10A10A), L1265–L1267 (2004).
    [CrossRef]
  8. R. W. Boyd, Nonlinear Optics, Third edition, (Academic Press, 2008), Chap.2.
  9. M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
    [CrossRef]
  10. A. K. Cousins, “Temperature and thermal stress scaling infinite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28(4), 1057–1069 (1992).
    [CrossRef]
  11. A. Sennaroglu, A. Askar, and F. M. Atay, “Quantitative study of laser beam propagation in a thermally loaded absorber,” J. Opt. Soc. Am. B 14(2), 356–363 (1997).
    [CrossRef]
  12. H. H. Lim, S. Kurimura, T. Katagai, and I. Shoji, “Temperature-Dependent Sellmeier Equation for Refractive Index of 1.0 mol% Mg-Doped Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 52(3R), 032601 (2013).
    [CrossRef]

2013

P. Zeil, A. Zukauskas, S. Tjörnhammar, C. Canalias, V. Pasiskevicius, and F. Laurell, “High-power continuous-wave frequency-doubling in KTiOAsO4.,” Opt. Express 21(25), 30453–30459 (2013).
[CrossRef] [PubMed]

H. H. Lim, S. Kurimura, T. Katagai, and I. Shoji, “Temperature-Dependent Sellmeier Equation for Refractive Index of 1.0 mol% Mg-Doped Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 52(3R), 032601 (2013).
[CrossRef]

2011

2010

2008

2007

S. V. Tovstonog, S. Kurimura, and K. Kitamura, “High power continuous-wave green light generation by quasiphase matching in Mg stoichiometric lithium tantalate,” Appl. Phys. Lett. 90, 0511115 (2007).

2004

N. E. Yu, S. Kurimura, Y. Nomura, and K. Kitamura, “Stable High-Power Green Light Generation with Thermally Conductive Periodically Poled Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 43(10A10A), L1265–L1267 (2004).
[CrossRef]

1997

1992

A. K. Cousins, “Temperature and thermal stress scaling infinite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28(4), 1057–1069 (1992).
[CrossRef]

1990

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

Askar, A.

Atay, F. M.

Byer, R. L.

Canalias, C.

Cousins, A. K.

A. K. Cousins, “Temperature and thermal stress scaling infinite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28(4), 1057–1069 (1992).
[CrossRef]

Devi, K.

Digonnet, M. J. F.

Ebrahim-Zadeh, M.

Fejer, M. M.

Fields, R. A.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

Fincher, C. L.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

Hum, D. S.

Innocenzi, M. E.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

Katagai, T.

Kitamura, K.

S. V. Tovstonog, S. Kurimura, and K. Kitamura, “High power continuous-wave green light generation by quasiphase matching in Mg stoichiometric lithium tantalate,” Appl. Phys. Lett. 90, 0511115 (2007).

N. E. Yu, S. Kurimura, Y. Nomura, and K. Kitamura, “Stable High-Power Green Light Generation with Thermally Conductive Periodically Poled Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 43(10A10A), L1265–L1267 (2004).
[CrossRef]

Kumar, S. C.

Kurimura, S.

H. H. Lim, S. Kurimura, T. Katagai, and I. Shoji, “Temperature-Dependent Sellmeier Equation for Refractive Index of 1.0 mol% Mg-Doped Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 52(3R), 032601 (2013).
[CrossRef]

H. H. Lim, T. Katagai, S. Kurimura, T. Shimizu, K. Noguchi, N. Ohmae, N. Mio, and I. Shoji, “Thermal Performance in High Power SHG Characterized by Phase-Matched Calorimetry,” Opt. Express 19(23), 22588–22593 (2011).
[CrossRef] [PubMed]

S. V. Tovstonog, S. Kurimura, I. Suzuki, K. Takeno, S. Moriwaki, N. Ohmae, N. Mio, and T. Katagai, “Thermal effects in high-power CW second harmonic generation in Mg-doped stoichiometric lithium tantalate,” Opt. Express 16(15), 11294–11299 (2008).
[CrossRef] [PubMed]

S. V. Tovstonog, S. Kurimura, and K. Kitamura, “High power continuous-wave green light generation by quasiphase matching in Mg stoichiometric lithium tantalate,” Appl. Phys. Lett. 90, 0511115 (2007).

N. E. Yu, S. Kurimura, Y. Nomura, and K. Kitamura, “Stable High-Power Green Light Generation with Thermally Conductive Periodically Poled Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 43(10A10A), L1265–L1267 (2004).
[CrossRef]

Laurell, F.

Lee, Y.

Lim, H. H.

H. H. Lim, S. Kurimura, T. Katagai, and I. Shoji, “Temperature-Dependent Sellmeier Equation for Refractive Index of 1.0 mol% Mg-Doped Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 52(3R), 032601 (2013).
[CrossRef]

H. H. Lim, T. Katagai, S. Kurimura, T. Shimizu, K. Noguchi, N. Ohmae, N. Mio, and I. Shoji, “Thermal Performance in High Power SHG Characterized by Phase-Matched Calorimetry,” Opt. Express 19(23), 22588–22593 (2011).
[CrossRef] [PubMed]

Mio, N.

Moriwaki, S.

Noguchi, K.

Nomura, Y.

N. E. Yu, S. Kurimura, Y. Nomura, and K. Kitamura, “Stable High-Power Green Light Generation with Thermally Conductive Periodically Poled Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 43(10A10A), L1265–L1267 (2004).
[CrossRef]

Ohmae, N.

Pasiskevicius, V.

Samanta, G. K.

Sennaroglu, A.

Shimizu, T.

Shoji, I.

H. H. Lim, S. Kurimura, T. Katagai, and I. Shoji, “Temperature-Dependent Sellmeier Equation for Refractive Index of 1.0 mol% Mg-Doped Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 52(3R), 032601 (2013).
[CrossRef]

H. H. Lim, T. Katagai, S. Kurimura, T. Shimizu, K. Noguchi, N. Ohmae, N. Mio, and I. Shoji, “Thermal Performance in High Power SHG Characterized by Phase-Matched Calorimetry,” Opt. Express 19(23), 22588–22593 (2011).
[CrossRef] [PubMed]

Sinha, S.

Suzuki, I.

Takeno, K.

Tjörnhammar, S.

Tovstonog, S. V.

S. V. Tovstonog, S. Kurimura, I. Suzuki, K. Takeno, S. Moriwaki, N. Ohmae, N. Mio, and T. Katagai, “Thermal effects in high-power CW second harmonic generation in Mg-doped stoichiometric lithium tantalate,” Opt. Express 16(15), 11294–11299 (2008).
[CrossRef] [PubMed]

S. V. Tovstonog, S. Kurimura, and K. Kitamura, “High power continuous-wave green light generation by quasiphase matching in Mg stoichiometric lithium tantalate,” Appl. Phys. Lett. 90, 0511115 (2007).

Urbanek, K. E.

Yu, N. E.

N. E. Yu, S. Kurimura, Y. Nomura, and K. Kitamura, “Stable High-Power Green Light Generation with Thermally Conductive Periodically Poled Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 43(10A10A), L1265–L1267 (2004).
[CrossRef]

Yura, H. T.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

Zeil, P.

Zukauskas, A.

Appl. Phys. Lett.

S. V. Tovstonog, S. Kurimura, and K. Kitamura, “High power continuous-wave green light generation by quasiphase matching in Mg stoichiometric lithium tantalate,” Appl. Phys. Lett. 90, 0511115 (2007).

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[CrossRef]

IEEE J. Quantum Electron.

A. K. Cousins, “Temperature and thermal stress scaling infinite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28(4), 1057–1069 (1992).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

H. H. Lim, S. Kurimura, T. Katagai, and I. Shoji, “Temperature-Dependent Sellmeier Equation for Refractive Index of 1.0 mol% Mg-Doped Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 52(3R), 032601 (2013).
[CrossRef]

N. E. Yu, S. Kurimura, Y. Nomura, and K. Kitamura, “Stable High-Power Green Light Generation with Thermally Conductive Periodically Poled Stoichiometric Lithium Tantalate,” Jpn. J. Appl. Phys. 43(10A10A), L1265–L1267 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Other

R. W. Boyd, Nonlinear Optics, Third edition, (Academic Press, 2008), Chap.2.

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Figures (7)

Fig. 1
Fig. 1

Schematic of the structure of the SHG material used in the simulation with a focused Gaussian beam. TEC is a thermoelectric cooler.

Fig. 2
Fig. 2

Measured TEC temperature versus SH power (a) and SH power versus F power (b).

Fig. 3
Fig. 3

Photograph of PPMgSLT modules that allow four-side heat spread.

Fig. 4
Fig. 4

Dependent of Cα (square) and ηnorm (triangle) on the focusing parameter, ξ. The error bar is the standard error in each fitting.

Fig. 5
Fig. 5

Calculated ΔT (r, z) for a strong (ξ = 2.84) (a) and a weak (ξ = 0.5) (b) focusing. (a-1), (b-1): ΔT (z) at r = 0 (solid) and r = ω (z) (dotted) for the same output SH powers, 1, 5, and 10 W. (a-2), (b-2): ΔT (r, z) - ΔT (r, 0).

Fig. 6
Fig. 6

(a) Calculated ΔT (r, z) needed to generate SH power of 30 W with F power of 80 W for different crystal lengths of 10, 20 and 40 mm at the smallest possible ξ. Solid: ΔT (0, z), dot: ΔT (ω (z), z). Horizontal straight lines indicate the calculated QPM temperature acceptance bandwidths at FWHM with the dispersion of MgSLT [12]. (b) Normalized ΔT (r, z) in each QPM temperature acceptance bandwidth versus normalized z for each length.

Fig. 7
Fig. 7

Calculated ΔT (0, z) for output SH power of 30 W at ξ = 1 (ω0 = 28.2 μm) for three focusing positions, referred as front (−25%), center (0%), and rear ( + 25%) in a 10-mm long crystal. The arrows indicate the focusing positions.

Tables (1)

Tables Icon

Table 1 Relevant physical parameters

Equations (21)

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2i k SH E SH z + T 2 E SH = ω SH 2 c 2 χ (2) E F 2 e iΔkz ,
E F (r,z)= A F 1+iτ exp( r 2 ω 0 2 (1+iτ) ),
E SH (r,z)= A SH (z) 1+iτ exp( 2 r 2 ω 0 2 (1+iτ) ),
τ= 2(z z 0 ) b = 2(z z 0 ) k ω 0 2 ,
A SH (z)= i2π λ F n SH χ (2) | A F | 2 z0 z exp(iΔk z ) 1+2i z /b d z ,
P SH (z)= 1 2 π n SH c ω 0 2 ε 0 | A SH (z) | 2 ,
1 r r ( r T r ) + 2 T z 2 = h κ ,
h ( r , z ) = α F 2 P F π ω F 2 ( z ) exp ( 2 r 2 ω F 2 ( z ) ) exp ( α F z ) + α S H 2 P S H ( z ) π ω S H 2 ( z ) exp ( 2 r 2 ω S H 2 ( z ) ) exp ( α S H z ) .
T ( r , z ) = T b + Δ T ( r , z ) ,
Δ T ( r , z ) = Δ T F ( r , z ) + Δ T S H ( r , z ) = α F P F exp ( α F z ) 4 π κ × [ ln ( r b 2 r 2 ) + E 1 ( 2 r b 2 ω F 2 ( z ) ) E 1 ( 2 r 2 ω F 2 ( z ) ) ] + α S H P S H ( z ) exp ( α S H z ) 4 π κ × [ ln ( r b 2 r 2 ) + E 1 ( 2 r b 2 ω S H 2 ( z ) ) E 1 ( 2 r 2 ω S H 2 ( z ) ) ] ,
T T E C = T T E C 0 Δ T T E C ,
Δ T T E C = 1 C α [ R P S H O u t η n o r m + P S H O u t ] ,
C α = C π ω 0 2 α S H ,
C α = C π ω 0 2 α S H = C π L α S H k ξ ,
C 2κ r b 2 ,
ΔT(r,z) α F P F exp( α F z) 2πκ ω F 2 (z) [ r b 2 r 2 ] + α SH P SH (z)exp( α SH z) 2πκ ω SH 2 (z) [ r b 2 r 2 ],
E 1 (z)=γlnz n=1 (1) n z n nn! .
ΔT(0, z 0 )= α SH r b 2 2κπ ω 0 2 [ R P F (1 α F z 0 )+2 P SH ( z 0 )( 1 α SH z 0 ) ],
T TEC = T TEC 0 ΔT(0, z 0 ),
ΔT(0, z 0 )= 1 C eff ( α SH ,κ, r b , ω 0 ) [ R P SH Out η norm + 1 2 P SH Out ],
C eff = 2κπ ω 0 2 α SH r b 2 ,

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