Abstract

Waveguide circuits play a key role in modern integrated optics and provide an appealing approach to scalability in quantum optics. We report on periodically poled ridge waveguides in z-cut potassium titanyl phosphate (KTiOPO4 or KTP), a material that has recently received growing interest due to its unique dispersion properties. Ridges were defined in surface-near rubidium-exchanged KTP by use of a precise diamond-blade dicing saw. We fabricated single-mode ridge waveguides at around 800 nm which exhibit widths of 1.9–3.2 μm and facilitated type-II second harmonic generation from 792 nm to 396 nm with high efficiency of 6.6 %/W·cm2. Temperature dependence of the second harmonic process was found to be 53 pm/K. The low temperature dependence and high nonlinear conversion efficiency make our waveguides ideally suited for future operations in classical nonlinear integrated optics and integrated quantum networking applications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. K. Kato, “Temperature Insensitive SHG at 0.5321 μm in KTP,” IEEE J. Quant. Electron. 28(10), 1974–1976 (2013).
    [Crossref]
  2. J. D. Bierlein and H. Vanherzeele, “Potassium titanyl phosphate: properties and new applications,” J. Opt. Soc. Am. B 6(4), 622–633 (1989).
    [Crossref]
  3. V. Ansari, E. Roccia, M. Santandrea, M. Doostdar, C. Eigner, L. Padberg, I. Gianani, M. Sbroscia, J. M. Donohue, L. Mancino, M. Barbieri, and C. Silberhorn, “Heralded generation of high-purity ultrashort single photons in programmable temporal shapes,” Opt. Express 26(3), 2764–2774 (2018).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. H. Karlsson and F. Laurell, “Electric field poling of flux grown KTiOPO4,” Appl. Phys. Lett. 71(24), 3474–3476 (1997).
    [Crossref]
  6. H. Karlsson, F. Laurell, and L. K. Cheng, “Periodic poling of RbTiOPO4 for quasi-phase matched blue light generation,” Appl. Phys. Lett. 74(11), 1519–1521 (1999).
    [Crossref]
  7. J. Hellström, R. Clemens, V. Pasiskevicius, H. Karlsson, and F. Laurell, “Real-time and in situ monitoring of ferroelectric domains during periodic electric field poling of KTiOPO4,” J. Appl. Phys. 90(3), 1489–1495 (2001).
    [Crossref]
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    [Crossref]
  10. M. Rüsing, C. Eigner, P. Mackwitz, G. Berth, C. Silberhorn, and A. Zrenner, “Identification of ferroelectric domain structure sensitive phonon modes in potassium titanyl phosphate: A fundamental study,” J. Appl. Phys. 119(4), 044103 (2016).
    [Crossref]
  11. M. F. Volk, C. E. Rüter, and D. Kip, “Rb/Ba side-diffused ridge waveguides in KTP,” Opt. Express 25(17), 19872–19877 (2017).
    [Crossref] [PubMed]
  12. M. F. Volk, C. E. Rüter, M. Santandrea, C. Eigner, L. Padberg, H. Herrmann, C. Silberhorn, and D. Kip, “Fabrication of low-loss Rb-exchanged ridge waveguides in z-cut KTiOPO4,” Opt. Mater. Express 8(1), 82–87 (2018).
    [Crossref]
  13. L. G. Carpenter, S. A. Berry, and C.B.E. Gawith, “Ductile dicing of LiNbO3 ridge waveguide facets to achieve 0.29 nm surface roughness in single process step,” Electron. Lett. 53(25), 1672–1674 (2017).
    [Crossref]
  14. P. T. Callahan, K. Safak, P. Battle, T. D. Roberts, and F. X. Kärtner, “Fiber-coupled balanced optical cross-correlator using PPKTP waveguides,” Opt. Express 22(8), 9749–9758 (2014).
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    [Crossref] [PubMed]
  16. R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, and O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
    [Crossref]
  17. A. Zukauskas, V. Pasiskevicius, and C. Canalias, “Second-harmonic generation in periodically poled bulk Rb-doped KTiOPO4 below 400 nm at high peak-intensities,” Opt. Express 21(2), 1395–1403 (2013).
    [Crossref] [PubMed]
  18. F. Laurell, J. B. Brown, and J. D. Bierlein, “Sum-frequency generation in segmented KTP waveguides,” Appl. Phys. Lett 60(9), 1064 (1992).
    [Crossref]
  19. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
    [Crossref]
  20. A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
    [Crossref]

2018 (2)

2017 (3)

L. G. Carpenter, S. A. Berry, and C.B.E. Gawith, “Ductile dicing of LiNbO3 ridge waveguide facets to achieve 0.29 nm surface roughness in single process step,” Electron. Lett. 53(25), 1672–1674 (2017).
[Crossref]

M. F. Volk, C. E. Rüter, and D. Kip, “Rb/Ba side-diffused ridge waveguides in KTP,” Opt. Express 25(17), 19872–19877 (2017).
[Crossref] [PubMed]

H. Rütz, K. H. Luo, H. Suche, and C. Silberhorn, “Quantum Frequency Conversion between Infrared and Ultraviolet,” Phys. Rev. Appl. 7(2), 024021 (2017).
[Crossref]

2016 (1)

M. Rüsing, C. Eigner, P. Mackwitz, G. Berth, C. Silberhorn, and A. Zrenner, “Identification of ferroelectric domain structure sensitive phonon modes in potassium titanyl phosphate: A fundamental study,” J. Appl. Phys. 119(4), 044103 (2016).
[Crossref]

2014 (2)

2013 (4)

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, and O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[Crossref]

A. Zukauskas, V. Pasiskevicius, and C. Canalias, “Second-harmonic generation in periodically poled bulk Rb-doped KTiOPO4 below 400 nm at high peak-intensities,” Opt. Express 21(2), 1395–1403 (2013).
[Crossref] [PubMed]

G. Harder, V. Ansari, B. Brecht, T. Dirmeier, C. Marquardt, and C. Silberhorn, “An optimized photon pair source for quantum circuits,” Opt. Express 21 (12), 13975–13985 (2013).
[Crossref] [PubMed]

K. Kato, “Temperature Insensitive SHG at 0.5321 μm in KTP,” IEEE J. Quant. Electron. 28(10), 1974–1976 (2013).
[Crossref]

2009 (1)

2001 (1)

J. Hellström, R. Clemens, V. Pasiskevicius, H. Karlsson, and F. Laurell, “Real-time and in situ monitoring of ferroelectric domains during periodic electric field poling of KTiOPO4,” J. Appl. Phys. 90(3), 1489–1495 (2001).
[Crossref]

1999 (1)

H. Karlsson, F. Laurell, and L. K. Cheng, “Periodic poling of RbTiOPO4 for quasi-phase matched blue light generation,” Appl. Phys. Lett. 74(11), 1519–1521 (1999).
[Crossref]

1997 (3)

H. Karlsson and F. Laurell, “Electric field poling of flux grown KTiOPO4,” Appl. Phys. Lett. 71(24), 3474–3476 (1997).
[Crossref]

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14(9), 2268–2294 (1997).
[Crossref]

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
[Crossref]

1992 (1)

F. Laurell, J. B. Brown, and J. D. Bierlein, “Sum-frequency generation in segmented KTP waveguides,” Appl. Phys. Lett 60(9), 1064 (1992).
[Crossref]

1989 (1)

Ansari, V.

Arie, A.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
[Crossref]

Barbieri, M.

Battle, P.

Berry, S. A.

L. G. Carpenter, S. A. Berry, and C.B.E. Gawith, “Ductile dicing of LiNbO3 ridge waveguide facets to achieve 0.29 nm surface roughness in single process step,” Electron. Lett. 53(25), 1672–1674 (2017).
[Crossref]

Berth, G.

M. Rüsing, C. Eigner, P. Mackwitz, G. Berth, C. Silberhorn, and A. Zrenner, “Identification of ferroelectric domain structure sensitive phonon modes in potassium titanyl phosphate: A fundamental study,” J. Appl. Phys. 119(4), 044103 (2016).
[Crossref]

Bierlein, J. D.

F. Laurell, J. B. Brown, and J. D. Bierlein, “Sum-frequency generation in segmented KTP waveguides,” Appl. Phys. Lett 60(9), 1064 (1992).
[Crossref]

J. D. Bierlein and H. Vanherzeele, “Potassium titanyl phosphate: properties and new applications,” J. Opt. Soc. Am. B 6(4), 622–633 (1989).
[Crossref]

Brecht, B.

Brown, J. B.

F. Laurell, J. B. Brown, and J. D. Bierlein, “Sum-frequency generation in segmented KTP waveguides,” Appl. Phys. Lett 60(9), 1064 (1992).
[Crossref]

Callahan, P. T.

Calmano, T.

Canalias, C.

Carpenter, L. G.

L. G. Carpenter, S. A. Berry, and C.B.E. Gawith, “Ductile dicing of LiNbO3 ridge waveguide facets to achieve 0.29 nm surface roughness in single process step,” Electron. Lett. 53(25), 1672–1674 (2017).
[Crossref]

Cassemiro, K. N.

Cheng, L. K.

H. Karlsson, F. Laurell, and L. K. Cheng, “Periodic poling of RbTiOPO4 for quasi-phase matched blue light generation,” Appl. Phys. Lett. 74(11), 1519–1521 (1999).
[Crossref]

Clemens, R.

J. Hellström, R. Clemens, V. Pasiskevicius, H. Karlsson, and F. Laurell, “Real-time and in situ monitoring of ferroelectric domains during periodic electric field poling of KTiOPO4,” J. Appl. Phys. 90(3), 1489–1495 (2001).
[Crossref]

Dirmeier, T.

Donohue, J. M.

Doostdar, M.

Eger, D.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
[Crossref]

Eigner, C.

Gawith, C.B.E.

L. G. Carpenter, S. A. Berry, and C.B.E. Gawith, “Ductile dicing of LiNbO3 ridge waveguide facets to achieve 0.29 nm surface roughness in single process step,” Electron. Lett. 53(25), 1672–1674 (2017).
[Crossref]

Gianani, I.

Haderka, O.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, and O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[Crossref]

Harder, G.

Hellström, J.

J. Hellström, R. Clemens, V. Pasiskevicius, H. Karlsson, and F. Laurell, “Real-time and in situ monitoring of ferroelectric domains during periodic electric field poling of KTiOPO4,” J. Appl. Phys. 90(3), 1489–1495 (2001).
[Crossref]

Herrmann, H.

Huber, G.

Ito, R.

Karlsson, H.

J. Hellström, R. Clemens, V. Pasiskevicius, H. Karlsson, and F. Laurell, “Real-time and in situ monitoring of ferroelectric domains during periodic electric field poling of KTiOPO4,” J. Appl. Phys. 90(3), 1489–1495 (2001).
[Crossref]

H. Karlsson, F. Laurell, and L. K. Cheng, “Periodic poling of RbTiOPO4 for quasi-phase matched blue light generation,” Appl. Phys. Lett. 74(11), 1519–1521 (1999).
[Crossref]

H. Karlsson and F. Laurell, “Electric field poling of flux grown KTiOPO4,” Appl. Phys. Lett. 71(24), 3474–3476 (1997).
[Crossref]

Kärtner, F. X.

Kato, K.

K. Kato, “Temperature Insensitive SHG at 0.5321 μm in KTP,” IEEE J. Quant. Electron. 28(10), 1974–1976 (2013).
[Crossref]

Katz, M.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
[Crossref]

Kip, D.

Kitamoto, A.

Kondo, T.

Kränkel, C.

Laiho, K.

Laurell, F.

S. Müller, T. Calmano, P. W. Metz, C. Kränkel, C. Canalias, C. Liljestrand, F. Laurell, and G. Huber, “Highly efficient continuous wave blue second-harmonic generation in fs-laser written periodically poled Rb:KTiOPO4 waveguides,” Opt. Lett. 39(5), 1274–1277 (2014).
[Crossref] [PubMed]

J. Hellström, R. Clemens, V. Pasiskevicius, H. Karlsson, and F. Laurell, “Real-time and in situ monitoring of ferroelectric domains during periodic electric field poling of KTiOPO4,” J. Appl. Phys. 90(3), 1489–1495 (2001).
[Crossref]

H. Karlsson, F. Laurell, and L. K. Cheng, “Periodic poling of RbTiOPO4 for quasi-phase matched blue light generation,” Appl. Phys. Lett. 74(11), 1519–1521 (1999).
[Crossref]

H. Karlsson and F. Laurell, “Electric field poling of flux grown KTiOPO4,” Appl. Phys. Lett. 71(24), 3474–3476 (1997).
[Crossref]

F. Laurell, J. B. Brown, and J. D. Bierlein, “Sum-frequency generation in segmented KTP waveguides,” Appl. Phys. Lett 60(9), 1064 (1992).
[Crossref]

Liljestrand, C.

Luo, K. H.

H. Rütz, K. H. Luo, H. Suche, and C. Silberhorn, “Quantum Frequency Conversion between Infrared and Ultraviolet,” Phys. Rev. Appl. 7(2), 024021 (2017).
[Crossref]

Machulka, R.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, and O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[Crossref]

Mackwitz, P.

M. Rüsing, C. Eigner, P. Mackwitz, G. Berth, C. Silberhorn, and A. Zrenner, “Identification of ferroelectric domain structure sensitive phonon modes in potassium titanyl phosphate: A fundamental study,” J. Appl. Phys. 119(4), 044103 (2016).
[Crossref]

Mahal, V.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
[Crossref]

Mancino, L.

Marquardt, C.

Metz, P. W.

Müller, S.

Oron, M.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
[Crossref]

Padberg, L.

Pasiskevicius, V.

A. Zukauskas, V. Pasiskevicius, and C. Canalias, “Second-harmonic generation in periodically poled bulk Rb-doped KTiOPO4 below 400 nm at high peak-intensities,” Opt. Express 21(2), 1395–1403 (2013).
[Crossref] [PubMed]

J. Hellström, R. Clemens, V. Pasiskevicius, H. Karlsson, and F. Laurell, “Real-time and in situ monitoring of ferroelectric domains during periodic electric field poling of KTiOPO4,” J. Appl. Phys. 90(3), 1489–1495 (2001).
[Crossref]

Perina, J.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, and O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[Crossref]

Roberts, T. D.

Roccia, E.

Rosenman, G.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
[Crossref]

Rüsing, M.

M. Rüsing, C. Eigner, P. Mackwitz, G. Berth, C. Silberhorn, and A. Zrenner, “Identification of ferroelectric domain structure sensitive phonon modes in potassium titanyl phosphate: A fundamental study,” J. Appl. Phys. 119(4), 044103 (2016).
[Crossref]

Rüter, C. E.

Rütz, H.

H. Rütz, K. H. Luo, H. Suche, and C. Silberhorn, “Quantum Frequency Conversion between Infrared and Ultraviolet,” Phys. Rev. Appl. 7(2), 024021 (2017).
[Crossref]

Safak, K.

Santandrea, M.

Sbroscia, M.

Shirane, M.

Shoji, I.

Silberhorn, C.

Skliar, A.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
[Crossref]

Soubusta, J.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, and O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[Crossref]

Suche, H.

H. Rütz, K. H. Luo, H. Suche, and C. Silberhorn, “Quantum Frequency Conversion between Infrared and Ultraviolet,” Phys. Rev. Appl. 7(2), 024021 (2017).
[Crossref]

Svozilík, J.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, and O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[Crossref]

Vanherzeele, H.

Volk, M. F.

Zrenner, A.

M. Rüsing, C. Eigner, P. Mackwitz, G. Berth, C. Silberhorn, and A. Zrenner, “Identification of ferroelectric domain structure sensitive phonon modes in potassium titanyl phosphate: A fundamental study,” J. Appl. Phys. 119(4), 044103 (2016).
[Crossref]

Zukauskas, A.

Appl. Phys. Lett (1)

F. Laurell, J. B. Brown, and J. D. Bierlein, “Sum-frequency generation in segmented KTP waveguides,” Appl. Phys. Lett 60(9), 1064 (1992).
[Crossref]

Appl. Phys. Lett. (2)

H. Karlsson and F. Laurell, “Electric field poling of flux grown KTiOPO4,” Appl. Phys. Lett. 71(24), 3474–3476 (1997).
[Crossref]

H. Karlsson, F. Laurell, and L. K. Cheng, “Periodic poling of RbTiOPO4 for quasi-phase matched blue light generation,” Appl. Phys. Lett. 74(11), 1519–1521 (1999).
[Crossref]

Electron. Lett. (1)

L. G. Carpenter, S. A. Berry, and C.B.E. Gawith, “Ductile dicing of LiNbO3 ridge waveguide facets to achieve 0.29 nm surface roughness in single process step,” Electron. Lett. 53(25), 1672–1674 (2017).
[Crossref]

IEEE J. Quant. Electron. (1)

K. Kato, “Temperature Insensitive SHG at 0.5321 μm in KTP,” IEEE J. Quant. Electron. 28(10), 1974–1976 (2013).
[Crossref]

J. Appl. Phys. (2)

M. Rüsing, C. Eigner, P. Mackwitz, G. Berth, C. Silberhorn, and A. Zrenner, “Identification of ferroelectric domain structure sensitive phonon modes in potassium titanyl phosphate: A fundamental study,” J. Appl. Phys. 119(4), 044103 (2016).
[Crossref]

J. Hellström, R. Clemens, V. Pasiskevicius, H. Karlsson, and F. Laurell, “Real-time and in situ monitoring of ferroelectric domains during periodic electric field poling of KTiOPO4,” J. Appl. Phys. 90(3), 1489–1495 (2001).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4), 265–268 (1997).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. A (1)

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, and O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[Crossref]

Phys. Rev. Appl. (1)

H. Rütz, K. H. Luo, H. Suche, and C. Silberhorn, “Quantum Frequency Conversion between Infrared and Ultraviolet,” Phys. Rev. Appl. 7(2), 024021 (2017).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 a) Waveguides were formed in periodically poled KTP by Rb in-diffusion and subsequent ridge definition. SEM image of b) a selectively etched surface of a periodically poled ridge (top view) and of a c) waveguide’s end facet; d) light image of a waveguide’s end facet.
Fig. 2
Fig. 2 a) Setup to investigate second harmonic generation in KTP ridge waveguides. The light was detected on a power meter. b) Experimentally obtained mode images of a 3.1 μm wide ridge waveguide at 800 nm, the calculated modes are indicated by white dashed lines, according to 20%, 40%, 60% and 80% of the simulated field amplitude.
Fig. 3
Fig. 3 a) Measured (blue) and calculated (red) phase-matching curve of a 2.6 μm wide and 7.9 mm long ridge waveguide for type-II conversion; the calculated curve (green) corresponds to a poling length equal to the sample length of 7.9 mm. The inset shows the Input-Output curve of fundamental to second harmonic power. b) Temperature dependence of the phase-matching wavelength.

Tables (1)

Tables Icon

Table 1 Comparison of efficiency for periodically poled bulk or waveguides in KTP.

Equations (5)

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

P SHG , norm = sinc 2 ( Δ k l 2 ) ,
Δ k = 2 π n y-eff ( λ SH ) λ SH 2 π n y-eff ( λ pump ) λ pump 2 π n z-eff ( λ pump ) λ pump 2 π Λ .
n i ( λ ) = n i ( bulk ) ( λ ) + Δ n i ( waveguide ) ( λ ) .
η exp = P SHG P pump 2 l 2 100 % = 6.6 % W cm 2 ,
η theo = 8 π 2 d QPM 2 S 2 n 3 c 0 λ pump 2 = 12.4 % W cm 2 .

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