Abstract

Mid-infrared lithium niobate cladding waveguides have great potential in low-loss on-chip non-linear optical instruments such as mid-infrared spectrometers and frequency converters, but their three-dimensional femtosecond-laser fabrication is currently not well understood due to the complex interplay between achievable depressed index values and the stress-optic refractive index changes arising as a function of both laser fabrication parameters, and cladding arrangement. Moreover, both the stress-field anisotropy and the asymmetric shape of low-index tracks yield highly birefringent waveguides not useful for most applications where controlling and manipulating the polarization state of a light beam is crucial. To achieve true high performance devices a fundamental understanding on how these waveguides behave and how they can be ultimately optimized is required. In this work we employ a heuristic modelling approach based on the use of standard optical characterization data along with standard computational numerical methods to obtain a satisfactory approximate solution to the problem of designing realistic laser-written circuit building-blocks, such as straight waveguides, bends and evanescent splitters. We infer basic waveguide design parameters such as the complex index of refraction of laser-written tracks at 3.68 µm mid-infrared wavelengths, as well as the cross-sectional stress-optic index maps, obtaining an overall waveguide simulation that closely matches the measured mid-infrared waveguide properties in terms of anisotropy, mode field distributions and propagation losses. We then explore experimentally feasible waveguide designs in the search of a single-mode low-loss behaviour for both ordinary and extraordinary polarizations. We evaluate the overall losses of s-bend components unveiling the expected radiation bend losses of this type of waveguides, and finally showcase a prototype design of a low-loss evanescent splitter. Developing a realistic waveguide model with which robust waveguide designs can be developed will be key for exploiting the potential of the technology.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Low-loss 3D-laser-written mid-infrared LiNbO3 depressed-index cladding waveguides for both TE and TM polarizations

Huu-Dat Nguyen, Airán Ródenas, Javier R. Vázquez de Aldana, Guillermo Martín, Javier Martínez, Magdalena Aguiló, Maria Cinta Pujol, and Francesc Díaz
Opt. Express 25(4) 3722-3736 (2017)

Low loss depressed cladding waveguide inscribed in YAG:Nd single crystal by femtosecond laser pulses

Andrey Okhrimchuk, Vladimir Mezentsev, Alexander Shestakov, and Ian Bennion
Opt. Express 20(4) 3832-3843 (2012)

Low-loss curved waveguides in polymers written with a femtosecond laser

Welm M. Pätzold, Ayhan Demircan, and Uwe Morgner
Opt. Express 25(1) 263-270 (2017)

References

  • View by:
  • |
  • |
  • |

  1. Y. Ren, G. Brown, A. Ródenas, S. Beecher, F. Chen, and A. K. Kar, “Mid-infrared waveguide lasers in rare-earth-doped YAG,” Opt. Lett. 37(16), 3339–3341 (2012).
    [Crossref] [PubMed]
  2. R. He, Q. An, Y. Jia, G. R. Castillo-Vega, J. R. Vázquez de Aldana, and F. Chen, “Femtosecond laser micromachining of lithium niobate depressed cladding waveguides,” Opt. Mater. Express 3(9), 1378–1384 (2013).
    [Crossref]
  3. Q. An, Y. Ren, Y. Jia, J. R. V. de Aldana, and F. Chen, “Mid-infrared waveguides in zinc sulfide crystal,” Opt. Mater. Express 3(4), 466–471 (2013).
    [Crossref]
  4. J. R. Macdonald, S. J. Beecher, P. A. Berry, G. Brown, K. L. Schepler, and A. K. Kar, “Efficient mid-infrared Cr:ZnSe channel waveguide laser operating at 2486 nm,” Opt. Lett. 38(13), 2194–2196 (2013).
    [Crossref] [PubMed]
  5. J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
    [Crossref]
  6. A. Ródenas, G. Zhou, D. Jaque, and M. Gu, “Direct laser writing of three-dimensional photonic structures in Nd:yttrium aluminum garnet laser ceramics,” Appl. Phys. Lett. 93(15), 151104 (2008).
    [Crossref]
  7. A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
    [Crossref]
  8. A. Rodenas, “Direct femtosecond laser writing of 3D photonic structures in rare-earth doped lithium niobate”, PhD Thesis 2009, ISBN 978–84–693–3869–8, http://hdl.handle.net/10486/4167
  9. A. Ródenas, L. M. Maestro, M. Ramirez, G. A. Torchia, L. Roso, F. Chen, and D. Jaque, “Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides,” J. Appl. Phys. 106(1), 013110 (2009).
    [Crossref]
  10. B. McMillen and Y. Bellouard, “On the anisotropy of stress-distribution induced in glasses and crystals by non-ablative femtosecond laser exposure,” Opt. Express 23(1), 86–100 (2015).
    [Crossref] [PubMed]
  11. H. Karakuzu, M. Dubov, S. Boscolo, L. A. Melnikov, and Y. A. Mazhirina, “Optimisation of microstructured waveguides in z-cut LiNbO3 crystals,” Opt. Mater. Express 4(3), 541–552 (2014).
    [Crossref]
  12. J. Burghoff, C. Grebing, S. Nolte, and A. Tünnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89(8), 081108 (2006).
    [Crossref]
  13. A. Rodenas, A. Benayas, J. R. Macdonald, J. Zhang, D. Y. Tang, D. Jaque, and A. K. Kar, “Direct laser writing of near-IR step-index buried channel waveguides in rare earth doped YAG,” Opt. Lett. 36(17), 3395–3397 (2011).
    [Crossref] [PubMed]
  14. S. Kroesen, W. Horn, J. Imbrock, and C. Denz, “Electro-optical tunable waveguide embedded multiscan Bragg gratings in lithium niobate by direct femtosecond laser writing,” Opt. Express 22(19), 23339–23348 (2014).
    [Crossref] [PubMed]
  15. A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG:Nd3+ crystal by femtosecond laser writing,” Opt. Lett. 30(17), 2248–2250 (2005).
    [Crossref] [PubMed]
  16. A. Okhrimchuk, V. Mezentsev, A. Shestakov, and I. Bennion, “Low loss depressed cladding waveguide inscribed in YAG:Nd single crystal by femtosecond laser pulses,” Opt. Express 20(4), 3832–3843 (2012).
    [Crossref] [PubMed]
  17. T. Gorelik, M. Will, S. Nolte, A. Tuennermann, and U. Glatzel, “Transmission electron microscopy studies of femtosecond laser induced modifications in quartz,” Appl. Phys., A Mater. Sci. Process. 76(3), 309–311 (2003).
    [Crossref]
  18. M. Will, J. Burghoff, S. Nolte, A. Tünnermann, F. Wunderlich, and K. Goetz, “Detailed investigations on femtosecond-induced modifcations in crystalline quartz for integrated optical applications,” Proc. SPIE 5714, 261–270 (2005).
    [Crossref]
  19. J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89(1), 127–132 (2007).
    [Crossref]
  20. Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40(11), 4637–4641 (1969).
    [Crossref]
  21. A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
    [Crossref]
  22. A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
    [Crossref]
  23. D. E. Zelmon, D. L. Small, and D. Jundt, “Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol.% magnesium oxide –doped lithium niobate,” J. Opt. Soc. Am. B 14(12), 3319–3322 (1997).
    [Crossref]
  24. Y. Tsuji and M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol. 18(4), 618–623 (2000).
    [Crossref]
  25. H. Karakuzu, M. Dubov, and S. Boscolo, “Control of the properties of micro-structured waveguides in lithium niobate crystal,” Opt. Express 21(14), 17122–17130 (2013).
    [Crossref] [PubMed]
  26. R. Scarmozzino and R. M. Osgood, “Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications,” J. Opt. Soc. Am. A 8(5), 724–731 (1991).
    [Crossref]
  27. R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6(1), 150–162 (2000).
    [Crossref]
  28. G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28(1), 363–370 (1992).
    [Crossref]
  29. S. Gross, N. Jovanovic, A. Sharp, M. Ireland, J. Lawrence, and M. J. Withford, “Low loss mid-infrared ZBLAN waveguides for future astronomical applications,” Opt. Express 23(6), 7946–7956 (2015).
    [Crossref] [PubMed]

2015 (2)

2014 (2)

2013 (4)

2012 (2)

2011 (1)

2009 (4)

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
[Crossref]

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

A. Ródenas, L. M. Maestro, M. Ramirez, G. A. Torchia, L. Roso, F. Chen, and D. Jaque, “Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides,” J. Appl. Phys. 106(1), 013110 (2009).
[Crossref]

2008 (1)

A. Ródenas, G. Zhou, D. Jaque, and M. Gu, “Direct laser writing of three-dimensional photonic structures in Nd:yttrium aluminum garnet laser ceramics,” Appl. Phys. Lett. 93(15), 151104 (2008).
[Crossref]

2007 (1)

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89(1), 127–132 (2007).
[Crossref]

2006 (2)

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

J. Burghoff, C. Grebing, S. Nolte, and A. Tünnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89(8), 081108 (2006).
[Crossref]

2005 (2)

A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG:Nd3+ crystal by femtosecond laser writing,” Opt. Lett. 30(17), 2248–2250 (2005).
[Crossref] [PubMed]

M. Will, J. Burghoff, S. Nolte, A. Tünnermann, F. Wunderlich, and K. Goetz, “Detailed investigations on femtosecond-induced modifcations in crystalline quartz for integrated optical applications,” Proc. SPIE 5714, 261–270 (2005).
[Crossref]

2003 (1)

T. Gorelik, M. Will, S. Nolte, A. Tuennermann, and U. Glatzel, “Transmission electron microscopy studies of femtosecond laser induced modifications in quartz,” Appl. Phys., A Mater. Sci. Process. 76(3), 309–311 (2003).
[Crossref]

2000 (2)

Y. Tsuji and M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol. 18(4), 618–623 (2000).
[Crossref]

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6(1), 150–162 (2000).
[Crossref]

1997 (1)

1992 (1)

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28(1), 363–370 (1992).
[Crossref]

1991 (1)

1969 (1)

Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40(11), 4637–4641 (1969).
[Crossref]

Agullo-Rueda, F.

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

An, Q.

Andrushchak, A. S.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
[Crossref]

Arias, I.

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

Beecher, S.

Beecher, S. J.

Bellouard, Y.

Benayas, A.

Bennion, I.

Berry, P. A.

Boscolo, S.

Brown, G.

Burghoff, J.

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89(1), 127–132 (2007).
[Crossref]

J. Burghoff, C. Grebing, S. Nolte, and A. Tünnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89(8), 081108 (2006).
[Crossref]

M. Will, J. Burghoff, S. Nolte, A. Tünnermann, F. Wunderlich, and K. Goetz, “Detailed investigations on femtosecond-induced modifcations in crystalline quartz for integrated optical applications,” Proc. SPIE 5714, 261–270 (2005).
[Crossref]

Cantelar, E.

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

Castillo-Vega, G. R.

Chen, F.

de Aldana, J. R. V.

Denz, C.

Dubov, M.

Glatzel, U.

T. Gorelik, M. Will, S. Nolte, A. Tuennermann, and U. Glatzel, “Transmission electron microscopy studies of femtosecond laser induced modifications in quartz,” Appl. Phys., A Mater. Sci. Process. 76(3), 309–311 (2003).
[Crossref]

Goetz, K.

M. Will, J. Burghoff, S. Nolte, A. Tünnermann, F. Wunderlich, and K. Goetz, “Detailed investigations on femtosecond-induced modifcations in crystalline quartz for integrated optical applications,” Proc. SPIE 5714, 261–270 (2005).
[Crossref]

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6(1), 150–162 (2000).
[Crossref]

Gorelik, T.

T. Gorelik, M. Will, S. Nolte, A. Tuennermann, and U. Glatzel, “Transmission electron microscopy studies of femtosecond laser induced modifications in quartz,” Appl. Phys., A Mater. Sci. Process. 76(3), 309–311 (2003).
[Crossref]

Grebing, C.

J. Burghoff, C. Grebing, S. Nolte, and A. Tünnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89(8), 081108 (2006).
[Crossref]

Gross, S.

Gu, M.

A. Ródenas, G. Zhou, D. Jaque, and M. Gu, “Direct laser writing of three-dimensional photonic structures in Nd:yttrium aluminum garnet laser ceramics,” Appl. Phys. Lett. 93(15), 151104 (2008).
[Crossref]

Hadley, G. R.

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28(1), 363–370 (1992).
[Crossref]

He, R.

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6(1), 150–162 (2000).
[Crossref]

Horn, W.

Hu, J.

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

Imbrock, J.

Ireland, M.

Jaque, D.

A. Rodenas, A. Benayas, J. R. Macdonald, J. Zhang, D. Y. Tang, D. Jaque, and A. K. Kar, “Direct laser writing of near-IR step-index buried channel waveguides in rare earth doped YAG,” Opt. Lett. 36(17), 3395–3397 (2011).
[Crossref] [PubMed]

A. Ródenas, L. M. Maestro, M. Ramirez, G. A. Torchia, L. Roso, F. Chen, and D. Jaque, “Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides,” J. Appl. Phys. 106(1), 013110 (2009).
[Crossref]

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

A. Ródenas, G. Zhou, D. Jaque, and M. Gu, “Direct laser writing of three-dimensional photonic structures in Nd:yttrium aluminum garnet laser ceramics,” Appl. Phys. Lett. 93(15), 151104 (2008).
[Crossref]

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

Jaque, F.

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

Jia, Y.

Jovanovic, N.

Jundt, D.

Kar, A. K.

Karakuzu, H.

Khrushchev, I.

Kim, Y. S.

Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40(11), 4637–4641 (1969).
[Crossref]

Kityk, A. V.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
[Crossref]

Koshiba, M.

Kroesen, S.

Laba, H. P.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
[Crossref]

Lamela, J.

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

Lawrence, J.

Lifante, G.

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

Macdonald, J. R.

Maestro, L. M.

A. Ródenas, L. M. Maestro, M. Ramirez, G. A. Torchia, L. Roso, F. Chen, and D. Jaque, “Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides,” J. Appl. Phys. 106(1), 013110 (2009).
[Crossref]

Mazhirina, Y. A.

McMillen, B.

Melnikov, L. A.

Mendez, C.

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

Menyuk, C. R.

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

Mezentsev, V.

Mitchell, J.

Mytsyk, B. G.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
[Crossref]

Nolte, S.

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89(1), 127–132 (2007).
[Crossref]

J. Burghoff, C. Grebing, S. Nolte, and A. Tünnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89(8), 081108 (2006).
[Crossref]

M. Will, J. Burghoff, S. Nolte, A. Tünnermann, F. Wunderlich, and K. Goetz, “Detailed investigations on femtosecond-induced modifcations in crystalline quartz for integrated optical applications,” Proc. SPIE 5714, 261–270 (2005).
[Crossref]

T. Gorelik, M. Will, S. Nolte, A. Tuennermann, and U. Glatzel, “Transmission electron microscopy studies of femtosecond laser induced modifications in quartz,” Appl. Phys., A Mater. Sci. Process. 76(3), 309–311 (2003).
[Crossref]

Okhrimchuk, A.

Okhrimchuk, A. G.

Osgood, R. M.

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6(1), 150–162 (2000).
[Crossref]

Ramirez, M.

A. Ródenas, L. M. Maestro, M. Ramirez, G. A. Torchia, L. Roso, F. Chen, and D. Jaque, “Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides,” J. Appl. Phys. 106(1), 013110 (2009).
[Crossref]

Ren, Y.

Rodenas, A.

Ródenas, A.

Y. Ren, G. Brown, A. Ródenas, S. Beecher, F. Chen, and A. K. Kar, “Mid-infrared waveguide lasers in rare-earth-doped YAG,” Opt. Lett. 37(16), 3339–3341 (2012).
[Crossref] [PubMed]

A. Ródenas, L. M. Maestro, M. Ramirez, G. A. Torchia, L. Roso, F. Chen, and D. Jaque, “Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides,” J. Appl. Phys. 106(1), 013110 (2009).
[Crossref]

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

A. Ródenas, G. Zhou, D. Jaque, and M. Gu, “Direct laser writing of three-dimensional photonic structures in Nd:yttrium aluminum garnet laser ceramics,” Appl. Phys. Lett. 93(15), 151104 (2008).
[Crossref]

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

Roso, L.

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

A. Ródenas, L. M. Maestro, M. Ramirez, G. A. Torchia, L. Roso, F. Chen, and D. Jaque, “Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides,” J. Appl. Phys. 106(1), 013110 (2009).
[Crossref]

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

Sahraoui, B.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
[Crossref]

Sanz Garcia, J. A.

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6(1), 150–162 (2000).
[Crossref]

R. Scarmozzino and R. M. Osgood, “Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications,” J. Opt. Soc. Am. A 8(5), 724–731 (1991).
[Crossref]

Schepler, K. L.

Sharp, A.

Shestakov, A.

Shestakov, A. V.

Small, D. L.

Smith, R. T.

Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40(11), 4637–4641 (1969).
[Crossref]

Solskii, I. M.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
[Crossref]

Tang, D. Y.

Torchia, G. A.

A. Ródenas, L. M. Maestro, M. Ramirez, G. A. Torchia, L. Roso, F. Chen, and D. Jaque, “Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides,” J. Appl. Phys. 106(1), 013110 (2009).
[Crossref]

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

Tsuji, Y.

Tuennermann, A.

T. Gorelik, M. Will, S. Nolte, A. Tuennermann, and U. Glatzel, “Transmission electron microscopy studies of femtosecond laser induced modifications in quartz,” Appl. Phys., A Mater. Sci. Process. 76(3), 309–311 (2003).
[Crossref]

Tunnermann, A.

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89(1), 127–132 (2007).
[Crossref]

Tünnermann, A.

J. Burghoff, C. Grebing, S. Nolte, and A. Tünnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89(8), 081108 (2006).
[Crossref]

M. Will, J. Burghoff, S. Nolte, A. Tünnermann, F. Wunderlich, and K. Goetz, “Detailed investigations on femtosecond-induced modifcations in crystalline quartz for integrated optical applications,” Proc. SPIE 5714, 261–270 (2005).
[Crossref]

Vázquez de Aldana, J. R.

Will, M.

M. Will, J. Burghoff, S. Nolte, A. Tünnermann, F. Wunderlich, and K. Goetz, “Detailed investigations on femtosecond-induced modifcations in crystalline quartz for integrated optical applications,” Proc. SPIE 5714, 261–270 (2005).
[Crossref]

T. Gorelik, M. Will, S. Nolte, A. Tuennermann, and U. Glatzel, “Transmission electron microscopy studies of femtosecond laser induced modifications in quartz,” Appl. Phys., A Mater. Sci. Process. 76(3), 309–311 (2003).
[Crossref]

Withford, M. J.

Wunderlich, F.

M. Will, J. Burghoff, S. Nolte, A. Tünnermann, F. Wunderlich, and K. Goetz, “Detailed investigations on femtosecond-induced modifcations in crystalline quartz for integrated optical applications,” Proc. SPIE 5714, 261–270 (2005).
[Crossref]

Yurkevych, O. V.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
[Crossref]

Zelmon, D. E.

Zhang, J.

Zhou, G.

A. Ródenas, G. Zhou, D. Jaque, and M. Gu, “Direct laser writing of three-dimensional photonic structures in Nd:yttrium aluminum garnet laser ceramics,” Appl. Phys. Lett. 93(15), 151104 (2008).
[Crossref]

Adv. Opt. Photonics (1)

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

Appl. Phys. A (1)

J. Burghoff, S. Nolte, and A. Tunnermann, “Origins of waveguiding in femtosecond laser structured LiNbO3,” Appl. Phys. A 89(1), 127–132 (2007).
[Crossref]

Appl. Phys. B (1)

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B 95(1), 85–96 (2009).
[Crossref]

Appl. Phys. Lett. (2)

A. Ródenas, G. Zhou, D. Jaque, and M. Gu, “Direct laser writing of three-dimensional photonic structures in Nd:yttrium aluminum garnet laser ceramics,” Appl. Phys. Lett. 93(15), 151104 (2008).
[Crossref]

J. Burghoff, C. Grebing, S. Nolte, and A. Tünnermann, “Efficient frequency doubling in femtosecond laser written waveguides in lithium niobate,” Appl. Phys. Lett. 89(8), 081108 (2006).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (1)

T. Gorelik, M. Will, S. Nolte, A. Tuennermann, and U. Glatzel, “Transmission electron microscopy studies of femtosecond laser induced modifications in quartz,” Appl. Phys., A Mater. Sci. Process. 76(3), 309–311 (2003).
[Crossref]

IEEE J. Quantum Electron. (1)

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28(1), 363–370 (1992).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6(1), 150–162 (2000).
[Crossref]

J. Appl. Phys. (4)

Y. S. Kim and R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40(11), 4637–4641 (1969).
[Crossref]

A. Ródenas, J. A. Sanz Garcia, D. Jaque, G. A. Torchia, C. Mendez, I. Arias, L. Roso, and F. Agullo-Rueda, “Optical investigations of femtosecond laser induced microstress in neodymium doped lithium niobate crystals,” J. Appl. Phys. 100(3), 033521 (2006).
[Crossref]

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106(7), 073510 (2009).
[Crossref]

A. Ródenas, L. M. Maestro, M. Ramirez, G. A. Torchia, L. Roso, F. Chen, and D. Jaque, “Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides,” J. Appl. Phys. 106(1), 013110 (2009).
[Crossref]

J. Lightwave Technol. (1)

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

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

Opt. Express (5)

Opt. Lett. (4)

Opt. Mater. Express (3)

Proc. SPIE (1)

M. Will, J. Burghoff, S. Nolte, A. Tünnermann, F. Wunderlich, and K. Goetz, “Detailed investigations on femtosecond-induced modifcations in crystalline quartz for integrated optical applications,” Proc. SPIE 5714, 261–270 (2005).
[Crossref]

Other (1)

A. Rodenas, “Direct femtosecond laser writing of 3D photonic structures in rare-earth doped lithium niobate”, PhD Thesis 2009, ISBN 978–84–693–3869–8, http://hdl.handle.net/10486/4167

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Simulated stress field of the 2-track structure. (a) for the σy component (b) for the σz component.

Fig. 2
Fig. 2

Profiles of 40 μm diameter core cladding waveguides: (a) geometry, (b) fabricated result, (c)(d) stress fields σy and σz, (e)(f) stress-optic refractive index change distributions ny and nz.

Fig. 3
Fig. 3

Fundamental mode near field intensity distribution of the 40 µm diameter core CLW as obtained by FEM (a and b), FD-BPM (c and d), and experiments (e, and f).

Fig. 4
Fig. 4

Comparison of near field TE mode cross sections of simulations and experiment. Horizontal cross sections are shown on the left and vertical cross sections are shown on the right. The best matching between simulated and measured cross sections was obtained for an index change inside tracks of Δn = −0.008.

Fig. 5
Fig. 5

Simulated (a and b) and measured (c) TE modes of the 40-CLW. (a) FEM, (b) FD-BPM and (c) experiment. Using complex RI change inside the cladding tracks: Δny = −0.008 + i0.0007. Scale bar in (c) is 30 µm and it is the same for the three Figs.

Fig. 6
Fig. 6

Straight waveguide propagation losses (a and d), s-bend with R = 125 mm (b and e), and s-bend with R = 100 mm (c and f). Propagation losses (PLs, dB/cm straight length) and bend losses (BLs, dB/mm arc length) are evaluated for TE and TM modes.

Fig. 7
Fig. 7

Straight waveguide PLs (a and d), s-bend with R = 125 mm (b and e), and with R = 100 mm (c and f).

Fig. 8
Fig. 8

Simulation of light propagation in the 50 μm diameter core straight waveguide and s-bend double ring CLW. Straight waveguide propagation losses (a and d), s-bend with r = 125 mm (b and e), and s-bend with r = 100 mm (c and f). Propagation losses (PLs, dB/cm straight length) and bend losses (BLs, dB/mm arc length) are evaluated for TE and TM modes.

Fig. 9
Fig. 9

a) cladding design of the splitter, b) light propagation simulation showing the field intensity distribution, and c) integrated power flux monitor of the two branches along the splitter length, blue and red curves show the left and right branches, respectively.

Equations (5)

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

σ ij = σ 0 + C ijkl :( ε kl ε 0 α kl θ ).
ε= 1 2 ( u+ u T ); ε mn = 1 2 ( u m u n + u n u m ).
Δ ( 1 n 2 ) ij = k,l π ijkl σ kl .
n PML (r)= n o,e i k max ( r r in L ) 2 , r in <r r in +L.
PLs(dB/cm)= 40π ln10.λ(μm) Im( n eff )× 10 4 .

Metrics