Skip to main content

Leaky Modes in Laser-Printed Integrated Optical Structures

  • Conference paper
  • First Online:
Distributed Computer and Communication Networks (DCCN 2019)

Abstract

Some features of a promising technology for creating complex profiles of smoothly irregular and stepped integrated optical waveguide structures, namely, the technology of laser printing, are briefly discussed. The relevance and importance of this direction is due to the widespread and promising technology of femtosecond recording, as well as the active use of elements (chips) created in this way in integrated optics and nanophotonics. Three-dimensional photon schemes have a wide range of applications, from quantum information processing and miniature lasers to opto-mechanics and optical fluids.

When designing bulk integrated optical structures, complex problems arise, both of a theoretical nature and of numerical simulation of the waveguide propagation of optical radiation, because the guided waveguide modes experience radiation and leakage losses. In this regard, the creation of new methods for theoretical and numerical analysis of waveguide processes, in particular those related to the leakage of modes, is undoubtedly important and relevant in the development of the technology of “laser printing”.

Our study shows that, first of all, the radiation outflow process should be considered as a wave process, and models should be built based on wave equations. Constructing a rigorous theory of waveguide leakage processes will make an important theoretical contribution to the theory of integrated optical waveguides and will contribute to improving the technology of “laser printing”.

The publication has been prepared with the support of the “RUDN University Program 5-100”(Sevastianov L.A., mathematical model development). The reported study was funded by RFBR, project number 19-01-00645 (Egorov A.A., physical model development). The reported study was funded by RFBR, project number 18-07-00567 (Divakov D.V., numerical analysis).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Salter, P.S., Jesacher, A., Spring, J.B., Metcalf, B.J., et al.: Adaptive slit beam shaping for direct laser written waveguides. Opt. Lett. 37, 470–472 (2012)

    Article  Google Scholar 

  2. Gross, S., Riesen, N., Love, J.D., Withford, M.J.: Three-dimensional ultra-broadband integrated tapered mode multiplexers. Laser Photonics Rev. 8(5), L81–L85 (2014)

    Article  Google Scholar 

  3. Heilmann, R., Greganti, C., Gräfe, M., Nolte, S., Walther, P., Szameit, A.: Tapering of fs Laser-written Waveguides (2017). arXiv:1707.02941

  4. Corrielli, G., Seri, A., Mazzera, M., Osellame, R., de Riedmatten, H.: An Integrated Optical Memory based on Laser Written Waveguides (2015). arXiv:1512.09288v1

  5. El Hassan, A., Kunst, F.K., Moritz, A., Andler, G., Bergholtz, E.J., Bourennane, M.: Corner states of light in photonic waveguides (2018). arXiv:1812.08185v1

  6. Pavlov, I., Tokelet, O., Pavlova, S., et al.: Femtosecond laser written waveguides deep inside silicon. Opt. Lett. 42, 3028–3031 (2017)

    Article  Google Scholar 

  7. Sherwood-Droz, N., Lipson, M.: Scalable 3D dense integration of photonics on bulk silicon Opt. Express 19(18), 17758–17765 (2011)

    Article  Google Scholar 

  8. Stuart, B.C., Feit, M.D., Herman, S., Rubenchik, A.M., Shore, B.W., Perry, M.D.: Nanosecond-to-femtosecond laser-induced breakdown in dielectrics. Phys. Rev. B 53(4), 1749–1761 (1996)

    Article  Google Scholar 

  9. Carr, C.W., Radousky, H.B., Rubenchik, A.M., Feit, M.D., Demos, S.G.: Localized dynamics during laser-induced damage in optical materials. Phys. Rev. Lett. 92(8), 087401 (2004)

    Article  Google Scholar 

  10. Stone, A., et al.: Direct laser-writing of ferroelectric single-crystal waveguide architectures in glass for 3D integrated optics. Sci. Rep. 5, 10391 (2015)

    Article  Google Scholar 

  11. Corrielli, G., et al.: Rotated waveplates in integrated waveguide optics. Nat. Commun. 5, 4249 (2014)

    Article  Google Scholar 

  12. Bellouard, Y., Said, A.A., Bado, P.: Integrating optics and micro-mechanics in a single substrate: a step toward monolithic integration in fused silica. Opt. Express 13, 6635 (2005)

    Article  Google Scholar 

  13. Osellame, R., Hoekstra, H.J.W.M., Cerullo, G., Pollnau, M.: Femtosecond laser microstructuring: an enabling tool for optofluidic lab-on-chips. Laser Photon. Rev. 5, 442 (2011)

    Article  Google Scholar 

  14. Ogusu, K., Miyag, M., Nishida, S.: Leaky TE modes in an asymmetic three-layered slab waveguide. J. Opt. Soc. Am. 70, 68–72 (1980)

    Article  Google Scholar 

  15. Marcuvitz, N.: On field representations in terms of leaky modes or eigenmodes. IRE Trans. Antennas Propag. 4(3), 192–194 (1956)

    Article  Google Scholar 

  16. Goldstone, L.O., Oliner, A.A.: Leaky-wave antennas I: rectangular waveguides. IRE Trans. Antennas Propag. AP 7, 307–319 (1959)

    Article  Google Scholar 

  17. Tamir, T., Oliner, A.A.: Guided complex waves, part I: fields at an interface. Proc. inst. Elec. Eng. 110, 310–324 (1963)

    Article  Google Scholar 

  18. Tamir, T., Oliner, A.A.: Guided complex waves, part II: relation to radiation patterns. Proc. Inst. Elec. Eng. 110, 325–334 (1963)

    Article  Google Scholar 

  19. Barone, S.: Leaky wave contributions to the field of a line source above a dielectric slab. Report R-532-546, PIB-462, Microwave Research Institute, Polytechnic Institute of Brooklyn, 26 November 1956

    Google Scholar 

  20. Barone, S., Hessel, A.: Leaky wave contributions to the field of a line source above a dielectric slab-part II. Report R-698-58, PIB-626, Microwave Research Institute, Polytechnic Institute of Brooklyn, December 1958

    Google Scholar 

  21. Cassedy, E.S., Cohn, M.: On the existence of leaky waves due to a line source above a grounded dielectric slab. IRE Trans. Microwave Theor. Tech. 9, 243–247 (1961)

    Article  Google Scholar 

  22. Gamow, G.: Zur quantentheorie de atomkernes. Z. Phys. 51, 204–212 (1928)

    Article  Google Scholar 

  23. Bohm, A., Gadella, M., Mainland, B.: Gamow vectors and decaying states. Am. J. Phys. 57, 1103–1108 (1989)

    Article  MathSciNet  Google Scholar 

  24. Siegert, A.F.J.: On the derivation of the dispersion formula for nuclear reactions. Phys. Rev. 56, 750–752 (1939)

    Article  Google Scholar 

  25. Tolstikhin, O.I., Ostrovsky, V.N., Nakamura, H.: Siegert pseudo-states as a universal tool: resonances, S matrix, green function. Phys. Rev. Lett. 79, 2026 (1997)

    Article  Google Scholar 

  26. Tolstikhin, O.I., Ostrovsky, V.N., Nakamura, H.: Siegert pseudostate formulation of scattering theory: one-channel case. Phys. Rev. A 58, 2077 (1998)

    Article  Google Scholar 

  27. Monticone, F., Alu, A.: Leaky-wave theory, techniques, and applications: from microwaves to visible frequencies. Proc. IEEE 103(5), 793–821 (2015)

    Article  Google Scholar 

  28. Divakov, D., Drevitskiy, A., Egorov, A., Sevastianov, L.: Numerical modeling of leaky electromagnetic waves in planar dielectric waveguides. Proc. SPIE 11066, 110660R (2019)

    Google Scholar 

  29. Divakov, D., Tiutiunnik, A., Sevastianov, A.: Symbolic-numeric computation of the eigenvalues and eigenfunctions of the leaky modes in a regular homogeneous open waveguide. MATEC Web Conf. 186, 4 p., Article ID 01009 (2018)

    Article  Google Scholar 

  30. Fock, V.A.: Electromagnetic Diffraction and Propagation Problems. Pergamon Press, London (1965)

    Google Scholar 

  31. Martínez-Ros, A.J., Gómez-Tornero, J.L., Clemente-Fernández, F.J., Monzó-Cabrera, J.: Microwave near-field focusing properties of width-tapered microstrip leaky-wave antenna. IEEE Trans. Antennas Propag. 61(6), 2981–2990 (2013)

    Article  Google Scholar 

  32. Egorov, A.A.: Theory of laser radiation scattering in integrated optical waveguide with 3D-irregularities in presence of noise: vector consideration. Laser Phys. Lett. 1(12), 579–585 (2004). https://doi.org/10.1002/lapl.200410140

    Article  Google Scholar 

  33. Egorov, A.A.: Use of waveguide light scattering for precision measurements of the statistic parameters of irregularities of integrated optical waveguide materials. Opt. Eng. 44(1), 014601–1-10 (2005). https://doi.org/10.1117/1.1828469

    Article  Google Scholar 

  34. Egorov, A.A.: Inverse problem of theory of the laser irradiation scattering in two-dimensional irregular integrated optical waveguide in the presence of statistic noise. Laser Phys. Lett. 2(2), 77–83 (2005). https://doi.org/10.1002/lapl.200410129

    Article  Google Scholar 

  35. Egorov, A.A.: Theoretical, experimental and numerical methods for investigating the characteristics of laser radiation scattered in the integrated-optical waveguide with three-dimensional irregularities. Quant. Electron. 41(7), 644–649 (2011). https://doi.org/10.1070/QE2011v041n07ABEH014560

    Article  Google Scholar 

  36. Egorov, A.A.: Study of bifurcation processes in a multimode waveguide with statistical irregularities. Quant. Electron. 41(10), 911–916 (2011). https://doi.org/10.1070/QE2011v041n10ABEH014683

    Article  Google Scholar 

  37. Egorov, A.A.: Theoretical and numerical analysis of propagation and scattering of eigen- and non-eigenmodes of an irregular integrated-optical waveguide. Quant. Electron. 42(4), 337–344 (2012). https://doi.org/10.1070/QE2012v042n04ABEH014809

    Article  Google Scholar 

  38. Egorov, A.A., Shigorin, V.D., Ayriyan, A.S., Ayryan, E.A.: Study of the effect of pulsed-periodic electric field and linearly polarized laser radiation on the properties of liquid-crystal waveguide. Phys. Wave Phenom. 26(2), 116–123 (2018). https://doi.org/10.3103/S1541308X18020012

    Article  Google Scholar 

  39. Egorov, A.A., Egorov, M.A., Tsareva, Y.I., Chekhlova, T.K.: Study of the integrated-optical concentration sensor for gaseous substances. Laser Phys. 17(1), 50–53 (2007). https://doi.org/10.1134/S1054660X07010100

    Article  Google Scholar 

  40. Egorov, A.A., Egorov, M.A., Chekhlova, T.K., Timakin, A.G.: Study of a computer-controlled integrated optical gas-concentration sensor. Quant. Electron. 38(8), 787–790 (2008). https://doi.org/10.1070/QE2008v038n08ABEH013589

    Article  Google Scholar 

  41. Egorov, A.A.: Theory of absorption integrated optical sensor of gaseous materials. Opt. Spectrosc. 109(4), 625–634 (2010). https://doi.org/10.1134/S0030400X1010022X

    Article  Google Scholar 

  42. Egorov, A.A., Andler, G., Sevastyanov, A.L., Sevastyanov, L.A.: On some properties of smoothly irregular waveguide structures critical for information optical systems. Commun. Comput. Inf. Sci. 919, 387–398 (2018). https://doi.org/10.1007/978-3-319-99447-5

    Article  Google Scholar 

  43. Egorov, A., Sevastianov, L., Shigorin, V., Andler, G., Ayriyan, A., Ayriyan, E.: Experimental and numerical study of properties of nematic liquid crystal waveguide structures. IEEE Xplore 8631282, 448–452 (2019). https://doi.org/10.1109/ICUMT.2018.8631282

    Article  Google Scholar 

  44. Wang, Y., H., Li, Zhao, L., Liu, Y., Liu, S., Yang, J.: Tapered optical fiber waveguide coupling to whispering gallery modes of liquid crystal microdroplet for thermal sensing application. Opt. Express 25(2), 918–926 (2017). https://doi.org/10.1364/OE.25.000918

    Article  Google Scholar 

  45. Liu, J.-M.: Photonic Devices. University Press, Cambridge (2005)

    Book  Google Scholar 

  46. Rigneault, H., Lourtioz, J.-M., Delalande, C., Levenson, A. (eds.): Nanophotonics. ISTE Ltd. (2006)

    Google Scholar 

  47. Davis, K.M., Miura, K., Sugimoto, N., Hirao, K.: Writing waveguides in glass with a femtosecond laser. Opt. Lett. 21(21), 1729–1731 (1996)

    Article  Google Scholar 

  48. Ams, M., et al.: Investigation of ultrafast laser-photonic material interactions: challenges for directly written glass photonics. IEEE Sel. Top. Quant. Electron. 14(5), 1370–1381 (2008)

    Article  Google Scholar 

  49. Nandi, P., et al.: Femtosecond laser written channel waveguides in tellurite glass. Opt. Express 14(25), 12145–12150 (2006)

    Article  Google Scholar 

  50. Nejadmalayeri, A.H., Herman, P.R.: Ultrafast laser waveguide writing: lithium niobate and the role of circular polarization and picosecond pulse width. Opt. Lett. 31, 2987–2989 (2006)

    Article  Google Scholar 

  51. Yang, W., Kazansky, P.G., Svirko, Y.P.: Non-reciprocal ultrafast laser writing. Nat. Photonics 2, 99–104 (2008)

    Article  Google Scholar 

  52. Eaton, S.M., Chen, W., Zhang, L., Iyer, R., Aitchison, J.S., Herman, P.R.: Telecom-band directional coupler written with femtosecond fiber laser. IEEE Photonics Technol. Lett. 18(20), 2174–2176 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. A. Sevastianov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Egorov, A.A., Divakov, D.V., Lovetskiy, K.P., Sevastianov, A.L., Sevastianov, L.A. (2019). Leaky Modes in Laser-Printed Integrated Optical Structures. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2019. Lecture Notes in Computer Science(), vol 11965. Springer, Cham. https://doi.org/10.1007/978-3-030-36614-8_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-36614-8_41

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36613-1

  • Online ISBN: 978-3-030-36614-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics