M.A. Abelmas1, O.V. Ivanov2

1 Ulyanovsk State Technical University (Ulyanovsk, Russia)

2 Ulyanovsk Branch of the V.A. Kotelnikov IRE RAS (Ulyanovsk, Russia)

1 abelmax1998@mail.ru

In modern fiber-optic sensors based on the interaction of modes in contacting optical fibers, the accuracy of calculating the coupling coefficient between the fibers is critically important. The widely used linearly polarized (LP) mode approximation, which ignores the longitudinal field components, can lead to significant errors.

To perform an accurate calculation of hybrid modes of optical fibers, taking into account the core, analyze the structure of surface electromagnetic fields, and determine the coupling coefficient between two contacting parallel fibers, considering all field components, including the longitudinal one.

Dependencies of the amplitudes of surface electric field components on the radial mode number for HE and EH hybrid modes in fibers with and without a core are presented. A comparison of the field structures for cases with and without the core has been conducted, revealing qualitative differences in component behavior. It is shown that the longitudinal field component at the cladding boundary is comparable to the transverse components, and its contribution to the mode coupling coefficient reaches a significant value. Field distribution profiles for the HE₁₁ mode in Cartesian coordinates are constructed, allowing the assessment of the amplitude ratio between the longitudinal and transverse components near the cladding boundary. Components of the coupling coefficient for two contacting parallel fibers are calculated, and regions of their maximum interaction are determined. A comparison of the coupling coefficient with and without considering the longitudinal field component is performed; it is demonstrated that neglecting it leads to an error in the coupling coefficient value of up to several tens of percent. Dependencies of the coupling coefficient on the mutual orientation of fiber polarizations, external refractive index, and radial mode number are investigated, revealing patterns of their influence on the efficiency of inter-fiber interaction.

The obtained results allow for improving the accuracy of calculations and the design of fiber-optic devices based on inter-fiber interaction through surface fields.

Abelmas M.A., Ivanov O.V. Interaction of cladding modes of optical fibers via surface fields. Radiotekhnika. 2026. V. 90. № 4.
P. 135−147. DOI: https://doi.org/10.18127/j00338486-202604-16 (In Russian)

1. Udd E. Volokonno-opticheskie datchiki. M.: Tekhnosfera. 2008. 17 s. (in Russian).
2. Chiang K. S., Liu Y., Liu Q., Rao Y. Optical sensing based on light coupling between two parallel long-period fiber gratings. Photonic Sensors. 2011. V. 1. № 3. P. 204–209.
3. Tripathi S. M., Kumar A., Varshney R. K., Kumar Y. B. P., Marin E., Meunier J.-P. Strain and Temperature Sensing Characteristics of Single-Mode–Multimode–Single-Mode Structures. J. Lightwave Technol. 2009. V. 27. № 13. P. 2348.
4. Kogelnik H., Schmidt R. Switched directional couplers with alternating Δβ. IEEE J. Quantum Elect. 1976. V. 12. № 7. P. 396–401.
5. Chiang K.S., Ng M. N., Liu Y., Li S. Evanescent-field coupling between two parallel long-period fiber gratings. Proc. Lasers Electro-Opt. Soc. 2000 Ann. Meeting. 15–16 Nov. Rio Grande. 2000. P. 836–837.
6. Hong Z., Li X., Zhou L., Shen X., Shen J., Li S., Chen J. Coupling characteristics between two conical micro/nano fibers: simulation and experiment. Opt. Express. 2011. V. 19. № 5. P. 3854.
7. Wu Q., Semenova Y., Ma Y., Wang P., Guo T., Long J., Farrell. G. Light Coupling Between a Singlemode-Multimode-Singlemode (SMS) Fiber Structure and a Long Period Fiber Grating. J. Lightwave Technol. 2011. V. 29. № 24. P. 3683–3688.
8. Baiad M. D., Gagné M., Lemire-Renaud S., De Montigny E., Madore W.-J., Godbout N., Kashyap, R. Capturing reflected cladding modes from a fiber Bragg grating with a double-clad fiber coupler. Opt. Express. 2013. V. 21. № 6. P. 6873.
9. Zhang C., Chiang K. S. Broadband optical fiber tap based on cladding-mode coupling. Opt. Eng. 2012. V. 51 № 7. p. 075001.
10. Kritzinger R., Meyer J., Burger J. Investigation of the power coupling of novel wavelength-selective couplers incorporating axially symmetric long-period fiber gratings. S. Afr. J. Sci. 2011. v. 107. № 5/6. Р. 703–705.
11. Zhang W., Huang L., Gao F., Bo F. Tunable broadband light coupler based on two parallel all-fiber acousto-optic tunable filters. Opt. Express. 2013. V. 21. № 14. P. 1358.
12. Fang L., Jia, H. Mode add/drop multiplexers of LP02 and LP03 modes with two parallel combinative long-period fiber gratings. Opt. Express. 2014. V. 22. № 10. P. 16621.
13. Chiang K.S., Chan F.Y.M., Ng M.N. Analysis of Two Parallel Long-Period Fiber Gratings. J. Lightwave Technol. 2004. V. 22. № 5.
    P. 1358–1366.
14. Abel'mas M.A., Suhov S.V., Ivanov O.V. Modelirovanie raspredeleniya poverhnostnogo elektromagnitnogo polya mod besserdcevinnogo opticheskogo volokna. Sb. trudov po materialam X Mezhdunar. konf. i molodezhnoj shkoly «Infor-macionnye tekhnologii i nanotekhnologii» (ITNT-2024). V 6-ti tomah. Samara. 2024. 10262 s. (in Russian).
15. Abel'mas M.A., Suhov S.V., Ivanov O.V. Issledovanie polyarizacii na granice obolochki opticheskogo volokna. Aktual'nye problemy fizicheskoj i funkcional'noj elektroniki. materialy 26-j Vseross. molodezhnoj nauch. konf. Ul'yanovsk. 2023. S. 100-102 (in Russian).
16. Abel'mas M.A., Ivanov O.V. Poverhnostnye elektromagnitnye polya obolochechnyh mod besserdcevinnyh volokonnyh sve-tovodov. Radiotekhnika i elektronika. 2024. T. 69. № 12. S. 1150-1161 (in Russian).
17. Abel'mas M.A., Ivanov O.V. Uchet prodol'noj komponenty elektricheskogo polya pri razrabotke volokonno-opticheskih datchikov. Materialy 25-j Vseross. molodezhnoj nauch. konf. «Aktual'nye problemy fizicheskoj i funkcional'noj elektroniki». Ul'yanovsk. 2022. S. 31-32 (in Russian).
18. Ivanov O.V., Abel'mas M.A. Osobennosti prodol'nogo polya mod vblizi poverhnosti opticheskogo volokna. Sb. materi-alov 56-j nauch.-tekhnich. konf. «Vuzovskaya nauka v sovremennyh usloviyah». V 2-h chastyah. Ul'yanovsk. 2022. S. 164-167 (in Russian).
19. Erdogan T. Cladding-mode resonances in short-and long-period fiber grating filters. J. Opt. Soc. Am. A. 1997. V. 14. № 8. 1760 р.
20. Iizuka K. Elements of the photonics. N.Y.: Wiley. 2002.
21. Kawano K., Kitoh T. Introduction to optical waveguide analysis: solving Maxwell’s equations and the schrodinger equation. N.Y.: Wiley. 2001.
22. Abel'mas M.A., Bakurov D.D., Ivanov O.V. Raschet prodol'noj, poperechnoj i azimutal'noj sostavlyayushchih poverhnostnogo polya obolochechnyh mod volokna v zavisimosti ot dliny volny. Materialy 24-j Vseross. molodezhnoj nauch. konf. «Aktual'nye problemy fizicheskoj i funkcional'noj elektroniki». Ul'yanovsk. 2021. S. 20-21 (in Russian).
23. Huang W.P. Coupled-mode theory for optical waveguides. J. Opt. Soc. Am. A. 1994. V. 11. № 3. P. 963-983.