Fibre Bragg grating sensors have emerged as a simple, inexpensive, accurate, sensitive and reliable platform, a viable alternative to the traditional bulkier optical sensor platforms.

In this work we present an extensive theoretical analysis of the tilted fibre Bragg grating sensor (TFBG) with a particular focus on its polarization-dependent properties.

We have developed a highly efficient computer model capable of providing the full characterization of the TFBG device in less then $3$~minutes for a given state of incident light polarization. As a result, the polarization-dependent spectral response, the field distribution at the sensor surface as well as the fine structure of particular resonances have become accessible for theoretical analysis.

As a part of this computer model we have developed a blazingly fast full-vector complex mode solver, capable of handling cylindrical waveguides of an arbitrary complex refractive index profile.

Along with the theoretical study we have investigated optical properties of the TFBG sensor with application to polarisation-resolved sensing.

We proposed a new method of the TFBG data analysis based on tracking the grating transmission spectra along its principle axes, which were extracted from the Jones matrix.

In this work we also propose a new method of enhancing the TFBG sensor refractometric sensitivity limits, based on resonant coupling between the TFBG structure resonances and the local resonances of nanoparticles deposited on the sensor surface. The $3.5$-fold increase in the TFBG sensor sensitivity was observed experimentally.

**TILTED FIBRE BRAGG GRATING**

**SENSORS WITH RESONANT**

**NANO-SCALE COATINGS**

**Simulation of optical properties**

**Aliaksandr Bialiayeu, PhD**

**1 A full-vector complex mode solver for circularly symmetric optical**

**waveguides**

**1**

**2 Modeling of tilted Bragg grating (TFBG) structures**

**39**

**3 Experimental polarization-based optical sensing with application**

**to TFBG sensors**

**89**

**4 Optical properties of materials**

**107**

**5 Optical properties of nanoparticles**

**125**

**6 The optimal parameters for a nanoparticle-based coating**

**137**

**7 Modification of the sensor surface with various types of nano-**

**scale coatings**

**157**

**8 Conclusion**

**175**

**v**

**1**

**A full-vector complex mode solver for circularly symmetric**

**optical waveguides**

**1**

**vii**

**viii**

**2**

**Modeling of tilted Bragg grating (TFBG) structures**

**39**

**3**

**Experimental polarization-based optical sensing with application**

**to TFBG sensors**

**89**

**4**

**Optical properties of materials**

**107**

**ix**

**5**

**Optical properties of nanoparticles**

**125**

**6**

**The optimal parameters for a nanoparticle-based coating**

**137**

**7**

**Modification of the sensor surface with various types of nano-**

**scale coatings**

**157**

**x**

**8**

**Conclusion**

**175**

**A**

**MatLab Code. The full vectorial complex mode solver.**

**179**

**B**

**Mathematica Code for Mie scattering**

**191**

**xi**

**xii**

**xiii**

**xiv**

**xv**

**xvi**

**xvii**

**xviii**

**xix**

**xxi**

**xxiii**

**xxiv**

**xxv**

**xxvi**

**xxvii**

**xxviii**

**xxix**

**xxx**

**xxxi**

**xxxii**

**xxxiii**

**xxxiv**

**xxxv**

**xxxvii**

**xxxviii**

**CHAPTER 1**

**1.1**

**Introduction**

**1**

**2**

**3**

**4**

**1.2**

**The solutions for a cylindrical waveguide**

**5**

**1.2.1**

**Weakly guided approximation**

**6**

**1.2.2**

**The exact solution for cylindrical waveguides**

**7**

**8**

**1.2.3**

**TE and TM modes in slab waveguides**

**9**

**10**

**1.3**

**The numerical method**

**1.3.1**

**The scalar modes**

**11**

**12**

**13**

**14**

**15**

**1.3.2**

**The vectorial modes**

**16**

**17**

**18**

**19**

**1.4**

**Discussion**

**20**

**21**

**22**

**23**

**24**

**25**

**26**

**27**

**28**

**29**

**1.5**

**The orthogonality of the basis functions**

**1.5.1**

**The orthogonality relation for the scalar modes**

**30**

**31**

**1.5.2**

**The orthogonality relation for the vectorial modes**

**32**

**33**

**34**

**1.5.3**

**Numerical verification**

**35**

**36**

**1.6**

**Conclusion**

**37**

**CHAPTER 2**

**2.1**

**Derivation**

**39**

**40**

**41**

**42**

**43**

**44**

**2.2**

**The matrix elements**

**45**

**46**

**47**

**48**

**49**

**50**

**51**

**52**

**53**

**54**

**55**

**56**

**2.3**

**Coupled-mode theory,**

**the two modes approximation**

**57**

**58**

**59**

**60**

**61**

**2.4**

**Coupling between the core mode and many cladding modes in the**

**TFBG**

**62**

**63**

**64**

**65**

**66**

**67**

**68**

**69**

**70**

**71**

**72**

**73**

**74**

**75**

**2.5**

**Polarization-dependent coupling**

**76**

**77**

**78**

**79**

**80**

**81**

**82**

**2.6**

**The electric field distribution at the fibre boundary**

**83**

**84**

**85**

**86**

**87**

**88**

**CHAPTER 3**

**89**

**90**

**91**

**3.1**

**The Optical Setup**