Long-Period waveguide grating couplers
Student thesis: Doctoral Thesis
Related Research Unit(s)
A long-period grating formed in a single-mode optical fiber or waveguide can cause light coupling between the guided mode and the co-propagating cladding modes at specific resonance wavelengths and, therefore, produce a transmission spectrum that consists of a series of rejection-bands centered at those wavelengths. A single long-period grating thus functions as a band-rejection filter. However, by placing two or more identical long-period gratings in parallel, light in the cladding modes dropped by the launching grating can be collected as outputs from the other gratings(s). Such a long-period grating coupler functions as an add/drop multiplexer. Long-period gratings formed in optical fibers, known as long-period fiber gratings (LPFGs), have been studied extensively and applied widely in optical communications and sensing. Couplers based on parallel LPFGs have also been demonstrated recently. However, the geometry and the constituent materials of the optical fiber impose severe constraints on the functions that LPFGs can achieve. Packaging of parallel LPFGs to achieve stable and efficient add/drop operation is also a serious challenge. To remove the constraints of the optical fiber, long-period gratings formed in planar waveguide structures, namely, long-period waveguide gratings (LPWGs), have been proposed. It is envisaged that a wide range of novel integrated-optic devices can be realized with LPWGs. Because waveguides and gratings can be formed on the same substrate, integration of many parallel LPWGs is a solvable problem. The present thesis provides a detailed study of the analysis, design, and fabrication of coupling devices based on parallel LPWGs. The thesis begins with the discussion of the coupled-mode theory and the derivation of the coupled-mode equations for the analysis of LPWG couplers. These equations are first solved analytically for a coupler that consists of two parallel identical uniform LPWGs, where the two gratings are allowed to be offset in the light propagation direction. The transmission characteristics of the coupler are studied in detail and the conditions for 100% coupling efficiency are highlighted. A practical design example is given to demonstrate the feasibility of constructing an efficient LPWG coupler with typical polymer channel waveguides. Furthermore, a transfer-matrix method for solving the coupled-mode equations is developed to study the effects of various forms of non-uniformity, such as pitch detuning, chirping, index apodization, and phase shifts introduced along the gratings, on the transmission characteristics of the LPWG coupler. The coupled-mode theory is next applied to the analysis of a more general coupler that consists of an arbitrary number of parallel uniform LPWGs with identical grating pitches. With the input light launched into only one of the gratings, the conditions for an arbitrary output power distribution among the gratings are derived. Several special cases of practical significance are discussed. A design example of a 3-dB power splitter based on a 3 × 3 LPWG coupler using typical polymer channel waveguides is presented. The transfer-matrix method is further extended to the analysis of a general LPWG array that consists of an arbitrary number of parallel dissimilar and non-uniform LPWGs. Finally, the effects of cladding-mode degeneracy on the transmission characteristics of a single LPWG and a 2 × 2 LPWG coupler are studied. On the experiment side, a 2 × 2 LPWG add/drop multiplexer is fabricated with polymer channel waveguides. The experimental results compare well with the simulation results based on the coupled-mode analysis. An array of ten parallel LPWGs is also demonstrated, which shows the possibility of achieving strong light coupling between widely separated waveguides with only the grating effect.
- Optical wave guides