Optical waveguide gratings : phase retrieval and unidirectional coupling
波導光柵之研究 : 相位重建和單向耦合
Student thesis: Doctoral Thesis
Related Research Unit(s)
Grating is a periodic structure formed in an optical fiber or waveguide for wavelength selection and reconfiguration. Being wavelength-selective elements, gratings have been widely used in optical communication and sensing systems. A number of grating-based devices, such as optical filters, add/drop multiplexers, and optical sensors, have been developed. The thesis contributes to the understanding of two specific characteristics of gratings: phase retrieval and unidirectional coupling. The first part of the thesis studies the retrieval of the phase spectra of gratings from their reflection or transmission amplitude spectra. While most applications of gratings explore their amplitude spectra, there are many applications that rely on the phase characteristics of gratings. A complete knowledge of a grating should consist of both its amplitude and phase spectra, obtained in both the reflection and the transmission directions. A simple and fast phase-retrieval method based on the Hilbert transform (HT) has been applied to fiber Bragg gratings (FBGs), which are narrow-band reflectors. The HT method makes use of the unique relation between the amplitude response and the phase response of a minimum-phase system. The method is applicable to the transmission of an FBG that has an arbitrary grating profile, but only works for the reflection of an FBG that has a strictly symmetric grating profile. In this thesis, we apply the HT method to long-period gratings (LPGs), which are broadband rejection filters. We demonstrate the method with numerical examples and experiments and discuss its limitations. For LPGs, the method is applicable to an arbitrary grating profile, provided that the sign of the modal dispersion factor is known and no over-coupling occurs at any wavelength. We also apply the HT method to Bragg gratings formed in metal waveguides that support surface plasma waves. Such metal Bragg gratings (MBGs) differ from FBGs in having a large propagation loss. We illustrate the operation and the performance of the HT method for MBGs with detailed numerical examples. For the retrieval of the reflection phase, the large propagation loss of an MBG breaks the symmetry requirement of the HT method and thus allows the method to tolerate a certain degree of asymmetry in the grating profile. For the retrieval of the transmission phase, there is no restriction on the grating-profile symmetry, but the large propagation loss can introduce significant errors in the retrieved phase spectrum. We can effectively remove such errors, however, by applying the HT method to the spectrum with the background propagation loss artificially taken away. The HT method provides a simple and effective way to obtain the phase and group-delay characteristics of LPGs and MBGs. The second part of the thesis investigates a special class of LPGs to achieve unidirectional coupling, where light is coupled between two propagating modes along only one propagation direction. Such gratings require carefully matched periodic modulations of the real part and the imaginary part of the relative permittivity of the waveguide and are referred to as complex LPGs (CLPGs). Previous analyses of CLPGs focus on the use of gain-and-loss modulations for the achievement of unidirectional coupling, which poses significant difficulty in the realization of such gratings. Triggered by a recent experimental demonstration of a silicon-based CLPG that does not involve any gain modulations, we analyze, in this thesis, CLPGs for unidirectional coupling that involve only loss modulations and propose a particularly simple structure based on two separate, balanced LPGs (a dielectric grating and a matched metal grating) to realize CLPGs. Our theoretical analyses with the coupled-mode theory and the mode-matching method reveal new propagation dynamics in CLPGs and new considerations for the design of CLPGs as one-way mode converters. We successfully fabricate CLPG samples in polymer waveguides based on our design approach with our in-house fabrication facilities and demonstrate unidirectional coupling with these samples using a prism coupler system set up specifically for the study. Our approach in the design and the fabrication of CLPGs is flexible and cost-effective and could be further developed into a practical platform for the implementation of CLPG-based photonic devices with new functionalities.
- Diffraction gratings