Optimal Design And Characterization Of Broadband Composite Waveplate With Applications In Spectroscopic Ellipsometry

The birefringent waveplate is one of the most important polarized components, which can be used to change the polarization states by introducing a phase shift named the retardance between the two orthogonal components of a polarized light. A composite waveplate, which consists of multiple single-waveplates with their optical axes aligned at different orientations, can compensate the deviations in its optical characteristics with the wavelength, the incident angle and the temperature. The composite waveplate is widely used to modify, modulate and analyze the polarization in many optical systems, such as polarimetry, ellipsometry, optical imaging, laser technique and optical communications. The polarization properties of the composite waveplate can be charaterized by its retardance, orientation of the optical axis, rotary angle, and the ratio of the transimissions in the directions of the fast axis and the slow axis, which have significant influences on the applicable wavelength range and the measurement accuracy and precision of the optical systems. These charateristic parameters depend on the structure of the composite waveplate, such as the materals, the thicknesses and the axis orientations of the the single-waveplates, and the application environments, such as the wavelength, the incident angle and the temperature. Therefore, it is of great importance to study the optimization, the charaterization, the error analysis, and the applications of the composite waveplate.Accordingly, this dissertation concerntrates on the above issues about the composite waveplates, including the optimal design, the charaterization of the optical properites, the accurate alignment of the optical axes and the calibration of the misalignment errors, and the applications in the broadband Mueller matrix ellipsometer (MME). The main contents and innovations of this dissertation are as following:An optical model based on Jones'equivalent theorem is constructed to describe an arbitrary composite waveplate, in which the composite waveplate is optically equivalent to a cascaded system containing a linear retarder and a rotator (circular retarder). Then, a method is proposed for the optimal design of a general composite waveplate (GCW). Both the retardances and azimuths of fast axes of the single-waveplates in the GCW are flexible parameters to be optimized. Compared with convential achromatic waveplates, the GCW is not limited to specific structures, and consequently will provide much more flexibilities to adapt to the optimization of achromatic retardance over a broad band.A simple and general formula is derived to calculate the retardance of the birefringent waveplate under arbitrary incident angle and azimuthal angle based on the theory of wave propagation. And then, a method is presented for the optimal design of a wide-view-angle waveplate by combining two positive waveplates and two negative waveplates. To ensure the design process repeatable and reliable, an approximate method to calculate the initial design parameters of the wide-view-angle waveplate is proposed based on the partial derivative of the effective refractive index to the incident angle.A method for the characterization of the optical properties of a composite waveplate using a spectroscopic MME is proposed. After defining the characteristic parameters of the composite waveplate, the equivalent theory is extended to describe a practical composite waveplate by using the Mueller matrix formalism. And then the relationships between the characteristic parameters and the Mueller matrix are derived. Experimental results performed on a house-developed MME demonstrate that the presented method has the advantage of obtaining all the characteristic spectrums of an arbitrary composite waveplate in a single measurment compared with the existing techniques.A general analytical model is constructed to describe the relations between the characteristic parameters and the misalignment errors in the axes of the composite waveplate. The oscillations in the the characteristic spectrums and their sensitivities to the axis misalignment errors of the composite waveplate are analyzed through simulations. Then, a method is presented to accurately align the optical axes and to quantitatively calibrate the residual misalignment errors in the axes of the composite waveplate using a spectroscopic MME. Experiments performed on a house-developed MME demonstrate that the presented method has a much higher accuracy in the axis alignment of the composite waveplate compared with the published mehtods. In addition, it gives access to quantitatively calibrate the misalignment errors in the axes of the composite waveplate.A novel design of an MME based on dual rotating-GCW is proposed. The basic principles for system measurement and system calibration of the GCW-based MME are presented. A condition-number-based method is proposed for the optimal design of the GCW-based MME system. Then, a broadband MME platform based on the presented principles and methods is set up convering the wavelength range of 200-1000nm. The house-developed MME platform not only verifies the correctness and effectiveness of the presented MME principles based on GCWs, but also can be used as a powerful tool to perform experiments for the other parts of this dissertation.