Phase Retrieval and Gaussian Beam Mode Decomposition of Gyrotron Beams

In this dissertation, we have developed the necessary basis for the characterization of the RF output of a gyrotron. The characterization includes the phase reconstruction and Gaussian beam mode decomposition. In order to analyze the phase reconstruction in detail, we have developed an accurate field propagation method using the complete Rayleigh-Sommerfeld scalar diffraction integral (RSDI) and the Huygens-Fresnel diffraction integral (HFDI), using a fast Fourier Transform (FFT) based approach. The discretization of the two diffraction integrals is analyzed analytically and numerically. In the case of the HFDI, a condition on the distance of propagation, where aliasing and replication are completely removed, is found. It relates the distance of propagation Δz, the number of sampling points M, the grid cell size Δx and the wavelength λ as: Δz = M(Δx)2 · 1/λ. The two formalisms are also studied using a zero-padding technique, which can be used to propagate the field to any arbitrary distance. These propagation methods are then used in the Iterative Phase Retrieval Algorithm (IPRA) for phase reconstruction. The effects of several parameters on the IPRA (the number of planes, the measurement plane size, the distance of propagation, the number of sampling points and the grid cell size, the misalignment along the optical axis, etc.) are then analyzed. For the theoretical field profiles used in this dissertation, the misalignment along the optical axis in the form of a transverse shift affects the IPRA most severely. The experimental procedure to measure the beam intensity patterns using infrared (IR) thermography is explored extensively. Out of the many target materials used, Robax is the most appropriate in terms of dynamic range, temperature linearity and for the possibility to perform measurements from the front side and the back side. Further, infrared image data processing is investigated for intensity pattern enhancement. This includes various steps: Fixed Pattern Noise (FPN) correction by subtracting the background image of the target taken before the microwave irradiation, defective pixels correction, perspective correction, image pattern enhancement by filtering and denoising. Further, the intermodal decomposition of the reconstructed phase and amplitude is analyzed in detail using two methods, in order to extract the Gaussian content: Finding a set of Gaussian beam parameters and a mode content matrix which maximizes the power in the fundamental mode |C00|2. This method is commonly used by the gyrotron tube developers. Finding a set of Gaussian beam parameters and a mode content matrix which minimizes the error between the corresponding reconstructed field and the input (theoretical and/or experimental) field. It is found that, the two methods may give significantly different results. As a general rule, the second method gives more precise and more reliable results, but the solution is unfortunately not unique and depends both on the measured profile and the measurement parameters. Therefore, the concept of Gaussian content adopted by the community seems to be incomplete, and the corresponding optimized parameters should be associated to it. The definition of Gaussian content should then be reexamined, and completed by an analysis of the power coupling coefficient of the microwave beam to the transmission line (corrugated waveguide or a quasi-optical line).

Huygens-Fresnel diffraction and evanescent waves

Demetri Psaltis

Based on a modified Huygens-Fresnel principle valid in the near field, we analytically verify the exponential wave decay of evanescent waves. This field decay along the propagation direction can be considered as the result of interference between elementary oscillating dipole sources rather than point sources. Specific examples where the modified Huygens-Fresnel principle is applicable are also examined. In particular, the diffraction through a single nano-slit, as well as, the propagation of an engineered input leading to a subwavelength focus are presented. (C) 2010 Published by Elsevier B.V.

2011

Development of Tunable Optical MEMS for Advanced Laser Beam Shaping, Homogenizing and Speckle Reduction

Jonathan Masson

In this thesis, the development, design, fabrication and characterization of three innovative laser beam shaping, homogenizing and speckle reduction devices are reported. Typical beam shaping devices are static and not easily adaptable to a large variety of optical setups. Furthermore, the main issues when shaping coherent light are diffraction effects, speckle patterns, interferences and wavelength dependency. The devices presented in this work solve these issues. The main subjects discussed are beam shaping of coherent light and speckle reduction. Beam shaping and speckle reduction are important in many applications like laser machining, illumination, laser displays and photolithography. The first device presented is a dynamic diffuser and homogenizer for line generation. The 1D linear diffuser consists of a large single crystal silicon membrane of 5x5, 10x10 or 15x15 mm2 areas and having a thickness of 5 μm to 10 μm. This optical surface has a 100 % fill factor. The goal is to deform the membrane in one dimension only so that the light is also diffused in one dimension. The free standing continuous silicon membrane has a bridge type configuration. The actuation of the device is made electromagnetically at resonance by the use of the Lorentz force. Stiffening beams are fabricated below the membrane to decouple the 1D and 2D modes and to prevents 2D dynamic deformations. The device is fabricated on SOI wafer using standard microfabrication technologies. The devices are characterized using a laser doppler vibrometer (LDV) and a goniometer. The LDV measurements have shown that 1D and 2D modes can be excited separately. The diffusion angle is tunable between 0 to 22 mrad. The device is used to smooth out the interference effects created by a static 1D beam shaping optical element. The relative optical power efficiency of is 99.8 %. The device is capable to sustain high optical load of at least 140 W/cm2. It is now being tested in an industrial environment with high power CO2 laser for sealing glass capillaries. The second device presented is a 2D dynamic diffuser. It has to fulfill several characteristics, namely to diffuse light with small and tunable angle with high efficiency, reduce the speckle contrast and interference patterns, have a simple driving and packaging scheme and handle high optical power. A device with a 5x5 mm2 optical surface is designed, fabricated and characterized. The mirror is made of a thin and large deformable a-Si membrane which is supported by an array of posts. The disposition of the posts determines how the membrane is deformed in smaller sub-reflecting elements. A periodic and a pseudo random arrangements of the post arrays are designed. Electrostatic actuation is used to deform the membrane. The whole v deformable mirror is fabricated over a scanning stage. Out of plane resonant comb drive actuators are used to actuate the scanning stage. The diffusion of the light is performed by the deformation of the membrane while the homogenization of the beam profile is accomplished by the simultaneous scanning of the whole deformed membrane. Optical simulations are successfully used to predict the optical properties of the diffuser and to set the requirements for the electro-mechanical part of the device design. The fabrication process is using parylene-C as a refilling material and as a sacrificial layer to enable the fabrication of a 100 % fill factor deformable mirror. The membrane is continuous and release hole free. It is aluminum coated and showed an absolute optical power efficiency of 81 % in the actuated state. The high optical power handling of the device could not be tested. Nevertheless , the material of the device is silicon and the stage is connected with large springs to the frame for high heat conductivity. The pseudo random devices showed ability to shape an incoming beam regardless of its intensity profile into a output beam having a Gaussian profile. Besides, the diffusion angle is small and tunable between 0 to 10 mrad FWHM. The periodic devices is able to transform an incoming Gaussian beam into a super Gaussian intensity profile. Finally, the dynamic diffuser is capable of reducing the speckle contrast of a laser beam projected on a diffusing screen. The speckle contrast is reduced from 0.7 to 0.21 using the device alone and it is reduced to 0.11 when the dynamic diffuser is used in combination with a static diffuser. Tunable diffusion angle, smoothing of interferences, tunable beam shaping and speckle re- duction is realized while keeping the degree of freedom of the device to a minimum. By taking advantage of the optical design of the pseudo random diffuser, only one control electrode is needed to deform the membrane and one signal is used to scan the diffuser. The result is a very compact device, simple actuation and a straightforward packaging schemes. The last device presented is a very small footprint speckle reduction device. A simple actuation scheme using comb drive actuators and four folded springs enable large in plane displacement of a random phase plate. 180 μm of in plane displacement is achieved with a driving voltage as low as 29 V. The speckle contrast is reduced to 0.21 when the device is translating at 314 Hz. A comprehensive study of the diffuser characteristics is made to understand the surface parameters of the diffuser that influence directly the performances on the speckle reduction. The surface profile of the binary height has to be well defined to insure a phase shift of π. This very small device is a good candidate for integration in any portable device where speckle reduction is needed.

EPFL2012

Near-field imaging

Libo Yu

Bloch surface waves (BSWs) are surface electromagnetic waves excited at the interface between a truncated periodic dielectric multilayer and a surrounding medium. This particular solution to the Maxwell equations in stratified media has been known since the late 1970s. However, few studies have been conducted till now on the manipulation and control of BSW propagation over 2D surfaces of photonic structures. There are several advantages provided by BSW propagation on almost flat surfaces. Due to the use of dielectric materials, losses are very low, thus allowing the propagation of BSWs over long distances. Another advantage in using BSWs is the possibility of operating within a broad range of wavelengths by properly designing a suitable multilayered structure. Furthermore, since the maximum intensity associated with BSWs can be tuned on the surface, a strong field intensity increased by several orders of magnitude can be achieved and can thereby enhance the field close to the structure's surface. This tunable localized field confinement is particularly attractive in fluorescence biosensing. In the following, we will use an exemplary BSW-sustaining multilayer as a general platform suitable for manipulating and controlling BSW propagation on its surface in the spectral range of telecom wavelengths. Several 2D optical photonic devices can be implemented starting from an ultra-thin (~ λ /15) polymer layer spun on the multilayer, which can be subsequently shaped as desired. The presence of the polymer modifies the local effective refractive index, enabling a direct manipulation of the BSWs. We experimentally and theoretically demonstrate that BSWs can be diffracted, focused, coupled and made resonating by locally shaping the geometries of 2D photonic devices—such as lenses, prisms, gratings, bended waveguides and waveguide couplers—on the multilayer. One of the main advantages is that these 2D photonic devices can have arbitrary shapes, which are difficult to obtain in 3D. The strong point of the platform concept is that a thin-film multilayer enables standard-wafer-scale production. The top surface can be modified to customize a 2D micro-system by, e.g., e-beam writing, optical lithography, stamping or other replication techniques. Since a BSW can be considered as a 2D wave and it is bounded at the surface of the multilayer, near-field imaging is one of the preferred tools to directly monitor and characterize the near field produced on the structured multilayered surface mentioned above. A multi-heterodyne scanning near-field optical microscope (MH-SNOM) developed in our lab (EPFL-OPT) makes near-field characterization possible. The operation wavelength is in the near infrared range (1460 nm–1580 nm). A polarization-retrieval method is developed in this thesis to measure and characterize the near-field polarization response for arbitrary polarization- sensitive photonic nano-devices, such as photonic crystal microcavities, waveguides, thin films, nanoparticles, spiral gratings and other near-field polarization-sensitive imaging applications. Polarization retrieval is easily accessible in far-field microscopy, but is challenging for the near field. This is because when a SNOM probe interacts with the near field and scatters the signal to the far field, the near-field polarization may be considerably altered. In this thesis, the developed method uses an isotropic region in the vicinity of the nanostructure as a calibration area, whose known polarization properties provide a global criterion to calibrate and quantify the polarization distortion induced by the detection system. It is then applied on the field measured above the structure of interest to compensate and reconstruct its complex field response. We experimentally show the effectiveness of the method on a silicon form- birefringent grating (FBG) with significant polarization diversity. Three spatial dimensional near-field measurements are in agreement with theoretical predictions obtained with rigorous coupled-wave analysis (RCWA). Pseudo-far- field (~10λ away from the surface) measurements are performed to obtain the effective refractive index of the FBG, emphasizing the validity of the proposed method. This reconstruction algorithm makes the MH-SNOM a powerful tool to analyze concurrently the polarization-dependent near-field optical response of any nanostructures with subwavelength resolution as long as a calibration area is available in close proximity.