| An important functionality in many optical systems is to manipulate the spectral content of light. Diffractive optics has been used widely for this purpose. Typically, in such systems a diffractive element essentially acts as an optical filter on the incident beam of light. However, no comprehensive theory of this type of filtering existed. Furthermore, recent advances in MEMS technology have enabled reconfigurable diffractive optical elements, which make it possible to create programmable spectral filters. Such devices can lead to significant advances in many applications and enable new classes of optical instruments and systems. Hence, a need arose to develop an understanding of the capabilities and limitations of such devices.; The theory presented in this work answers three main questions: (1) how does one synthesize a diffractive optical element (DOE) for a desired filter; (2) what are the capabilities and limitations on such filters; and (3) what is the best device to use? We present two analytical algorithms to compute the DOE for any complex-valued linear filter, and thus answer question 1. The theory also leads to an understanding that there are fundamental trade-offs between filter complexity, power, error, and spectral range, which answers question 2. We then show that a fully arbitrary DOE is very redundant as a filter, and that we can maintain full functionality by a much simpler device, answering question 3. We then apply the theory to existing devices, which leads to the understanding of their capabilites and limitations. Furthermore, the theory led to the discovery that some well-known MEMS devices, such as the Texas Instruments DMD array, can be used as arbitrary spectral filters.; Using the DMD, we demonstrate three applications that can benefit from this technology: correlation spectroscopy, femtosecond pulseshaping, and tunable lasers. In all three applications, we enable functionality never achieved before. The most significant achievement is our demonstration of continuous tuning of an external cavity laser (ECL) with no mechanical motion except for micromirror tilts on the order of a wavelength. This kind of ECL tuning enables integration and volume manufacturing, potentially making this the technology of choice for tunable lasers. |
