In this thesis, I will describe the polarization properties of two separate but similar optical systems. I will begin by showing anisotropy in a dielectric photonic crystal slab patterned with a periodic circular hole array. This anisotropy can be utilized in manipulating the gain properties of surface emitting photonic crystal lasers. I will then describe a metallic, planar metamaterial patterned similarly with a 2d periodic array of holes. The enhanced optical transmission of this system is demonstrated computationally and experimentally, with a good agreement between the two. I will also demonstrate polarization rotation in this array. The effect is shown to minimize the background contribution to the transmission resulting in the narrowing of the line width and improvement between on and off resonance contrast. I then provide a theory behind the polarization rotation in transmission through a metamaterial based upon a Jones matrix formulation, which is dependent only upon the existence of separate s and p resonances in a photonic system. / text

Three problems at the forefront of microwave radiometry are solved using probability theory and inverse problem formulations which are heavily based in probability theory. Probability theory is able to capture information about random phenomena, while inverse problem theory processes that information. The use of these theories results in more accurate estimates and assessments of estimate error than is possible with previous, non-probabilistic approaches. The benefits of probabilistic approaches are expounded and demonstrated. The first problem to be solved is a derivation of the error that remains after using a method which corrects radiometric measurements for polarization rotation. Yueh [1] proposed a method of using the third Stokes parameter TU to correct brightness temperatures such as Tv and Th for polarization rotation. This work presents an extended error analysis of Yueh's method. In order to carry out the analysis, a forward model of polarization rotation is developed which accounts for the random nature of thermal radiation, receiver noise, and (to first order) calibration. Analytic formulas are then derived and validated for bias, variance, and root-mean-square error (RMSE) as functions of scene and radiometer parameters. Examination of the formulas reveals that: 1) natural TU from planetary surface radiation, of the magnitude expected on Earth at L-band, has a negligible effect on correction for polarization rotation; 2) RMSE is a function of rotation angle Ω, but the value of Ω which minimizes RMSE is not known prior to instrument fabrication; and 3) if residual calibration errors can be sufficiently reduced via postlaunch calibration, then Yueh's method reduces the error incurred by polarization rotation to negligibility. The second problem addressed in this dissertation is optimal estimation of calibration parameters in microwave radiometers. Algebraic methods for internal calibration of a certain class of polarimetric microwave radiometers are presented by Piepmeier [2]. This dissertation demonstrates that Bayesian estimation of the calibration parameters decreases the RMSE of the estimates by a factor of two as compared with algebraic estimation. This improvement is obtained by using knowledge of the noise structure of the measurements and by utilizing all of the information provided by the measurements. Furthermore, it is demonstrated that much significant information is contained in the covariance information between the calibration parameters. This information can be preserved and conveyed by reporting a multidimensional pdf for the parameters rather than merely the means and variances of those parameters. The proposed method is also extended to estimate several hardware parameters of interest in system calibration. The final portion of this dissertation demonstrates the advantages of a probabilistic approach in an empirical situation. A recent inverse problem formulation, sketched in [3], is founded on probability theory and is sufficiently general that it can be applied in empirical situations. This dissertation applies that formulation to the retrieval of Antarctic air temperature from satellite measurements of microwave brightness temperature. The new method is contrasted with the curve-fitting approach which is the previous state-of-the-art. The adaptibility of the new method not only results in improved estimation but is also capable of producing useful estimates of air temperature in areas where the previous method fails due to the occurence of melt events.

Master of Science / Department of Physics / Brian R. Washburn / This thesis reports our attempt towards achieving a phase stabilized free-space nonlinear polarization rotation (NPR) mode locked erbium doped fiber laser frequency comb system. Optical frequency combs generated by mode-locked femtosecond fiber lasers are vital tools for ultra-precision frequency metrology and molecular spectroscopy. However, the comb bandwidth and average output power become the two main limiting elements in the application of femtosecond optical frequency combs. We have specifically investigated the free-space mode locking dynamics of erbium-doped fiber (EDF) mode-locked ultrafast lasers via nonlinear polarization rotation (NPR) in the normal dispersion regime. To do so, we built a passively mode-locked fiber laser based on NPR with a repetition rate of 89 MHz producing an octave-spanning spectrum due to supercontinuum (SC) generation in highly nonlinear fiber (HNLF). Most significantly, we have achieved highly stable self-starting NPR mode-locked femtosecond fiber laser based frequency comb which has been running mode locked for the past one year without any need to redo the mode locking. By using the free-space NPR comb scheme, we have not only shortened the cavity length, but also have obtained 5 to 10 times higher output power (more than 30 mW at central wavelength of 1570 nm) and much broader spectral comb bandwidth (about 54 nm) compared to conventional all-fiber cavity structure with less than 1 mW average output power and only 10 nm spectral bandwidth. The pulse output from the NPR comb is amplified through a 1 m long EDF, then compressed by a length of anomalous dispersion fiber to a near transform limited pulse duration. The amplified transform limited pulse, with an average power of 180 mW and pulse duration of 70 fs, is used to generate a supercontinuum of 140 mW. SC generation via propagation in HNLF is optimized for specific polling period and heating temperature of PPLN crystal for SHG around 1030 nm. At last, we will also discuss the attempt of second harmonic generation (SHG) by quasi phase matching in the periodically polled lithium niobate (PPLN) crystal due to nonlinear effect corresponding to different polling period and heating temperature.