TM-polarized Modes Research Articles

Compact terahertz wave polarizing beam splitter

We designed a compact terahertz (THz) wave polarizing beam splitter based on a periodic bilayer structure, which operates over a wide THz wavelength range. Within a short length (about 1 mm), this polarizing beam splitter separates THz wave TE- and TM-polarized modes into orthogonal output waveguides. Results of simulations with the finite-element method show that 99.99% of the TE-polarized THz wave is deflected by the periodic bilayer structure (with 39.9 dB extinction ratio), whereas 99.58% of the TM-polarized THz wave propagates through the structure (with a 23.7 dB extinction ratio). Tolerance analysis reveals a large tolerance to fabrication errors.

Back-propagating surface polaritons of a one-dimensional photonic crystal containing single negative metamaterials

The existence of the surface polaritons at the interface separating a semi-infinite uniform left-handed metamaterial and a one-dimensional photonic crystal composed of alternating layers of two kinds of single-negative materials is theoretically investigated. The dispersion characteristics of the surface polaritons are analyzed and demonstrated that in the presence of metamaterial, the surface polaritons are sensitive to light polarization, so that there exist only backward TM-polarized (or TE-polarized) kind of the surface polaritons depending on the ratio of the thicknesses of the two periodic stacking layers. The existence regions of the surface polariton modes are determined for both TM-polarized and TE-polarized surface polariton modes.

Ultra-high-Q TE/TM dual-polarized photonic crystal nanocavities

We demonstrate photonic crystal nanobeam cavities that support both TE- and TM-polarized modes, each with a Q factor greater than one million and a mode volume on the order of the cubic wavelength. We show that these orthogonally polarized modes have a tunable frequency separation and a high nonlinear spatial overlap. We expect these cavities to have a variety of applications in resonance-enhanced nonlinear optics.

Surface Bloch waves in metamaterial and metal-dielectric superlattices

We study the properties of electromagnetic Bloch waves in semi-infinite periodic structures created by alternating metamaterial and dielectric layers. We derive and analyze the dispersion relations in the long-wavelength limit for both TE- and TM-polarized surface Bloch modes for magnetic metamaterials with negative refraction and metal-dielectric plasmonic superlattices. We reveal that in the subwavelength regime, the bulk modes are characterized by three different refractive indices (“trirefringence”), while the surface modes can propagate parallel to the Bloch wavevector and along the interface between superlattice and semi-infinite dielectric.

Properties of waveguide modes in a photon crystal based on slotted silicon with a defect

The properties of localized modes in Bragg waveguides based on grooved silicon are treated theoretically. For structures with different widths of the channel, the dispersion curves for the TE-and TM-polarized waveguide modes as well as the localization coefficient and the group velocity of wave packets formed of the modes are calculated. The calculations were carried out by the method of expansion of the electromagnetic field in terms of plane waves with the use of the approximation of periodic continuation of the solutions. It is shown that, in the structures, the properties of the TE-and TM-polarized waveguide modes are substantially different. The TE modes are found to be most localized in the waveguide channel, with the degree of localization close to unity in the structures with a wide channel. The group velocity of wave packets formed of such modes reach a value close to the speed of light in free space. This is due to the fact that the power of the waveguide mode is almost totally concentrated in the channel, whose permittivity is unity.

Casimir Energy of the Evanescent Field between Inhomogeneous Dielectric Slabs

Using the mode-by-mode summation technique, we study the contribution of the evanescent modes to the Casimir energy between semi-infinite dielectric slabs whose plasma frequencies change linearly near their surfaces. The vacuum energy is defined as the summation of the zero-point energy over all possible TM-polarized evanescent modes, and the dispersion relation is numerically obtained using multilayer approximation and the transfer matrix method. In contrast to homogeneous dielectric slabs, the number of allowed modes between inhomogeneous dielectric slabs diverges in the continuous limit; however, our computational method affords the convergent Casimir energy. Furthermore, the effect of inhomogeneity in dielectric permittivity on the Casimir energy is evaluated.

Dependence of spectral width of TM-polarization lasing modes on pumping intensity in two-dimensional random media

The spectral width of transverse magnetic (TM) lasing modes in two-dimensional random media is theoretically investigated by using the time-dependent theory. The evolution curve of the spectral width of TM-polarization modes versus the pump intensity is obtained from which one can calculate some characteristic parameters of the emission, e.g. the threshold. The results show that, from the view of spectral width, the emission of the TM-polarization lasing modes have better out-put property than that obtained previously with TE-polarization.

Properties of Pump-Laser Modules Exposed to Polarization-Dependent and Wavelength-Selective Feedback From Fiber Bragg Gratings

The performance of fiber Bragg grating (FBG) stabilized pump-laser modules is strongly influenced by changes of the state of polarization (SOP) arising from intrinsic and/or induced birefringence of the fiber. Birefringence changes the SOP as the light propagates back and forth between laser and FBG, which are separated by a distance of 1 to 2 m. As a result, the effective wavelength-selective feedback provided by the FBG varies accordingly. Based on the steady-state solution of a set of multimode rate equations we present a new model allowing us to calculate the output characteristics of a grating-stabilized pump-laser module as function of effective feedback. An effective-reflector approach is applied to describe the external cavity between the front mirror and the FBG on the module's front side. The polarization- and wavelength-dependent effective feedback from the grating is taken into account by a feedback parameter in the equations for the effective reflector. We present an extended traveling-wave amplifier model for calculating the TE- and TM-polarized contributions to the power from all output ports of the module. Our model is verified by comparison of simulation results with experimental data for a typical FBG-stabilized pump-laser module. The output characteristics are analyzed as function of effective feedback for both the principal TE-polarization as well as the residual TM-polarization modes.

Almost-common path interferometer using the separation of polarization states for digital phase-shifting shearography

An original experimental setup for shearography with metrological applications is presented. The simplicity and the efficiency of the setup are provided by a shearing device, a prism that separates the TE and TM polarization modes with a coating and a thin glass plate placed on its face. The use of this shearing device enables an in-line and almost-common path configuration for the shearing interferometer, a path that leads to high stability and a low sensitivity to external disturbances. Moreover, the sensitivity of the interferometer can be easily adjusted for different applications by varying the shearing amount with glass plates of different thicknesses or by moving the shearing device between two lenses along the optical axis. The temporal phase-shifting method is applied through the use of a liquid crystal variable retarder.

Polarization-dependent Talbot effect

The term "polarization-dependent Talbot effect" means that the Talbot self-imaging intensity of a high-density grating is different for TE and TM polarization modes. Numerical simulations with the finite-difference time-domain method show that the polarization dependence of the Talbot images is obvious for gratings with period d between 2 lambda and 3 lambda. Such a polarization-dependent difference for TE and TM polarization of a high-density grating of 630 lines/mm (corresponding to d/lambda=2.5) is verified through experiments with the scanning near-field optical microscopy technique, in which a He-Ne laser is used as its polarization is changed from the TE mode to the TM mode. The polarization-dependent Talbot effect should help us to understand more clearly the diffraction behavior of a high-density grating in nano-optics and contribute to wide application of the Talbot effect.

Efficient antiguiding of TE and TM polarizations in low-index core waveguides without the need for an omnidirectional reflector

While an omnidirectional bandgap is necessary to reflect arbitrary polarized light with a planar periodic reflector at any angle of radiation incidence, we demonstrate that omnidirectionality is not at all necessary for efficient antiguiding of modes of any polarization in low-index core photonic bandgap (PBG) fibers and waveguides. For a given radiation decay rate into the reflector and multilayer bandgap size we characterize the phase space of fiber materials leading to the same effective guiding conditions. We demonstrate that low- and high-index-contrast PBG waveguides can antiguide problematic TM-like modes equally effectively. Finally, the possibility of TE-like guidance of a TM-polarized mode is described.

High transmission efficiency for surface plasmon resonance by use of a dielectric grating

The efficiency of the transmission of surface plasmon waves by use of a dielectric diffraction grating is discussed. The Kretschmann device allows us to obtain a surface plasmon resonance that consists of an absorption peak in the reflection spectrum. When surface plasmon resonance occurs, the TM-polarization mode of the incident electromagnetic wave is neither transmitted nor reflected. The procedure to transform an 4bsorption peak into a transmission peak is described. Transmittivity of 68% is obtained for a simple structure that consists of a thin-film layer of Ag coated on a volume diffraction grating and embedded between two dielectric media. The results presented herein were obtained by numerical simulations that were carried out by use of an algorithm based on the rigorous coupled-wave theory.

Finite element and perturbative study of buffered leaky planar waveguides

The effects of the presence of a high-index medium in the proximity of planar waveguiding structures that makes up buffered leaky waveguides, were studied using a finite element method (FEM) leaky mode solver and a perturbation method. Various phenomena observed in the FEM results were interpreted through the approximate analytical expressions derived using the perturbation method. The effect of the buffer layer thickness, the high-index medium refractive index, and the quasi-confinement of the modal field were investigated. The results show that the perturbation due to the high-index medium can lead to either an increase or a decrease of the real part of the effective index, and that the leakage loss of a TE-polarized mode is not always lower than TM-polarized mode of the same order. It was found that if the refractive index of the high-index medium goes to infinity, a leaky-wave structure evolves into a guided-wave structure.

Application of an approximate vectorial diffraction model to analysing diffractive micro-optical elements

Scalar diffraction theory, although simple and efficient, is too rough for analysing diffractive micro-optical elements. Rigorous vectorial diffraction theory requires extensive numerical efforts and is not a convenient design tool. In this paper we employ a simple approximate vectorial diffraction model which combines the principle of the scalar diffraction theory with an approximate local field model to analyse the diffraction of optical waves by some typical two-dimensional diffractive micro-optical elements. The TE and TM polarization modes are both considered. We have found that the approximate vectorial diffraction model can agree much better with the rigorous electromagnetic simulation results than the scalar diffraction theory for these micro-optical elements.

Compact and integrated TM-pass waveguide polarizer

A novel integrated TM-pass waveguide polarizer with a subwavelength-wide slot is introduced and theoretically analyzed. With a proper design of the slot, the waveguide can be used as a single polarization waveguide to guide only TM polarization modes of the light signal. With 26 microm length of this TM-pass polarizer, our computer simulations predict the insertion loss of 0.54 dB for the TM polarization mode with the extinction ratio of 20.3 dB at the wavelength of 1.55 microm.

Waveguide-coupled octagonal microdisk channel add-drop filters.

We report planar waveguide-coupled octagonal microdisk channel add-drop filters on silicon nitride-on-silica substrates. Using ray optics, we show that discrete octagonal cavities have wave-front-matched four- and eight-bounce ray orbits. From a planar waveguide-coupled 50-microm-sized octagonal microdisk filter, our experiment demonstrates TM-polarized eight-bounce modes with a coupling efficiency of approximately 56%, Q approximately equal to 1150, and a finesse of approximately 5. Using the two-dimensional finite-difference time-domain method, we obtain qualitative agreement between measurement and simulation of a smaller-sized waveguide-coupled octagonal microdisk filter.

Analysis of the birefringence of a silicon-on-insulator rib waveguide.

A detailed analysis of the polarization characteristics (birefringence) of a silicon-on-insulator (SOI) rib waveguide is given. The fundamental TE- and TM-polarized modes of the SOI rib waveguide are calculated by a semivectorial finite-difference method. The rib width and the slab height of the SOI rib waveguide are normalized with respect to the total height of the silicon layer. A general relation between the two normalized parameters for a nonbirefringent SOI rib waveguide is obtained. According to this relation a nonbirefringent SOI rib waveguide can easily be designed. The fabrication tolerance for a nonbirefringent SOI rib waveguide is also analyzed, revealing that the tolerance can be increased by use of a larger total height of the silicon layer.

Analysis of polarization properties of lateral antiresonant reflecting optical waveguides

Polarization properties of lateral antiresonant reflecting optical waveguides (ARROWs) with many periods have been investigated in a high index contrast material based on silicon-on-insulator platform. Two designs, one based on grazing incidence and a second one incorporating Brewster angle condition, with depressed and non-depressed index cores are compared. The numerical simulations with a 3D semi-vectorial beam propagation method presented demonstrate that depressed and non-depressed index core in the two analyzed designs have very different polarization properties. With non-depressed index core TE and TM polarization modes are efficiently supported, whereas with the depressed index core both designs perform well as TE mode polarizers with a TE to TM extinction ratio of better than 22 dB/mm. Attenuation properties have also been studied for different number of periods in the ARROW design.

Silicon-based optical waveguide polarizer using photonic band gap

Based on different photonic band structures of TE and TM polarization modes in periodic multilayers, a method to realize the waveguide polarizer is proposed. The waveguide structure contains a SiO2 core layer sandwiched between two multilayers of alternately stacked poly-Si and SiO2, and the whole structure can be grown on a Si substrate. Its propagation characteristics are studied theoretically. High extinction ratio over 40 dB at a light wavelength of 1.3 μm is expected in the waveguide of only 40 μm long, accompanied with very low propagation loss of the passive TE mode. These characteristics are very suitable for the applications in integrated optics. The fabrication of this polarizer structure by using the magnetron sputtering method is demonstrated.

A comparison of the Colton–Kirsch inverse scattering methods with linearizedtomographic inverse scattering

We present a numerical comparison of the so-called ‘linear sampling’ inversescattering methods developed by Colton and Kirsch, published in this journal, andlinearized tomographic inverse scattering algorithms based on either holographicfiltered backpropagation principles or a plain matrix inversion scheme. Althoughwe restrict ourselves to two-dimensional obstacle scattering, we investigate boththe transverse magnetic (TM) and the transverse electric (TE) polarizationmodes. The comparison of the TM-polarization mode is performed with a specificfiltered backpropagation algorithm derived here whereas the comparison of theTE-polarization mode is performed with a matrix inversion scheme. Bothsuggested schemes, with which we compare the linear sampling method, make useof linearizing approximations whereas the linear sampling method does notintroduce any such approximations.Numerical examples are given for a monofrequent plane wave excitation inangular diversity mode with either full or limited aperture data. In theseparticular experiments, the linearized tomographic methods appear to provideclearer visual results than the linear sampling methods.