Controlling the polarization dependence of dual-channel directional couplers formed by silicon-on-insulator slot waveguides

The polarization dependence of directional couplers (DC) formed by silicon-on-insulator (SOI) slot waveguides was studied, and its applications as highly efficient polarization beam splitters (PBSs) and polarization-independent directional couplers (PIDCs) were investigated. The coupling lengths for the quasi-TE and quasi-TM modes may vary with the waveguide geometry due to structural birefringence; thus numerical simulations of the coupling effects in the directional couplers with different aspect ratios and waveguide spacing were conducted to obtain the optimal design parameters for high efficiency as well as compact device size. The lengths of the coupling regions of the designed PBS and PIDC are 47.61 and 23.13 μm, respectively, and they delivered good performance, with an extinction ratio greater than 20 and 1 dB bandwidth larger than 100 nm. The tolerance of fabrication error in the practical device is also discussed.     

Spectral characteristics of asymmetric directional couplers in graded index channel waveguides analyzed by coupled-mode and normal-mode techniques

We present a detailed analysis of the spectral characteristics of asymmetric directional couplers (ADC's) formed by K(+) -Na(+) ion exchange in BK7 glass and compare the results obtained by the use of normal-mode theory with those obtained by the use of the coupled-mode approach. Maximum power transfer is observed to occur at the wavelength at which the propagation constants of the perturbed component arms are equal. This is attributed to the strong coupling inherent in these devices. Strong coupling and asymmetry are observed to result in unequal confinement of the normal modes, leading to reduce power transfer, even when both arms of the coupler are synchronized. Additionally, significant polarization dependence is observed because of birefringence induced by both the K(+) -Na(+) exchange process and the chosen device structure. Polarization extinction ratios of 11.9 and 26.1 dB are obtained for the arms of the directional couplers. ADC's are observed to operate as bandpass filters, and by adjustment of structural parameters, the peak transmission wavelength can be tuned, with spectral bandwidths of 25-55 nm and coupling lengths of 6-12 mm. Over 90% of the input power in the TE polarization at 1.07 μm can be transferred to the second arm of the coupler, whereas power either in the TM polarization or at wavelengths outside the passband is relatively unaffected. We also show that within the bandpass, where the two arms are phase matched, exact normal-mode analysis yields the same results as the quasi-normal-mode approach, in which the normal modes are expressed in terms of the individual modes.     

Polarization dependence of the coupling ratio in LiTaO3 directional couplers

The effect of design and fabrication parameters on the polarization dependence of the splitting ratio in directional couplers produced in LiTaO3 by Zn diffusion has been investigated experimentally at a wavelength of 1558 nm. The directional couplers featured various combinations of waveguide width, separation gaps between waveguides, bending angle, and diffusion conditions. In each case the coupling region was 3.5 mm long. Of particular interest was the identification of parameter sets for which the sum of power splitting ratios from TE and TM inputs equals unity at the output, as needed for electro-optic tunable filters with relaxed beam-splitter requirements.     

Laser direct writing polymeric single-mode waveguide devices with a rib structure

A focused argon-ion laser beam is used on a spin-coated polymeric thin-film deposited upon a SiO2/Si substrate to polymerize the core for fabrication of Gaussian profile optical channel waveguides. A rib structure that allows only the fundamental mode to propagate even with its higher dimension and high-index contrast between the core and the cladding was fabricated. When the thickness of the core-index region outside the rib section decreases, the waveguide produces higher-order modes at the output. The waveguide reported here has cross-sectional dimensions and numerical apertures that match the single-mode fibers for efficient coupling. I used a mixture of two intermiscible acrylate monomers for the cladding and the core of the waveguides. The polymerization process and its dependent dwell time or scan speed and the laser power intensity are shown. I present the operational characteristics of directional couplers using a rib waveguide structure with a core-cladding index difference.     

Polarization dependence in Ti-diffused LiNbO3 directional couplers

The effect of design and fabrication parameters on the dependence on polarization of the splitting ratio in directional couplers produced by Ti diffusion in LiNbO3 has been investigated experimentally at a wavelength of 1.54 microm. The parametric study was carried out at a diffusion temperature of 1025 degrees C, which was found to suppress outdiffusion effects. The directional couplers were produced by use of various combinations of waveguide separation, Ti film thickness, and diffusion time. Of particular interest was the identification of parameter sets for which the sum of TE and TM splitting ratios equals unity, as required for electro-optic and acousto-optic tunable filter designs with relaxed beam-splitter requirements. Directional couplers that closely match this criterion were obtained by diffusion of 3.5-mm-long, 7-microm-wide Ti strips separated by 11 microm for 11 h. It was found that a bending angle of 0.6 degrees for input and output waveguides produces lower transmission loss for both polarizations than a 1.0 degree bend angle (>1-dB loss reduction).     

Empirical relations for the propagation characteristics of diffused channel waveguides

Empirical relations for the propagation constant and the field profile parameters of integrated optical diffused channel waveguides have been developed. The field profile used is the evanescent secant-hyperbolic field, which has been shown earlier to be a very good approximation for diffused channel-waveguide modes. Least-square fitting has been used to obtain the empirical relations. The results show that the error in empirical relations for the propagation constant is within 2% for a broad range of waveguide parameters. The obtained empirical relations for the field profile and the propagation constant have been used, as an example, to calculate the coupling length of diffused channel-waveguide-based directional couplers.     

Optical field-strength generalized polarization of non-stationary quantum states in waveguiding photonic devices

A quantum analysis of the generalized polarization properties of multimode non-stationary states based on their optical field-strength probability distributions is presented. The quantum generalized polarization is understood as a significant confinement of the probability distribution along certain regions of a multidimensional optical field-strength space. The analysis is addressed to quantum states generated in multimode linear and nonlinear waveguiding (integrated) photonic devices, such as multimode waveguiding directional couplers and waveguiding parametric amplifiers, whose modes fulfill a spatial modal orthogonality. In particular, the generalized polarization degree of coherent, squeezed and Schrödinger’s cat states is analyzed.     

Enhancement of the precision of fiber-optic interferometers by using couplers with high spectral power or antisymmetric supermode cutoff

It is shown that in 2×2 single-mode optical-fiber directional couplers operating with cutoff of the antisymmetric normal mode of a composite waveguide, the additional stray phase shift of the waves in the forward and cross channels (found in normal couplers) vanishes. Thus, by using these couplers (instead of the usual ones) in various interferometers, the precision can be enhanced substantially. It has also been shown that the precision of interferometers with wide-band radiation sources (such as white-light interferometers and fiber-optic gyroscopes) can be improved by replacing the usual couplers with couplers of high spectral power whose splitting ratio can execute a large number of oscillations within the radiation line width, efficiently eliminating the afore-mentioned stray phase shift. Pis’ma Zh. Tekh. Fiz. 23, 76–80 (July 26, 1997)     

Traveling waves in two parallel infinite linear point-scatterer arrays

Traveling waves in two coupled parallel infinite linear point-scatterer arrays are studied analytically for the first time to our knowledge. The two arrays are considered to be generally offset in the axial direction. It is found that slow quasi-even/odd supermodes are supported, as a result of the coupling-induced splitting of the modes of the single array, in direct analogy to standard optical waveguide couplers. Exactly even/odd supermodes are supported when the axial offset is zero. Mode splitting, dispersion curves, and coupling length are numerically investigated versus the inter-element spacing, the inter-array distance, and the axial offset. Potential applications of the concept are in directional optical couplers made of metallic or dielectric nanoparticle chains.     

Analysis of mode size transformation with a tapered directional coupler

A simple tapered directional coupler with a five-layered structure is employed for mode conversion between a single-order and higher-order modes. We investigate coupling from higher-order modes to a single-order field theoretically and experimentally. As a result, we confirm that the first two modes in the tapered waveguide are coupled with a single-order mode in another waveguide by computer simulation using the beam propagation method. Furthermore, we fabricated the actual device and observed the streak patterns of the first three modes.     

Design considerations for a higher-order-mode dielectric-loaded power extractor set for millimeter-wave generation

The design of an electron-beam excited device for millimeter-wave generation is presented. Referred to as a dielectric-loaded power extractor, it is based on the higher-order-mode operation of a dielectric-loaded waveguide. With a matching transition, the unit can deliver power to the output waveguide at one of two frequencies, 20.8 and 35.1 GHz, corresponding to the TM₀₂ and TM₀₃ modes, respectively. By properly choosing the thickness of the dielectric lining, both modes are tuned to synchronize with an ultra-relativistic electron beam traversing the unit so that the wakefield generated by the beam is excited at these modes, chosen to be at 20.8 and 35.1 GHz, respectively, both corresponding to a harmonic of the 1.3 GHz operating frequency at an accelerator facility. Power generated in the unintended TM₀₁ mode is effectively suppressed for bunch train operation by a novel technique. The device consists of a dielectric-loaded decelerating structure and two changeable output couplers to deliver the millimeter-wave power to a standard waveguide. For a drive beam with 50 nC of charge per bunch, power levels of 90.4 and 8.68 MW are expected to be delivered by the device at 20.8 and 35.1 GHz, respectively.     

Theoretical study of coaxial fibers

A mathematical solution of the wave equation for coaxial fibers having four different refractive-index profiles is presented. The transcendental equations are obtained under LP approximation and calculated for comparison of HE(mn)-mode-dispersion characteristics. Attention is paid to the HE(11) and HE(12) modes because of their importance for modeling directional couplers, and calculations are carried out to obtain dispersion dependence on dimensional parameters of the fibers. The field expressions also are given, and the spatial distributions of the HE(11) and HE(12) modal fields of all coaxial structures for different conditions of propagation are calculated.     

Volume grating couplers: polarization and loss effects

We analyze the polarization-dependent performance and the loss performance of volume grating couplers using a leaky-mode approach in conjunction with rigorous coupled-wave analysis for two configurations: the volume grating in the cover layer and the volume grating in the waveguide. The angular dependence of TE and TM polarization coupling efficiency is studied, and designs for polarization-dependent and polarization-independent couplers are presented for both configurations. Polarization-dependent couplers are obtained with an outcoupling angle close to normal. Polarization-independent couplers are obtained with outcoupling angles away from normal, 46.7 deg in the case of a volume grating in the cover layer and 54.4 deg in the case of a volume grating in the waveguide. The effect of loss on coupler performance is also analyzed. It is found that, for cases of practical importance, the effect of lossy coupler materials is small. The estimated loss for a commercially available material is 5 dB/cm. For TE-polarized light and the volume grating in the waveguide, a loss of this magnitude reduces the coupling efficiency by less than 3%, whereas in the case of the volume grating in the cover layer, it reduces the coupling efficiency by less than 0.3%.     

Input waveguide grating couplers designed for a desired wavelength and polarization response

Input grating couplers are used to couple light from free space into a waveguide and can provide additional functions such as focusing and beam splitting of the light into arbitrary desired positions in the waveguide. We show that it is possible to design the couplers so that they perform different desired functions depending on the polarization or wavelength of the incident light. We demonstrate experimentally a number of couplers that may be of interest, e.g., in optical fiber communications. Examples are polarization-independent couplers, designed to have the same response for two orthogonal polarizations of the incident light, and couplers for demultiplexing in wavelength division multiplexing applications, designed to separate and focus different input wavelengths to different positions in the waveguide.     

Excitation of waveguide modes in organic light-emitting diode structures by classical dipole oscillators

Analytical techniques known in the literature are used to (i) identify all the planar waveguide modes in four top-emitting organic light-emitting diode (OLED) structures over the visible spectrum, and (ii) compute both TM and TE power spectra for classically radiating dipoles in the emissive layers of these OLED structures. Peaks in the computed power spectra are identified with the waveguide modes in the OLED devices, and areas associated with these peaks are used to estimate the excitation probability of the waveguide modes. In cases where ambiguities arise because of overlapping peaks, it is shown that computed power spectra can be approximated as sums of Lorentzian line shapes. It is found that for all four structures, the dipoles couple almost 80% of their radiant energy into TM modes with only about 20% going into TE modes. Furthermore, except for a narrow spectral band, the excited TM modes are primarily short-range surface plasmon polaritons. Excitations in the narrow spectral band correspond to TM and TE Fabry-Perot microcavity modes. Finally, the analysis shows that, in the absence of grating couplers, only light in the microcavity modes escapes into the air cover.     

Polarization eccentricity of the transverse field for modes in chiral core planar waveguides.

The general solution for modes in an asymmetric planar waveguide with a homogeneous and isotropic chiral core is given in terms of a pair of parameters related to the eccentricity of the polarization ellipse for the transverse electric field. This formulation provides insight into the transition, with increasing chirality of the core, from TE/TM modes to right-handed and left-handed circular polarization modes. Mode polarization as a function of waveguide thickness and of frequency is discussed in detail. Beyond a mode-dependent maximum thickness (or frequency), the left-handed elliptical modes consist of a slow-wave component whose cutoff properties are examined. The limiting case of a symmetric waveguide is also discussed.     

Characteristics of polymeric optical passive single-mode waveguiding devices fabricated by an argon-ion laser

The fabrication of polymeric single-mode Gaussian profile optical waveguides is described. We used poly(methyl methacrylate) and a mixture of two intermiscible monomers for the cladding and the core, respectively, of the waveguides. The cores of the waveguides were fabricated by with an argon-ion laser beam. The waveguides had single-mode Gaussian refractive-index profiles. By using such waveguides, we fabricated directional couplers for power coupling to the adjacent waveguides and also parallel waveguide arrays for preventing power coupling to adjacent waveguides for use in interconnect chips. We analyzed the characteristics of these couplers by using the coupled-mode theory and compared the results with those obtained with the beam propagation method. Experimental results showed good correlation with the theoretical values. We designed optical bus arrays for interconnect chips, considering the variation of normalized frequency V, the power penalty, and the dimensions of the waveguides and the separation between them. The number of waveguides in the bus array increased with increasing V. For a known value of V, a waveguide's density increases with a decrease of its dimensions. The theoretical maximum number of waveguides is ~1490/cm and ~846/cm for 2 mum x 2 mum and 4 mum x 4 mum single-mode waveguides, respectively, to satisfy a 1-dB power penalty criterion at bit-error rate of 10(-9). We fabricated interconnect bus arrays with fifteen 4 mum x 4 mum waveguides for a 3-cm coupling length, and the experimental results were verified to be in good agreement with the theoretical values.     

A Multistate Reflectometer

Precise measurement of complex reflection coefficient and power sensor effective efficiency is reported using a reflectometer comprising two detectors and two directional couplers, one coupler having connected to it a reflector able to switch to different stable states. Results were obtained in three waveguide bands spanning 8.2-26.5 GHz.     

Angular output of hollow, metal-lined, waveguide Raman sensors

Hollow, metal-lined waveguides used as gas sensors based on spontaneous Raman scattering are capable of large angular collection. The collection of light from a large solid angle implies the collection of a large number of waveguide modes. An accurate estimation of the propagation losses for these modes is required to predict the total collected Raman power. We report a theory/experimental comparison of the Raman power collected as a function of the solid angle and waveguide length. New theoretical observations are compared with previous theory appropriate only for low-order modes. A cutback experiment is demonstrated to verify the validity of either theory. The angular distribution of Raman light is measured using aluminum and silver-lined waveguides of varying lengths.     

Design of phased-array wavelength division multiplexers using multimode interference couplers

Novel designs for phased-array wavelength-division multiplexers based on self-imaging properties of multimode interference (MMI) couplers are presented. These devices, which operate on N equally spaced wavelength channels, consist of two MMI couplers connected by an array of N monomode waveguides. The MMI couplers function as power splitters/combiners, and the waveguide array is the dispersive element. The excellent characteristics of MMI couplers offer the possibility of designing small-size devices with low loss and with high uniformity among different channels. A general theoretical formulation for an N-channel multiplexer is presented, and a simple procedure for finding an optimum set of lengths for the array guides is given. We show that these multiplexers can function as N x N wavelength-selective interconnecting components. The simulated performance of three variations of a five-channel device, designed in a rib waveguide system, is given. It is demonstrated that sidelobes in the multiplexer spectral response can be suppressed by weighting the power samples in the array waveguides through appropriate design of a nonuniform MMI power splitter.