Leaky-mode Loss Research Articles

Wavelength dependent transmission in W-type plastic optical fibers with graded index core distribution

This paper investigates the wavelength dependence of the equilibrium mode distribution (EMD) and steady state distribution (SSD) in W-type plastic optical fibers (POFs) with graded index (GI) core distribution for parametrically varied width of the fiber's intermediate optical layer and refractive index of the outer cladding. The numerical solution of the time-independent power flow equation is used to determine the transmission characteristics of the W-type GI POF. We demonstrated that the coupling length Lc required to achieve an EMD in W-type GI POF is shorter than the length determined experimentally for the original SC GI POF at 633 nm. We also demonstrated that as the wavelength increases, the EMD and steady-state distribution (SSD) are achieved at shorter W-type GI POF lengths. This is explained by the increase in leaky mode losses as wavelength increases. This makes it easier to tailor W-type GI POFs to a specific application at different wavelengths.

Power flow in multimode W-type plastic optical fibers with graded index core distribution

A method is proposed for investigation of transmission along a multimode W-type (doubly clad) plastic optical fiber (POF) with graded index (GI) distribution of the core. The multimode W-type GI POF is designed from a multimode singly clad (SC) GI POF fiber upon modification of the cladding layer of the latter. The transmission characteristics of such proposed W-type GI POF are determined from the numerical solution of the power flow equation. We have shown that coupling length Lc at which an equilibrium mode distribution (EMD) is achieved in W-type GI POF is shorter than this length experimentally determined for the original SC GI POF. This is a consequence of leaky mode losses which reduce the number of higher guided modes involved in the coupling process, thus reducing the length Lc. We have shown that the shorter the length Lc, the earlier the bandwidth switches from the functional dependence of 1/z to 1/z1/2. We found that bandwidth improves with thinner and shallower intermediate layers. Finally, the bandwidth of the W-type GI POF analyzed in this work is greater if compared to the bandwidth of the original SC GI POF.

Influence of wavelength on equilibrium mode distribution and steady state distribution in W-type plastic optical fibers

Wavelength dependence of equilibrium mode distribution (EMD) and steady state distribution (SSD) in W-type plastic optical fibers (POFs) is investigated in this paper for parametrically varied width of the fiber’s intermediate optical layer and refractive index of the outer cladding. We have shown that with increasing the wavelength EMD and SSD are achieved at shorter W-type POF lengths. This is explained by the rise of the leaky mode losses with increasing wavelength. This facilitates tailoring W-fibers to a specific application at hand at different wavelengths.

Wavelength dependence of equilibrium mode distribution and steady state distribution in W-type plastic-clad silica fibers

Abstract Wavelength dependence of equilibrium mode distribution (EMD) and steady state distribution (SSD) in W-type plastic-clad silica fibers (PCSFs) is investigated in this paper for parametrically varied width of the fiber’s intermediate optical layer and refractive index of the outer cladding. We have shown that the W-type PCSF has better transmission characteristics at longer infrared wavelengths. This is explained by the rise of the leaky mode losses with increasing wavelength. This facilitates tailoring W-fibers to a specific application at hand in the infrared wavelength region.

Controlling the attenuation of leaky modes in multimode W-type photonic crystal fibers in the infrared wavelength domain

Leaky mode losses for a range of parameters such as the spacing and size of air holes, as well as the wavelength in W-type multimode glass photonic crystal fiber, are reported. Using an effective index approach by numerical solution of the time-independent power flow equation, we obtained that the leaky mode losses increase as the wavelength increases, and this rise of losses is greater in the case of narrower inner cladding. This user-friendly, simple approach of computing leaky losses could be used by experimentalists and system users.

Infrared wavelength dependence of leaky mode losses and steady state distribution in W-type glass optical fibers

Infrared wavelength dependence of leaky mode losses and steady state distribution (SSD) in W-type glass optical fibers (doubly clad fibers with three layers) is investigated in this paper for parametrically varied depths and widths of the fiber’s intermediate optical layer. This enables a tailoring of configuration of the W-type fiber to suit an application at hand. We have shown that the proposed W-type fiber has better transmission characteristics at longer infrared wavelengths.

Impact of fiber outer boundaries on leaky mode losses in leakage channel fibers

In a leakage channel fiber, the desired fundamental mode (FM) has negligible waveguide loss. Higher-order modes (HOM) are designed to have much higher waveguide losses so that they are practically eliminated during propagation. Coherent reflection at the fiber outer boundary can lead to additional confinement especially for highly leaky HOM, leading to lower HOM losses than what are predicted by conventional FEM mode solver considering infinite cladding. In this work, we conducted, for the first time, careful measurements of HOM losses in two leakage channel fibers (LCF) with circular and rounded hexagonal boundary shapes respectively. Impact on HOM losses from coiling, fiber boundary shapes and coating indexes were studied in comparison to simulations. This work, for the first time, demonstrates the limit of the simulation method commonly used in the large-mode-area fiber designs and the need for an improved approach. More importantly, this work also demonstrates that a deviation from circular fiber outer shape may be an effective method to mitigate HOM loss reduction from coherent reflection from fiber outer boundary, even in double-clad fibers, with HOM losses in excess of 20 dB/m measured in the hexagonal LCF with ~50 µm core diameter while keeping FM loss negligible.

Analysis of leaky-mode losses for optical fibers

We present a direct, rigorous, and fast numerical method for obtaining leaky-mode losses in optical fibers by solely solving complex propagation constants of the characteristic equation of leaky modes. Both the modified Bessel function and the Hankel function of the second kind are individually used to express the field component of leaky modes in the outermost cladding. The characteristic equation of cylindrically symmetric fiber structures, which consist of uniform and graded layers, is derived by combining the Runge-Kutta method and the exact solution of a homogeneous layer. Since complex root searching is the key technique in this method, we also present a numerical algorithm for solving the characteristic equation of optical fibers. Moreover, because for both guided and leaky modes the field distributions in the outermost cladding region have the same expression, the leaky mode can be easily obtained by choosing an improper solution, and therefore the calculation of leaky modes demonstrates the simplicity of this method. An approximation rule of branch choices for lossy material is also derived. The approach we present is consistent with the results of previously published papers.

A Semianalytical Technique for Leaky-Mode Loss Calculation in Hollow Dielectric Waveguides With Arbitrary Cross Sections

We present an approximate semianalytical technique for the calculation of the loss coefficient of leaky modes in 3-D hollow dielectric waveguides having an arbitrary cross section. The hollow waveguides are assumed to have an axis of symmetry and to have a cladding with a higher refractive index than the core. An expression for the modal loss coefficient is derived using a ray-optics approach with paraxial approximation. For the special cases of specific cross sections with known solutions, our technique gives results that are identical to the available analytical solutions. The technique is then applied on practical waveguide geometries, allowing the calculation of polarization- and wavelength-dependent losses. Full numerical alternatives to the technique involve time-consuming simulations and, sometimes, difficulty in incorporating a suitable boundary condition to obtain leaky-mode solutions.

Leaky mode propagation in planar multi-layer inhomogeneous birefringent waveguides: polar dielectric tensor configuration

The lightwave propagation characteristics in planar inhomogeneous multi-layered anisotropic waveguides having a polar dielectric tensor configuration are investigated. The transition from guided modes to leaky modes is found to be dependent on the azimuth angle theta and on the type and thickness of the embedded metal and buffer layers. The guided mode losses assume the lowest values (about 10dB cm-1) for a Ag layer. The leaky mode losses exhibit a peak near the critical angle theta c and then decrease with increasing azimuth angle. This effect can be advantageously exploited to build integrated optical devices such as angle deviation detectors. For a structure with a Ni layer the authors find theta c approximately=25.5 degrees and the loss value is the highest calculated to date ( alpha approximately=1280 dB cm-1).

Power coupling equations for single-mode, single-polarization optical fibers with effects of leaky modes and broad-band light source

A set of coupled equations for single-mode single-polarization (SMSP) optical fibers applicable to the case with effects of leaky modes and broadband light sources has been derived. The power coupling coefficients are related not only to the birefringence of the SMSP fiber, but also to the leaky mode loss and the spectral linewidth of the light source.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Polarization coupling in single-mode single-polarization optical fibers with a broadband light source

A set of coupled power equations that is applicable to the general case of a quasi-monochromatic light source is derived from the set of coupled amplitude equations for single-mode single polarization (SMSP). The spectral densities of Lorentzian-shaped and Gaussian-shaped distributions are characterized for the quasi-monochromatic light source. Our final results show that the power coupling coefficients are related not only to the birefringence of the SMSP fibers but also to the leaky-mode loss and the spectral half-width of the light source.

Leaky-mode loss in coated depressed-cladding fibers

A simple formula for the leaky-mode loss in realistic depressed-cladding (DC) fibers is presented. It takes the finite dimension of the substrate cladding and the presence of the coating into account. The losses show oscillations versus both the wavelength and the width of the substrate cladding. Additional small humps occurring in the transmission curves of cutoff measurements are well explained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Polarization coupling in single-mode single-polarization optical fibers: Power coupling

A set of coupled power equations derived from that of amplitude equations for single-polarization (SMSP) optical fibers has been presented. Our results show that the power coupling coefficients are related not only to the effect of the birefringence of SMSP fibers, but also to the leaky mode loss.

Polarization coupling power in single-mode single-polarization optical fibers

A set of coupled power equations has been derived from a set of coupled amplitude equations for a single-mode single-polarization (SMSP) optical fiber. Our results indicate that the power coupling coefficients are related not only to the birefringence of the SMSP fiber but also to the leaky-mode loss.

Anisotropic fiber with a depressed-cladding profile

Anisotropic fibers of the depressed-cladding type are analyzed by employing an iterative perturbation technique in a simple and straightforward way. An analytic expression is obtained for calculating the leaky-mode losses of an anisotropic depressed-cladding fiber. Numerical results show that such fibers possess much higher losses than those predicted earlier for a step-index model and hence are more advantageous for use in achieving singlepolarization, single-mode operation.

Leaky-mode loss of the second propagating mode in single-mode fibers with index well profiles

Radiation loss characteristics are calculated for the first two LP modes of a double-clad lightguide structure in which the inner cladding forms a low refractive-index well between the core and the outer cladding. The higher-order mode is defined to be effectively cut off at wavelengths where the LP(11) mode power is sufficiently attenuated to ensure negligible modal noise due to interference between LP(01) and LP(11) modes. Calculations apply for various deposited cladding thicknesses and findings can be easily extrapolated if specifications are changed for system requirements on the minimum unspliced fiber length or the extinction ratio between P(11) and P(01) mode powers, Re = 10 log P(11)/P(01). The latter is specified at points such as splice joints where modal noise is generated. Theoretical results are correlated with measurements in order to determine the effective cutoff wavelength for fibers in which leaky-mode loss mechanisms dominate. The procedure should be extremely useful for determining the shortest usable wavelength for single-mode lightwave systems.

Depressed index substrate tubes to eliminate leaky-mode losses in single-mode fibers

Silica tubing to be used as substrate tubes for MCVD has was demonstrated for a fiber having only one-fourth the deposited clad-merical tubing in that it is both dehydrated and fluorinated during processing to yield a silica which is dry and whose refractive index is lower than that of silica. These tubes are advantageously used to prepare single-mode fibers having fluorinated-silica cladding which controls dispersion and reduces scattering losses. In this case, the refractive index of the deposited cladding can be matched to that of the outer tube thus avoiding leaky-mode losses commonly encountered in depressed-index clad fibers. Using such an approach, low loss (0.28 dB/km at 1.55 μm) was demonstrated for a fiber having only one-fourth the deposited cladding required when a commercial silica tube is used. Such tubes could provide ecomomies to the processing of and the performance of complex cladding single-mode structures and impact multimode fiber designs.

Light Propagation in Proton-Exchanged LiNbO3 Waveguides

Summary Light propagation in X-cut LiNbO3 waveguides fabricated by proton exchange is analyzed theoretically. Simple formulae are given for both (real) effective refractive indices and leaky mode loss of guided and leaky modes. An example of dispersion and loss curves for a typical proton-exchanged waveguide is presented. The similarities and differences with respect to titanium-indiffused and out-diffused LiNbO3 waveguides are pointed out.

Length dependence of the effective cutoff wavelength in single-mode fibers

The effective cutoff wavelength of a depressed cladding single-mode fiber in either a cabled or a loose state depends upon the length of the fiber. This dependence can be accurately represented by a linear function of the logarithm of the fiber length for lengths between 1 m and 1 km. Cutoff will shift 55-66 nm per decade length for slightly and moderately depressed cladding designs, respectively. Neglecting all sources of differential mode attenuation except leaky-mode loss, the computed behavior of cutoff as a function of fiber length agrees reasonably well with the observed behavior for a moderately depressed cladding design. On the other hand, agreement is poor for a slightly depressed cladding design. A knowledge of the length dependence of cutoff is essential for establishing a production requirement for cutoff based upon the needs of the system.