Self-phase modulation and dispersion in high data rate fiber-optictransmission systems

The theoretical transmission limits imposed by the interaction of first- and second-order group velocity dispersion and intensity-dependent self-phase modulation (SPM) effects for a range of wavelengths around the zero dispersion wavelength (λ₀) for fibers in which polarization dispersion is negligible are investigated. It is found that increasing the peak input power to 30 mW reduces the transmission distance for data rates greater than 50 Gb/s, if operating at wavelengths shorter than λ₀. Operating at wavelengths longer than λ₀ improves the performance due to the cancellation of first-order dispersion by self-phase modulation. For example, at 50 Gb/s and 30 mW peak input power, the maximum transmission distance is 255 and 162 km, if operating at wavelengths 1 nm longer or shorter than λ₀, respectively. Above 100 Gb/s, higher-order dispersion limits the transmission distance even at wavelengths equal to, or longer than, λ₀. Linear dispersion compensation using a grating-telescope combination can significantly improve system performance for wavelengths where first-order dispersion dominates     

Pressure-dependent Sellmeier coefficients and material dispersionsfor silica fiber glass

The pressure-dependent Sellmeier coefficients are essential to characterize the optical design parameters for the optical fiber communication systems under deep sea environmental conditions. These coefficients are calculated for densified silica glass for the first time to compute the pressure dependence of material dispersion at any wavelength from the ultraviolet (UV) to 1.71 μm. The zero dispersion wavelength λ₀ (1.2725 μm at 0.1 10⁶ N m ^-2) varies linearly with pressure, and dλ₀/dP is 0.0027 nm/(10⁶ N m^-2). The calculated value is approximately one-third of the experimental value of 0.0076 nm/(10⁶ N m^-2) for a germanium-doped dispersion shifted fiber having λ₀=1.5484 μm and -0.0070 nm/(10⁶ N m^-2) for a pure silica-core fiber cable having λ₀ =1.2860 μm. Since, the refractive indexes are increased with pressure, the negative value of shift of the zero-dispersion wavelength is erroneous. The explanations are due to Ge-doping in silica glass, a possible temperature fluctuation of 0.16°C in the pressure-dependent measurement system of the zero dispersion wavelength and different experimental conditions of the silica glass and the optical fibers. This anomaly can also be attributed to the internal strain development at the core-cladding and fiber-jacketing boundaries due to pressure, which shows a larger experimental value. It accounts for the experimental values satisfactorily     

Temperature-dependent Sellmeier coefficients and chromaticdispersions for some optical fiber glasses

Temperature-dependent Sellmeier coefficients are necessary to optimize optical design parameters of the optical fiber transmission system. These coefficients are calculated for fused silica (SiO₂ ), aluminosilicate, and Vycor glasses for the first time to find the temperature dependence of chromatic dispersion at any wavelength from UV to 1.7 μm. The zero dispersion wavelength λ₀ (1.273 μm for SiO₂, 1.393 μm for aluminosilicate, and 1.265 μm for Vycor glasses at 26°C) varies linearly with temperature, and dλ₀/dT is 0.03 nm/K for aluminosilicate and Vycor glasses, whereas for SiO₂ it is 0.025 nm/K. This study interprets the recently observed experimental value of dλ₀/dT for two dispersion shifted optical fibers; and the dominantly material origin of dλ₀/dT is confirmed here as a fundamental property of the optical fiber glasses     

High-nonlinearity fiber optical parametric amplifier with periodicdispersion compensation

Theory shows that the maximum gain and bandwidth of one-pump fiber optical parametric amplifiers made from high-nonlinearity fiber, operated with a pump wavelength λ_p far from the fiber zero-dispersion wavelength λ₀ can greatly be improved by periodic dispersion compensation. We have performed experiments and obtained good agreement with theory: for λ_p=1542 and λ₀=1591 nm, we have increased the bandwidth from 7 to 28 nm, and the maximum gain from 15 to 20 dB, by splicing three pieces of standard fiber at regular intervals in a 40-m long nonlinear fiber     

Spectral gain hole-burning at 1.53 μm in erbium-doped fiberamplifiers

Spectral gain hole-burning at λ₀=1.53 μm was observed in an erbium-doped fiber amplifier at temperatures between 4.2 and 77 K. The hole width was found to broaden with temperature for T ⩾20 K according to a T^1.73 law. From the data, the room-temperature homogeneous linewidth associated with the 1.531-μm transition in the ⁴I_13/2-⁴I_15/2 laser system was determined to be Δλ_h=11.5 nm for aluminosilicate fibers     

Merged Sagnac-Michelson interferometer for distributed disturbancedetection

An interferometric technique is described to detect and locate perturbations along an optical fiber. This distributed sensor has a position dependent response to time-varying disturbances such as strain or temperature. These disturbances cause a phase shift which is detected and converted to spatial information, The sensor consists of a Sagnac interferometer merged with a Michelson interferometer. This is achieved by a frequency selective mirror in the center of the Sagnac-loop. The sensor is illuminated by two light sources with wavelengths λ₁ and λ₂, respectively. The mirror reflects λ₁ and transmits λ₂, causing the interferometer to operate as a Michelson at wavelength λ₁ and as a Sagnac at wavelength λ₂. Any time-varying perturbation on, the fiber will, result in a signal at λ₂ proportional to the product of the rate of phase change caused by the perturbation and the distance of the perturbation relative to the position of the mirror. The output of the Michelson interferometer at wavelength λ₁ is proportional to the phase change caused by the unknown perturbation. By dividing the output of the Sagnac interferometer by the time rate of change of the Michelson interferometer signal, the position of the disturbance relative to the mirror is located. Results obtained with a 200 m-distributed fiber sensor are discussed     

Design optimization for efficient erbium-doped fiber amplifiers

The gain and pumping efficiency of aluminosilicate erbium-doped fiber amplifiers (EDFAs) are analyzed as a function of guiding parameters and Er-doping profile for two pump wavelengths of λ _p=980 nm and λ_p=1.47 μm. Three designs of fiber-amplifier waveguides are considered: one with the same mode size as standard 1.5-μm communication fibers (type 1); one with the same mode size as standard 1.5-μm dispersion-shifted fibers (type 2); and one with mode size smaller than those of communication fibers (type 3). For the 1.47-μm pump, fundamental LP₀₁ mode excitation is assumed, while for the λ_p=980-nm pump, concurrent excitation of LP₁₁ modes is considered. It is shown that excitation of higher-order pump modes at 980 nm does not significantly affect the amplifier gain performance. The effect of concentrating the Er³⁺ doping near the center of the fiber core is shown to increase the amplifier gain coefficients by a factor of 1.5 to 2     

Wave propagation through curved shells and the validity of theplane-slab approximation

A variety of results is presented for the transmission of microwaves through curved shells. Cylindrical shells with line sources and spherical shells with dipole sources, located in the shell cavity, are considered, and ray theory is applied in systematic computation following G.H. Deschamps' procedure (1972). The ray tracing procedure implemented in the program includes the contribution of multiple reflections between the shell dielectric and free-space medium interface. These results are compared with the local plane-slab approximation described by G. Tricoles (1964). Errors <1% in magnitude are found for radii of curvature >10 λ₀, and thickness <1% λ₀. For the extreme case of shells with radii <5 λ₀ and thickness greater than 1 λ₀, the plane-slab approximation appears to have significant error. Typically, for a shell of radius 5 λ₀ and thickness of 1 λ₀, the error in the normalized far field is less than 4%. The procedure of P.D. Einziger and L.B. Felsen (1983) is extended to provide a basis for the plane-slab approximation     

Optimal pump wavelength in the4I15/2-4I13/2 absorption band for efficient Er3+-doped fiberamplifiers

The authors report the measured gain of a highly efficient erbium-doped fiber amplifier pumped at wavelengths between 1.46 and 1.51 μm. The optimal pump wavelength, λ_opt, was determined to be 1.475 μm. At this wavelength, the maximum gain coefficients for signals at 1.531 and 1.544 μm were 2.3 and 2.6 dB/mW, respectively. At λ_opt, high gains ranging from 32 dB at pump power P_p=20 mW up to 40 dB at P _p=80 mW were obtained. These modest pump powers are within the capabilities of currently available 1.48-μm diode lasers. The width about λ_opt for 3-dB gain variation exceeded 27 nm for P_p=10 mW and 40 nm for P_p >20 mW. With this weak dependence on pump wavelength, single-longitudinal-mode lasers do not have a significant advantage over practical Fabry-Perot multimode pump lasers     

Singlemode channel waveguides and electrooptic modulators in KTiOPO4 for the short visible wavelength region

Single-mode channel waveguides at short visible wavelengths have been fabricated in KTiOPO₄ by Rb&rlhar2;K ion exchange in mixed melts of RbNO₃-KNO₃-Ba(NO₃)₂ . The technological parameters have been chosen by means of theoretical WKB- and “effective index” calculations concerning the singlemode region of the effective channel waveguide index N₀₀ at the given wavelength. Great diffusion anisotropy and small dispersion of the surface refractive index change guarantee singlemode operation of the very same channel waveguide from the blue up to the red. Typical attenuation of about 2.0 dB/cm for TM- and 1.5 dB/cm for TE polarization was obtained at λ=0.5145 μm. Light-induced refractive index changes (photorefractive effect) have been determined as a function of time, wavelength, guided optical mode intensity and temperature. The light-induced effects in Rb&rlhar2;K ion-exchanged channel waveguides in KTiOPO₄ are about two orders of magnitude smaller than those in annealed proton-exchanged channel waveguides in LiNbO₃. Electrooptic phase modulators have been successfully investigated concerning dynamic V_π measurements, the electric-optical field overlap and dc-drift phenomena. Design, fabrication and experimental results of integrated-optic Mach-Zehnder-interferometer modulators for short visible wavelengths are presented     

Tensile-strained AlGaAsP and InGaAsP-(AlGa)0.5In0.5P quantum well laser diodes for TM-mode emission in the wavelengthrange 650 <λ<850 nm

TM-polarized laser emission is demonstrated at wavelengths longer than 650 nm, for (AlGa)_0.5In_0.5P-based laser diodes. These structures contain tensile-strained AlGaAsP or InGaAsP quantum well active regions, which are capable of spanning a wavelength range of roughly 650-850 nm, for TM-mode lasers on GaAs substrates. This represents an extension of the wavelength range available from typical GaInP-(AlGa)_0.5In_0.5P lasers, where the requirement for biaxial tension limits the TM-mode wavelengths to less than 650 nm. In addition, compared to AlGaAs confining structures, the high-bandgap (AlGa)_0.5In_0.5P confinement structure used here makes AlGaAs(P) active regions feasible at shorter wavelengths, with good performance maintained for 670<λ<700 mn. Likewise, the wavelength range 700<λ<750 nm, where AlGaAs laser characteristics are diminished, becomes accessible using these materials     

A curved spiral antenna above a conducting cylinder

A curved spiral antenna above a finite hollow conducting cylinder is analyzed using the method of moments. The effects of cylinder length 2H and cylinder radius r_cy on the radiation characteristics of the spiral are evaluated. As 2H increases, the cross-polarization component of the radiation field in the broadside direction decreases to a constant value (approximately -18 dB). When 2H is greater than one wavelength (λ₀), the input impedance of the spiral above a cylinder of radius r_cy=0.25 λ₀ is almost constant (250-j20 Ω) with a gain of approximately 7 dB. The spiral above a cylinder of (2H, r_cy)=(2.7 λ₀, 0.25 λ₀) shows a 3-dB axial ratio bandwidth of approximately 23%, which is wider than a flat spiral antenna above a flat ground plane of infinite extent     

Tilted- and axial-beam formation by a single-arm rectangular spiralantenna with compact dielectric substrate and conducting plane

A single-arm rectangular spiral antenna is analyzed using the finite-difference time-domain method. The spiral is printed on a finite-size dielectric substrate backed by a finite-size conducting plane. Both the substrate and conducting planes are square with a side length L of less than 0.6λ₀ (λ₀: wavelength in free space). The radiation pattern is dependent on the outermost arm peripheral length C. The spiral whose peripheral length is within 2λ_gg (λ_g: the guided wavelength of the current) radiates a tilted beam of circular polarization. When the peripheral length is decreased to λ_gg, the spiral radiates an axial beam. The axial beam has a wide half-power beam width of approximately 102° (for L≈0.369λ₀) with a gain of approximately 6.7 dB. The axial beam shows a 15% frequency bandwidth for a 3 dB axial ratio criterion. Over this bandwidth, the voltage standing-wave ratio (VSWR) is less than two, as desired. The experimental results for the radiation pattern, gain, axial ratio, and VSWR are also presented     

Fabrication of variable bandwidth filters using arrayed-waveguidegratings

Variable bandwidth filters have been fabricated using silica-based N×N arrayed-waveguide gratings. The centre wavelengths are λ₀=1.55 μm for all channels. The 3 dB bandwidths are 40, 78, 116 and 154 GHz, for the filter with a path length difference ΔL=63 μm. In the filter with ΔL=8.6 μm, the 3 dB bandwidths are 414, 769, 1198 and 1608 GHz. The on-chip losses are 2.1-2.9 dB and sidemode suppression ratios are larger than 27 dB     

Anomalous dispersion in Er3+ and Yb3+-dopedfibers

In experimental and theoretical study of anomalous dispersion in Er³⁺and Er³⁺-Yb³⁺-doped fibers has been developed. Anomalous time delay caused by both absorption and emission at 1.535 μm has been theoretically calculated and experimentally measured. A pump power dependence of anomalous time delay in rare-earth-doped fibers has been theoretically calculated and experimentally investigated. It has been shown that pump power fluctuations lead to propagation time jitter in Er³⁺-doped fiber amplifiers. The pulse interaction due to refractive index change caused by gain saturation is predicted. It has been shown that for Er ³⁺-doped fibers with SiO₂-GeO₂ core composition, the anomalous dispersion per 1-dB gain is twice that of fibers with SiO₂-Al₂O₃ core, which is caused by gain curve form difference. A scheme of mutual compensation of intrinsic fiber dispersion and anomalous dispersion caused by Er³⁺ in the region 1.532-1.537 μm has been suggested     

New converses in the theory of identification via channels

New converses for identification via arbitrary single-user and multiple-access channels, with finite first- and second-type probabilities of error, are developed. For the arbitrary single-user channel, it is shown that (λ₁, λ₂)-identification capacity is upper-bounded by λ-capacity, and optimistic (λ₁,λ₂ )-identification capacity is upper-bounded by optimistic λ-capacity, for any λ>λ₁+λ₂. The bounds become tight at the limit of the vanishing probabilities of error, thus generalizing previous results by Han and Verdu (1992), who showed that the identification capacity is equal to transmission capacity for channels satisfying the strong converse of the channel coding theorem. A by-product of the new identification converses is a general formula for optimistic λ-capacity. An outer bound on the (λ₁, λ₂)-identification capacity region of an arbitrary multiple-access channel is developed. A consequence of this bound is that the identification capacity region is equal to the transmission capacity region for any stationary, finite-memory multiple-access channel. The key tool in proving these bounds is the partial resolvability of a channel, a new notion in resolvability theory, which deals with approximation of the output statistics on a suitably chosen part of the output alphabet. This notion of approximation enables us to get sharp bounds on identification for arbitrary channels, and to extend these bounds to the multiple-access channel     

Optical fiber for deep ultraviolet light

Deep ultraviolet optical fibers are fabricated using modified SiO ₂ glasses containing 2000-ppm fluorine for the clad and 200 ppm for the core. The transmission at 193 nm is improved to more than 60%/m by optimizing the fiber drawing condition. The H₂-inpregnation into the fiber suppresses the degradation of the transmission by irradiation of ArF excimer laser (50 mJ/cm² /pulse). Further improvement may be expected by reducing oxygen-deficient center (I) defect generation in the drawing process     

Narrow-band directional couplers made of dissimilar single-modefibers with different cladding refractive indexes

A wavelength-selective directional coupler, consisting of two polished single-mode fibers with different cladding refractive indexed, has been fabricated. In contrast to symmetrical couplers, where the power transfer characteristic is a quasiperiodic function of the wavelength, couplers made of dissimilar fibers show a true bandpass-filter characteristic. They consist of two fibers with different core diameters and refractive-index profiles, having the same cladding refractive index. The parameters of the fibers must be chosen in such a way that if their propagation constants β₁, β₂ are plotted over the wavelength, the curves intersect at a cross-over wavelength λ₀ equal to the center wavelength of the filter. The 3-dB bandwidth of the coupler's power transfer characteristic is 13.6 nm, the best value achieved up to now     

Gigabit/s optical receiver sensitivity and zero-dispersion single-mode fiber transmission at 1.55 µm

High-speed pulse response and receiver sensitivity at 1.55 μm were measured at data rates ranging from 400 Mbits/s to 2 Gbits/s, in order to elucidate characteristics of a reach-through p+nn- Ge APD. The p+nn- Ge APD receiver provided a 2 Gbit/s received optical power level of -32.0 dBm at 1.55μm and a 10^-9error rate, which was 4 dB better than the receiving level with a p+n Ge APD. Detector performance at 1.3μm was also studied for comparison with performance at 1.55μm. Single-mode fibers, which have 0.54 dB/km loss and zero dispersion at 1.55μm, and an optical transmitter-receiver, whose repeater gain is 29.2 dB, have enabled 51.5 km fiber transmission at 2 Gbits/s. The transmission system used in this study has a data rate repeater-spacing product of 103 (Gbits/s) . km at 1.55μm. Optical pulse broadening and fiber dispersion were also studied, using 1.55 and 1.3μm dispersion-free fibers. Future repeater spacing prospects for PCM-IM single-mode fiber transmission systems are discussed based on these experimental results.     

Optimal probability-of-error thresholds and performance for twoversions of the sign detector

Expressions are obtained for specifying the optimal error probability (minimum P_e) thresholds λ₀₁ and λ₀₂ for the traditional and modified sign detectors, respectively. These thresholds are shown to depend on the parameters p, P₁, and M where: M is the number of observations z_i used in the test statistic; P₁=P(H₁ ) is the prior probability for hypothesis H₁ that signal s₁ is present and 1-P₁ =P(H₀) corresponds to the hypothesis H₀ that signal s₀ is present; and p=Pr{z_i⩾0|H₁} with s₀=0 for the traditional sign detector and p=Pr{z_i⩾λ|H₁ }=Pr{z_i<λ|H₀} with λ =(s₀+s₁)/2 for the modified sign detector. The expressions for λ₀₁ and λ₀₂, are given explicitly, and shown to be independent of P₁ for sufficiently large M. Optimal P_e versus M performance curves, corresponding to both versions of the sign detector, are obtained for a representative range of values for p and P₁