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Usually, noise characteristics of optical amplifiers are described by the theory of Shimoda, Takahashi, and Towns (STT theory). This theory deals only with lumped amplifiers whose noise parameters are spatially uniform. However, it is not the case with fiber amplifiers. In this paper, first, a novel noise theory of three-dimensionally distributed amplifiers based on the STT theory is presented and the fundamental equations for calculations of the gain and noise characteristics of a fiber amplifier and systems with fiber amplifiers are obtained. Next, this noise theory is applied to a practical fiber amplifier and an example of the gain and noise characteristics is shown. The backward propagated spontaneous emission is shown to degrade the noise characteristics severely, and the total noise characteristics are shown to be better at 1.553 μm than at 1.530 μm. Finally, a low erbium-doped fiber system whose gain is balanced with the background loss of the system fiber is analyzed as the system optimizing the signal-to-noise ratio. Nearly ideal characteristics are shown to be realized in this system with the bi-directional pumping.

Nondestructive measurement of the axially nonsymmetrical refractive-index distribution of an optical fiber preform is described. A new method, called the triangular mask, is employed to measure the deflection angle of the probing rays that travel through the preform. This method is somewhat similar to, but a little simpler than, the spatial filtering technique used in the measurement of axially symmetrical preforms by Sasaki et al. Most of the data collections and processing are automated. The 2-D index distribution is computed from the deflection angles. The accuracy of the computer algorithm is estimated by computer simulations. Examples of experimental results are compared with the results of a destructive measuring technique.

The periodic mode coupling between the LP(01) and counterpropagating LP(02) modes induced by a reflective fiber grating is investigated by using the coupled-mode theory. The properties of the mode conversion by the reflective fiber grating are compared with those by a transmissive grating that couples LP(01) and LP(02) modes in a same direction. Our results show that the former has a narrower power conversion spectrum than the latter.

Temporal signatures (reflection impulse responses) of optical fibers are obtained as the inverse Fourier transforms of the optical-frequency-domain reflectometry (OFDR) data. In this OFDR system, the entire process is automated. The modulation frequency is changed stepwise to obtain an exact inverse Fourier transform. The experimental results are in good agreement with those obtained by computer simulations.

A direct amplitude-modulation technique of semiconductor lasers featuring good frequency-modulation-component suppression was developed for ASK heterodyne optical communications. A slave laser strongly injection-locked by a highly stabilized master laser is directly modulated through the driving current. The signal is then demodulated by optical heterodyning. It has been shown that the frequency-modulation component of the slave laser is effectively suppressed by the injection locking.

The double-stage phase-diversity (DSPD) scheme we have proposed features a phase-diversity-type optical homodyne detection followed by a phase-diversity-type electrical frequency up-conversion, giving a heterodyne-like intermediate frequency (IF) signal. It has the advantages of both heterodyning and homodyning. In this paper, we first calculate the sensitivity penalty due to the optical circuit (hybrid) imbalance in a DSPD receiver. It is shown that the penalty is as small as that in a conventional phase-diversity receiver and that the optical circuit requirement is not severe. The DSPD experiment with an adjustable imbalance is then performed to confirm the theory; experimental results are in good agreement with the theory. Finally, the possibility of compensation of the optical imbalance at the electronic stage of the receiver is shown.

A theoretical analysis of a new type of erbium-doped fiber amplifier with an isolator in its midway is presented. It is shown that the noise characteristics as well as the gain characteristics are improved by the midway isolator. The optimization of the isolator position is also discussed. >

A group delay in an optical fiber is one of the major factors limiting the transmission distance of a long-distance, high bit-rate optical fiber communication system using in-line erbium doped fiber amplifiers (EDFAs). The group delay can be compensated by a delay equalizer (a stripline section, for instance) inserted in the intermediate frequency stage of a coherent receiver. The purpose of this paper is to propose a method for compensating the fiber group- delay precisely by adjusting the width distribution of a nonuniform, open-type stripline compensator and thus optimizing its group-delay characteristics. It is shown that, by using the optimized nonuniform stripline, the overall group-delay dispersion is reduced to approximately 1/20 of the value obtained with an ordinary, uniform stripline compensator. The effectiveness of the optimized stripline was confirmed by a computer simulation of the entire system.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

It is known that the stimulated Brillouin scattering (SBS) causes an excess loss by reflecting the launched signal light back into the transmitter. This effect limits the maximum transmitted power in optical fiber communication systems. In this paper we describe another harmful effect that may be caused by the SBS. We show that if the SBS occurs in fiber, the transmitted and scattered light have intensity fluctuations, which is explained as the noise partly from amplified spontaneous Brillouin scattering and partly from the optical chaos.

The conventional noise theory of an optical amplifier is based on the semiclassical master equation which is known as Shimoda, Takahashi and Towns' (STT) theory. However, this theory deals only with lumped amplifiers. The present paper shows first that the noise formulas for distributed nonuniform amplifiers can be derived in a simple way by using the STT theory.

The spectral properties of a LP(01) ? LP(02) mode converter by using a photoinduced fiber grating are investigated. A fiber with given parameters is considered, and the wavelength dependence of power conversion between the two modes is calculated. The results show that the spectrum can be narrowed by selecting the operating wavelength close to the cutoff wavelength of the LP(02) mode. The methods for obtaining a mode converter with a broadband spectrum and a mode converter with a spectrum having two peaks are also discussed.

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.

An accurate theoretical analysis of multichannel DPSK coherent optical communication system is presented for the first time. The analysis accounts for the crosstalk caused by an adjacent channel and for the influence of laser phase noise. It is found that the electrical domain channel spacing can be as small as 2.3 times the bit rate for a 1 dB penalty.

In a previous paper, two of the authors proposed a closed-form dispersion formula for α-power graded-core fibers. However, it was found later that an important approximation implied in the analysis had been overlooked. In this paper, the same formula is newly derived in a correct manner but as an approximation. The overlooked approximation is clarified and stated explicitly. The derived approximate formula is relatively accurate for near-uniform-core fibers (such as those with α = 4 or α = 8), but the error increases appreciably for quadratic-core fibers (α = 2), which are of practical importance. A modification of the dispersion formula is proposed to improve its accuracy for the quadratic-core case. In the final part of this paper, the accuracy of the derived formulas (including the modified one) is investigated by comparing the computed characteristics with rigorous solutions.

Vectorial wave analyses of uniform-core optical fibers using a boundary integral method that does not use Green's function are presented. The expansion of the electromagnetic field on the boundary, the selection of the weight function, and the method for giving boundary conditions are discussed. By using the formulation obtained, the propagation characteristics of elliptical-core optical fibers are analyzed. The effect of the boundary shape on the numerical results is also investigated through analyses of rectangular-core fibers. It is found that the boundary integral method can easily be applied to solve vectorial wave boundary value problems. >

In a multimode optical fiber, the so-called multimode dispersion (mode-delay difference) is the principal cause that widens the transmitted pulse. The multimode dispersion can be controlled by the refractive-index profile. However, the optimum profile that minimizes the multimode dispersion has not yet been determined. This paper describes the computer-aided trial-and-error synthesis of the optimum refractive-index profile. It is shown that the group delay is reduced to about 10/sup -3/ times the value obtained with the uniform core fiber, to about 10 ps/km. This value is comparable to the material dispersion obtained with an ordinary fused-silica fiber and a typical semiconductor laser. It is also shown that the optimum profile is a smoothed W-shaped one.

A vectorial wave analysis of the propagation characteristics of radially inhomogeneous optical fibers is presented. The vectorial wave equation is first translated into a variational problem, and then it is solved by using the finite element method. The results are compared with those of the scalar wave analysis. The error caused by the scalar wave approximation is discussed for wide variety of refractive index profiles. It is shown that the error caused by the scalar wave approximation is about 0.1 percent for eigenvalues and 1 percent for delay time, when the relative index difference between core and cladding is 1 percent.

A method of computer analysis of planar (two-dimensional) circuits having an arbitrarily shaped short boundary is proposed. The proposed method is based upon the contour integral representation of the two-dimensional wave equation. Results of the computer analyses for simple circuits are compared with analytical solutions to show the validlty and accuracy of the proposed method. Some examples of analyses of practical circuits are also presented.

When two different wavelengths are used for recording and reading in a volumetype hologram memory, construction of a space modulator and photodiode array becomes difficult because unwanted patches appear on a reconstructed image. This can be avoided in a one-dimensional hologram; however, storage density is reduced. This paper proposes a quasi-one-dimensional volume-type hologram which preserves thick film memory (high density memory) while configuration of a space modulator and a photodiode array is simplified and simultaneous reading at different wavelengths is possible. With a PMMA film with thickness 400 μm a storage density of (0.3 ∼ 1.0) × 105 bits/mm2 was realized, Conditions for simultaneous reading at a different wavelength have been clarified.

A fully computer-oriented synthesis of the optimum circuit pattern of a 3-dB hybrid ring based upon the planar circuit concept is described. In the synthesis process, the contour-integral method, and Powell's method are used for the circuit analysis, the optimization, respectively. The synthesized optimum patterns are given in normalized curves, parameters which can directly be used in practical circuit design. The validity of the theory is confirmed by experiment. It is shown both theoretically, experimentally that the planar circuit approach can, not only prevent the deterioration of the hybrid characteristics due to the widening of the circuit, but bring forth hybrid characteristics somewhat better than the distributed constant model. It is also shown that the obtained optimized characteristics can further be improved by addition of simple external circuits.

1年にわたってオムニバス方式で連載してきた講座『光通信技術』の最終回として, 「光通信の将来」と題し, 光通信方式, デバイス等に関する課題のうちから, いくつかを取り上げて将来を展望する.

A new method for solving electromagnetic boundary-value problems is presented. The new method is a modification of the conventional boundary-element method; the conventional method is modified by using the reciprocity theorem derived from Green's identity, making the use of Green's function unnecessary. To confirm the validity of the new method, numerical analyses are presented for Dirichfet- and Neumann-type boundary-value problems of a two-dimensional scalar wave equation.

The variational method is used to determine the propagation characteristics of an optical fiber consisting of a core with an arbitrary refractive-index distribution and a uniform cladding. The problem is first translated into a variational problem; the factional is computed upon the TEM-approximation basis. The variational problem is then solved by using the Rayleigh-Ritz method. The computed propagation characteristics are presented for refractive-index distributions of practical interest. The single-mode condition for a quadratic self-focusing fiber is obtained as v < 3.53 where v denotes the conventionally used normalized frequency; this result agrees with the numerical analysis by Dil and Blok. The obtained characteristic equations for the simplest case (uniform core case) are compared with analytic solutions to ensure the validity of the analysis.

A planar chart for expressing a state of polarization of an arbitrarily polarized light is proposed. The proposed chart is equivalent to the Poincare sphere, but has an advantage over the Poincare sphere in that it can be printed on a flat paper. The characteristics of the proposed chart are investigated. The computer-drawn exact chart is shown with important parameter values. Finally, an example of the application of the proposed chart is described.

Research and development of coherent optical fiber communications have been accelerated mainly because of the possibility of receiver sensitivity improvement reaching 20 dB, and partly because of the possibility of frequency-division multiplexing (FDM) with very fine frequency separation. In this paper, recent advances in the research on coherent optical fiber communication systems are reviewed, with emphasis on those reported in the past two years. The bit-error rate measurements so far reported are classified and investigated in four categories: PCM-ASK, PCM-FSK, PCM-PSK, and PCM-DPSK. The states-of-the-art of polarization-state stabilization techniques is also discussed.

In an axially symmetrical single-mode optical fiber, the polarization plane of the propagated HE11 mode is subject to unstable rotation due to slight changes in ambient conditions. Such an instability can be prevented by making the refractive index distribution in the fiber axially nonsymmetrical. This paper describes a two-dimensional, vectorial-wave finite-element method calculation of the propagation characteristics of such axially nonsymmetrical fibers. It is an improved version of Yeh's program; the field outside the central core region is expanded by a series of modified Bessel functions. Some numerical examples are described.

High-accuracy data of normalized cutoff frequencis, propagation constants, and delay time of LP/sub ml/ modes for alpha-power graded-core fibers (alpha= 1, 2, 4, and 10) are obtained by using two entirely different methods: power-series expansion and finite element methods, and the results are compared. The difference between cutoff frequencies obtained by these methods is less than 0.005 percent for most of the LP modes. The obtained data are accurate enough to be used as the standard for estimating the accuracy of other various analyses.

新しい半導体マイクロ波発振器として, 最近大きな関心をもたれているガン (Gunn) 発振器について, 出力, スペクトル純度など, 応用上重要な性能の現状と将来の発展の見通しを述べた.出力は近い将来, 連続波でワットレベルまで増大すると推算される.スペクトル純度は, 応用上要求される水準に近づきつつある.

A method of computing demagnetizing factors using a resistance network analog or an electrolytic tank has been devised, and the demagnetizing factors for spheres, rods, disks, and tubes have been computed for the case μ = ∞. When the size of the model on the analog is appropriate, the value obtained for a sphere is within 1% of the theoretical value of ⅓. Although the demagnetizing factor is not a precise concept for rods, disks, or tubes, in which the induced magnetization is not uniform, this term is often used for convenience. In this paper, the ``ballistic demagnetizing factor'' (defined in terms of the mean magnetization over the median cross section of the object) is considered. The values obtained for rods and disks are compared with those found in the literature, principally with Bozorth and Chapin's compiled values. Typical results are 0.37 (0.47), 0.223 (0.27), 0.117 (0.14), and 0.052 (0.056) for (L/d) = ½, 1, 2, and 4, respectively, where (L/d) denotes the length‐to‐diameter ratio and the values in the brackets are the previously used values. The axial nonuniformity of the magnetization in rods and tubes is also measured and discussed.

The measurement of the Raman scattering in a single-mode optical fiber using optical time-domain reflectometry (OTDR) is reported. The OTDR technique makes it possible to determine the power level of the pump and Stokes components along the fiber without cutting it back, and to estimate Raman scattering parameters in a reliable manner. The measurement method is described and experimental results are discussed. It is concluded that the power conversion process to higher Stokes components has been clearly displayed without cutting back the fiber. >

The double-stage phase-diversity (DSPD) scheme proposed in this paper features phase-diversity-type optical homodyne detection, and phase-diversity-type frequency up-conversion producing heterodyne-like second IF signal. It has the advantages of both heterodyning and homodyning. Results of a simulation experiment are presented.

The analysis and design of a planar circuit having an anisotropic spacing medium are the subjects of this chapter. What is actually considered is a tri-plate-type planar circuit having ferrite spacers magnetized perpendicularly with respect to the circuit conductors. The analysis of an arbitrarily shaped ferrite planar circuit of this type is discussed first, aiming at the determination of the parameters of the equivalent multiport circuit.