A new concept σ-inverse" of a matrix is proposed. The σ-inverse of a matrix A is defined as the matrix X satisfying the following two equations:AXAσ2X*A,(XA)*XA,were σ is a given positive real number. The σ-inverse of A is denoted by Aσ. This matrix gives minimum-variance estimation in linear systems, while in contrast the Moore-Penrose inverse gives best linear unbiased estimation. The spectral properties of the σ-inverse can be represented by a complex-valued function /(zσ2). This function is continuous and bounded, which reflects the properties of the σ-inverse.

It is well-known that the Schwarz Theorem for one-variable function has been applied to the theory of one-variable positive real function. In this short note, the Theorem is generalized to the case of multi-variable function, and its application is shown.

The TJS lasers which have the kink-free behavior and good proportionalities in the outputs between the front mirror and the rear mirror have been tested by cw aging. After 12,000-hour cw againg, a TJS laser has been found to still lase in a single longitudinal mode as well as in the fundamental transverse mode. The life of TJS lasers at 25 is estimated to be at least 80,000 hours on the basis that the laser is still alive after 3,000-hour aging at 60. By considering that the spatial homogeneity in the active region of the TJS laser is maintained for long time cw aging, the reason why the single mode behavior is kept even after the aging can be explained. Here, the spatial homogeneity in the active region of the TJS laser may be due to a small size of the region and to high hole concentration of the region.

We report a performance analysis and experimental results of an optical intensity modulator using a pair of optical gate couplers and conventional electro-optic phase shifters. The modulator involves only three straight waveguides. The optical gate coupler consists of three coupled waveguides. At the input gate coupler, input light is equally divided and fed into parallel arms of the phase shifters. A retardation φ between the two arms of the phase shifters is controlled electro-optically by applied voltage. At the output gate coupler, both lights are re-combined according to the phase shifts. The modulator is fabricated monolithically by diffusing Ti into a z-cut LiNbO3. Each patterned waveguide is about 6 µm wide and spacing is 2.9 µm at the gate coupler. The lenght of the gate coupler is 6 mm and a pair of electrodes are 7 mm long and the spacing is 12 µm. For Ey00mode (r13) the half-wave voltage is 21 V, the extinction ratio is 11.3 dB and insertion loss is 9.8 dB at 1.15 µm.

Semiautomated measurement of the refractive-index profiles of single-mode fibers using the scattering-pattern method developed by the same authors is described. The scattering-pattern method features very high resolution, typically 0.2 µm: hence at present it is the only method suitable for single-mode fibers. The measurement have been performed by using a semiautomated system. This system consists of an automated measuring apparatus of the scattering pattern and softwares for calculating the refractive-index profile. The obtained profiles are compared with those of preforms.

It is very important to choose appropriate fiber parameters such as core and outer diameters and refractive index difference of fiber for obtaining low loss and stable fiber cables for practical use. Several problems related to determine the fiber parameters must be taken into concideration for a design of fiber structures. Many theoretical and experimental studies on the relationship between fiber parameters and transmission characteristics to show fiber parameters dependence on excess loss useful for the design of practical fiber cables. In this paper, we made clear experimentally the relationship between excess losses and fiber parameters for jacketed step-index fibers with various combinations of core and outer diameters, index difference and jacket diameter. As the results, we found that the excess loss caused by winding uniformly on the mandrel is proportional to (a/)2-3 and is independent of fiber diameter and that the loss due to microbending by external forces remarkably affected by both a/ and the fiber and jacket diameters. The results obtained by the investigations are utilised for manufacturing low loss and stable optical fiber cables.

Optical waveguiding phenomena at 10.6 µm have been observed in evaporated amorphous Se films with Au-cladding. The far-field analysis has shown that the fundamental TE0 mode is most dominantly confined. The results show that amorphous Se can be used to form planar waveguides for the 10.6 µm radiation of a CO2 laser. It has been also observed that the attenuation of TM modes is much larger than that of TE modes in accordance with the theory of the metal-clad optical waveguides. As an application, a photoelastic modulator utilizing a piezoelectric resonance of the Au-clad amorphous Se waveguide has been fabricated. The PZT piezoelectric ceramics is used as the substrate to excite mechanical vibration. The modulator is operated around its fundamental length-expanding resonance of 211.2 kHz. The band-width and the half-wave voltage are determined to be 5.4 kHz and 55 V, respectively.

From theoretical or experimental point of view, graded-index multimode fibers are interesting and promissing transmission lines for future optical communication systems. Their transmission characteristics, however, have not been well recognized so far. Therefore, it is necessary to clarify the characteristics before considering graded-index multimode fibers for practical uses. Among the characteristics, optical loss and pulse dispersion are of paramount importance. This paper presents baseband frequency characteristics of recently produced graded-index multimode fibers in the frequency range from DC to 1.7 GHz. The characteristic dependence of graded-index multimode fibers on wavelength and excitation condition is also studied in comparison with that of a step-index multimode fiber. Wavelength, rather than excitation condition, is shown to be an important factor that determines the characteristics of the fiber. The wavelength dependence of the bandwidth has been found to be critically influenced by the profile of the fiber. In order to understand the detailed characteristics of graded-index multimode fibers, the measurement covering a wide frequency range, e. g., from DC to over 2 GHz, is necessary.

An initial trial of the optical fiber transmission system in NTT is reported in this paper. In NTT's transmission networks, the shorthaul application appears attractive in the near future. The laboratory test is primarily targeted to 32 Mb/s bit rate and 8 km long repeater spacing. We report here the design philosophy of step-index multimode fibers and repeaters for this trial. Through the design and manufacturing of fibers, the fundamental and common characteristics of fibers are clarified. Stable, compact and low power consuming optical repeaters are realized. Trere is no trouble of optical repeatered line and all repeaters in the line are operating with sufficient optical power margin. Multi-repeatered test has confirmed that experimental results are in good agreement with the design values.

DH lasers are believed to be one of the most suitable light sources for optical fiber transmission. However, the light output of DH lasers has usually such detrimental effects as a relaxation oscillation and a spectral broadening during pulse response. For high bit rate and long-distance fiber transmission, lasers need to have a high performance pulse responce and a narrow spectral width. We examined the dynamic characteristics of GaAs/GaAlAs DH lasers, which had an internally striped planar (ISP) structure using sulfur diffusion, by changing the stripe width. By narrowing the stripe width to the range of 5 to 7 µm of ISP lasers with an undoped active region and the cavity length of about 150 µm, significant improvement was achieved in frequency response, pulse response and spectral behavior as well. The frequency response was flat up to 2 GHz without a resonant-like peak. The relaxation oscillation was suppressed up to 10-mW light output. The spectral width at 400-Mb/s modulation was controlled within 20 without degradation of extinction ratio. Threshold currents were in the range of 55 to 70 mA. The light output increased linearly up to 10 mW without a kink. The external differential quantum efficiency was about 60 %. These lasers are operating stably after more than 1,000 hours at 70 under 3-mW light output. A narrow stripe-geometry ISP laser has a promising feature in that it can be used in high bit rate and long-distance fiber transmission.

A method to estimae the coupling length of the fiber in which modes couple each other due to the random bending of fiber axis is given. The coupling length is estimated from the comparison of the measured transfer function to the theoretical one which is derived previously. The coupling length of a graded-index fiber is estimated to be about 0.8 km using this method. Further, the coupling length of recent graded-index fibers is presumed to be about several Km. For step-index fibers, it is estimated to be in the range between 0.5-5 Km.

We describe the use of integrated optical waveguides for the study of locally illuminated superconductors. The creation of optically controlled Josephson junctions is discussed.

This method can reduce the measuring time considerably and can improve spatial resolution by using a Q (quasi)-fiber in comparison with an usual fiber-polishing method. The overall measuring error was less than 0.03% for the case of index difference1%.

The sides of strip waveguides create TE-TM coupling which has so far been neglected in published analyses. For all TM" modes and for higher TE" modes on strip waveguides under suitable conditions, this coupling produces interesting new effects, such as leakage and resonance, which have implications for device performance.

High strength fiber optical waveguides have been prepared by hermetically coating the pristine fiber surface with a metallic jacket. The static fatigue characteristics of these fibers at high stress levels have been observed to be orders of magnitude superior to plastic jacketed fibers.

Experimental and theoretical studies have been carried out on propagation in curved single-mode optical fibres. Mode conversion at the start of a bend produces a transition region which affects the bend loss, transverse energy distribution and gives rise to ray emission. It is shown that the modes of a curved multimode fibre can be conveniently and simply described using parabolic cylindrical co-ordinaces.

A directional coupler type light modulator connected to a single mode optical fiber, was fabricated using Ti-diffused LiNbO3 waveguides. Two 8 µm wide parallel waveguides separated by 5 µm with 15 mm interaction length were used. Modulation characteristics at the infrared wavelength of 1.15 µm were as follows; 4.0 V modulation voltage, 1.0 GHz 3 dB bandwidth, 17.6 dB extinction ratio and 8.2 dB optical insertion loss.

It is shown that the resonance-like phenomena or the relaxation oscillations in the light output of the directly modulated injection lasers is suppressed by a non-resonant π-type electric circuit connected to the laser diode. Application of this suppressor circuit is not sensitive to the bias current of laser diode and the cut-off frequency of modulation is sufficiently large. It is pointed out that the use of this method at the narrow stripe laser is the most effective.

Two strip-waveguides, with and without a function of light intensity modulation, have been monolithically integrated with an embedded stripe DH laser. The strip-waveguides are constructed with guide films of high resistivity GaAs0.9 P0.1 and surroundings of slightly lower refractive index GaAs0.85 P0.15. The intensity of spontaneous light output from the stripe Ga0.97 Al0.03 As laser can be modulated by a voltage applied to the waveguide-modulator through an isolated electrode. It is seen that the maximum modulation occurs at a wavelength shorter than the peak wavelength of emission spectrum as a result of the Franz-Keldysh effect.