Abstract:
An optical signal processing apparatus includes a first optical waveguide and a first slab waveguide configured to equally distribute an output light of the first optical waveguide. A first arrayed waveguide includes an aggregate of optical waveguides changing in optical length by a constant interval for dividing the output light. A second slab waveguide focuses the optical output of the first arrayed waveguide. A spatial filter receives incident light focused by the second slab waveguide and distributes the incident light on a straight line. The spatial filter also modulates the light into a desired amplitude according to the position on the straight line. The apparatus also includes a second arrayed waveguide and an aggregate of optical waveguides changing in optical length by a constant interval for applying light modulated by the spatial filter to the second arrayed waveguide. Structure is provided for converging the output light of said second arrayed waveguide to a single point. The resulting output light is then appiled to a second optical waveguide.

Description:
This application is a divisional of U.S. patent application Ser. No. 0/921,844, now U.S. Pat. No. 6,122,419 filed Sep. 2, 1997, issued Sep. 19, 2000 which for purposes of disclosure is incorporated herein by specific reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     This invention relates to a method and an apparatus for processing, measuring or storing high-speed optical signals. 
     2. Description of the Prior Art 
     An example of prior art optical signal processing circuit is shown in FIG.  1 . In the Figure, the reference numerals  201  and  205  indicate diffraction gratings,  202  and  204  are lenses, and  203  is a spatial filter or an optical storage medium. When a time series signal light is applied to his optical circuit, a Fourier transformation of the time series signal light, that is, a frequency spectrum distribution thereof is formed on the spatial filter  203  by the frequency decomposition function of the diffraction grating  201  and the Fourier transformation function of the lens  202 . When the frequency spectrum distribution is modulated by means of the spatial filter  203 , the waveform of the time series signal can be modulated. Here the wave form can be controlled by the spatial filter  203  even when the time series signal is very high in speed. 
     As an example, when an optical signal of a pulse width of 200 fs and a pulse interval of 5 ps shown in the upper part of FIG. 2 is applied, the incident optical spectrum has a shape as shown in the upper part of FIG. 3, having an optical power distribution shown by the broken line in the middle part of FIG. 3 on the spatial filter  203  after passing through the diffraction grating  201  and the lens  202 , and when this is modulated by the spatial filter  203 , it has a shape as shown in the lower part of FIG. 3 in the spectrum after passing through the spatial filter  203 . A time-dependent waveform corresponding to the spectrum is the pulse sequence shown in the lower part of FIG.  3 . Thus, optical signal processing can be achieved by modulating the frequency spectrum of optical signal by the spatial filter  203 . That is, various waveform shaping according to the filter is possible. 
     Further, with  203  shown in FIG. 1 used as an optical storage medium, by applying time series signal light and reference light simultaneously, an interference fringe of both lights is hologram recorded on the optical storage medium  203 . After the recording, when only the reference light is incident, the signal light is reproduced and output. Such studies are reported, for example, in A. M. Weiner, “Programable shaping of Femtosecond optical pulses by use of 128-Element Liquid Crystal Phase Modulator,” IEEE J Quntun Electronics, Vol . 28 No. 4, pp. 908-920 (1992); A. Weiner et al., “Spectral holography of Shaped femtosecond pulses”, Optics Letters, vol. 17, pp. 224-226 (1992). 
     With the advance in optical communication technology, pulse widths of optical signals utilized in optical transmission are 100 ps (ex; FA-10G system) in the practical application stage, and those of next-generation very large capacity transmission apparatus are considered to utilize picosecond pulses of 1-10 ps. Optical pulses of femtosecond region are application region of the time being in the research and development and material evaluation of stable light sources, and considered not to be applied in optical communications immediately. That is, basic apparatus and method enabling optical pulse generation, waveform shaping, waveform measurement, waveform recording, correlation processing, and the like are required for constructing next-generation very high capacity systems. 
     However, the above-described prior art has the following problems. That is, in the modulation or hologram recording, all of the diffraction gratings  201 ,  203 , the lenses  202  and  204 , and the spatial filter  203  must be laid out in high precision, are liable to be affected by the external environment, are thus difficult to be modular structured, and are nearly impossible to operate other than in a so-called experimental-environment. Therefore, it is not practicable at present stage. 
     Still further, when treating a time series signal, signal processing is in principle possible by single dimensional diffraction grating and lens. However, the diffraction grating and the lens have a redundant two-dimensional structure, which requires tedious positioning which is inherently unnecessary. 
     Yet further, when treating a long pulse sequence of over 10 ps or a pulse of large pulse width, it is required to increase the incident beam diameter which, in turn, requires large-sized diffraction grating or lens, and thus a large sized apparatus. 
     That is, the prior art structure using the diffraction grating pair and the lens effective for femtosecond pulses requires a very large sized apparatus for picosecond pulses, and is difficult to be packaged in a transmission apparatus of about 30×40×3 cm. Further, it is required to use a connection optical system with the optical fiber, and flexible apparatus design according to the pulses is Impossible. 
     Heretofore, a semiconductor mode-locked laser is known as picosecond pulse generation means. 
     FIG. 4 shows the structure of a prior art mode-locked laser for use as a short pulse light source. 
     In the Figure, the mode-locked laser comprises an optical gain medium  51 , an pumping circuit  52  for forming a population inversion to the optical gain medium  51 , mirrors  53 - 1  and  53 - 2  constituting an optical resonator, an optical modulator  54  placed in the optical resonator, and a clock generator  55  for driving the optical modulator  54 . In this construction, when the clock generator  55  drives the optical modulator  54  at a clock frequency equal to the resonance mode spacing of the optical resonator or an integer multiple thereof, an optical short pulse sequence of a repetition frequency equal to the clock frequency or an integer multiple thereof. 
     FIG. 5 shows the structure of a multi-wavelength light source for simultaneously oscillating light of a plurality of wavelengths. 
     In the Figure, the multi-wavelength light source comprises an optical gain medium  61 , an arrayed-waveguide grating  62 , a lens  63  for coupling the optical gain medium  61  with the arrayed-waveguide grating  62 , a high reflection mirror  64  and a low reflection mirror  65  disposed at both end surfaces of the optical gain medium  61 , and a high reflection mirror  66  disposed at the other end of the arrayed-waveguide grating  62 . 
     The arrayed-waveguide grating  62  comprises an input waveguide  71 , an arrayed waveguide  73  including a plurality of waveguides gradually increasing in length by a waveguide length difference ΔL, a plurality of output waveguides  75 , a slab waveguide  72  for connecting the input waveguide  71  and the arrayed waveguide  73 , and a slab waveguide  74  for connecting the arrayed waveguide  73  and the output waveguide  75 , which are formed on a substrate  70 . 
     Light incident into the input waveguide  71  spreads by diffraction in the slab waveguide  72 , and incident and distributed in equal phase into individual waveguides of the arrayed waveguide  73 . The light-transmitted in the individual waveguides of the arrayed waveguide  73  and reaching the slab waveguide  74  has a phase difference corresponding to the waveguide length difference ΔL. Since the phase difference varies with the wavelength, when focused on the focal plane by the lens effect of the slab waveguide  74 , the light is focused at different positions by wavelengths. Therefore, light of different wavelengths are taken out from the individual waveguides of the output waveguide  75 . 
     In the multi-wavelength light source using such an arrayed waveguide grating  62 , an optical resonator is formed between the high refection mirror  64  and the high reflection mirror  66 , and light of a plurality of wavelengths can be simultaneously oscillated by steadily exciting the optical gain medium  61 . 
     However, the prior art mode-locked laser has the following problems. 
     (1) The oscillation mode envelope spectrum is largely varied by the operation condition, and it is difficult to set the central wavelength and the pulse width. 
     (2) Since the amplitude and phase of each mode cannot be independently controlled, pulse shape design is difficult. 
     (3) A very large number of modes are excited, however, correlation between modes is insufficient due to dispersion and nonlinear effect of the semiconductor medium of the long resonator, and it is difficult to generate a transform limit optical short pulse sequence. 
     Further, since the phase to each mode is not controlled in the multi-wavelength as shown in FIG. 5, it is impossible to generate an optical short pulse sequence of high repetition frequency by mode locking. 
     As described above, there has heretofore been a semiconductor mode-locked laser as picosecond pulse generation-means, however, to utilize it as a light source for optical communications, it is required that the phase and intensity are stable, the central wavelength and pulse width and pulse shape can be set (in design and fabrication), and a high quality pulse close to the transform limit is generated. However, present semiconductor mode-locked lasers are difficult to simultaneously meet these requirements. Further, it is very difficult to incorporate the prior art shown in FIG. 1 in a semiconductor mode-locked light source, and no studies have been reported on the problems. 
     In a very high speed optical transmission apparatus, distortion of waveform due to group velocity dispersion in the optical fiber is a first factor that limits the transmission distance. Dispersion characteristics of a transmission line (optical fiber) depend on ambient temperature, on material and cover with passage of time. Further, the dispersion characteristics are changed when the optical fiber is changed to another optical fiber in association with a malfunction or replacement of the transmission line. Or. even if the dispersion of the optical fiber is unchanged, the dispersion value applied to the optical signal is changed by changes in light source wavelength or filter characteristics. 
     Since even dispersion shift optical fibers of small dispersion, which are generally used, have a dispersion of about ±1 ps/nm/km, a transmission section of 80 km has a dispersion of ±80 ps/nm. Since an optical band width of optical signal of pulse width of 10 ps at 20 Gbit/s is about 1 nm, a pulse broadening of a maximum of 80 ps is generated. However, the time slot of 20 Gbit/s signal is 50 ps, a large inter-symbol interference is generated to produce large errors. Therefore, an apparatus for compensating (equalizing) the dispersion of transmission line is indispensable for a very high speed transmission apparatus. 
     An example of prior art is shown in FIG.  6 . In FIG. 6,  01  is an optical amplifier,  02  is an optical switch, and  03  is a dispersion compensation fiber. 
     In the prior art, the optical signal is passed through another optical fiber having dispersion characteristics reverse to the dispersion of the transmission line to compensate the dispersion, thereby obtaining a good waveform. 
     Since dispersion characteristics of the dispersion compensation fiber  03  are not variable, it is general to provide fibers of different dispersion characteristics for compensating the dispersion according to changes in dispersion characteristics of the transmission line. 
     However, the prior art has the following problems. 
     (i) compensation is difficult for high order dispersion. 
     (ii) A number of fibers must be provided to compensate the dispersion. In particular, since the tolerance of dispersion is narrow in a very high speed optical signal, fibers of small increment in dispersion value are required. As a result, the apparatus becomes large in size, and an optical switch of multiple switches is required. 
     (iii) Since the dispersion compensation fiber is switched by an optical switch, a momentary disconnection of optical signal occurs during switching. 
     Further, as other prior art examples, there are constructions of chirped fiber grating and multiple-connected MZ interferometer, however, these have the. following problems. 
     (iv) Control width of central wavelength of dispersion compensation is small, and the compensation band width is narrow. 
     In a very high speed optical transmission apparatus, a second factor of limiting the transmission distance is distortion of waveform due to self-phase modulation in the optical fiber. Another example of prior art is shown in FIG.  7 . In FIG. 7, the symbol  04  indicates an optical transmitter,  05  is a high dispersion fiber,  06  is an optical-amplifier,  07  is an optical transmission line,  08  is a dispersion compensation circuit, and  09  is an optical receiver. 
     This construction provides a transmission method in which an optical signal is previously passed through a high dispersion medium on the assumption of compensation to increase the pulse width, thereby reducing the self-phase modulation. Since the self-phase modulation is generated nearly proportional to the optical pulse peak intensity, the modulation can be reduced by increasing the pulse width to decrease the peak power. Since, dispersion can be compensated to reproduce the waveform, however, degradation of waveform due to self-phase modulation, which is a nonlinear phenomenon, cannot be reproduced by a normal linear waveform equalization method, a transmission apparatus is required which does not generate a nonlinear phenomenon in the transmission line. 
     However, the prior art has the following problems. 
     (v) Since changes in dispersion in the transmission line cannot be previously estimated, there is a possibility that dispersion is equalized by chance in the course of the transmission line, resulting in self-phase modulation leading to an increase in waveform degradation and errors. 
     As described above, as picosecond pulse waveform shaping (e.g., dispersion compensation) means, there are other optical fibers having reverse dispersion characteristics to the dispersion in the transmission line, a chirped fiber grating, and a multiple-connected MZ interferometer. However, these means are difficult to achieve compensation for high order dispersion, variable dispersion compensation, and wide band compensation. Further, the prior art shown in FIG. 1 is very small in compensatable dispersion amount. For example, for an optical pulse of 2 ps in pulse width, it can provide only a compensation of about 5 ps/nm. 
     The optical signal processing apparatus as described above is required to measure waveform of optical signals of higher speed. 
     Heretofore, as waveform measuring and recording means, there is a very high speed O/E converter or a streak camera. However, the band width of the O/E converter is as much as 50 GHz and impossible to measure picosecond pulses of 1-10 ps. Further, since the streak camera is low in sensitivity in the optical communication wavelength region, a sufficient S/N is not obtained by a single sweeping, and a real-time waveform cannot be observed. There is no report of study using the prior art shown in FIG.  1 . When the prior art is applied, as is, since light is distributed two-dimensionally on the Fourier transformation plane, measurement of high S/N is difficult unless a specific optical system is devised. 
     SUMMARY OF THE INVENTION 
     An object of the present invention, as described above, is to provide an optical signal processing apparatus and optical signal processing method which enables generation, waveform shaping, waveform measurement, waveform recording, correlation processing, and the like of optical pulses of 1-10 ps. 
     Basic construction of the optical signal processing apparatus according to the present invention suitable for such problems comprises an optical waveguide, first means for equally distributing an output of the optical waveguide, a arrayed waveguide comprising an aggregate of optical waveguides changing in optical length by a constant interval for spectrally dividing the output light, second means for focusing the optical output of the arrayed waveguide, and a mirror for receiving and reflecting incident light focused by the second means. 
     Or, the optical signal processing apparatus according to the present invention comprises an optical waveguide, first means for equally distributing an output of the optical waveguide, a arrayed waveguide for dividing the output light, second means for focusing the optical output of the arrayed waveguide, and a spatial filter for receiving incident light focused by the second means and spectrally dividing the incident light on a straight line and for modulating the incident light into a desired amplitude or phase according to the position on the straight line, thereby reflecting the incident light. 
     Further, another construction of the optical signal processing apparatus according to the present invention comprises a first optical waveguide, first means for equally distributing an output of the first optical waveguide, a first arrayed waveguide comprising an aggregate of optical waveguides changing in optical length by a constant interval for dividing the output light, second means for focusing the optical output of the first arrayed waveguide, a spatial filter for receiving incident light focused by the second means and distributing the incident light on a straight line and for modulating the light into a desired amplitude according to the position on the straight line, third means comprising an aggregate of optical waveguides changing in optical length by a constant interval for applying light to the second arrayed waveguide, fourth means for converging the output light of the second arrayed waveguide to a single point, and a second optical waveguide to which the output light of the fourth means is applied. 
     A yet further construction of the optical signal processing apparatus according to the present invention comprises a reflective type spatial filter, a arrayed waveguide comprising an aggregate of optical waveguides changing in optical length by a constant interval, first means for applying coherent light to the reflective type spatial filter and inputting the coherent light modulated by the reflective type spatial filter into the arrayed waveguide, and second means for converging output light of the arrayed waveguide to a single point. 
     A yet further construction of the optical signal processing apparatus according to the present invention comprises a transmission type spatial filter, a arrayed waveguide comprising an aggregate of optical waveguides changing in optical length by a constant interval, first means for applying coherent light to the transmission type spatial filter, second means for applying the coherent light modulated by the transmission type spatial filter into the arrayed waveguide, and third means for converging output light of the arrayed waveguide to a single point. 
     The optical signal processing method according to the present invention is characterized in that an optical signal is input to an optical signal processing apparatus having a arrayed waveguide and a spatial filter, to convert the optical signal into a frequency spectral image, the frequency spectral image is subjected to a desired modulation by the spatial filter, and the modulated frequency spectral image is converged to a single point to obtain a new optical signal. 
     In the optical signal processing method, the optical signal processing apparatus used is preferably the above-described optical signal processing apparatus. 
     Another arrangement of the optical signal processing method according to the present invention is characterized in that coherent light is input in an optical signal processing apparatus having a arrayed waveguide and a spatial filter written with a hologram image corresponding to the frequency spectrum of a desired optical signal to generate an optical signal. 
     Still further, in the present invention, by combining the optical signal processing apparatus of the basic structure with predetermined parts, generation of a short pulse is possible. 
     The basic construction of such optical signal processing apparatus is characterized by comprising in the optical signal processing apparatus of the basic structure having the above-described mirror, at the input side of the optical waveguide, optical modulation means for modulating an oscillation light in an optical resonator with a frequency nearly equal to the resonance mode spacing or an integer multiple thereof, and optical gain means, wherein the modulation means, the gain means, and the optical waveguide are sequentially coupled by optical coupling means, an optical reflection mirror is disposed on the end surface not facing the coupling means of the optical modulator, the mirror formed on the end surface of the second means is a high reflection type, a resonator is formed between these high reflection type mirrors, thereby enabling generation of a short pulse light. 
     In the construction for generating short pulses, a plurality of output waveguides may be disposed at predetermined spacings between the focal plane of one slab waveguide of the arrayed waveguide grating and the high reflection mirror. 
     Similarly, the plurality of output waveguides may be disposed at equal spacings. 
     Similarly, the high reflection mirrors corresponding to the individual output waveguides may be different in reflectivity from each other. 
     Similarly, the plurality of output waveguides may be set with predetermined waveguide length differences for compensating dispersion in the optical resonator. 
     Similarly, in place of the high reflection mirrors, a plurality of lens arrays disposed at a predetermined spacing, and a liquid crystal light modulator having a high reflection mirror on one side may be provided. 
     Similarly, an optical synthesizer for synthesizing part or all of a plurality of output waveguides. 
     Similarly, gratings formed in the individual output waveguides may be different in diffractive efficiency from each other. 
     Similarly, a plurality of high reflection mirrors may be disposed at predetermined spacings on the focal plane of one slab waveguide of the arrayed waveguide grating. 
     Similarly, a plurality of high reflection mirrors may be disposed at equal spacings. 
     Similarly, the plurality of high reflection mirrors may be different in reflectivity from each other. 
     Similarly, in place of the high reflection mirrors, a plurality of diffraction gratings may be formed at a predetermined spacing in the focal plane of the slab waveguide. 
     Similarly, the plurality of diffraction gratings may be disposed at equal spacings. 
     Similarly, the plurality of diffraction gratings may be different in diffractive efficiency from each other. 
     Similarly, the individual positions of the plurality of diffraction gratings may be dislocated in the normal direction of the focal plane of the slab waveguide. 
     Similarly, in place of the high reflection mirrors, a groove may be formed on the focal plane of the slab waveguide, and films formed by stacking a plurality of mirrors may be disposed at a predetermined spacing in the groove. 
     Similarly, the optical modulation means and the optical gain means may be integrated. 
     Similarly, part of the individual components may be connected with an optical fiber. 
     Similarly, the position of the high reflection mirror may be controlled by a fine control mechanism. 
     Similarly, the spacing of the high reflection mirrors may be varied in the normal direction of the slab waveguide. 
     Further, based on the optical signal processing apparatus of the basic structure according to the present invention, an apparatus for observing the waveform of the optical signal to be processed can be constructed. 
     Such a waveform observable optical signal processing apparatus comprises an optical waveguide, an arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, distribution means for distributing output light of the optical waveguide to the arrayed waveguide, focusing means for focusing the output light of the arrayed waveguide, a spatial filter disposed in the vicinity of the focal plane of the focusing means for modulating the light image, reflection means for reflecting light modulated by the spatial filter, and optical division means for taking out the reflected light from the reflection means in the optical waveguide. 
     Or, the apparatus comprises a first optical waveguide, a first arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, distribution means for distributing the output light of the first optical waveguide to the first arrayed waveguide, first focusing means for focusing the output light of the first arrayed waveguide, a spatial filter disposed in the vicinity of the focal plane of the first focusing means for modulating the light image, and further comprising a second arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, second focusing means for focusing the light modulated by the spatial filter to the second arrayed waveguide, a second optical waveguide, and wave synthesis means for synthesizing the output light of the second arrayed waveguide and coupling to the second optical waveguide. 
     Still further, the apparatus comprises a first optical waveguide, a first arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, distribution means for distributing output light of the first optical waveguide to the first arrayed waveguide, a reference light input optical waveguide, a second arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, second distribution means for distributing the output light of the reference light input optical waveguide to the second arrayed waveguide, focusing means for focusing the output light of the first arrayed waveguide and the output light of the second arrayed waveguide, an optical recording medium disposed in the vicinity of the focal plane of the focusing means, and optical division means for taking out the reflected light from the first optical waveguide. 
     A yet further construction of the waveform observable apparatus comprises a first optical waveguide, a first arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, first distribution means for distributing the output light of the first optical waveguide to the first arrayed waveguide, a third arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, second distribution means for distributing the output light of the reference light input optical waveguide to the third arrayed waveguide, first focusing means for focusing the output light of the first arrayed waveguide and the output light of the third arrayed waveguide, an optical recording medium disposed in the vicinity of the focal plane of the first focusing means, a second arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, second focusing means for focusing the light modulated by the optical recording means to the second arrayed waveguide, a second optical waveguide, and wave synthesis mans for synthesizing the output light of the second arrayed waveguide and coupling to the second optical waveguide. 
     Yet further, another construction of the waveform observable apparatus comprises a first optical waveguide, a first arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, first distribution means for distributing the output light of the first optical waveguide to the first arrayed waveguide, a first reference light input optical waveguide, a second arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, second distribution means for distributing the output light of the first reference light input optical waveguide to the second arrayed waveguide, a second reference light input optical waveguide, first focusing means for focusing the output light of the first arrayed waveguide and the output light of the second arrayed waveguide and the output light of the second reference light input optical waveguide, an optical recording medium disposed in the vicinity of the focal plane of the first focusing means, second focusing means for focusing the light modulated by the optical recording medium, and a light receiver array disposed in the vicinity of the focal plane of the second focusing means. 
     In the waveform observable apparatus, the focusing means may be a slab waveguide having a circular end surface. 
     Similarly, the focusing means may comprise a slab waveguide and a phase spatial modulation device. 
     Similarly, the spatial filter may be a phase filter, or an amplitude filter, or a spatial filter formed of amplitude filters and phase filters connected in multiple stages. 
     Similarly, the focal length of the phase spatial modulation device may be equal to the focal length of the slab waveguide of the coupling means. 
     Similarly, the spatial filter and the reflection means may be combined to form a pattern mirror comprising a number of partial mirrors. 
     Similarly, the spatial filter may be a spatial filter combining with a function of a phase spatial modulation device. 
     Similarly, the focusing means may be a lens. 
     Similarly, the focusing means may be a slab waveguide of the focal plane, having a phase adjusting arrayed waveguide at the end of the slab waveguide, and the phase adjusting arrayed waveguide end may be connected to the spatial filter. 
     Similarly, the focusing means may be a slab waveguide of the focal plane, having a phase adjusting arrayed waveguide at the slab waveguide end, and the phase adjusting arrayed waveguide may have an optical modulator array. 
     Similarly, phase difference between waveguides of the phase adjusting arrayed waveguide may be an integer multiple of 2π. 
     Similarly, the optical division means may be an optical circulator. 
     Similarly, the focusing means is a slab waveguide, having optical bend means at the slab waveguide end for bending light in direction perpendicular to the waveguide. 
     Similarly, the spatial filter may be a liquid crystal spatial modulator comprising a glass substrate, a transparent electrode, a liquid crystal, and a liquid crystal alignment film. 
     Similarly, a quarter-wave plate may be provided in the liquid crystal spatial modulator. 
     Similarly, the liquid crystal of the liquid spatial modulator may be a twist nematic type. 
     Further, the optical signal processing method by the waveform observable optical signal processing apparatus is characterized in that a time series optical signal is input in the optical waveguide to convert the time series optical signal into a frequency spectrum image, the frequency spectrum image is subjected to desired phase or amplitude or both modulations, and the modulated light is synthesized to obtain a new time series optical signal. Or, filter characteristics of the spatial filter may be a hologram image of a pattern corresponding to the frequency spectrum of a desired time series optical signal, and coherent pulse light is applied to the optical waveguide to generate the desired optical signal. Still further, an optical signal may be input in the optical waveguide, a reference light of coherent pulse light is applied to the reference light input waveguide, hologram recording is made on the recording medium, a reference light of another coherent pulse light is applied to the reference light input waveguide, to output a phase conjugate light of the signal light. Yet further, signal light is input in the optical waveguide, a reference light of coherent pulse light is applied to the reference light input waveguide, hologram recording is made on the recording medium, no a reference light of another coherent pulse light is applied to the reference light input waveguide, to output a signal light or a correlated light of the signal light and the reference light. Yet further, a signal light is input in the optical waveguide, a reference light of coherent pulse light is applied to the first reference light input waveguide, a reference light of single color is applied to the second reference light input waveguide to form reference light of coherent pulse light in the first reference light input waveguide to observe the pulse waveform. 
     Yet further, the present invention, based on the optical signal processing apparatus of the above-described basic structure, can provide an optical signal processing apparatus which enables dispersion compensation of the processed optical signal. The optical signal processing apparatus that enables such dispersion compensation comprises a first optical amplifier, an optical wavelength filter, a first optical waveguide, a first arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, distribution means for distributing the output light of the first optical waveguide to the arrayed waveguide, first focusing means for focusing the output light of the first arrayed waveguide, a spatial filter disposed in the vicinity of the focal plane of the first focusing means for modulating optical image, reflection means for reflecting light modulated by the spatial filter, optical division means for taking out the reflected light from the first optical waveguide, and a second optical amplifier. 
     Another construction of the dispersion compensatable optical signal processing apparatus comprises a first optical amplifier, an optical wavelength filter, a first arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, distribution means for distributing the output light of the first optical waveguide, first focusing means for focusing the output light of the first arrayed waveguide, a spatial filter disposed in the vicinity of the focal plane of the first focusing means for modulating the optical image, a second arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length, second focusing means for focusing light modulated by the spatial filter to the second arrayed waveguide, a second optical waveguide, optical synthesis means for synthesizing the output light of the second arrayed waveguide and coupling to the second optical waveguide, and a second optical amplifier. 
     Yet further, an optical signal processing apparatus can be constituted of the dispersion compensatable optical signal processing apparatus, a light source, and an optical modulation signal generation circuit. 
     Yet further, an optical signal processing apparatus can be composed of the dispersion compensatable optical signal processing apparatus and an optical receiver. 
     Similarly, an optical signal processing apparatus can comprise the dispersion compensatable optical signal processing apparatus, an optical signal transmitter circuit comprising a light source, an optical modulator, an optical signal receiver circuit comprising the dispersion compensatable optical signal processing apparatus and an optical receiver, and an optical transmission line. 
     In the dispersion compensatable optical signal processing apparatus, the spatial filter may be a phase filter in which a relative phase φ may have a characteristic approximating 
     
       
         φ( x )=Mod[ ax   2 , π]  (a: constant) 
       
     
     with respect to the position (x) on the spatial filter. (wherein Mod[u, v] indicates a remainder using v as a modulus.). 
     Similarly, the spatial filter may be a phase filter in which a relative phase φ may have a characteristic approximating 
     
       
         φ( x )=Mod[ ax   2 , 2π]  (a: constant) 
       
     
     with respect to the position (x) on the spatial filter. (wherein Mod[u, v] indicates a remainder using v as a modulus.). 
     Similarly, the spatial filter may be a phase filter in which a relative phase φ has a characteristic approximating 
     
       
         φ( x )=π/2 ( x &gt;0) and φ ( x )=0 ( x &lt;0), or 
       
     
     
       
         φ( x )=0 ( x &gt;0) and φ( x )=π/2 ( x &lt;0) 
       
     
     with respect to the position (x) on the spatial filter, thereby achieving amplitude modulation—angular modulation conversion. 
     Similarly, the spatial filter may be a phase filter in which a relative phase φ has a characteristic approximating 
     
       
         φ( x )=π( x &gt;0) and φ( x )=0 ( x &lt;0), or 
       
     
     
       
         φ( x )=0 ( x &gt;0) and φ( x )=π ( x &lt;0) 
       
     
     with respect to the position (x) on the spatial filter, thereby achieving amplitude modulation—angular modulation conversion. 
     Yet further, in the dispersion compensatable optical signal processing apparatus, the spatial filter may comprise a phase filter and an amplitude filter. 
     Similarly, the spatial filter may be a liquid crystal spatial modulator comprising a glass substrate, a transparent electrode, a liquid crystal, and a liquid crystal alignment film. 
     Yet further, an optical signal processing method by the above dispersion compensatable optical signal processing apparatus is characterized in that frequency spectral chase of optical signal generated by the optical signal transmitter circuit is modulated, and dispersion in the optical fiber and frequency spectral phase modulation by the optical signal transmitter circuit are compensated by the optical receiver circuit. 
     Another arrangement of the optical signal processing method is characterized in that the frequency spectral amplitude of the optical signal generated by the optical signal transmitter circuit is modulated, dispersion in the optical fiber and frequency spectral amplitude modulation by the optical signal transmitter circuit are compensated by the optical signal receiver circuit. 
     Similarly, a further arrangement is characterized in that frequency spectral phase and frequency spectral amplitude of the optical signal generated by the optical signal transmitter circuit are modulated, and dispersion in the optical fiber and frequency spectral phase modulation and frequency spectral amplitude modulation are compensated by the optical receiver circuit. 
     A yet further construction of the dispersion compensatable optical signal processing apparatus comprises a first optical signal processing apparatus comprising: 
     a short pulse light source; 
     a first optical amplifier; 
     a first optical wavelength filter; 
     a first optical splitting means for dividing the output light of the first optical wavelength filter into n(integer) units of light; 
     first n units of optical modulation circuits; 
     a first arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length; 
     first distribution means for distributing the output light of the first n units of input/output optical waveguides to the first arrayed waveguide; 
     first focusing means for focusing the output light of the first arrayed waveguide; 
     a first spatial filter disposed in the vicinity of the focal plane of the first focusing means for modulating light image; 
     first reflection means for reflecting light modulated by the first spatial filter; 
     optical splitting means for taking out the reflected light from the first n units of input/output optical waveguides; 
     optical combining means for synthesizing the reflected light from the n units of second optical splitting means; and 
     a second optical amplifier; 
     and a second optical signal processing apparatus comprising: 
     an optical transmission line; 
     a third optical amplifier; 
     a second optical wavelength filter; 
     third optical splitting means for dividing the output light of the second optical wavelength filter into n (integer) units of light; 
     second n units of input/output optical waveguides; 
     a second arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length; 
     second distribution means for distributing the output light of the second input/output optical waveguides to the second arrayed waveguide; 
     second focusing means for focusing the output light of the second arrayed waveguide; 
     a second spatial filter disposed in the vicinity of the focal plane of the second focusing means for modulating light image; 
     second reflection means for reflecting light modulated by the second spatial filter; 
     fourth optical splitting means for taking out the reflected light from the second input/output optical waveguide; and 
     n units of optical receivers for receiving the reflected light from the n units of fourth optical splitting means. 
     A yet further construction of the dispersion compensatable optical signal processing apparatus comprises a first optical signal processing apparatus comprising: 
     a short pulse light source; 
     a first optical amplifier; 
     a first optical wavelength filter; 
     a first optical splitting means for dividing the output light of the first optical wavelength filter into n(integer) units of light; 
     first n units of optical modulation circuits; 
     first n units of input/output optical waveguides a first arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length; 
     first distribution means for distributing the output light of the first input/output optical waveguides to the first arrayed waveguide; 
     first focusing means for focusing the output light of the first arrayed waveguide; 
     a first spatial filter disposed in the vicinity of the focal plane of the first focusing means for modulating light image; 
     a second arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length; 
     second focusing means for focusing the light modulated by the first spatial filter to the second arrayed waveguide; 
     first n units of output optical waveguides; 
     first optical combining means for synthesizing the output light of the second arrayed waveguide and coupling to the first n units of output optical waveguides; 
     second optical combining means for coupling output of the first n units of output optical waveguides; 
     a second optical amplifier; and a second optical signal processing apparatus comprising: 
     an optical transmission line; 
     a third optical amplifier; 
     a second optical wavelength filter; 
     third optical splitting means for dividing the output light of the second optical wavelength filter into n (integer) units of light; 
     second n units of input/output optical waveguides; 
     a third arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length; 
     second distribution means for distributing the optical waveguide output light of the second input/output optical waveguide to the third arrayed waveguide; 
     third focusing means for focusing the output light of the third arrayed waveguide; 
     a second spatial filter disposed in the vicinity of the focal plane of the third focusing means for modulating light image; 
     a fourth arrayed waveguide comprising a plurality of optical waveguides gradually increasing in waveguide length; 
     fourth focusing means for focusing light modulated by the second spatial filter to the fourth arrayed waveguide; 
     second n units of output optical waveguides; 
     third optical coupling means for coupling the output light of the fourth arrayed waveguide and coupling to the second n units of output optical waveguides; and 
     n units of optical receivers for receiving output light from the second output optical waveguide. 
     Yet further, the present invention, based on the optical signal processing apparatus of the above-described basic structure, can provide an optical signal processing apparatus which enables real-time observation of waveform of the processed optical signal. 
     Such a waveform observable optical signal processing apparatus comprises first time—space conversion means for converting time series optical signal of the signal light into spatial signal light, second time—space conversion means for converting time series optical signal of reference light into spatial signal light, focusing means for focusing the spatial signal light individually output from the first time—space conversion means and the second time—space conversion means to make interference with each other, light receiving means disposed in the vicinity of the focal plane of the focusing means for receiving an interference light image of a plurality of optical signals incident into the focusing means, and an optical signal restoration circuit for restoring a time series signal of the signal light from the detection signals of the light receiving means. 
     In the waveform observable optical signal processing apparatus, the first and second time—space conversion means may comprise arrayed waveguide gratings, and the focusing means may comprise a slab waveguide having a function for making Fourier transformation of the spatial signal light. 
     Similarly, in the waveform observable optical signal processing apparatus, the first and second time—space conversion means may comprise diffraction gratings, and the focusing means may comprise a lens for making Fourier transformation of the spatial signal light. 
     Similarly, in the waveform observable optical signal processing apparatus, the light receiving means may comprise a photodiode array. 
     Similarly, in the waveform observable optical signal processing apparatus, the optical signal restoration circuit may restore electric field distribution of optical pulse of the signal light by calculation from electric field distribution of the Fourier transform hologram detected by the light receiving means. 
     A signal processing method by the waveform observable optical signal processing apparatus is characterized by comprising a step of converting a time series optical signal of unknown signal light into spatial signal light, a step of converting time series optical signal of known reference light into spatial signal light, a step of focusing individually the spatial signal of the signal light and the spatial signal of the reference light to make interference with each other, thereby forming a hologram image of a pattern corresponding to the frequency spectrum of time series signal, a step of receiving the hologram image to be converted into an electrical signal, and a step of restoring the unknown signal light from the hologram image converted to electrical signal using a predetermined calculation formula. 
     In the optical signal processing method, the step of restoring the unknown signal light from the hologram image may have a mathematical calculation operation for multiplying the hologram image formed on the focal plane with electric field distribution of reconstructing light mathematically derived from the electric field distribution of known reference light, followed by Fourier transformation operation and space—time conversion operation. 
     Further, in the signal processing method, the electric field distribution of reconstructing light on the focal plane to be multiplied with the hologram image may include a factor of dividing by the square of absolute value of amplitude distribution of electric field distribution at the focal plane of the known reference light. 
    
    
     The above and other objects, effects, features and advantages of the present invention will become more apparent from the following description of embodiments thereof taken in conjunction with the accompanying drawings. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic view showing an example of an optical signal processing apparatus; 
     FIG. 2 is a diagram showing pulse amplitude of input optical signal and output signal in the prior art apparatus; 
     FIG. 3 is a diagram showing optical spectrum of input optical signal, spatial filter transmittance of the optical signal, and optical spectrum of output optical signal in the prior art apparatus; 
     FIG. 4 is a schematic view showing the structure of a mode locked laser used as a prior art short pulse light source; 
     FIG. 5 is a schematic view showing a prior art multi-wavelength light source for simultaneously oscillating light of multiple wavelengths; 
     FIG. 6 is a schematic view showing the structure of a prior art dispersion compensatable optical signal processing apparatus; 
     FIG. 7 is a schematic view showing the structure of another prior art dispersion compensatable optical signal processing apparatus; 
     FIG. 8 is a schematic view showing the structure of the optical signal processing apparatus according to a first embodiment of the present invention; 
     FIG. 9 is a schematic view showing another structure of the optical signal processing apparatus according to the first embodiment of the present invention; 
     FIG. 10 is a schematic view showing a still further structure of the optical signal processing apparatus according to the first embodiment of the present invention; 
     FIG. 11 is a schematic view showing the structure of the optical signal processing apparatus according to a second embodiment of the present invention; 
     FIG. 12 is a schematic view showing a modification example of the optical signal processing apparatus according to the second embodiment of the present invention; 
     FIG. 13 is a schematic view showing another modification of the optical signal processing apparatus according to the second embodiment of the present invention; 
     FIG. 14 is a schematic view showing the structure of the optical signal processing apparatus according to a third embodiment of the present invention; 
     FIG. 15A is a schematic view showing the arrayed waveguide part of the optical signal processing apparatus according to the third embodiment of the present invention; 
     FIG. 15B is a schematic enlarged view showing the star coupler part of the optical signal processing apparatus shown in FIG. 15A; 
     FIG. 16 is a diagram showing pulse waveform of input light to the optical signal processing apparatus according to a fourth embodiment of the present invention, for explaining the present embodiment; 
     FIG. 17 is a diagram showing pulse waveform of output light to the optical signal processing apparatus according to the fourth embodiment of the present invention, for explaining the present embodiment; 
     FIG. 18 is a diagram showing pulse waveform of output light to the optical signal processing apparatus according to the fourth embodiment of the present invention, for explaining the present embodiment; 
     FIG. 19 is a diagram showing the relationship between treated optical pulse and the number of maximum processable optical pulses when using the apparatus according to the fourth embodiment according to the present invention and the prior art apparatus; 
     FIG. 20 is a schematic view showing the optical signal processing-apparatus according to an embodiment 5 of the present invention; 
     FIG. 21A is a schematic enlarged cross sectional view of a Fresnel lens of the optical signal processing apparatus according to the present invention; 
     FIG. 21B is a schematic plan view showing the structure of the optical signal processing apparatus according to the embodiment 5 of the present invention; 
     FIG. 22 is a diagram showing pulse amplitude of input signal and output signal in the optical signal processing apparatus according to the embodiment 5 of the present invention; 
     FIG. 23 is a diagram showing the relationship between optical spectrum of input optical signal, relative position of phase filter, and optical spectrum of output optical signal in the optical signal processing apparatus according to the embodiment 5 of the present invention; 
     FIG. 24A is a schematic enlarged view of the Fresnel lens part of a modification example of the optical signal processing apparatus according to the embodiment 5 of the present invention; 
     FIG. 24B is a schematic enlarged view of the Fresnel lens part of another modification example of the optical signal processing apparatus according to the embodiment 5 of the present invention; 
     FIG. 24C is a schematic enlarged view of the Fresnel lens part of a still further modification example of the optical signal processing apparatus according to the embodiment 5 of the present. invention; 
     FIG. 24D is a schematic enlarged view of the Fresnel lens part of a yet further modification example of the optical signal processing apparatus according to the embodiment 5 of the present invention; 
     FIG. 24E is a schematic enlarged view of the Fresnel lens part of a yet further modification example of the optical signal processing apparatus according to the embodiment 5 of the present invention; 
     FIG. 25A is a schematic cross sectional view showing spatial filter part comprising liquid crystal of the optical signal processing apparatus according to an embodiment 6 of the present invention; 
     FIG. 25B is a schematic plan view showing a transparent electrode forming the spatial filter of the optical signal processing apparatus according to the embodiment 6 of the present invention; 
     FIG. 26A is a schematic plan view showing the structure in the vicinity of output of a slab waveguide of the optical signal processing apparatus according to an embodiment 7 of the present invention; 
     FIG. 26B is a schematic cross sectional view showing the structure in the vicinity of output of the slab waveguide of the optical signal processing apparatus according to an embodiment 7 of the present invention; 
     FIG. 27 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 8 of the present invention; 
     FIG. 28 is a schematic enlarged cross sectional view in the vicinity of spatial filter provided at a central part of the optical signal processing apparatus according to the embodiment 8 of the present invention; 
     FIG. 29A is a schematic enlarged cross sectional view in the vicinity of spatial filter of a modification example of the optical signal processing apparatus according to the embodiment 8 of the present invention; 
     FIG. 29B is a schematic enlarged cross sectional view in the vicinity of spatial filter of another modification example of the optical signal processing apparatus according to the embodiment 8 of the present invention; 
     FIG. 29C is a schematic enlarged cross sectional view in the vicinity of spatial filter of a still further modification example of the optical signal processing apparatus according to the embodiment 8 of the present invention; 
     FIG. 29D is a schematic enlarged cross sectional view in the vicinity of spatial filter of a yet further modification example of the optical signal processing apparatus according to the embodiment 8 of the present invention; 
     FIG. 30 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 9 of the present invention; 
     FIG. 31 is a schematic enlarged view showing the structure of the optical signal processing apparatus according to the embodiment 9 of the present invention; 
     FIG. 32 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 10 of the present invention; 
     FIG. 33 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 11 of the present invention; 
     FIG. 34 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 12 of the present invention; 
     FIG. 35 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 13 of the present invention; 
     FIG. 36 is a schematic cross sectional view in the vicinity of Fresnel lens of the optical signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 37A is a schematic top view showing spatial filter of the optical signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 37B is a schematic cross sectional view showing spatial filter of the optical signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 38A is a schematic vertical cross sectional view showing Fresnel lens of the optical signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 38B is a schematic top view showing Fresnel lens of the optical-signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 38C is a schematic horizontal cross sectional view showing Fresnel lens of the optical signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 39 is a diagram showing exposure dependence of development depth of PMGI used in spatial filter and Fresnel lens of the optical signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 40 is a schematic cross sectional view showing Fresnel lens formed by etching a quartz substrate using PMGI as a mask in the optical signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 41 is a diagram showing filter characteristic (positive dispersion) of the optical signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 42 is a diagram showing filter characteristic (negative dispersion) of the optical signal processing apparatus according to the embodiment 13 of the present invention; 
     FIG. 43 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 15 of the present invention; 
     FIG. 44 is a block diagram showing a broad sense optical signal processing apparatus in the present invention, according to an embodiment 16; 
     FIG. 45 is a diagram showing a time-waveform of output light amplitude of modulator of the optical signal processing apparatus according to the embodiment 16 of the present invention, and an output waveform after passing through the optical signal processing apparatus as one of subject matter of the present apparatus; 
     FIG. 46 is a diagram showing characteristic of spatial filter (using third and higher order terms) when using the apparatus of the embodiment 13 as the optical signal processing apparatus of subject matter in the embodiment 16 of the present invention; 
     FIG. 47 is a diagram showing characteristic of spatial filter (completely random phase changes) when using the apparatus of the embodiment 13 as the optical signal processing apparatus of subject matter in the embodiment 15 of the present invention; 
     FIG. 48 is a diagram showing characteristic of amplitude filter when using a filter for reducing only the vicinity of the central frequency as the amplitude filter of the reception side optical signal processing apparatus of subject matter in the embodiment 16 of the present invention; 
     FIG. 49A is a diagram showing characteristic of phase filter in the case of reflection-type construction of the optical signal processing apparatus of according to an embodiment 17 of the present invention; 
     FIG. 49B is a diagram showing characteristic of phase filter in the case of reflection type construction of the optical signal processing apparatus of according to the embodiment 17 of the present invention; 
     FIG. 50A is a diagram showing frequency spectrum amplitude of amplitude modulation signal in the embodiment 17 of the present invention; 
     FIG. 50B is a diagram showing frequency spectrum amplitude of angular modulation signal in the embodiment 17 of the present invention; 
     FIG. 51 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 18 of the present invention; 
     FIG. 52 is a diagram showing average optical amplitude distribution on filter plane in the embodiment 18 of the present invention; 
     FIG. 53 is a diagram showing waveforms of modulation signal, phase modulated signal, and demodulated signal after reproduction in the embodiment 18 of the present invention; 
     FIG. 54 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 19 of the present invention; 
     FIG. 55 is a schematic view showing the structure of the optical signal processing apparatus (short pulse light source) according to an embodiment 20 of the present invention; 
     FIG. 56 is a diagram showing the relationship between frequency of incident light to slab waveguide  72  and focusing position x on focal plane of slab waveguide  74  in the optical signal processing apparatus according to an embodiment 20 of the present invention; 
     FIG. 57 is a diagram showing reflection spectrum when spacing of output waveguide  75  is set to 50 μm and core width to 10 μm in the embodiment 20 of the present invention; 
     FIG. 58 is a diagram showing oscillation wavelength spectrum of the optical signal processing apparatus according to the embodiment 20 of the present invention; 
     FIG. 59 is a diagram showing oscillation pulse wavelength of the optical signal processing apparatus according to the embodiment 20 of the present invention; 
     FIG. 60 is a diagram showing an example of oscillation frequency spectrum that can be achieved by the optical signal processing apparatus according to the embodiment 19 of the present invention; 
     FIG. 61 is a schematic enlarged view showing part of the optical signal processing apparatus (short pulse light source) according to an embodiment 21 of the present invention; 
     FIG. 62A is a schematic enlarged view showing part of the optical signal processing apparatus (short pulse light source) according to an embodiment 22 of the present invention; 
     FIG. 62B is a schematic view showing the structure in the vicinity of phase filter used for making dispersion compensation in resonator in the optical signal processing apparatus (short pulse light source) according to the embodiment 22 of the present invention; 
     FIG. 63 is a schematic enlarged view showing part of the optical signal processing apparatus (short pulse light source) according to an embodiment 23 of the present invention; 
     FIG. 64 is aschematic enlarged view showing part of the optical signal processing apparatus (short pulse light source) according to an embodiment 24 of the present invention; 
     FIG. 65 is a schematic view showing the structure of the optical signal processing apparatus (short pulse light source) according to an embodiment 25 of the present invention; 
     FIG. 66 is a schematic enlarged view showing the apparatus shown in FIG. 65; 
     FIG. 67 is a schematic enlarged view showing part of the optical signal processing apparatus (short pulse light source) according to an embodiment 26 of the present invention; 
     FIG. 68A is a schematic enlarged view showing part of the optical signal processing apparatus (short pulse light source) according to an embodiment 27 of the present invention; 
     FIG. 68B is a schematic cross sectional view taken along line A-A′ of FIG. 68A; 
     FIG. 69 is a schematic enlarged view showing part of the optical signal processing apparatus (short pulse light source) according to an embodiment 28 of the present invention; 
     FIG. 70 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 29 of the present invention; 
     FIG. 71A is a schematic plan view showing the structure of high reflection mirror of the optical signal-processing apparatus according to the embodiment 29 of the present invention; 
     FIG. 71B is a schematic cross sectional view showing the structure of high reflection mirror of the optical signal processing apparatus according to the embodiment 29 of the present invention; 
     FIG. 72 is a schematic view showing layout in the vicinity of high reflection mirror of the optical signal processing apparatus according to the embodiment 29 of the present invention; 
     FIG. 73A is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 30 of the present invention; 
     FIG. 73B is a schematic view showing the structure of a modification example of the optical signal processing apparatus according to the embodiment 30 of the present invention; 
     FIG. 73C is a schematic enlarged view showing the structure shown in FIG. 73B; 
     FIG. 73D is a schematic view showing the structure of photo diode array used in the optical signal processing apparatus according to the embodiment 30 of the present invention; and 
     FIG. 74 is a schematic view showing the structure of the optical signal processing apparatus according to an embodiment 31 of the present invention. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Embodiment 1 
     A method and arrangement thereof for processing an optical signal according to a first embodiment of the present invention will be described with reference to FIG.  8 . 
     As shown in FIG. 8, an input optical signal u(t), after being incident to a quartz waveguide  1 , is divided to an arrayed grating  3  of N waveguides by a star coupler  2 . The arrayed waveguide  3  is set so that individual waveguides have an optical length difference of ΔL between an incident surface S 1  and an output surface S 2 . 
     In this case, best-performance spectroscopic characteristics are shown when S 1  is on the circumference about the input end to the star coupler  2  of the quartz waveguide  1 , and S 2  is disposed on the circumference about the center of S 3 . 
     As a result, since adjacent light beam has a phase difference of nΔL (n being a refractive index of waveguide) at the output end from the arrayed waveguide  3  to a slab waveguide  4 , the structure is known to have the same wave division function as a diffraction grating (for example, H. Takahashi et al., IEEE J. Lightwave Tech. Vol. 12 (No. 6), pp. 989-995 (1994); M. K. SMIT Electron. Lett. vol.24, pp.385-386 (1988); C. Dragone et al., IEEE Photon. Technol. Lett., vol. 3, pp.896-899 (1991)). 
     Heretofore, use of such a arrayed waveguide is well known as an optical wavelength demultiplexer in wavelength division multiplexing optical transmission systems. 
     The inventors have found that when a time series optical signal is applied to the arrayed waveguide  3 , time-frequency spectrum of the optical signal can be formed as a spatial image even without using a lens. Further, the inventors have found a high-resolution arrayed waveguide designing method and devised applications thereof in optical signal processing based on this principle. 
     That is, when an arrayed waveguide is used, Fourier transformation U(n) of the incident optical signal can be focused on a focal plane S 3  of the slab waveguide  4 . 
     It has been found that when a m′th order diffraction light is used, the frequency resolution is proportional to Nm. Wherein N is the number of waveguides of the arrayed waveguide  3 . Therefore, when m is increased, an increased resolution can be obtained as compared with an ordinary diffraction grating in which the frequency resolution is proportional to N. When optimally designed according to the guideline, a waveguide array with a very high optical resolution can be obtained, thereby enabling spectral division of a high-speed long optical pulse sequence. 
     When a reflective spatial filter  5  is disposed on the focal plane S 3  of the above-described high resolution arrayed waveguide, an optical pattern of U(v)H(v) is reflected, returned through the star coupler  2 , and output from the quartz waveguide  1 , wherein H(v) is a spatial pattern of the spatial filter  5 . 
     The output optical signal is u(t)*h(t), wherein * indicates a convolution of two signals. 
     Specifically, by disposing the optional spatial filter  5 , processing can be made in the frequency region of the incident signal light. Input/output between the external and the quartz waveguide  1  is made, for example, by using an optical fiber with a coupler. 
     Since, in the configuration shown in FIG. 8, the focal plane S 3  is on the circumference about the center of S 2 , when the spatial filter  5  is flat, generally a distortion occurs in the output waveform. When the phase is quadratically changed with respect to the central frequency, the distortion is approximated, this configuration is approximately has a quadratic dispersion characteristics. To compensate this, the input light or output light may be passed through a dispersion medium having the same magnitude and reverse sign. Or, the spatial filter  5  may be designed to include the dispersion compensation. 
     As a practical application example of this method, a case is considered in which the optical signal u(t) is passed through an apparatus, for example, a long distance optical fiber transmission line, and subjected to a distortion such as f(t)=u(t)*h(t). 
     To reshape the distorted signal f(t) back to the original signal u(t), an optical signal processing apparatus as shown in FIG. 9 can be used. A reflective type structure is shown in FIG. 8 showing the principle of optical signal processing, whereas the apparatus shown in FIG. 9 is a transmission type. 
     As shown in FIG. 9, the optical signal f(t) having a certain distortion is applied to a quartz optical circuit  8  from an optical fiber  7  through an optical connector  6 . 
     The quartz optical circuit  8 , as shown in FIG. 10, comprises waveguides  9  and  13 , star couplers  10  and  14 , arrayed waveguides  11  and  15  and slab waveguides  12  and  16 , which are symmetrically disposed to a spatial filter  17 . 
     The arrayed waveguides  11  and  15  are as necessary provided halfway with half wave plates  18  and  18  to eliminate polarization dependence. 
     The input signal light, after transmitting in the waveguide  9 , is incident to the arrayed waveguide  11  by the star coupler  10 , and focuses Fourier transformation F(v)=U(v)H(v) on the focal plane S 3  in the slab waveguide  12 . 
     Here, one which has the following pattern is disposed as the spatial filter  17  on the focal plane, U(v) is given by the product with the signal. 
     
       
         H*( v )/|H( v )| 2   
       
     
     When it is passed through the slab waveguide  16 , the arrayed waveguide  15 , and the star coupler  14 , the signal is inverse Fourier transformed, and the restored optical signal u(t) can be taken out from the waveguide  13 . When amplitude damping is large, the signal is output to the outside by the optical connector  6  through an optical amplifier  19 . 
     Here, the spatial filter  17  may be a fixed or rewritable pattern. In the case of a fixed pattern, one which is formed with a pattern of a predetermined phase or transmittance formed by deposition or the like on a substrate such as a glass substrate may be disposed. For a rewritable pattern, an optical modulator comprising a liquid crystal or semiconductor is used as a spatial filter, phase or transmittance of each pixel on the optical modulator is controlled by a voltage output from a spatial filter controller  20 . 
     In effect, using the optical circuit of the structure of FIG. 10, it has been confirmed that shaping is possible of distortion of optical pulse sequence of 1500 nm in wavelength comprising 100 pulses of a single pulse width of 0.2 ps and a period of 0.5 ps, by a spatial filter of fixed pattern formed on a glass substrate. 
     Embodiment 2 
     A method and arrangement thereof for generating an optical pulse according to a second embodiment of the present invention will be described with reference to FIG.  11 . 
     In the present embodiment, a reflective type computer generated hologram (CGH)  21  is disposed on the focal plane S 3 . In this computer generated hologram  21 , for example, Fourier transformation U(t) of an optical pulse sequence u(t) is written as a spatial frequency pattern. 
     Therefore, when read light is applied to a slab waveguide  23  from an optical waveguide  22 , the optical pattern U(v) reflected from the hologram is transmitted in the order of the slab waveguide  23 , a arrayed waveguide  24 , and a star coupler  25 , Fourier transformed by the principle described in Embodiment 1, and the optical pulse sequence u(t) is output from a waveguide  26 . 
     In the present embodiment, only by applying an optical pulse as a read light, a desired optical pulse sequence written in the computer generated hologram can be generated. 
     As a modification of the present embodiment, for example, as shown in FIG. 12, read light may be applied to a arrayed waveguide  43  through a waveguide  41  and a star coupler  42 , and applied to the computer generated hologram  21  as a Fourier transformed image. However, the read light may be a short optical pulse. 
     Further, as another modification of the present embodiment, for example, as shown in FIG. 13, a transmission type computer generated hologram  31  can be used. That is, when read light is applied to a slab waveguide  34  from a arrayed waveguide  32  and a waveguide  33  at the opposite side, the optical pattern u(v) passed through the hologram is transmitted in the order of a slab waveguide  35 , a arrayed waveguide  32 , and a star coupler  36 , inverse Fourier transformed as described above, and the optical pulse sequence u(v) is output from an optical waveguide  37 . 
     In effect, using an optical circuit of the structure of FIG. 11, generation of an optical pulse sequence has been confirmed which comprises 100 pulses of a single pulse width of 0.2 ps and a period of 0.5 ps. 
     Embodiment 3 
     A method and arrangement thereof for temporarily storing an optical pulse according to a third embodiment of the present invention will be described with reference to FIG.  14 . In the present embodiment, a photosensitive optical recording medium  51  is disposed on the focal plane S 3 . 
     As shown in FIG. 14, the input optical signal u(t) is introduced into the apparatus from the external by an optical connector  52 , and amplified by an optical amplifier  53 . Then, the signal is divided by an optical coupler  54  into signal light and reference light, and the signal light is applied, as is, to a quartz optical circuit  55 . 
     In the quartz optical circuit  55 , as shown in FIG. 15, the signal light, after being applied to a waveguide  56 , is divided into a arrayed waveguide  58  by a star coupler  57 . 
     Light output from each arrayed waveguide  58  is transmitted in a slab waveguide  59 , spatially focuses Fourier transformation U(v) of the input optical signal on the focal plane S 3 . 
     On the other hand, the reference light divided from the signal light is divided by the optical coupler  54 , after passing through an optical modulator  60 , is applied to the quartz optical circuit  55 , as shown in FIG. 15, passing through a reference waveguide  61 , and then applied to the slab waveguide  59 . 
     FIG. 15B shows an enlarged view of the star coupler  57  in FIG.  15 A. In this case, the input waveguide end of the arrayed waveguide is disposed on a circumference, on one of a circumference about the input end from the reference waveguide  61  to the star coupler  57 , and a circumference about the input end from the waveguide  56  to the star coupler  57 . Normally, the number of waveguides disposed on each circumference is set nearly equal to each other. 
     As a result, by interference of the reference light with the signal light, U(v) is recorded as a hologram on the optical recording medium  51 . 
     After that, when light of the same wavelength as the reference light is applied as a read light from a waveguide W 2 , U(v) recorded on the hologram is read, inverse Fourier transformed during transmitting in the order of the slab waveguide  59 , the arrayed waveguide  58 , and the star coupler  57 , and the optical pulse sequence u(t) is output from the waveguide  56 . 
     In this case, the optical modulator  60  serves to cut an optical pulse for reference light or read light from part of the signal light. 
     Thus, the optical pulse sequence is stored by the above described principle. 
     While the present embodiment shows a reflective type arrangement, it is also possible to use a construction using a transmissive type hologram in which the read waveguide is disposed at the opposite side of the hologram. Further, as in FIG. 12, an arrangement is also possible in which the reference light and the read light are applied through a arrayed waveguide. 
     The optical recording medium  51  can be, for example, a photo refractive device of a semiconductor multiple quantum well structure or a photosensitive film. 
     Still further, it is also possible to provide a plurality of reference light waveguides, so that a number of optical pulse sequence patterns are recorded on the hologram according to the individual reference light. 
     Yet further, when an optical sensor array is disposed in place of the hologram medium on the focal plane and only the signal light is introduced without introducing the reference light, power spectrum of the signal light can be adjusted. 
     Embodiment 4 
     Using the arrangement of FIG. 8, the number N of the arrayed waveguides is set to 340, and the order m of diffraction is set to 59. Input light is the output of a Cr/YAG laser which is band limited by a wavelength filter to produce a pulse with a central wavelength of 1549 nm, a spectral width of 2.3 nm, and a pulse width of 1.1 ps. 
     A pulse waveform of the input light when optical signal generation is made with the above arrangement is shown in FIG.  16 . An output waveform when processed by providing reflective type amplitude filters for pulse generation on the focal plane is shown in FIGS. 17 and 18. It has been confirmed from FIGS. 17 and 18 that the optical signal processing apparatus and the optical signal processing method according to the present invention function as designed. 
     The relationship between the treated pulse width and the maximum number of processable pulses, when using a arrayed waveguide and when using a prior art diffraction grating, is shown in FIG.  19 . 
     A first effect of the present invention is that the signal processing capacity (processable pulse sequence length) is high. As can be seen from FIG. 18, the arrangement according to the present invention is long in processable pulse sequence length as compared with the prior art arrangement, and design according to the pulse width of optical pulse to be processed by changing the diffraction order (m). Using numerical formulae, maximum processable pulse sequence length (T 0 ) and minimum pulse width (τ) are as follows. 
     T 0 ≅mN/2v 0  (however, in the prior art, m=1, vo: central frequency, N: number of waveguides, in the prior art τ is the number of diffraction gratings irradiated with optical beam) 
     τ≅(2fλ 0 /v 0 Hd)α (prior art, d: groove spacing of diffraction grating, λ 0 : central wavelength, f: lens focal length, H: filter size, α: constant (normally 0.3-0.4, depending on pulse waveform) 
     τ≅(m/2v 0 )α (present invention) 
     When making dispersion compensation and the like using the present invention, processing capacity is proportional to the processable pulse sequence length. That is, the circuit of the present invention has about 10 times the capacity of the prior art. 
     A second effect of the present invention is that the apparatus can be made compact in structure. In the prior art, as can be seen from FIG. 1, the total length is  4   f . However, with the assumption of small distortion of the lens, at least f=10 cm and a diameter of 10 cm are required to obtain the performance of FIG. 18, and the total length is about 60-70 cm and the width/height is about 30 cm. When the optical fiber input/output optical system is included, the apparatus is very large in dimensions, which is impossible to be equipped on an optical communication apparatus. However, in the present invention, the optical circuit can be bent and disposed, and since the waveguide material is higher in refractive index than the air, the apparatus can be constructed smaller in size, an apparatus having the performance of FIG. 19 can be fabricated with a quartz substrate of about 10 cm square. With a semiconductor waveguide, the size is about 5 cm square. 
     A third effect is that integration with other optical circuits is possible. For example, an optical amplifier is incorporated, thereby achieving optical signal processing with reduced loss. 
     An effect when the present invention is applied to picosecond pulse generation means is that a pulse sequence close to the transform limit can be easily generated by dispersion compensation in the resonator, and that the pulse shape can be designed by control over individual modes. 
     An effect when the present invention is applied to a dispersion compensation circuit is that high-order dispersion compensation, variable dispersion compensation, and wide band compensation are possible. To an optical pulse of 2 ps in pulse width, compensation of up to about 100 ps/nm is possible. Further, it is possible to dispose a kinoform (Fresnel lens) between the slab waveguide and filter/mirror to achieve waveform shaping without distortion. 
     An effect when the present invention is applied to a transmission apparatus is that dispersion compensation following a change in the dispersion of the transmission line is possible, system construction is possible with reduced transmission waveform degradation due to self-phase modulation, and that an amplitude modulation—angular modulation conversion circuit can be easily constructed. 
     Embodiment 5 
     FIG. 20 shows an embodiment 5 according to the present invention. In the apparatus of the present embodiment, a first slab waveguide  105  for distributing output of an optical waveguide  104 , an arrayed waveguide  106  formed of a plurality of optical waveguides gradually increasing in waveguide length for generating phase difference by differing the optical length of distributed light of the slab waveguide  105 , and a second slab waveguide  107  having a circular end surface and a lens function are integrated on a quartz substrate  101 . In the Figure,  200  is an arrayed waveguide grating. 
     At the optical input side to the quartz substrate  101 , signal light is input through an optical fiber  103 , an optical circulator  102  for taking out return reflected light is disposed in the course of the optical fiber  103 . In this case, an optical fiber coupler has the same function and can be used, however, it has an extra loss of at least 6 dB. 
     On the other hand, at the optical output side of the quartz substrate  101 , a phase spatial modulation device represented by a Fresnel lens  108  or kinoform, a spatial filter  109 , and a mirror  110  as reflection means are present. 
     FIG. 21 is a schematic enlarged view showing the Fresnel lens  108  as a phase spatial modulation device, the spatial filter  109 , and the like disposed on the quartz substrate  101 , as shown in FIG. 21A, the Fresnel lens (kinoform)  108 , a holding substrate  113 , the spatial filter  109 , and the mirror  110  are provided to be disposed between quartz substrates  111  a low reflection filer  112  is stuck on the surface of the Fresnel lens (kinoform)  108  and the surface of the spatial filter  109 . In this case, the side-surface shape of the Fresnel lens (kinoform)  108  is, as shown in FIG. 21B, is formed so that the contour part is elliptical, and curvature in the minor diameter direction is equal to the focal length of the slab waveguide  107 , which can be fabricated by etching a material which is transparent in the operation wavelength region. The structure and production method of the Fresnel lens will be described in detail in a later embodiment. 
     Although greater in film thickness than a Fresnel lens, it may be fabricated by etching a spheric or an aspheric lens or the like, and used in place of the Fresnel lens  108 . The fabrication method is similar to the Fresnel lens. 
     The function of the structure shown in FIGS. 20 and 21 is substantially equivalent to the function of the prior art structure shown in FIG. 1, as to the large size which is a problem in the prior art, for example, in an example of repetition signal (FIG. 22 upper part) of a pulse interval 50 ps and a pulse with 2 ps, an optical system of a beam diameter of, for example, at least 15 mm is required, an apparatus of about 50×100 cm in size is required considering the effective diameter of the lens. On the other hand, in the present embodiment, an optical length difference of a maximum of about 10 mm may be provided in the quartz waveguide, which can be integrated on a substrate of about 5×5 cm, thus there is a big difference in size. 
     The first slab waveguide  105 , the arrayed waveguide  106 , and the second slab waveguide  107  are integrated on the quartz substrate, of which the arrayed waveguide  106  differs in waveguide length by ΔL between adjacent individual waveguides to have a optical path difference of nΔL, wherein n is a refractive index of the waveguide. That is, the arrayed waveguide  106  has a wave division function same as a diffraction grating. 
     Output end of the arrayed waveguide is formed in a circumferential form of a radius f and connected to the second slab waveguide  107 , the second slab waveguide  107  functions as a lens of a focal length f. That is, in the case of a lens, whereas it has a Fourier transformation function of image between focal planes of both ends of the lens in the vicinity of the optical axis, the second slab waveguide  107  also has a single dimensional Fourier transformation function of output image of the arrayed waveguide  106 . Since the focus of the second slab waveguide is positioned on the circumferential surface on the optical axis of the second slab waveguide  107 , the Fresnel lens (kinoform)  108  is provided at the output side to make the focal plane flat. The focal length in the waveguide surface of the Fresnel lens (kinoform)  108  is set equal to the above described f. The arrangement of the spatial filter  109  for modulating through the low reflection coating  112  and the mirror for reflection is as shown in FIG. 21A, however, the Fresnel lens (kinoform)  108  and the spatial filter (in the case of a phase filter) can be fabricated by etching a material which is transparent to the operating wavelength, or can be fabricated in a desired shape by adjusting exposure to the photosensitive material by direct depicting of electron beam, since the developed thickness is determined in inverse proportion to the exposure. Further, it is also possible to fabricate the Fresnel lens  108  and the spatial filter  109  by etching the substrate using the photosensitive material as a mask to process the substrate form. Still further, in the case of an amplitude filter, the light absorption film can be etched into strips with controlled line—space ratio. As to whether a phase filter or an amplitude filter is selected, the former has a problem of difficult in design, the latter has a problem of high loss, it may be selected according to the purpose, or both are provided. 
     FIG. 22 shows an input pulse waveform of a repetition signal of a pulse interval 50 ps and a pulse width 2 ps. The input signal light is passed through the circulator shown in FIG. 20, applied to the optical waveguide  104 , and distributed to individual waveguides of the arrayed waveguide  106  by the first slab waveguide  105 . Then, the signal light is divided by the arrayed waveguide  106  according to the optical length difference, Fourier transformed by the second slab waveguide  107 , phase modulated by the spatial filter (in this case, tentatively a phase filter)  109  through the Fresnel lens (kinoform)  108 , returned by reflection of the mirror  110 , inverse Fourier transformed, and taken out as an output light from the optical circulator  102 . FIG. 22 lower part shows the-output light waveform, which has 5 times pulse repetitions. 
     In this case, the spatial filter has a positional dependence of relative phase as shown in FIG. 23 middle part. 
     Where t 1  is a pulse width of processed optical pulse, and v 0  is a central frequency, the amplitude vibrates n times in the pulse. 
     
       
           n =v 0    t   1   
       
     
     In this case, when a phase variation d satisfies the following formula, 
     
       
           n≧d/ 2π 
       
     
     the phase variation may be approximated as 
     d′≡Mod[d, 2π] (wherein [u, v] indicates a remainder using v as a modulus.). 
     That is, in a reflective arrangement, since light passes two times through the phase filter, the filter can be fabricated with a maximum phase change of π. Further, for the case of a transmission type, the phase variation may be approximated as d″≡Mod[d, 2π], and the filter can be fabricated with a maximum phase change of 2π. 
     Of course, although increasing in film thickness, it is needless to say that a phase filter for obtaining a necessary phase variation may be used. 
     FIG. 23 upper part shows a frequency spectrum of incident signal, and FIG. 23 lower part shows a frequency spectrum of signal light after passing through the spatial filter  109 . FIG. 23 lower part is only phase modulation, and has no spectral change. 
     Thus, a time series waveform can be modulated. 
     When representing the modulation by numerical formulae, incident signal light is u(t), transmission function of filter (forward and reverse) is h(x), t is time, x is a structural position on the filter. Frequency spectral image is represented as U(V(x)) using Fourier transformation U of u. Wherein, V shows a frequency relating to the repetition structure of the filter. 
     Spectrum after passing through the filter is S(V(x))=U(V(x))·h(x). Waveform of the output light is inverse Fourier transformed to s(t)=u(t)*H(t). Wherein * indicates convolution integration. 
     As shown in FIG. 22, the repetition frequency of pulse is increased 5 times, constituted by repetitions of the same pattern in the phase filter. Where pattern is g(x), and repetition period is V 1 (x 1 ), the repetition period of the pulse is 1/V 1 (x 1 ). 
     Further, in general, pulse amplitude in the period differs. To align the pulse amplitude, each pattern may be binary phase according to M series, for example, repetition period may be divided into 15 parts (π, 0, 0, 0, π, 0, 0, π, π, 0, π, 0, π, π, π). 
     Where a desired waveform is s(t), and Fourier transformation thereof is S(V(x)), a desired waveform can be obtained with a filter having a transmission function represented by h(x)=S(V (x))/U(V(x)). 
     FIG. 24 shows a modification in structure (Embodiment 5) of FIG.  20  and FIG. 21, FIG. 24A shows an example provided with both a phase filter  109   a  and an amplitude filter  109   b  for the spatial filter  109 , the optical signal processing range is expanded by controlling both filters, rather than controlling one of the two filters, phase and amplitude. 
     FIG. 24B shows an example which is the same in function as FIG. 21, but the Fresnel lens (kinoform)  108  is mounted on the upper surface of the filter, which is simple in fabrication. However, the focal length of the Fresnel lens (kinoform)  108  must be f/ns wherein ns is a refractive index of the slab waveguide  107 . 
     FIG. 24C shows an example in which a pattern mirror  114  serving as both the mirror  110  shown in FIG.  21  and the amplitude filter  109 , which is simple in fabrication. 
     FIG. 24D shows an example which, in place of the slab waveguide  107  and the Fresnel lens (kinoform)  108 , is provided with a lens  115  only in this part, which has slightly larger in size but high precision Fourier transformation is possible. 
     Further, FIG. 24E shows an example provided with a phase filter  116  which serves as both the Fresnel lens  108  and the spatial filter (phase filter)  109 . This construction is difficult in design but simple in fabrication. 
     While Embodiment 5 is described assuming the use of quartz waveguides, it is needless to say that the same optical circuit can be fabricated with semiconductor waveguides such as InP, GaAs, or Si, or dielectric material optical waveguide such as LiNbO 3 , or organic material optical waveguides such as polyimide. In particular, semiconductor optical waveguides are possible to construct even further compact apparatus due to their high refractive index, and an optical amplifier can be incorporated in the optical circuit. 
     Embodiment 6 
     FIG. 25A shows an example in which the spatial filter shown in FIG. 21 is made from a liquid crystal,  301   a  and  301   b  are transparent electrodes,  302  is an alignment film,  303  is a spacer,  304  is a nematic liquid crystal, and  305  is a quarter-wave plate. The quarter-wave plate is necessary for eliminating polarization dependence when using a polarization-dependent spatial filter, and f axis and s axis of the quarter-wave plate are disposed with a 45-degree inclination to the waveguide facet (A-A′ line in FIG.  25 A). Orientation of the liquid crystal is homogeneous orientation parallel or perpendicular to the waveguide facet (A-A′ line in FIG.  25 A). 
     FIG. 25B shows the structure of the transparent electrode  301   a , which has strip-formed electrodes and the individual electrode can be applied with an optional voltage. By applying a voltage, orientation of crystal is changed, phase difference is changed between the transparent electrodes  301   a  and  301   b , since the electrodes are provided in strips, a desired spatial phase filter can be achieved. That is, in this example, it is possible to make optical signal processing as necessary by adjusting the phase filter. Further, a twist nematic liquid crystal may be used as the liquid crystal. In this case, the quarter-wave plate is unnecessary. When the applied voltage is sufficiently high, this arrangement functions as a polarization independent phase modulator. 
     Embodiment 7 
     FIG. 26 shows an embodiment 7 of the present invention, in which the optical path is bent to form an even smaller sized apparatus. In FIG. 26,  401  is a core of optical waveguide,  402  is a mirror,  403  is a groove on a slanted (7-8 degrees) end surface. In the present embodiment, an optical bend unit is formed of the groove  403  for bending light and the mirror  402  so that the focal plane of the slab waveguide  107  is on the mirror  110 . In the present embodiment, since the filter can be disposed on the quartz substrate, an even smaller sized apparatus can be constructed. The groove can be easily formed using a reactive on etching apparatus. 
     Embodiment 8 
     FIG. 27 shows a transmission type structure, in which a first quartz substrate  101 A having the first arrayed waveguide  106  and a second quartz substrate  101 B having a second arrayed waveguide  505  are disposed on a heat sink  501 . The two quartz substrates  101 A and  101 B are symmetrical in structure. That is, the quartz substrate  101 A is integrated thereon with a first slab waveguide  105  for wave division, a first arrayed waveguide  106 , and a second slab waveguide  107  for focusing, the second quartz substrate is also integrated thereon with a first slab waveguide  504 , a second arrayed waveguide  505 , and a second slab waveguide  506  for wave synthesis. A spatial filter and the like are disposed between the quartz substrates  101 A and  101 B.  502  denotes an optical amplifier. 
     An arrayed waveguide grating  200 A is formed on the quartz substrate  101 A on the heat sink  501 , and similarly a second arrayed waveguide grating  200 B is formed on the quartz substrate  101 B on the heat sire;  501 , disposed symmetrically about tale spatial filter. The first arrayed waveguide grating  200 A comprises an optical waveguide  104 , a first slab waveguide  105 , and arrayed waveguide  106 , and a second slab waveguide  107 . The other second arrayed waveguide grating  200 B similarly comprise a first slab waveguide  504 , an arrayed waveguide  505 , a second slab waveguide  506 , and an optical waveguide  507 . 
     FIG. 28 is an enlarged view, the spatial filter is one which is similar to that of FIG. 25, but since it is a transmission type, it is required to obtain at least a phase difference (2π). Further, the mirror  110  and the quarter-wave plate  305  of FIG. 25 are unnecessary and omitted. Since this construction has a polarization dependence, when eliminating the dependence, two stages of filters may be connected perpendicularly. The transmission type construction of the present embodiment is equivalent in operation to the construction shown in FIG.  20 . While the apparatus becomes large, the circulator  102  of FIG. 20 is unnecessary and the loss can be reduced.  503  in FIG. 27 denotes a filter control unit. 
     FIG. 29 shows a modification of the embodiment 8 shown in FIGS. 27 and 28, FIG. 27A is an example using a fixed spatial filter, FIG. 29B is an example using the Fresnel lens (kinoform)  108  formed on the substrate, FIG. 29C is an example using a phase filter  116  which serves as both Fresnel lens (kinoform) and phase filter, and FIG. 29D is an example using a lens  115  in place of the first slab waveguides  107  and  504 . In this case, since the spatial filter is transmission type, at least a phase difference of 2π can be obtained. 
     Embodiment 9 
     FIG. 30 shows another example of transmission type, in which phase adjustment is achieved by heating. That is,  601  is an arrayed waveguide,  602  is a heating electrode,  603  is a wiring, and  604  is a control unit. FIG. 31 shows an enlarged view of the arrayed waveguide. Here,  605  is a groove provided in the waveguide,  606  is a taper structure for reducing connection loss, and  607  is a half-wave plate. The groove  605 , the taper  606 , and the half-wave plate are a structure for reducing polarization dependence of she waveguide, which can also be used in other arrayed waveguide as necessary. Since, in general, refractive index of a material has a temperature dependence, optical length of waveguide, that is, the phase, can be modulated by heating. In this case, the phase of each waveguide of the arrayed waveguide  601  can be adjusted by adjusting the current in the electrode  602 . That is, when it is disposed so that input end of the arrayed waveguide  601  is Fourier transformation plane by the slab waveguide  107 , the arrayed waveguide  601 , the heating electrode  602 , the groove  605 , the taper  606 , and the half-wave plate  607  function as a variable phase filter. To facilitate phase control, fabrication is made so that the phase difference between individual waveguides of the arrayed waveguide  601  is an integer multiple of 2π. Also in the present embodiment, same as in the case of FIG. 25, optional phase variation and flexible optical signal are achieved. 
     Further, as indicated by the virtual line in FIG. 31, a construction is possible in which the spatial filter and the half-wave plate are disposed at the center to be connected to the phase adjustment arrayed waveguide end. 
     Embodiment 10 
     FIG. 32 shows an example for hologram recording, in which  701  is a reference light input waveguide,  702  is a slab waveguide as distribution means,  703  is a second arrayed waveguide, and  704  is an optical recording medium. For  704 , a photo refractive crystal such as semiconductor MQW or barium titanate, a thermoplastic can be used. In this case, optical system  104 - 106  of the signal light is the same in construction as optical system  701 - 703  of the reference light. When a signal light is input into the circulator  102  and a coherent short pulse reference light into the optical waveguide  701 , the signal light and reference light are Fourier transformed and undergo interference on the medium  704 , and hologram recorded. After the recording, when a coherent short pulse reference light is input again, phase conjugate light of signal light is output from the circulator  102 . That is, the present embodiment has a function of recording high speed optical signal and generating phase conjugate light. 
     Embodiment 11 
     FIG. 33 is another example of hologram recording, showing a transmission type. In the Figure,  801  is a slab waveguide as second focusing means,  802  is an arrayed waveguide,  803  is a slab waveguide as wave synthesis means, and  804  is an optical waveguide. As in the example of FIG. 32, when signal light is input into the first waveguide  104  and reference light into the waveguide  701 , optical signal is hologram recorded on the waveguide  704 . After the recording, when coherent short pulse reference light is input again, signal light is reproduced from the waveguide  804 . When another signal light is input in place of the reference light, a correlated signal between the two signal light can be output. 
     Embodiment 12 
     FIG. 34 shows a waveform observation example of a very high speed optical signal, in which  901  is a CW light source of monochromatic light,  902  is an optical waveguide,  903  is a slab waveguide, and  904  is an optical receiver array. When signal light is input into the waveguide  104  and reference light into the waveguide  701 , diffraction is made by hologram on the medium  704 . When the diffracted light is focused on the array  904 , temporal waveform is formed as a spatial optical amplitude distribution. By conversion into electrical signal by the array  904 , and by conversion to time series signal by a parallel—serial conversion circuit  905 , a very high speed optical signal can be observed. An optical filter  906  is to set the wavelength of the CW light source to a wavelength different from signal light and control light to block input of signal light and reference light into the array  904 . 
     In the description of the above drawings, similar reference numerals indicate similar parts. 
     The slab waveguides  107  and  504  and the like as focusing means are to make the focal plane flat in combination with the Fresnel lens (kinoform), generally a large distortion occurs unless optical signal processing in frequency space is made on the focal plane, but the Fresnel lens and the like can be eliminated depending on the curvature of the focal plane. 
     Further, as described above, the spatial filter of phase filter or amplitude filter or both may be provided. 
     Still further, it is described that in the example of FIG. 20, the focal length of the Fresnel lens (kinoform) is equal to the focal length of the slab waveguide of the coupling means, however, it is not necessarily equal to each other, but can be determined according to whether dispersion is generated or dispersion compensation is made. 
     Yet further, the vertical direction bending means shown in FIG. 26B can be applied, for example, in FIG. 32, in this case, the spatial filter  109  and the mirror  110  shown in FIG. 26B are replaced with an optical recording medium. 
     As can be seen from the above examples, embodiments of the individual figures can be applied to each other as necessary. 
     Embodiment 13 
     An embodiment 13 of the present invention is shown in FIG.  35 . The embodiment 13 is similar in basic structure to the apparatus of the embodiment 4, but differs in that an optical amplifier  120 , an optical filter  121 , and an optical amplifier  122  are provided at the light source side. 
     A detailed construction in the vicinity of the Fresnel lens is shown in FIG.  36 . In FIG. 36, the reference numeral  111  indicates a quartz substrate,  112  is a low reflection coating film, and  113  is a holding substrate. 
     The Fresnel lens  108  can be fabricated by etching a material which is transparent in the operating wavelength region. Contour of the Fresnel lens is elliptical. The curvature of the Fresnel lens  108  in the minor axis direction is set to have a focal length of optical length of the lens surface and the end surface of the slab waveguide  107 . The curvature in the major axis direction of the Fresnel lens  108  is set equal to the focal length of the slab waveguide  107 . 
     Signal light input into the optical fiber  103  is amplified by the optical amplifier  120 , after removing unnecessary ASE light by the optical filter, passed through the circulator  121 , and input into the optical waveguide  104 . Then, the signal light is distributed by the first slab waveguide  105  to individual waveguides of the arrayed waveguide  106 . The adjacent individual waveguides of the arrayed waveguide  106  differ in waveguide length by ΔL. Therefore, wherein n is a refractive index of the waveguide, adjacent waveguides have a phase difference of nΔL. That is, the arrayed waveguide  106  has a wave division function same as a diffraction grating. 
     Therefore, the arrayed waveguide grating  200  comprising the first slab waveguide  105 , the arrayed waveguide  106  and the second slab waveguide  107  has heretofore been used as a wavelength demultiplexer in a wavelength division multiplexing transmission apparatus. 
     Output end of the arrayed waveguide  106  is connected to the second slab waveguide  107 , and disposed on a circle of a radius f. That is, the second slab waveguide  107  functions as a lens having a focal length of f. 
     Focal plane of the second slab waveguide  107  is located on a circle with the center at the output end of the arrayed waveguide  106  on the optical axis of the second slab waveguide  107 . 
     Optical signal processing in frequency space according to the present invention generally produces a large distortion unless carried out on the focal plane. Therefore, the Fresnel lens  108  is disposed at the output side of the slab waveguide  107 . The focal plane is converted to a flat plane by the Fresnel lens  108 . Focal length in the waveguide surface of the Fresnel lens  108  is set equal to f. 
     Input light is passed through the spatial filter  109 , reflected by the mirror  110 , and again passed through the spatial filter  109 . 
     FIGS. 37 and 38 show details of the spatial filter  109  and the Fresnel lens  108 . In this case, the spatial filter  109  and the Fresnel lens can be fabricated by the same process. Thickness of the spatial filter  109  is equal to λ 0 /(2n L ) because a maximum of phase difference 2π is necessary in the forward and reverse directions in a reflection type, wherein λ 0  is a tube center wavelength of the signal, and n L  is a refractive index of the material of the spatial filter  109 . 
     Further, since, in the Fresnel lens, light is output from the lens into the air, the lens thickness is designed to have a focal length equal to the second slab waveguide  107  in order to convert the focal plane of the second slab waveguide  107  into a flat plane. 
     Still further, the curvature in the direction (y) perpendicular to the waveguide substrate is set so that focal length in the quartz substrate  111  is equal to the thickness of the quartz substrate  11 , in order to convert output light from the lens into parallel light. Where curvatures in x direction and y direction are Rx and Ry, elliptical ring of the Fresnel lens  108  is shown by the following formula (1). 
     m 1, 2, . . . (integer) corresponds to discontinuity of the curved surface.                      R   y       R   x                       x   m   2       +     y   m   2       =     2      m                     λ   o       n   L                       R   y               (   1   )                                
     Further, the curvature R and the focal length f are converted by the following formula (2). 
     
       
         R=(n L −1)f  (2) 
       
     
     The spatial filter  109  and the Fresnel lens  108  can be fabricated, for example, by exposing PMGI (PolyMethiGlutarImide) by means of an electron beam exposure apparatus, followed by developing. 
     FIG. 39 shows a graph of exposure dependence of developing depth of PMGI. 
     Further, fabrication is also possible using PMGI as a mask by etching the quartz substrate  111 . This is shown in FIG.  40 . 
     It is needless to say that a replica may be made based on the quartz substrate  111 . 
     For representing by mathematical formulae, incident signal light is assumed as u(t), and a transmission function (forward and reverse) of the spatial filter  109  as h(x). 
     Wherein, f is time, and x is a position on the spatial filter  109 . 
     The signal light u(t) is divided by the arrayed waveguide  106 , and focused at a different position x on the spatial filter  109 . The divided frequency spectral image is represented as U(ω(x)) using Fourier transformation U of u. Spectrum after passing of the spatial filter  109  where the central frequency of the signal corresponds to x=0 is shown as the following formula (3) 
     
       
           U (ω( x ))·( x )  (3) 
       
     
     The reflected light is again passed through the arrayed waveguide  106  and inverse Fourier transformed. 
     When light passes through a medium having a group velocity dispersion, input/output relation in the frequency space is shown by the following formulae (4) and (5). 
     
       
           U   out (ω)= U   in (ω)·Exp( i φ(ω))  (4) 
       
     
     
       
         
           
             
               
                 
                   
                     φ 
                      
                     
                       ( 
                       ω 
                       ) 
                     
                   
                   ≅ 
                   
                     
                       φ 
                       o 
                     
                     + 
                     
                       
                         φ 
                         1 
                       
                        
                       
                         ( 
                         
                           ω 
                           - 
                           
                             ω 
                             0 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         
                           
                             φ 
                             2 
                           
                            
                           
                             ( 
                             
                               ω 
                               - 
                               
                                 ω 
                                 o 
                               
                             
                             ) 
                           
                         
                         2 
                       
                       2 
                     
                     + 
                     ⋯ 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     wherein ω is an angular frequency, ωo is a central angular frequency, the first term of the phase term shows an absolute phase, the second term is a position on the time base, and the third term and after indicate a high order dispersion effect. Pulse broadening is generated mainly by the effect of the third term. 
     However, since, when a phase filter shown by the following formula (6) is provided, and passed through the phase filter after Fourier transformation by the optical circuit of the present embodiment, the third term can be canceled from the formula (3), waveform degradation due to group velocity dispersion can be equalized.                h        (     ω        (   x   )       )       =     Exp                   (       -                            φ   2            {     ω        (   x   )       }     2       2       )               (   6   )                                
     The phase filter, as shown in FIG. 40, can be fabricated by etching a material which is transparent in the operation wavelength region. Since fabrication of a filter of a large phase difference is difficult, in the construction of reflection type, the filter may be fabricated by folding with a phase difference π. In the case of reflection type, since light is passed two times, the characteristic formula of the dispersion compensation filter is shown by the following formula (6′).                h        (     ω        (   x   )       )       =     Exp                   (       -                            φ   2            {     ω        (   x   )       }     2       4       )               (     6   ′     )                                
     Approximation of formulae (6) and (6′) is effective for light of pulse width of more than 100 fs. It is needless to say that a filter having a thickness equal to the phase difference may be fabricated. 
     FIGS. 41 and 42 show an example of filter characteristics of embodiment 13. In this case, it is assumed that characteristic of dispersion compensation filter for compensating a change in Fourier phase in the medium having a group velocity dispersion is ax 2  in the Fourier transformation plane. 
     FIG.  41  and FIG. 42 correspond positive and negative of dispersion. 
     As a result, for the case of relative phase φ being position (x) on the spatial filter, it is possible to fabricate an optical circuit having a characteristic approximating φ(x)=Mod[ax 2 , π] (a: constant) 
     (wherein Mod[u, v] indicates a remainder using v as a modulus.). 
     While the present embodiment can only compensate a fixed dispersion value, when a filter for compensating up to higher order term of the formula (5) is provided, higher order dispersion can be compensated from the formula (3) to formula (6′). 
     Embodiment 14 
     An embodiment 14 of the present invention will be described with reference to FIG. 25A, FIG. 25B, and FIG.  35 . The spatial filter of the apparatus of the present embodiment is shown in FIG.  25 A and FIG.  25 B. Other parts are similar to those in the embodiment 1 shown in FIG. 35, and detailed description thereof is omitted. 
     The quarter-wave plate is necessary, when using a spatial filter having a polarization dependence, for making it polarization independent. The liquid crystal can be homogeneously oriented parallel or perpendicular to the waveguide facet (A-A′ line in FIG.  25 A). f axis and s axis of the quarter-wave plate  305  are slanted by 45 degrees to the waveguide surface. 
     As shown in FIG. 25B, the transparent electrode  301 - a  is a strip-formed electrode, and each strip electrode can be applied with an optional voltage. When a voltage is applied, orientation of the liquid crystal is changed, and phase difference between the transparent electrodes  301 - a  and  301 - b . Since the electrode is provided in strips, a desired spatial phase filter can be achieved. That is, in the present embodiment, by adjusting the phase filter, it is possible to change the central wavelength of dispersion compensation, change the dispersion compensation amount, or make dispersion compensation according to the requirement. 
     Embodiment 15 
     An embodiment 15 of the present invention will be described with reference to FIG.  43  and above-shown FIG.  28 . In FIG. 43,  200 A is a first arrayed waveguide grating,  200 B is a second arrayed waveguide grating,  501  is a heat sink,  503  is a filter control unit,  504  is a slab waveguide as second focusing means,  505  is a second arrayed waveguide,  506  is a slab waveguide as wave synthesis means, and  507  is a second optical waveguide. 
     The optical waveguide  104 , the first slab waveguide  105 , the arrayed waveguide  106  and second slab waveguide  107 ; and the first slab waveguide  404 , the arrayed waveguide  505 , the second slab waveguide  506 , and the optical waveguide  507  are symmetrical in construction. 
     While the spatial filter (FIG. 28) is a filter same as used in the embodiment 14, since it is a transmission type, it is required to obtain twice the phase difference (2π). Further, the mirror and the quarter-wave plate are omitted since they are unnecessary. Since this construction has a polarization dependence, to make it polarization independent, the filters for obtaining phase difference may be connected perpendiculy in two stages. The transmission type construction of the present embodiment is equivalent in operation to the reflection type construction shown in the embodiments 13 and 14. 
     Embodiment 16 
     FIG. 44 shows an embodiment 16 of the present invention. 
     In FIG. 44,  1001  is a light source,  1002  is an optical modulator,  1003  is an optical modulation signal generator,  1004  is an optical signal processing apparatus as one of those shown in the embodiment 13 to embodiment 15,  1005  is a transmission line comprising an optical fiber, and optical filter, an optical amplifier, and the like,  1006  is an optical signal processing apparatus as one of those shown in the embodiment 13 to embodiment 15, and  1007  is an optical receiver. 
     Self-phase modulation which is a major factor of signal degradation in the transmission line is generated nearly in proportion to the optical pulse peak power. The pulse width can be increased to reduce the peak power while maintaining the average power, thereby reducing the self-phase modulation. 
     In the present embodiment, phase modulation is made in the optical signal processing apparatus  1004  to scramble the waveform to flatten the optical power, thereby reducing the peak power of the optical signal. 
     FIG. 45 shows examples of a time waveform of modulator output optical amplitude and an output waveform after passing through the optical signal processing apparatus  1004 . 
     Dispersion in the transmission line is mainly a group velocity dispersion of the third term of the formula (3) which is a square term with respect to the frequency. 
     When scramble by phase filter of the optical signal processing apparatus is made mainly by the square term, compensation is made with the dispersion characteristic of the transmission line in the course of the transmission line to reproduce the waveform, considerable self-phase modulation may occur resulting in uncompensatable degradation of waveform. Therefore, the phase filter characteristic is adapted to generate dispersion of the same sign as the dispersion of the transmission line for the square term. Or, tertiary or higher term is used, or a filter having a quite random phase changes is used. 
     For the case using the optical signal processing apparatus of the embodiment 13, examples of phase filter are shown in FIG. 46 (using tertiary or higher term) and FIG. 47 (quite random phase change). The phase filter of the reception side optical signal processing apparatus is designed to compensate dispersion by the transmission line and phase scramble previously given by the optical signal processing apparatus  1004 . To represent by mathematical formulae, signal light output from the optical modulator  1002  is assumed as u(t), phase filter characteristic of the optical signal processing apparatus (forward and reverse for reflection type) as h 1 (ω(x)), Fourier transformation as H 1 (t)), and waveform distortion generated by dispersion of the transmission line as J(t), signal light s(t) incident to the optical signal processing apparatus  1006  is approximated by the following formula (7), wherein * means convolution. 
     
       
           S ( t )= u ( t )*H 1 ( t )*J( t )  (7) 
       
     
     To reproduce the original waveform, phase filter characteristics of the optical signal processing apparatus  506  may be set as the following formula (8).                  h   2          (     ω        (   x   )       )       =           h   1          (     ω        (   x   )       )               *            ·   j                     (     ω        (   x   )       )               *                    h   1          (     ω        (   x   )       )            2                 j                   (     ω        (   x   )       )            2                 (   8   )                                
     Further, there may be a case in which modulation at the transmitter side of optical spectral amplitude can optical S/N at the receiver side. That is, since S/N is not uniform to the frequency, the optical signal processing apparatus  504  emphasizes low s/N frequency signal using an amplitude filter and makes transmission, a phase filter for compensating dispersion of the transmission line at the receiver side, and an amplitude filter having the reverse characteristics to the transmission side are used to equalize S/N with respect to the frequency, thereby enhancing the receiver sensitivity. 
     Still further, a filter for reducing only the vicinity of the central frequency is used as the amplitude filter of the receiver side optical signal processing apparatus  1006  to attenuate the low frequency component of time waveform, and interference between codes generated due to nonlinear effect and the like is reduced, thereby enhancing the reception sensitivity. Characteristics of such an amplitude filter are shown in FIG.  48 . 
     Embodiment 17 
     Characteristics of phase filter of an embodiment 17 of the present invention is shown in FIG.  49 A and FIG. 49B for reflection type configuration. Configuration other than the filter is the same as the embodiments 13 to 14. Input signal light is assumed to be an amplitude modulated signal light. Spectral amplitude of the amplitude modulated signal is shown in FIG.  50 A and FIG.  50 B. There are side bands above and below the carrier frequency. On the other hand, spectral amplitude of angular modulated signal light has the shape as shown in FIG. 20B. A difference from the frequency spectral amplitude of amplitude modulation is that the upper and lower side bands are reverse in phase. 
     That is, as shown in FIG.  50 A and FIG. 50B, when phase filter characteristics are as follows in the case of reflection type: 
     
       
         φ( x )=π/2 ( x &gt;0) and φ( x )=0 ( x &lt;0), or 
       
     
     
       
         φ( x )=0 ( x &gt;0) and φ( x )=π/2 ( x &lt;0) 
       
     
     conversion of modulation mode is made from amplitude modulation to angular modulation. It is needless to say that inverse conversion is achieved by using a phase inversed filter. Further, a transmission type filter has twice the phase change amount, it may be set as 
      φ( x )=π( x &gt;0) and φ( x )=0 ( x &lt;0), or 
     
       
         φ( x )=0 ( x&gt; 0   ) and φ( x )=π ( x &lt;0). 
       
     
     Since angular modulated light is nearly constant in optical average amplitude, it is hard to generate a nonlinear effect, and the transmission distance can be increased. 
     Yet further, as in the embodiment 16, it is possible that also using an amplitude filter, low S/N frequency signal is emphasized and transmitted, an amplitude filter having the reverse characteristics to the transmission side is used at the receiver side to enhance the receiver sensitivity. 
     Embodiment 18 
     An embodiment 18 of the present invention is shown. In FIG. 51,  1011  is a short pulse light source,  1012  is an optical amplifier,  1013  is an optical wavelength filter,  1014  is an optical splitter,  1015  is n units of optical modulation circuits,  1016  is n units of optical circulators,  1017  is n units of input waveguides,  1018  is an optical combiner,  1019  is an optical amplifier,  1020  is an optical transmission line,  1021  is an optical amplifier,  1022  is an optical wavelength filter,  1023  is an optical splitter,  1024  is n units of optical circulators, and  1025  is n units of optical receiver circuits. 
     This arrangement differs from the above described embodiment 17 in that the present embodiment mainly makes multiplexing of optical signal. 
     In optical communications using a short pulse, optical band width is mainly determined by the pulse width. 
     If the minimum pulse interval can be narrowed to about the pulse width, the band width can be efficiently utilized. 
     However, since operation speed of the modulation circuit is as high as 50 Gbit/s, the band width (about 400 GHz for Gaussian waveform) of pulse width 1 ps cannot be efficiently utilized. Therefore, in the present embodiment, to make it within the operation speed range of the modulation circuit, the pulse is divided into n units of modulation circuit to achieve modulation. 
     In the present embodiment, each modulation signal is differently phase modulated in frequency regions, and synthesized and multiplexed. 
     In this case, it is arranged so that phase modulation to each modulation signal is reduced in correlation with each other. 
     For such phase modulation, for example, different or shifted PN (Pseudorandom Noise) sequence or M (Maximum Length code) sequence may be used. 
     In the reflection type construction, spatial filter phase is changed in relative phase of [0, π/2] according to [1, 0] of the sequence. 
     An envelope of average optical amplitude distribution on the filter plane is shown in FIG.  52 . 
     Although the central frequencies of the individual modulation signals are the same, on the filter plane, focused at different positions reflecting different positions of the input waveguides. 
     The envelope of optical intensity distributions corresponding to k−1, k, and k+1′th channel are separated at intervals equal to the interval din at the connection of the input optical waveguide to the slab waveguide  105 . 
     Therefore, it is possible to make different phase modulation to each modulation signal in the frequency region phase modulated light is waveguided by the optical circulator  1016  to the optical synthesis device  1018 . 
     At the reception side, while the optical signal is divided into n units, each divided signal is demodulated in the frequency region using a spatial filter which is phase conjugate with the transmission side optical signal processing apparatus. 
     When correlation is small between individual phase modulations, other signal waveform is not reproduced, only an average background noise is present. 
     To determine the presence of a pulse from background noise, the receiver circuit is required to have a high performance for sufficiently responding the pulse. For very high speed discrimination, a nonlinear device, a nonlinear optical receiver, or a high speed opto-electric conversion device and a flip-flop circuit is used. 
     FIG. 53 shows waveforms of modulation signal, after phase modulation, and demodulated signal after reproduction. That is, the present embodiment functions as a spectrum spread transmission apparatus in the optical frequency region. Since, as the number of multiplexing increases, it becomes difficult to reduce correlation of phase modulation for all combinations, background noise increases, and multiplexing becomes difficult, however, it is possible to utilize a band width corresponding to the pulse width with an efficiency of about 50%. 
     For example, using a pulse of 1 ps, it is possible to construct a transmission apparatus having 4 channels at a channel modulation velocity of 50 Gbit/s, totally about 200 Gbit/s. 
     Embodiment 19 
     An embodiment 19 of the present invention is shown. In FIG. 54,  1031  is a short pulse light source,  1032  is an optical amplifier,  1033  is an optical splitter,  1034  is an optical division device,  1035  is n units of optical modulation circuits,  1036 ,  1037 , and  109  are the same transmission type optical signal processing apparatus as shown in FIG. 43, increasing the input/output waveguides to n units,  1038  is an optical combiner,  1039  is an optical amplifier,  1040  is an optical transmission line,  1041  is an optical amplifier,  1042  is an optical wavelength filter,  1043  is an optical splitter,  1044 ,  1045 , and  109  are the same transmission type optical signal processing apparatus as shown in FIG. 43 as described above, and  1046  is n units of optical receiver circuits. 
     In the present embodiment, the embodiment 18 is constructed with a transmission type phase modulation circuit, and the operation is the same as the embodiment 18. 
     However, since it is transmission type, relative phase of the spatial filter is changed at [0, π]. 
     Embodiment 20 
     FIG. 55 shows an embodiment 20 of the present invention, which is a short pulse light source. In the Figure, the short pulse light source according to the present invention comprises an optical modulator  2011 , a drive circuit  2012  for driving the optical modulator  1011 , an optical gain medium  2013 , n an pumping circuit  2014  far forming population inversion on the optical gain medium  2013 , an arrayed waveguide grating  2015  with eliminated the input waveguide  71  from the arrayed waveguide grating  62  shown in FIG. 5, optical coupling means  2016  for coupling the optical modulator (optical modulation means)  2011  and the optical gain medium (optical gain means)  2013 , and optical coupling means  2017  for coupling the optical gain medium  2013  and the arrayed waveguide grating  2015 . The optical coupling means  2016  side of the optical modulator  2011  is provided with a low reflection coating  2018 , and a high reflection mirror  2019  is disposed at the opposite side (outside). The optical coupling means  2017  side of the arrayed waveguide grating  2015  is provided with a low reflection coating  2020 , and a high reflection mirror  2021  is disposed at the opposite side (outside). 
     The optical modulator  2011  can be an MQW modulator, an LN modulator, or the like. The optical gain medium  2013  can be a traveling wave type semiconductor optical amplifier, rare earth doped optical fiber amplifier, or the like. The pumping circuit  1014  is a current source when the optical gain medium  1013  is a traveling wave type semiconductor optical amplifier, and an pumping light source for the case of the rare earth doped optical fiber amplifier. Further, the substrate  70  of the arrayed waveguide grating  2015  can be a semiconductor substrate such as InP or GaAs in addition to quartz substrate. 
     The arrayed waveguide grating  2015  comprises a slab waveguide  72 , an arrayed waveguide  73  comprising a plurality of waveguides gradually increasing in length by waveguide length difference ΔL, a slab waveguide  74 , and a plurality of output waveguides, formed on the substrate  70 . 
     Wherein ns is a refractive index of the slab waveguides  72  and  74 , nc is a refractive index of the arrayed waveguide  73 , d is a spacing of the arrayed waveguide  73  on the slab waveguide end surface, θ is a focusing direction with respect to the central axis of the slab waveguide  74 , fs is a focal length, and λ is wavelength of light, the focusing position is given by: 
     
       
           n   s   ·d  sin θ+ n   c ΔL= m λ( m= 1, 2, . . . ) 
       
     
     The value of m is generally several tens to several hundreds. The relationship between the optical frequency incident to the slab waveguide and the focusing position x on the focal plane of the slab waveguide is as shown in FIG.  56 . Linear dispersion (dx/df=fs·dθ/df) is 1 [μm/GHz]. 
     Light incident to the slab waveguide  72  is reflected by the high reflection mirror  2021  through the output waveguide  75  connected at an interval of Δx to the end surface of the slab waveguide  74 , and again output in the reverse direction from the slab waveguide  72 . The reflection spectrum of such an arrayed waveguide grating  2015  is according to the interval Δx and the core width of the output waveguide  75 . For example, a reflection spectrum when Δx is 50 μm and the core width is 10 μm is shown in FIG.  57 . According to the position of the output waveguide  75 , a comb-formed reflection spectrum having reflection peaks at every 50 GHz is obtained. 
     In the construction of the present embodiment, an optical resonator is formed between the high reflection mirror  2017  and the high reflection mirror  2021 , thereby simultaneously oscillating light of a plurality of wavelengths when the gain of the optical gain medium is sufficiently high. Further, when a sufficiently deep modulation is applied by driving the optical modulator with a sine wave of frequency f by the drive circuit  2012 , coupling occurs between oscillation modes to make mode locked oscillation. The driving frequency f is represented as 
     
       
           f=k·c /(2·L eff )=Δ x /( dx/df ) 
       
     
     wherein Leff is an equivalent optical distance between the high reflection mirror  2019  and the high reflection mirror  2021 , and k is an integer. In this case, phase relation of each vertical mode is maintained constant, an optical short pulse sequence of a repetition frequency f is generated. The oscillation spectrum is shown in FIG.  58  and the oscillation pulse waveform is shown in FIG.  59 . 
     The prior art mode locked type laser has been difficult to set the frequency of each mode. However, in the construction of the present embodiment, since frequency of each mode is determined by the interval Δx of the output waveguide  75  of the arrayed waveguide grating  2015 , frequency of each mode can be set in detail. Further, when the arrayed waveguide grating  2015  is formed on a quartz substrate, oscillation is possible at a frequency stable to temperature changes. 
     Still further, the prior art mode locked laser has been difficult to set the pulse width. However, in the construction of the present embodiment, by controlling the number of output waveguides  75  of the arrayed waveguide grating  15  and the reflectivity, of the high reflection mirror  2021 , that is, by setting the oscillation pulse width, the pulse width can be previously set. For example, a Gaussian type envelope spectrum as shown in FIG. 60 can be achieved. In this case, the pulse waveform on the time base is also Gaussian type. 
     Embodiment 21 
     FIG. 61 shows an embodiment 21 of the present invention, which is a short pulse light source. 
     The basic structure is the same as the embodiment 20 shown in FIG.  55 . Here, an enlarged view of the slab waveguide  74  and the output waveguide  75  part of the arrayed waveguide grating  2018  is shown. 
     The present embodiment is characterized in that lengths of individual waveguides of the output waveguide  75  are changed so that dispersion in the optical resonator can be compensated. 
     In general, a semiconductor material has a large dispersion, most of dispersion in the optical resonator of the present invention is considered to be semiconductor material dispersion in the optical modulator  2011  and the optical gain medium  2013 . The dispersion is about 0.005 ps/nm. When the output waveguide  75  is disposed with an interval of 50 μm to the arrayed waveguide  73  having a linear dispersion of 1 μm/GHz, if the adjacent waveguide length difference is 0.4 μm, it is possible to compensate the dispersion in the optical resonator. In this case, each waveguide length can be set so that a phase difference in the resonator to each mode is 2 mπ(m=1, 2, . . . ). 
     So, adjacent waveguide length difference can be set as follows; 
     
       
         0.4 μm± mλ   k /2n eff   
       
     
     wherein λ k  is the wavelength of k&#39;s mode and n eff  is the effective refractive index of the output waveguide. 
     This generates a pulse close to the transform limit. When the arrayed waveguide grating  2015  having a high free spectral range is used, a very short pulse sequence of sub-picosecond can be generated. 
     Embodiment 22 
     FIG. 62 shows an embodiment 22 of the present invention, which is a short pulse optical light source. 
     The basic structure is the same as the embodiment 20 shown in FIG.  55 . Here, an enlarged view of the output waveguide  75  part of the arrayed waveguide grating  2015  in the embodiment 20 is shown. 
     The present embodiment is characterized by a lens array and a liquid crystal spatial modulator having a high reflection mirror on one side in place of the high reflection mirror  2021  at the end surface of the output waveguide  75 . The lens array comprises a gradient refractive index lens  2022  disposed at spacings of Δx. The liquid crystal spatial modulator comprises a polarizer plate  2023 , a glass substrate  2024 - 1 , a twist nematic liquid crystal  2027  placed between a transparent electrode  2025  and a polarizer plate  2026  disposed at a spacing of Δx, a high reflection mirror  2028 , and a glass substrate  2024 - 2 , which are stacked. End surface of the output waveguide  75 , and both surfaces of the gradient refractive index lens  2022  and the polarization plate  2023  are provided with a low reflection coating  2029 . 
     The liquid crystal spatial modulator can control the reflectivity from the high reflection mirror  2028  to the output waveguide  75  by applying a voltage between opposing transparent electrode  2025 . This enables mode control dynamically, and can change the pulse waveform as necessary. 
     The spatial modulator in this case is not limit to the liquid crystal spatial modulator, but another modulator such as an MQW modulator, a modulator by Franz-Keldysh effect, an LN modulator, or a modulator by a nonlinear material can be utilized. 
     Further, it is needless to say that, to make dispersion compensation in the resonator, the above described dispersion compensation phase filter may be used. A cross sectional structure in this case is shown in FIG.  62 B. In the Figure,  74  is a slab waveguide,  2024  is a holding substrate,  2028  is a high reflection mirror, and  3000  is a dispersion compensation phase filter. 
     Embodiment 23 
     FIG. 63 shows an embodiment 23 of the present invention (short pulse light source). 
     Basic construction of the present embodiment is the same as embodiment 20 shown in FIG.  55 . Here, an enlarge view of the slab waveguide  74  of the arrayed waveguide grating  2015  and the output waveguide  75  part is shown. 
     The present embodiment is characterized in that a diffraction grating  2030  is formed in the output waveguide instead of using the high reflection mirror  2021 . This diffraction grating  2030  can be functioned as a very narrow band high reflection mirror. Since it has a spectroscopic characteristic, it enables very detailed mode wavelength setting. Further, by disposing the diffraction grating at an appropriate position, dispersion compensation in the optical resonator is possible as in the embodiment 20, and can generate a pulse close to the transform limit. 
     Embodiment 24 
     FIG. 64 shows an embodiment 24 of the present invention (short pulse light source). 
     Basic construction of the present embodiment is the same as embodiment 19 shown in FIG.  55 . Here, an enlarge view of the slab waveguide  74  of the arrayed waveguide grating  2015  and the output waveguide  75  part is shown. 
     The present embodiment is characterized in that two or three or more units of the output waveguides provided with the diffraction grating  2030  as in the embodiment 22 are connected to an optical coupler  2031 . By coupling light from the predetermined waveguides of the output waveguide  75  by the optical coupler  2031 , it is possible to couple a predetermined mode when mode locked oscillation is being made, thereby generating various pulse waveforms. For example, when coupling only an odd or even numbered mode to be output, an optical short pulse sequence of twice the repetition frequency of mode locked frequency can be generated. 
     Embodiment 25 
     FIG. 65 shows an embodiment 25 of the present invention (short pulse light source). 
     In the Figure, an arrayed waveguide grating  2032  has a construction in which the output waveguide  75  is eliminated from the arrayed waveguide grating  2015  in the embodiment 20, and a plurality of high reflection mirrors  2021  are disposed at spacings of Δx on the focal plane of the slab waveguide  74 . Other construction is the same as the embodiment 20. 
     FIG. 66 shows an enlarged view of the slab waveguide  74  part of the arrayed waveguide grating  2032 . 
     In the Figure, end surface of the substrate  70  of the arrayed waveguide grating  2032  is cut along the focal plane of the slab waveguide  74 , and a plurality of high reflection mirrors  2021  are disposed at spacings of Δx on the end surface. Further, to reduce end surface reflection from parts other than the high reflection mirrors  2021 , the entire end surface of the substrate  70  is provided with a low reflection coating. 
     Embodiment 26 
     FIG. 67 shows an embodiment 26 of the present invention (short pulse light source). 
     Basic construction of the present embodiment is the same as embodiment 25 shown in FIG.  65 . Here, an enlarged view of the slab waveguide  74  part of the arrayed waveguide grating  2032  is shown. 
     The present embodiment is characterized in that a diffraction grating  2033  is formed on the focal plane of the slab waveguide  74  instead of using the high reflection mirror  2021 . 
     The diffraction grating can be written by using ultraviolet light as in a diffraction grating formed in an optical fiber. Since a quartz substrate is small in coupling constant of diffraction grating and small in loss, the diffraction grating can be functioned as a very narrow band high reflection mirror. Further, in addition to the spectroscopic function of the arrayed waveguide grating, since the high reflection mirror by the diffraction grating  2033  in the slab waveguide  74  has a spectroscopic characteristic, a very detailed mode wavelength car be set. Still further, by dislocating individual positions of the diffraction grating  2033  on the normal line of the focal plane, dispersion compensation in the optical resonator as in the embodiment 20, thereby generating a pulse close to the transform limit. 
     Embodiment 27 
     FIG. 68 shows an embodiment 27 of the present invention (short pulse light source). 
     Basic construction of the present embodiment is the same as embodiment 26 shown in FIG.  67 . Here, an enlarged view of the slab waveguide  74  part of the arrayed waveguide grating  2032  is shown. FIG. 68A is a plan view, and FIG. 68B is a cross sectional view of FIG. 68A along line A-A′. The reference numeral  76  indicates a waveguide core. 
     The present embodiment is characterized in that, instead of using the high reflection mirror  2021 , a groove  2034  perpendicular to the substrate  70  is formed along the focal plane of the slab waveguide  74 , and a polyimide film  2036  formed with a plurality of mirrors  2035  is inserted in the groove. 
     The polyimide film  2036 , to eliminate unnecessary reflected light from the waveguide end surface, is fixed with an adhesive which is transparent in the operating wavelength and small in refractive index difference from the equivalent refractive index of the waveguide. Further, to eliminate reflected light from part without the mirror  2035  of the polyimide film  2036 , the surface is provided with low reflection coating  2038 . Still further, to avoid reflection from the back surface, the back side is laminated with a light absorption film  2039 . Yet further, in the present embodiment, various films can be used other than polyimide film. 
     Yet further, the arrayed waveguide gratings in the embodiments 20 to 26 are set in a short pulse light source, the arrayed waveguide grating of these embodiments can also be applied in other applications such as waveform shaping and dispersion compensation 
     Embodiment 28 
     FIG. 69 shows an embodiment 28 of the present invention (short pulse light source). 
     The present embodiment shows a construction in which the optical modulator  2011  and the optical gain medium  2013  are integrated. An n-InP substrate  2040  is stacked with an optical modulation MQW layer  2041 , an i-etch stop layer  2042 , a laser MQW layer  2043 , an n-InP layer  2044 , an n-InGaAsP layer  2045 , and an AuZnNi electrode  2046 , and an AuGeNi electrode  2047  is mounted on the backside of the n-InP layer  2040 . End surface at the optical modulator  2011  side is provide with a high reflection mirror  2048  ( 2019 ), and end surface of the optical gain medium  2013  is provided with a low reflection coating  2049 . By such integration, the number of parts of the pulse light source is reduced, optical coupling means is sufficient at only one position between the arrayed waveguide gratings  2015  and  2032 , thereby achieving an economical and reliable short pulse light source. 
     Embodiment 29 
     In FIG. 70,  2011  is a fiber output type optical modulator provided with a low reflection structure at the output surface and with a high reflection structure on the opposite surface,  2102  is a modulator drive circuit,  2103  is a fiber output type optical gain medium,  2104  is a gain medium pumping circuit,  2105  is a 4-terminal type optical circulator,  2106  is a non-reflection terminator,  2107  is an optical coupler,  2108  is a polarization maintaining optical fiber,  2109  is an arrayed waveguide grating,  2110  is an optical waveguide,  2111  is a first slab waveguide,  2112  is a waveguide array,  2113  is a second slab waveguide,  2114  is a lens,  2115  is a high reflection mirror, and  2116  is a fine movement table. 
     An enlarged view of the high reflection mirror  2115  of FIG. 70 is shown in FIG.  71 . FIG. 71A is a structural plan view, FIG. 71B is an end surface view. Here,  2117  is a quartz substrate,  2118  is a point reflection coating,  2119  is a high reflection mirror such as Au/Cr. Each mirror is constant in width, adapted to change the adjacent mirror spacing in y-direction of FIG.  71 A. 
     FIG. 72 shows layout in the vicinity of the mirror  2115 . In the Figure,  2120  is a lens substrate,  2114  is a lens, having a function to convert the cylindrical focusing plane of  2109  into a flat plane. The surface having the mirror  2115  is disposed to be in line with the focusing plane. In the figure, a direction vertical to the paper surface is y-direction, and rotation angle about the y-axis is θ. By the fine movement table  2116  connected to the mirror  2115 , the mirror can be finely moved in the x and y-directions and θ-direction. In the present embodiment, by moving the mirror  2115  in the x-direction, central frequency during mode locked oscillation and oscillation frequency of each mode can be controlled. By moving in the y-direction, since the spacing of the mirror  2119  is changed, mode interval, that is, repetition period of the pulse can be controlled. Further, to facilitate generation of mode locked state, the θ-direction is controlled so that the delay time in the resonator is an integer multiple or inverse thereof of the repetition period of the pulse. 
     The present embodiment 29 is characterized in that the repetition period and central frequency of the pulse sequence can be easily controlled. While individual parts are shown to be connected to the optical fiber, it is needless to say that they may be connected to the lens as in other embodiments. Further, in other embodiments, the parts may be connected to the optical fiber as in the present embodiment. 
     Embodiment 30 
     FIG. 73 shows an embodiment 30 of the present invention. The present embodiment relates to an optical signal processing apparatus which can provide observation of real-time waveform of optical signal. 
     In FIG. 73,  3101  is a signal light input waveguide for inputting signal light.  3102  is a slab waveguide, which has a function to distribute output light of the signal light input waveguide to an arrayed waveguide  3103 . The arrayed waveguide  3103  has a function for time—space conversion of incident signal light. 
     Further,  3104  is a reference light input waveguide for inputting reference light.  3105  is a first slab waveguide for the reference light, and has a function of distributing the output light of the reference light input waveguide  3104  to an arrayed waveguide  3106 . The arrayed waveguide  3106  has a function of time—space conversion of incident reference light. 
       3107  is a second slab waveguide, which has a function of Fourier transformation of output light individually from the arrayed waveguide  3103  and the arrayed waveguide  3106 .  3108  is an photo diode (PD) array, which detects electrical field amplitude distribution of Fourier transform hologram formed on the focal plane of the second slab waveguide  3107  by interference of the signal light Fourier transformed by the second slab waveguide  3107  with the reference light.  3109  is an optical signal restoration circuit for restoring the input signal light from the electrical field strength distribution of the Fourier transformed hologram detected by the PD array  3108 . Further,  200  is an arrayed waveguide grating comprising the waveguides  3101  and  3104 , the slab waveguides  3102 ,  3105 , and  3107 , and the arrayed waveguides  3103  and  3106 . In this case, when making time—space conversion of the signal light by the arrayed waveguide  3103  and the arrayed waveguide  3106 , since a hologram is not obtained if the spatial base is inversed to each other with respect to the time base, the two arrayed waveguides  3103  and  3106  are bent in the same direction as shown in FIG. 73, thereby aligning the sign of the spatial base to the time base on the output surface of the arrayed waveguides. 
     Yet further, in the present embodiment 30, while the PD array  3108  is nearly close contacted with the focal plane of the second slab waveguide  3107 , a lens may further be provided on the focal plane of the second slab waveguide  107  to make phase compensation. Yet further, when designing the two waveguide arrays, as shown in FIG. 73, the signal light arrayed waveguide  3103  is provided at the output side, the reference light arrayed waveguide is provided at the input side individually with a straight arrayed waveguide of about 1 cm, thereby preventing the arrayed waveguides from being overlapped with each other. 
     Yet further, as a construction having the same function, a construction shown in FIG. 73B is also possible. In FIG. 73B,  3110  is a second slab waveguide for reference light, and  3111  is a half mirror. The half mirror  3111  is introduced, after, forming the waveguide, by forming a groove in the substrate by a dicing saw and inserting. The position of the half mirror is determined so that reference light incident to the slab waveguide  3110  is reflected at the half mirror  3111 , and focused on the focal plane of the slab waveguide  3107 . In this case, to achieve an off-axis hologram arrangement, the optical axis of the reference light is required to be set in an angle of 3 to 30 degrees with respect to the optical axis of signal light. Although the resolution is improved when the angle between the signal light and reference light is as small as possible, to separate the signal light from the reference light, as shown in FIG. 73C, it is necessary to set so that individual beams of the reference light and signal light are not overlapped with each other. 
     The waveguide in FIG. 73 is formed as an example as shown below. First, a lower clad layer and a core layer are stacked in this order by a flame hydrolysis decomposition method (FHD method) on a single crystal silicon substrate, heated to a high temperature in an annealing furnace to form a transparent glass film covering the silicon substrate. After that, patterning is made to the shape of waveguide, unnecessary core layer is removed by dry etching, an upper clad layer is again stacked using the FHD method, and heated to a high temperature to make the upper clad layer transparent. Although the above described method is used in the present embodiment 30, it is apparent that a semiconductor waveguide structure fabricated by epitaxial growing of semiconductor higher in refractive index than a clad of InGaAsP as a core layer of a semiconductor layer such as of InP, after patterning and etching, again growing InP as an upper clad layer has the same function. In this case, it is desirable that the materials are transparent in the operating wavelength region. 
     Further, a detailed view of the photo diode array used in the present embodiment is shown in FIG.  73 D. The size of one piece of the photo diode in 256 units of single dimensional array is 200 μm in length and 30 μm in width, and individual pixels are arranged in a period of 50 μm. Electrical charge generated in each pixel is accumulated in the charge integrator  3114 . The accumulated charge is read by sequentially operating the pixels by the CMOS shift register  3115 . 
     Still further, the optical signal restoration circuit  3109  comprises a computer and hologram for making mathematical operation, which will be described later, on the distribution of hologram interference pattern detected by the photo diode array, and a display device for displaying the electrical field distribution of the restored original optical signal. 
     When signal light s 1 (t) to be observed is input in the waveguide  3101 , and known reference light r 1 (t) is input in the waveguide  3104 , at the output ends of the individual waveguides  3103  and  3106 , when the coordinate axis is x 1 , the signal light and the reference light are time—space converted individually into s 2 (x 1 ) and r 2 (x 1 ). These optical signals s 2 (x 1 ) and r 2 (x 1 ) are Fourier transformed by diffraction during transmitting the waveguide  3107 , the signal light and reference light are converted individually into S(ξ) and R(ξ), wherein ξ is a spatial frequency axis in the focal plane coordinates. Wherein S(ξ) and R(ξ) are Fourier transformation of s 2 (x 1 ) and r 2 (x 1 ). On the focal plane of the slab waveguide  3107 , S(ξ) and R(ξ) interfere with each other to form a hologram. Electrical field strength distribution G(ξ) can be represented as: 
     
       
           G (ξ)=| S (ξ)+ R (ξ)| 2   =|S (ξ)| 2   +|R (ξ)| 2   +S (ξ)× R *(ξ)+ S *(ξ)× R (ξ)  (1) 
       
     
     In the formula (1), S*(ξ) and R*(ξ) individually represent complex conjugate of S(ξ) and R(ξ). By detecting the distribution of such hologram G(ξ) and making mathematical operation, by multiplying G(ξ)/|R(ξ)| 2 , 
     
       
           G (ξ)× R (ξ)/| R (ξ)| 2 =(| S (ξ)| 2   /|R (ξ)| 2+1 )× R (ξ)+ S (ξ)×{ R (ξ)} 2   /|R (ξ)| 2   (2) 
       
     
     can be derived. Although not expressly shown in the formula (2), since, in the slab waveguide  3107 , signal light S 2 (x 1 ) and reference light r 2 (x 1 ) are applied from different positions, this is a construction equivalent to off-axis method in the holography. 
     Therefore, individual terms appearing in the formula (2) 
     
       
         (| S (ξ)| 2   /|R (ξ)| 2+1 )× R (ξ) 
       
     
     
       
           S (ξ) 
       
     
     
       
           S *(ξ)× R (ξ) 2   /|R (ξ)| 2   
       
     
     individually correspond to 0&#39;th order, +1st order, and −1st order diffraction components, differing in diffraction direction. Therefore, it is possible to separate an electrical component to be observed on the mathematical formulae to be derived in the optical restoration circuit  3109 . 
     Further, in practice, the focal plane of the second slab waveguide  3107  is an arc, however, in the present embodiment, it is cut on a straight line in the vicinity of the focal plane, the focal plane and the cut surface are not strictly in line with each other. That Y, the time—spatially changed signal light is not a strict Fourier transformation image on the straight cut plane. Therefore, when the original signal waveform is reproduced from hologram interference pattern received by the photo diode array, an error occurs at the time of making inverse Fourier transformation. 
     In the present embodiment, as a method for solving the problem with such an error, a compensation is made by sticking a Fresnel lens for compensating dispersion due to a phase shift on the cut surface of the second slab waveguide  3107 , however, when reproducing the waveform of the signal light by the calculation as described above, even without the Fresnel lens, it is also possible to make correction by compensating the dispersion due to the phase shift to make calculation of diffraction light, using more common diffraction formula, rather than Fourier transformation in the process of calculating the diffraction by the lens, that is, in the process of making inverse Fourier transformation. 
     In effect, using the optical system of FIG. 73, from the electrical field strength distribution when a set of  13  pulses of about 42 ps in pulse interval is input as a signal light from the signal light input waveguide  3101 , and single optical pulse close to transform limit of 1 ps in pulse width is input as a reference light from the reference light input waveguide  3104 , it has been confirmed that the electrical field distribution of the input signal optical pulse sequence can be mathematically restored. 
     Embodiment 31 
     FIG. 74 shows an embodiment 31 of the present invention, which relates to a waveform observable optical signal processing apparatus. In FIG. 74,  3201  is a diffraction grating, which has a function of time—space converting input signal light  3204  and input reference light  3205 .  3202  is a lens, which has a function of Fourier transforming the signal light and reference light diffracted by the diffraction grating  3201 .  3203  is an photo diode (PD) array disposed in the vicinity of the focal plane of the lens  3202 , for detecting electrical field strength distribution of the Fourier transform hologram formed on the focal plane of the lens  3202  by interference of the Fourier-transform signal light and reference light.  3206  is an optical restoration circuit for restoring the input signal light from the electrical field strength distribution of the Fourier-transform hologram detected by the PD array  3203 . Similarly to the embodiment 30, it is possible to derive the signal light by mathematical operation from the Fourier-transform hologram of the off-axis method. 
     It has been confirmed that electrical field distribution of input signal light can be restored from the electrical field strength distribution of the Fourier transform hologram when the optical system as shown in FIG. 74 is disposed, the optical system is input with a random signal obtained by appropriate modulation to a 100-unit pulse sequence of 0.3 ps in pulse width and about 8.3 ps in pulse interval, and a single pulse close to the transform limit of 0.1 ps in pulse width is input. 
     The present invention has been described in detail with respect to preferred embodiments, and it will now be apparent from the foregoing to those skilled in the art that changes and modifications may be made without departing from the invention in its broader aspects, and it is the intention, therefore, in the appended claims to cover all such changes and modifications as fall within the true spirit of the invention.