Patent Document

BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention relates to a waveform dispersive compensation method having a function, such as pulse waveform shaping, and, more particularly, to an adaptive dispersion compensating element used in ultrahigh-speed optical fiber communication.  
           [0003]    2. Description of Prior Art  
           [0004]    Recently, in optical fiber communication, its introduction into an optical access system is advancing, to say nothing of a trunk line system. In many 1.3 micron band zero dispersion fibers laid at present, when transmission is performed using light having a wavelength in a 1.5 micron band, a wavelength dispersion of about 17 ps/km−nm can be found in an optical fiber. Accordingly, when the transmission distance is made longer or when the transmission rate becomes fast, a means for controlling dispersion becomes necessary to prevent deterioration of an optical signal.  
           [0005]    A typical means that controls conventional dispersion is a dispersion compensator that uses a chirp Bragg grating having the structure in which a cycle of refractive index modulation is continuously changed. A fiber Bragg grating that forms a diffraction grating in a core of this optical fiber becomes an element whose position of reflection depends on an optical wavelength by forming a diffraction grating (chirp Bragg grating) that has a characteristic of reflecting light of a specific wavelength and continuously changes a pitch toward the major axis direction of an optical fiber. A dispersion compensator can be constituted using this feature. This chirp Bragg fiber grating becomes compact and has the same function as a dispersion compensating fiber by combining with an optical circulator.  
           [0006]    However, in most chirp Bragg gratings, dispersion and reflection characteristics were static. Desirably, they should have a diffraction grating that can change a band or dispersion with satisfactory control against many applications, such as dispersive compensation.  
           [0007]    One of the attempts that introduces a dynamically adjustable chirp into a chirp Bragg fiber grating as a conventional example can be found in an “Optical Diffraction Device Having an Adjustable Chirp” disclosed in Japanese Unexamined Patent Publication No. 2000-137197.  
           [0008]    [0008]FIG. 1 shows a process useful for providing an example in which a chirp diffraction grating is adjusted using a block diagram. In FIG. 1, Process A is a “Preparation of a waveguide including a diffraction grating”, Process B is “Coating of a diffraction grating area using a variable-resistance thin film”, or Process C is “Packaging of a device”.  
           [0009]    In FIG. 1, the operation is described below. As shown in Process A, the first process is to prepare an optical waveguide of a fixed length including an optical diffraction grating. Desirably, a waveguide should be an uncoated fiber, but can include an electrically insulated resistor thin film of uniform resistance. The waveguide ought to be either single mode or multi mode. The diffraction grating ought to be either a Bragg diffraction grating or a long cycle diffraction grating. The next process, as shown in Process B, is to coat a waveguide with a thin film of a resistance material in which local resistance increases substantially in succession along the length of a diffraction grating. The third process (Process C) (this is performed as occasion demands) is to package a device for operation.  
           [0010]    [0010]FIG. 2 shows a schematic sectional view of a waveguide diffraction grating device having an adjustable chirp as a specific configuration example. In FIG. 2, number  10  is an optical fiber,  11  is a diffraction grating,  12  is refractive index perturbation,  13  is a substrate, and  14 ,  15  are electrodes.  
           [0011]    An optical waveguide diffraction grating having an adjustable chirp includes a waveguide diffraction grating that thermally contacts an electrically controllable thermal conversion substrate whose temperature changes along the length of a diffraction grating. Because a thermal conversion substrate generates a temperature gradient along a diffraction grating, it generates heat on a fiber or can remove the heat from the fiber. As an example, the thermal conversion substrate is a resistive coat in which local resistance changes along the length of the diffraction grating. A current that passes through a thin film generates a temperature gradient along a diffraction grating that is almost proportional to the local resistance of the thin film and the size of a chirp can be adjusted by the current. A device that is obtained is simple and compact, and the power is efficient.  
           [0012]    However, in a means that uses the chirp diffraction grating, it is unknown how chirp characteristic control for compensating dispersion is performed in accordance with a change of the transmission state and a change of the transmission distance. Accordingly, the means had a problem that cannot flexibly be solved in accordance with the optical pulse transmission of practical optical communication. Further, a resistor element that generates a temperature gradient has the configuration in which heat output is controlled by changing a value of resistance in accordance with a change in the local thickness of a thin film. However, the means had a problem that it is difficult to control higher order diffusion (exceeding tertiary diffusion) than wavelength diffusion (secondary diffusion) in such configuration.  
         SUMMARY OF THE INVENTION  
         [0013]    The present invention has been made in view of solving the above prior art and provides a device that adaptively performs decentralized control in an optical fiber transmission path, such as performing dispersive compensation and waveform shaping in an optical fiber transmission.  
           [0014]    To attain this object, according to an aspect of the present invention, the adaptive dispersion compensating element is provided with a chirp Bragg grating formed in an optical fiber, a temperature gradient impressing means that impresses a temperature gradient along the longitudinal direction of the chirp Bragg grating, a spectral resolving means that spectrally resolves the output light from the chirp Bragg grating, a detecting means that detects the output light from the spectral resolving means, and a controlling means that performs feedback control of the temperature gradient impressing means based on the output from the detecting means.  
           [0015]    According to another aspect of the present invention, the adaptive dispersion compensating element can provide a compact and high-stability adaptive dispersion compensating element that adaptively performs dispersive compensation monitoring an optical signal in an optical fiber transmission path, such as performing dispersive compensation or waveform shaping in optical fiber transmission in accordance with the above configuration.  
           [0016]    According to another aspect of the present invention, the adaptive dispersion compensating element is provided with a chirp Bragg grating formed in an optical fiber, a temperature gradient impressing means that impresses a temperature gradient along the longitudinal direction of the chirp Bragg grating, a spectral resolving means that spectrally resolves the output light from the chirp Bragg grating, a detecting means that detects the output light from the spectral resolving means, and a controlling means that performs feedback control of the temperature gradient applying means based on the output from the detecting means, and has operation that adaptively performs dispersive compensation monitoring an optical signal in an optical fiber transmission path, such as performing dispersive compensation or waveform shaping in optical fiber transmission.  
           [0017]    Further, according to another aspect of the present invention, the adaptive dispersion compensating element is an adaptive dispersion compensating element whose temperature gradient is a nonlinear gradient that is impressed to the longitudinal direction of a chirp Bragg grating and has operation that adaptively performs dispersive compensation monitoring an optical signal in an optical fiber transmission path, such as performing dispersive compensation or waveform shaping in optical fiber transmission.  
           [0018]    Moreover, according to another aspect of the present invention, the adaptive dispersion compensating element has multiple areas in which a chirp Bragg grating is provided with a nonlinear chirp characteristic and a temperature gradient impressing means independently impresses a temperature gradient to the multiple areas respectively, and has operation that compensates residual dispersion, such as higher order dispersion.  
           [0019]    Besides, the same effect can also be obtained in an adaptive dispersion compensating element whose side of an optical fiber in which a chirp Bragg grating is formed is polished.  
           [0020]    Further, the same effect can also be obtained in an adaptive dispersion compensating element whose side of an optical fiber in which a chirp Bragg grating is formed has an uneven shape.  
           [0021]    Moreover, according to another aspect of the present invention, the adaptive dispersion compensating element has a first chirp Bragg grating formed in an optical fiber, a first temperature gradient impressing means that impresses a temperature gradient along the longitudinal direction of the first chirp Bragg grating, a second chirp Bragg grating formed in the optical fiber that receives the output light from the first chirp Bragg grating, a second temperature gradient impressing means that impresses a temperature gradient along the longitudinal direction of the second chirp Bragg grating, a spectral resolving means that spectrally resolves the output light from the second chirp Bragg grating, a detecting means that detects the output light from the spectral resolving means, and a controlling means that performs feedback control of the first temperature gradient impressing means and the second temperature gradient impressing means based on the output from the detecting means, and the first chirp Bragg grating and the second chirp Bragg grating are adaptive dispersion compensating elements that form a chirp in the reverse direction and have operation that cancels secondary dispersion generated in these dispersion compensating elements and compensates only higher order dispersion, such as tertiary dispersion.  
           [0022]    Further, according to another aspect of the present invention, the adaptive dispersion compensating element is an adaptive dispersion compensating element whose temperature gradient impressed along the longitudinal direction of a first chirp Bragg grating and a second chirp Bragg grating is a nonlinear gradient and has operation that adaptively performs dispersive compensation monitoring a signal in an optical fiber transmission path, such as performing dispersive compensation and waveform shaping in optical fiber transmission.  
           [0023]    Moreover, according to another aspect of the present invention, the adaptive dispersion compensating element has multiple areas in which a first chirp grating and a second chirp grating have a nonlinear chirp characteristic respectively and a first temperature gradient impressing means and a second temperature gradient impressing means independently impress a temperature gradient to the multiple areas respectively and has operation that compensates residual dispersion, such as higher order dispersion.  
           [0024]    Besides, the same effect can also be obtained in an adaptive dispersion compensating element whose side of an optical fiber in which a chirp Bragg is formed is polished.  
           [0025]    Further, the same effect can also be obtained in an adaptive dispersion compensating element whose side of an optical fiber in which a chirp Bragg has an uneven shape is polished.  
           [0026]    According to another aspect of the present invention, the adaptive dispersion compensating element is an adaptive dispersion compensating element in which a spectral resolving means is provided with a grating coupler having an optical fiber and a diffraction grating formed in the optical fiber and has operation that simply performs the optimum control by easily performing spectral resolution of an ultrahigh speed optical pulse of femto-second levels and performing decentralized control based on the result.  
           [0027]    As described above, according to another aspect of the present invention, the adaptive dispersion compensating element has a means that impresses a temperature gradient along the longitudinal direction of a chirp Bragg grating provided in an optical fiber, a means that applies a tensile force to the longitudinal direction of the chirp Bragg grating, a means that detects a signal light passing through the chirp Bragg grating through spectral resolution, and a means that performs feedback control based on spectral components of a detected optical frequency. Consequently, an adaptive controlling element that becomes a compact and high-stability device and performs dispersive compensation in an optical fiber transmission path with adaptability, such as performing dispersive compensation and waveform shaping in optical fiber transmission can be realized.  
           [0028]    Such objects and advantages of the present invention will further evident from the following embodiments described with reference to the appended drawings. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0029]    The present invention will be described in detail based on the followings, wherein:  
         [0030]    [0030]FIG. 1 is a drawing showing a production process of a conventional adaptive dispersion compensating element;  
         [0031]    [0031]FIG. 2 is a drawing showing the configuration of the conventional adaptive dispersion compensating element;  
         [0032]    [0032]FIG. 3 is a drawing showing the adaptive dispersion compensating element according to a first embodiment of the present invention;  
         [0033]    [0033]FIG. 4 ( a ) is a drawing showing a residual dispersion value in the input light position according to the first embodiment of the present invention;  
         [0034]    [0034]FIG. 4 ( b ) is a drawing showing a residual dispersion value in the output light position according to the first embodiment of the present invention;  
         [0035]    [0035]FIG. 5 ( a ) is a drawing showing a pulse time width in the input light according to the first embodiment of the present invention;  
         [0036]    [0036]FIG. 5 ( b ) is a drawing showing a pulse time width in the output light according to the first embodiment of the present invention;  
         [0037]    [0037]FIG. 6 ( a ) is a perspective view of a spectral resolution device according to a second embodiment of the present invention;  
         [0038]    [0038]FIG. 6 ( b ) is a top view of the spectral resolution device according to the second embodiment of the present invention;  
         [0039]    [0039]FIG. 6 ( c ) is a side view of the spectral resolution device according to the second invention;  
         [0040]    [0040]FIG. 7 is a drawing showing the configuration of a chirp Bragg grating according to a third embodiment of the present invention;  
         [0041]    [0041]FIG. 8 ( a ) is a drawing showing a group delay versus waveform characteristic of the chirp Bragg grating according to the third embodiment of the present invention;  
         [0042]    [0042]FIG. 8 ( b ) is a drawing showing a secondary dispersion versus wavelength characteristic of the chirp Bragg grating according to the third embodiment of the present invention;  
         [0043]    [0043]FIG. 8 ( c ) is a drawing showing a tertiary dispersion versus waveform characteristic of the chirp Bragg grating according to the third embodiment of the present invention; and  
         [0044]    [0044]FIG. 9 is a drawing showing the adaptive dispersion compensating element according to a fourth embodiment of the present invention. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0045]    (First Embodiment)  
         [0046]    A first embodiment of the present invention is described with reference to the drawings. FIG. 3 is a drawing that schematically shows the entire configuration of an adaptive dispersion compensating element according to the first embodiment of the present invention. In FIG. 3, number  101  is input light,  102  is an optical circulator,  103  is an optical coupler,  104  is a chirp Bragg fiber grating,  105  is a temperature gradient impression device,  106  is a spectral resolution device,  107  is a spectrum analyzer,  108  is a controller,  109  is an optical fiber, and  110  is output light.  
         [0047]    The operation of the adaptive dispersion compensating element constituted as described above is described.  
         [0048]    The input light  101  passes through the optical circulator  102  and is incident on the chirp Bragg fiber grating  104  and reflected as light whose dispersion is compensated, then returns to the circulator  102  again. Subsequently, signal light is branched by the optical coupler  103 . The branched monitor light on the one side is incident on the spectral resolution device  106  and a frequency is analyzed by the spectrum analyzer  107 , then an electric signal that is the output of the spectrum analyzer  107  enters the controller  108 . Further, the branched signal light on the other hand changes to the output light  110 .  
         [0049]    For example, if very-short-frequency pulse light is input, the light is provided with a broad frequency spectral component and necessarily susceptible to waveform dispersion. The light whose frequency is resolved by the spectral resolution device  106  is analyzed for the frequency by the spectrum analyzer  107 . If control is performed based on the signal, a high-speed light receiver is not necessary for compensation control of a dispersion value. The temperature gradient impression device  105  is controlled via the controller  108  so as to decrease a residual dispersion value in a desired waveform band.  
         [0050]    [0050]FIG. 4 ( a ) is a graphical representation showing a residual dispersion value in the input light. FIG. 4 ( b ) is a graphical representation showing a residual dispersion value in the output light. Further, FIG. 5 ( a ) is a graphical representation showing a pulse time width in the input light. FIG. 5 ( b ) is a graphical representation showing a pulse time width in the output light.  
         [0051]    As described above, according to this embodiment, an adaptive dispersion compensating element that performs decentralized control in an optical fiber transmission path, such as performing dispersive compensation and waveform shaping in optical fiber transmission, can be realized.  
         [0052]    Besides, in this embodiment, it is evident that the present invention is validated by suitably setting and executing structural parameters, such as the number of the chirp Bragg fiber gratings  104  and temperature gradient impression devices  105  and the control of the distance between the chirp Bragg fiber grating  104  and the temperature gradient impression device  105  by polishing the side of an optical fiber in which a chirp Bragg grating is formed and forming a fine uneven shape by etching in accordance with characteristics, such as a bandwidth and a dispersion amount of an optical fiber to be compensated.  
         [0053]    (Second Embodiment)  
         [0054]    A second embodiment of the present invention is described with reference to the drawings. FIG. 6 ( a ) is a perspective view showing the entire configuration of a grating coupler used for spectral resolution. FIG. 6 ( b ) is a top view of the grating coupler equally and FIG. 6 ( c ) is a side view of the grating coupler equally. In FIG. 6( a ), a number  201  is input light,  202  is a chirp Bragg fiber grating,  203  is an optical fiber in which the chirp Bragg fiber grating is formed,  204  is a top substrate,  205  is an optical fiber,  206  is a bottom substrate, and  207  is output light.  
         [0055]    The operation of the grating coupler constituted as shown above is described.  
         [0056]    The top substrate  204  that buries the optical fiber  203  in which the chirp Bragg fiber grating  202  is formed and the surface of the bottom substrate  206  that buries the optical fiber  205  are smoothly worked to the vicinity of the optical fiber core by abrasion respectively. When the respective worked surfaces are stuck, both the optical fibers draw nearer and five fiber couplers are formed in FIG. 6 ( a ). Each of the fiber couplers has such structure as shown in the top drawing of FIG. 6 ( b ) and the side view of FIG. 6( c ). However, this fiber coupler differs from a usual fiber coupler in that a grating is formed in the fiber on the one side. For example, in FIGS.  6  ( b ) and  6  ( c ), a spectrum that is equivalent to a reflected wavelength which corresponds to a grating pitch among the output light from Pin can be taken out from a P 2  port in a narrow band (less than 1 nm). Beside, the crossing angle θ of both fibers at this time will be set to about several degrees.  
         [0057]    When the input light  201 , such as very-short-frequency pulse light, is incident on the optical fiber  203  in which the chirp Bragg fiber grating  202  is formed, a grating pitch depends on a location. Accordingly, a spectrum that is equivalent to a reflected wavelength which corresponds to the grating pitch at the location of each fiber coupler can be taken out respectively. Consequently, the respective different spectrums whose wavelengths λ 1  to λ 5  can be taken out to the five optical fibers  205 .  
         [0058]    Even if a grating coupler constituted of an optical fiber and an optical fiber in which a diffraction grating is formed is used for spectral resolution of the input light as shown above, the operation of an adaptive dispersion compensating element is the same operation as the first embodiment. The spectral resolution of an ultrahigh speed optical pulse of femto-second levels is simply performed by performing control based on the size of each spectral component taken out using a grating coupler and the optimum control is simply performed by performing decentralized control based on the result.  
         [0059]    As described above, an adaptive dispersion compensating element that performs dispersive compensation in simple and optimum conditions can be realized by the control based on the spectral resolution in optical fiber transmission.  
         [0060]    Besides, in this embodiment, it is evident that the present invention is validated by suitably setting and executing structural parameters, such as the number of the chirp Bragg fiber gratings  104  and temperature gradient impression devices  105  and the control of the distance between the chirp Bragg fiber grating  104  and the temperature gradient impression device  105  by polishing the side of an optical fiber in which a chirp Bragg grating is formed and forming a fine uneven shape by etching in accordance with characteristics, such as a bandwidth and a dispersion amount of an optical fiber to be compensated.  
         [0061]    (Third Embodiment)  
         [0062]    An embodiment of the present invention is described with reference to the drawings. FIG. 7 is a drawing showing a configuration of a chirp Bragg grating. The configuration consists of areas (areas a and b) having two nonlinear chirp characteristics and a temperature gradient can independently be impressed to each area. A number  301  is a first nonlinear chirp Bragg grating,  302  is a first temperature gradient impression device,  303  is a second nonlinear chirp Bragg grating, and  304  is a second temperature gradient impression device.  
         [0063]    [0063]FIG. 8 ( a ) is a drawing showing a group delay versus waveform characteristic of the chirp Bragg grating according to the third embodiment of the present invention.  
         [0064]    [0064]FIG. 8 ( b ) is a drawing showing a secondary dispersion versus wavelength characteristic of the chirp Bragg grating according to the third embodiment of the present invention.  
         [0065]    [0065]FIG. 8 ( c ) is a drawing showing a tertiary dispersion versus waveform characteristic of the chirp Bragg grating according to the third embodiment of the present invention.  
         [0066]    The band of a chirp fiber diffraction grating is assumed to be 5 nm and the temperature characteristic (wavelength change) of a chirp fiber Bragg grating is assumed to be 0.01 nm/° C. respectively. FIG. 8 ( a ) is a drawing showing a group delay versus waveform characteristic of the chirp Bragg grating according to the third embodiment of the present invention. The solid line of FIG. 8 ( a ) shows an example of the wavelength dependence of a group delay of a nonlinear chirp Bragg grating in the areas a and b. Hereupon, when the temperature gradient of 50° C. is assigned to the area a, as shown in a dotted line, the reflection characteristic according to the temperature characteristic of the fiber diffraction grating changes from 1,555 nm to 1,554.5 nm by 0.5 nm. Accordingly, FIG. 8 ( b ) is a drawing showing a secondary dispersion versus wavelength characteristic of the chirp Bragg grating according to the third embodiment of the present invention. As shown in FIG. 8 ( b ), the group velocity slope (secondary dispersion) changes from −30 ps/nm to −37.5 ps/nm. Further, FIG. 8 ( c ) is a drawing showing a tertiary dispersion versus waveform characteristic of the chirp Bragg grating according to the third embodiment of the present invention. As shown in FIG. 8 ( c ), the tertiary dispersion (secondary dispersion slope) changes from −4 ps/nm 2  to −6.1 ps/nm 2 .  
         [0067]    Accordingly, if a group velocity gradient can be changed by assigning the temperature gradient of 50 degrees to a specific part of the area a, the tertiary dispersion can be controlled in the order of several ps/nm 2 .  
         [0068]    As described above, a chirp Bragg grating is constituted of multiple areas having a nonlinear chirp characteristic. When a wavelength dispersive characteristic is also controlled by independently impressing a temperature gradient to each area, the operation of an adaptive dispersion compensating element is the same operation as the first embodiment, and it can be realized that residual dispersion, such as higher order dispersion, is compensated.  
         [0069]    As described above, this embodiment has operation that compensates the residual dispersion, such as higher order dispersion, by controlling a wavelength dispersion characteristic finely and adaptively.  
         [0070]    Besides, in this embodiment, it is evident that the present invention is validated by suitably setting and executing structural parameters, such as the number of the chirp Bragg fiber gratings  104  and temperature gradient impression devices  105  and the control of the distance between the chirp Bragg fiber grating  104  and the temperature gradient impression device  105  by polishing the side of an optical fiber in which a chirp Bragg grating is formed and forming a fine uneven shape by etching in accordance with characteristics, such as a bandwidth and a dispersion amount of an optical fiber to be compensated.  
         [0071]    (Fourth Embodiment)  
         [0072]    An embodiment of the present invention is described with reference to the drawings. FIG. 9 shows an outline of the entire configuration of an adaptive dispersion compensating element. In FIG. 9, a number  401  is input light,  402  is a first optical circulator,  403  is a first chirp Bragg fiber grating,  404  is a first temperature gradient impression device,  405  is an optical fiber, and  406  is a second optical circulator. Further, number  407  is a second chirp Bragg fiber grating,  408  is a second temperature gradient impression device,  409  is an optical fiber,  410  is an optical coupler,  411  is a spectral resolution device,  412  is a spectrum analyzer,  413  is a controller,  414  is an optical fiber, and  415  is output light.  
         [0073]    The operation of the adaptive dispersion compensating element constituted as shown above is described.  
         [0074]    The input light  401  passes through the optical circulator  402  and is incident on the chirp Bragg fiber grating  403  and reflected as light whose dispersion is compensated, then returns to the circulator  402  again. Subsequently, the input light passes through the second optical circulator  406  and is incident on the first chirp Bragg fiber grating  407  and reflected as light whose dispersion is compensated, then returns to the second circulator  406 . At this time, the first chirp Bragg fiber grating and the second chirp Bragg fiber grating are connected so that the chirping direction will be reverse in the connection with each optical circulator and has the configuration in which the secondary dispersion generated in this dispersion compensating element can be cancelled.  
         [0075]    Subsequently, signal light is branched by the optical coupler  410 . The branched monitor light on the one side is incident on the spectral analytical device  411  and a frequency is analyzed by the spectrum analyzer  412 . An electric signal that is the output from the spectrum analyzer  412  enters the controller  413 . Further, the branched signal light on the other side changes to the output light  415 . For example, when very-short-frequency pulse light is input, the light is provided with a broad frequency spectrum component and necessarily susceptible to waveform dispersion. The light whose frequency is analyzed by the spectral resolution device  411  is analyzed for the frequency by the spectrum analyzer  412 . If control is performed based on the signal, a high-speed light receiver is not necessary for compensation control of a dispersion value. The temperature gradient impression device  410  and the second temperature gradient impression device  408  are controlled via the controller  413  so as to decrease a residual dispersion value in a desired waveform band.  
         [0076]    As described above, according to the present embodiment, an adaptive dispersion compensating element that performs decentralized control in an optical fiber transmission path, such as performing dispersive compensation and waveform shaping in optical fiber transmission, can be realized.  
         [0077]    Besides, in this embodiment, it is evident that the present invention is validated by suitably setting and executing structural parameters, such as the number of the chirp Bragg fiber gratings  104  and temperature gradient impression devices  105  and the control of the distance between the chirp Bragg fiber grating  104  and the temperature gradient impression device  105  by polishing the side of an optical fiber in which a chirp Bragg grating is formed and forming a fine uneven shape by etching in accordance with characteristics, such as a bandwidth and a dispersion amount of an optical fiber to be compensated.  
         [0078]    The present invention is described based on desirable embodiments shown in the drawings. However, it is evident that a person skilled in the art can easily change and alter the present invention, and such changing part is also included within the scope of the invention.

Technology Category: 3