Patent Application
20070248303
The foregoing and other objects, features and advantages of the present invention will be better understood from the following description taken in connection with the accompanying drawings, in which:
Embodiments of the present invention will now be described with reference to the drawings. Each drawing, however, is for illustrating one configuration example of the present invention, and a cross-sectional profile and the positional relationship of each composing element are shown roughly, only to assist in understanding the present invention, and therefore shall not limit the present invention to the illustrated examples. Also in the following description, specific materials and conditions may be used, but these materials and conditions are only one of the preferred examples, and the present invention shall never be limited to these.
In the following description, the case of forming the phase control means using an optical fiber will be used, but the phase control means is not limited to optical fiber, but may be formed using a flat type optical wave guide, for example.
<Reflectance of Unit FBG>
The optical pulse time spreader of the present invention is an optical pulse time spreader comprising a phase control means for time-spreading an optical pulse to be a string of chip pulses sequentially arrayed on the time base by encoding using an optical phase code, and generating and outputting the chip pulse string. The optical pulse time spreader of the present invention is an optical pulse time spreader which uses an SSFBG comprised of unit FBGs arrayed along the wave guide direction of the optical fiber as the phase control means.
The characteristic of the SSFBG of the present invention is that the unit FBGs, which correspond to the code values constituting the optical phase code one-to-one, are arrayed in a row along the wave guiding direction of the optical wave guide, and the phase difference between the Bragg-reflected lights from the two unit diffraction gratings, which are laterally adjacent to each other, is set as follows.
The phase difference between the Bragg-reflected lights from the two unit diffraction gratings which are laterally adjacent to each other and provide same code values is set to be
2Mπ (1).
The phase difference between the Bragg-reflected lights from the two unit diffraction gratings which are laterally adjacent to each other and provide different code values is set to be
(2N+1)π (2).
In the SSFBG of this invention, each reflectance of the unit diffractive gratings is set so that all the intensities of the chip pulses constituting the chip pulse string which is generated and output are equalized.
Now a method of calculating each reflectance of the unit diffraction gratings so that all the chip pulse intensities are equalized will be described with reference to
When the phase τ is converted into an actual geometric interval L, τ=(2π/λ)neffL, so L=τλ/(2πneff). Here neff is an effective refractive index when the light propagates the optical wave guide (core in the case of optical fiber). In the following description, interval τ is used regardless whether the value is a phase value or a value when the phase value is converted into a geometric interval, since it is not necessary to strictly distinguish a phase value τ and value τλ/(2πneff) when the phase value τ is converted into an actual geometric interval.
The interval τ between adjacent unit FBG i and unit FBG (i+1) is determined by the optical code, which is set for SSFBG 60, which is the phase control means. Generally the interval τi between adjacent unit FBG i and unit FBG (i+1), and the interval τj between adjacent unit FBG j and unit FBG (j+1) are different, that is τi≠τj. Here i and j are integers which satisfy 1≦i≦(j−1) and 1≦j≦(j−1) respectively, and i±j. However in the following description, the interval of adjustment unit FBG i and unit FBG (i−1) is not noted as τi adding the identification parameter i, but the intervals of adjacent unit FBGs are all noted as τ, regardless parameter i, since it is not necessary to identify τi and τj.
The first chip pulse and second chip pulse to be output from SSFBG 60 line up with the time interval when the phase 2τ is converted into time on the time base. This is because of the following reason. When an optical pulse is input to SSFBG 60, the first chip pulse is Bragg-reflected by FBG 1 and output, and the second chip pulse is Bragg-reflected by FBG 2 and output. Therefore the second chip pulse delays by the time when phase 2τ, to pass back and forth between FBG 1 and FBG 2, is converted into time. In other words, the i-th chip pulse and the (i+1)th chip pulse, which are adjacent to each other, line up with a time interval when the phase 2τ is converted into time on the time base.
Generally when phase τ is converted into time t, 2π (neff/λ) t=τ, so t=τλ/(2πneffC). Here neff is an effective refractive index when light propagates the optical wave guide (core in the case of optical fiber), and c is a speed of light in a vacuum. In the following description, it is not necessary to strictly distinguish phase τ and the value when the phase is converted into time, that is τλ/(2πneffc), so time interval τ or delay time τ is used without commenting that the value is a phase value or a value when the phase value is converted into time.
In SSFBG 60, as shown in
R
1
=P
c
/P
in (a′)
R
2
=P
c/(1−R1)2 (b)
R
k=(Pc1/2−Pk1/2)2/{(1−R1)2·(1−R2)2 . . . (1−Rk-1)2} (c-1)
R
k=(Pc1/2+Pk1/2)2/{(1−R1)2·(1−R2)2 . . . (1−Rk-1)2} (c-2)
Here Pin is an intensity of the optical pulse to be input to the phase control means, and if Pin is specified as Pin=1, then the above formula (a) is given by
R
1
=P
c(constant) (a)
The formula (a′) is expressed with parameter Pin remaining, so as to clearly know that R1 is reflectance, but the respective reflectances R2 and Rk of the second and k-th unit diffraction gratings are expressed with specifying Pin=1, as mentioned later.
The constant Pc is a value which is set as the intensity of the chip pulse, which is reflected from the first unit diffraction grating, and is output from the phase control means, and in the present invention, the reflectance of each unit diffraction grating is set so that all the intensities of the chip pulses to be output from the phase control means are equalized to this value.
Pk is an intensity of the triple reflection chip pulse to be output from the phase control means. Formula (c-1) and Formula (c-2) express the reflectance of the k-th unit diffraction grating when the phase difference between the single reflection chip pulse which is generated by a single reflection and is output for the k-th time and the triple reflection chip pulse which is generated by a triple reflection and is output for the k-th time is 0 (same phase), and is π (opposite phase) respectively.
The cases when the phase difference between a chip pulse generated by a single reflection and a chip pulse generated by a triple reflection is 0 (same phase) and π (opposite phase) generally means the case when the phase difference is 2Pπ, where P is an integer, and the case when the phase difference is (2Q+1)π, where Q is an integer respectively. However in the following description, the contents of the description are not changed even if P=Q=0, so cases when the phases of the chip pulse generated by a single reflection and the chip pulse generated by a triple reflection are the same and opposite (phase difference is π) means that the cases when the phase difference thereof is 0 and π respectively.
By setting the respective reflectances of the unit diffraction gratings as above, the intensities of all the chip pulses constituting the chip pulse string to be generated and output are equalized, and the reason for this will now be described.
If an optical pulse of which intensity if Pin is input to SSFBG 60, Bragg reflection occurs by the FBG 1, and the first chip pulse of which intensity is Pc is generated and output. The reflectance of FBG 1 at this time is given by R1=Pc/Pin. The second chip pulse is a chip pulse generated by Bragg reflection by the FBG 2. The generation steps of the second chip pulse are as follows.
An optical pulse of which intensity is Pin is input to the SSFBG 60, passes through the FBG 1, is Bragg-reflected by FBG 2, and passes through FBG 1 again, and is output. When the optical pulse of which intensity is Pin passes through FBG 1 first, the intensity thereof becomes (1−R1)Pin, and when the optical pulse is Bragg-reflected by FBG 2, the intensity thereof becomes (1−R1)·R2·Pin. When this optical pulse passes through FBG 1 again, the intensity thereof becomes (1−R1)·R2·(1−R1)·Pin=(1−R1)2·R2·Pin. This intensity (1−R1)2·R2·Pin must be the same as Pc, (1−R1)2·R2·Pin=Pc, which means the reflectance R2 of FBG 2 is given by R2=Pc/{(1−R1)2·Pin}.
To simplify the calculation herein below, the intensity Pin of the input optical pulse is set to 1 for description. Since Pin=1, R2=Pc/{(1−R1)2·Pin}=Pc/(1−R1)2. The respective reflectances R1, R2 and Rk of the first, second and k-th unit diffraction gratings are values which are defined without depending on the intensity Pin of the input optical pulse, so setting the intensity Pin of the input optical pulse to 1 does not influence the calculation result.
Then the reflectance R3 of FBG 3 is determined. The intensity P3′ of a chip pulse which is to be output by Bragg reflection occurred once in FBG 3, that is a single reflection chip pulse which is generated by a single reflection and is output for the third time, is given by Formula (3).
P
3′=(1−R1)2·(1−R2)2·R3 (3)
P
3=(R22·R1)·(1−R1)2 (4)
This triple reflection chip pulse is a chip pulse which is transmitted through FBG 1 (transmittance 1−R1), Bragg-reflected by FBG 2 (reflectance R2, first reflection), Bragg-reflected by FBG 1 (reflectance R1, second reflection), Bragg-reflected again by FBG 2 (reflectance R2, third reflection), and is transmitted through FBG 1 (transmittance 1−R1), and is output.
In other words, if the intensity of the input optical pulse is 1, the intensity thereof becomes (1−R1) when the optical pulse transmits through FBG 1. When the optical pulse of which intensity is (1−R1) is Bragg-reflected by FBG 2, the intensity of the reflected light becomes (1−R1)×R2. When the optical pulse of which intensity is (1−R1)×R2 is Bragg-reflected the second time by FBG 1, the intensity thereof becomes (1−R1)×R2×R1. When the optical pulse of which intensity is (1−R1)×R2×R1 is Bragg-reflected the third time by FBG 2, the intensity thereof becomes (1−R1)×R2×R1×R2. When the optical pulse of which intensity is (1−R1)×R2×R1×R2 transmits through FBG 1, the intensity thereof becomes (1−R1)×R2×R1×R2×(1−R1).
Therefore the intensity P3 of the triple reflection chip pulse which overlaps the single reflection chip pulse which is output for the third time becomes (1−R1)×R2×R1×R2×(1−R1)=(R22·R1)·(1−R1)2, and the Formula (4) is acquired.
The intensity of the chip pulse generated as a result of the single reflection chip pulse overlapping the triple reflection chip pulse is given by a square of the sum of the amplitudes of both chip pulses if the phases of the single reflection chip pulse and the triple reflection chip pulse are the same (phase difference is 0). In other words, the amplitude of the intensity P3′ of the chip pulse which is generated by the single reflection and is output for the third time is P3′1/2, and the amplitude of the intensity P3 of the chip pulse generated by the triple reflection is P31/2, so the intensity of the chip pulse generated as a result of the chip pulse generated by a single reflection overlapping the chip pulse generated by a triple reflection is given by the following Formula (5).
(P3′1/2+P31/2)2 (5)
If the phases of the single reflection chip pulse and the triple reflection chip pulse are the opposite (phase difference is π), the intensity of the chip pulse is given by the square of the difference of the amplitudes of these chip pulses. Therefore the intensity of the chip pulse generated as a result of the chip pulse generated by a single reflection overlapping the chip pulse generated by a triple reflection is given by the following Formula (6).
(P3′1/2−P31/2)2 (6)
The intensity of the chip pulse generated as a result of the single reflection chip pulse overlapping the triple reflection chip pulse at the same phases is given by Formula (5), that is (P31/2+P3′1/2)2. So this value must be the same as the intensity Pc of the chip pulse which is reflected from the first unit diffraction grating and is output, for the intensities of the chip pulse string to be equalized.
In other words, Pc=(P31/2+P3′1/2)2 is the condition for the intensities of the chip pulse string to be output to be equalized. This is transformed into P3′=(Pc2−P31/2)2. Since the intensity P3′ of the single reflection chip pulse to be output for the third time is given by Formula (3), the following Formula (7) can be acquired by substituting Formula (3) for this formula that is, Pc=(P31/2+P3′1/2)2.
(1−R1)2·(1−R2)2·R3=(Pc1/2−P31/2)2 (7)
therefore
R
3={(Pc1/2−P31/2)2}/{(1−R1)2·(1−R2)2} (8)
In the same way, if the phases of the single reflection chip pulse and the triple reflection chip pulse are opposite (phase difference is π), then
R
3={(Pc1/2+P31/2)2}/{(1−R1)2·(1−R2)2} (8′)
Now the intensity of the fourth and later chip pulses to be output from the SSFBG 60 will be considered. Table 2 shows a list of unit FBGs related to the generation of chip pulses generated by the triple reflection out of the fourth and later chip pulses to be output from SSFBG 60.
The fourth chip pulse is output after the first chip pulse with a 6τ delay time. The fifth chip pulse is output after the first chip pulse with an 8τ delay time. The sixth and later chip pulses are also output in the same way.
The fourth chip pulse, which is generated by a single reflection and is output for the fourth time, is a chip pulse generated by Bragg reflection by FBG 4. The chip pulse which is generated by the triple reflection and is output for the fourth time is output via three types of reflection routes, as shown in Table 2. For example, on the top level concerning the chip pulse which is output for the fourth time in Table 2, R2, R1 and R3 are shown as the first, second and third. This means that these chip pulses are reflected by FBG 2, FBG 1 and FBG 3 sequentially, and are output. This is the same for the other two combinations.
The interval τ between adjacent unit FBGs is 0 or π, so the phase difference between a chip pulse which is generated and output by a single reflection and a chip pulse which is generated and output by a triple reflection is also 0 or π. The reason is as follows.
The delay time differences between the chip pulses which are output for the third, fourth and fifth times and the chip pulse which is output for the first time are 4τ, 6τ and 8τ respectively, as shown in Table 2. For example, in the case of the third chip pulse of which delay time difference is 4τ, 24(=16) combinations are possible from 4τ=τ+τ+τ+τ=0+0+0+0=0 to 4τ=τ+τ+τ+τ=π+π+π+π=4π, including 4τ=τ+τ+τ+τ=π+0+0+0=π and 4τ=τ+τ+τ+τ=π+π+π+0=3π, and for all these cases, the delay time difference can be converted into phase difference which is either 0 (same phase) or π (opposite phase). In other words, 2π and 4π are equivalent to phase difference 0, and 3π is equivalent to phase difference π. This is the same in the case of delay time differences 6τ and 8τ.
In the case of a chip pulse generated by a single reflection, on the other hand, the delay time differences between the chip pulse which is output for the first time and the chip pulses which are output for the third, fourth and fifth times are 4τ, 6τ and 8τ respectively, just like the above mentioned case of triple reflection chip pulses. However the path is different between a chip pulse which is generated and output by a single reflection and a chip pulse which is generated and output by a triple reflection. For example, the chip pulse which is generated by a single reflection and is output for the fourth time is transmitted through FBG 1 to FBG 3, is reflected by FBG 4, is transmitted through FBG 3 to FBG 1, and is output. The chip pulse which is generated by a triple reflection and is output for the fourth time, on the other hand, propagates three types of path combinations, which are different from the single reflection chip pulse, as shown in Table 2.
Therefore depending on this difference of paths, the phase difference between a chip pulse which is generated and output by a single reflection and a chip pulse which is generated and output by a triple reflection becomes either 0 or π.
Generally in the case of a k-th chip pulse, the reflectance Rk of FBGk is given by the above Formulas (c-1) and (c-2). In other words, the intensity Pk′ of a single reflection chip pulse which is generated and output by a single reflection is given by
P
k=(1−R1)2·(1−R2)2 . . . (1−Rk-1)2·Rk (9)
N
k
=N
k-1+(k−2) (10)
The intensities of a chip pulse generated as a result of a chip pulse which is generated and output by a single reflection overlapping a chip pulse which is generated and output by a triple reflection, when the chip pulse which is generated and output by a single reflection and a chip pulse which is generated and output by a triple reflection have the same phases, and when they have opposite phases, are given by
(Pk′1/2+Pk1/2)2 (11) and
(Pk′1/2−Pk1/2)2 (11′)
respectively.
These values must be the same as the intensity Pc of the chip pulse, which is reflected and output from FBG 1 in order to equalize the intensities of the chip pulse string to be output. Since the condition to equalize the intensities is Pc=(Pk′1/2+Pk1/2) and Pc=(Pk′1/2−Pk1/2), then
Pk′=(Pc1/2−Pk1/2)2=(1−R1)2·(1−R2)2 . . . (1−Rk-1)2·Rk
and
Pk′=(Pc1/2+Pk1/2)2=(1−R1)2·(1−R2)2 . . . (1−Rk-1)2·Rk
by Formula (9). Therefore
R
k=(Pc1/2−Pk1/2)2/{(1−R1)2·(1−R2)2 . . . (1−Rk-1)2} (c-1)
and
R
k=(Pc1/2+Pk1/2)2/{(1−R1)2·(1−R2)2 . . . (1−Rk-1)2} (c-2)
are acquired.
Based on the result of considering the determined reflectances R1, R2 and Rk of the first, second and k-th unit diffraction gratings respectively, the case of setting optical phase code of which code length is 15 will be described as an example. In other words, an example of the case of J=15 will be described.
With reference to
In
Therefore according to the present invention, the reflectance of each unit FBG is determined considering that the chip pulses to be output from the SSFBG are not only those generated and output from each unit FBG by a single reflection, but include those generated and output by a triple reflection, and the result of determining the reflectance of each unit FBG according to this invention is indicated by the black dots in
In the reflectances indicated by black dots in
According to the phase control means of the optical pulse time spreader of the present invention, the reflectances of the unit diffraction gratings which are arrayed in a row along the wave guiding direction of the optical wave guide are determined considering the presence of chip pulses generated and output by a triple reflection, as mentioned above. For certain chip pulses generated and output by 5 times or more of odd count of multiple reflections also exist, but as mentioned later, it was confirmed that it is sufficient to consider the presence of chip pulses generated and output by a triple reflection.
Based on the reflectances determined using the above mentioned Formulas (a), (b), (c-1) and (c-2), the level Δn of the refractive index modulation of each unit diffraction grating is set, and the characteristic of the chip pulse string to be output was checked, and the result will be described below.
The structure of an SSFBG 40 as a phase control means of an optical pulse time spreader of a first embodiment will be described with reference to
The relationship between the reflectance of the unit FBG to be installed in the SSFBG of the first embodiment and the level Δn of the refractive index modulation will be described with reference to
Using the relationship between the reflectance of the unit FBG and the level Δn of the refractive index modulation of the unit FBG, shown in
The encoding characteristic of the SSFBG of the first embodiment will be described with reference to
The difference A between the maximum and minimum of the intensities of chip pulses which are output from the SSFBG of the prior art shown in
The auto-correlation waveform which is formed by decoding an optical pulse encoded by the SSFBG of the first embodiment will be described with reference to
In
It is desirable that the auto-correlation waveform is generated such that the side peak is as small as possible. In other words, a decoder is for regenerating the optical pulse before encoding, so an ideal is regenerating a single optical pulse. This means that the ratio of the peak and sub-peak of the auto-correlation waveform, which is a signal to noise ratio (S/N ratio), is larger the better.
As
The structure of the SSFBG 50 as a phase control means of an optical pulse time spreader of the second embodiment will be described with reference to
The difference between the refractive index modulation structure of the SSFBG 50 and the refractive index modulation structure of the SSFBG 40 of the first embodiment is that the refractive index modulation intensity of the periodic refractive index modulation structure of the unit FBG constituting the SSFBG 50 is apodized by a window function. In the second embodiment, a Gaussian error function is used for this window function.
A method of apodizing the refractive index modulation intensity of the periodic refractive index modulation structure of the unit FBG using the window function will now be described with reference to
As the extreme right side in
(Δn/2)·sin(2πx/Λ) (3)
A unit FBG having a periodic refractive index modulation structure given by a new function which is Formula (3) multiplied by a window function given by the following Formula (4) is referred to as a unit FBG apodized by the function given by Formula (4).
exp[−1n2[2(x−(L−2))/LB]2] (4)
Here 1n2 indicates a natural logarithm of 2. exp indicates an exponential function of which exponent is the base of the natural logarithm. Here, just like the first embodiment, it is assumed that the length L of the unit FBG is 2.4 mm, the average of the effective refractive index of the optical fiber is 1.4473, and the refractive index modulation period Λ of the unit FBG is 535.5 nm. Therefore the wavelength λ of the Bragg-reflected light given by λ=2neff×Λ is 1550 nm. B is a coefficient for band adjustment, and it is set to B=0.5 here.
By apodization, a concentrated Bragg reflection occurs at the center of each FBG, and as a result, the half width of the time-based waveform of the generated Bragg-reflected light becomes small. In other words, the half width of the chip pulse constituting the encoded optical pulse string becomes small, so overlapping of the bottom areas of chip pulses constituting the encoded optical pulse string on the time base can be decreased. If overlapping of the bottom areas of chip pulses can be decreased, the effect of interference due to overlapping of the bottom areas of chip pulses on the time base can be decreased. As a result, the intensity difference of chip pulses can be decreased compared with the case of encoding and decoding using the optical pulse time spreader of the first embodiment.
The function for the apodization corresponding to Formula (4) is not limited to a Gaussian error function. Any function that can apodize the level of amplitude of the periodic refractive index modulation structure of the unit FBG given by Formula (3), so as to be maximum at the center area of the unit FBG, can be used. For example, a function used for the signal processing technology field, such as Raised cosine, Tan h, Blackman, Hamming, Hanning, etc., can be used.
Now a method for determining the level Δn of the refractive index modulation of each unit FBG will be described. For this, the reflectance to be set for each unit FBG must be determined. The method for determining this reflectance was explained in the first embodiment, and is therefore omitted here. In the second embodiment as well, the code being set for the SSFBG 50 is the same code as the code being set for the SSFBG 40 of the first embodiment. Therefore the reflectance to be set for each unit FBG is the same as the case of the first embodiment.
So the relationship between the reflectance to be set for each FBG and the level Δn of the refractive index modulation in the case of the second embodiment must be determined. This relationship is shown in
The encoding characteristic of the SSFBG of the second embodiment will be described with reference to
The difference A between the maximum and minimum of the intensities of chip pulses which are output from the SSFBG of the prior art shown in
Also as mentioned above, according to the SSFBG of the second embodiment, the overlapping of the bottom areas of chip pulses constituting the encoded optical pulse string on the time base decreases. In other words, interference between adjacent chip pulses decreases, and each chip pulse is clearly separated. This means that the input optical pulse is evenly spread within the spreading time on the time base. In this way, the input optical pulse being spread evenly within the spreading time on the time base has the following advantages.
An auto-correlation waveform which is formed by decoding an optical pulse encoded by the SSFBG of the second embodiment will be described with reference to
It is desirable that the auto-correlation waveform is generated such that the side peak is as small as possible. In other words, a decoder is for regenerating the optical pulse before encoding, so the ideal is regenerating a single optical pulse.
While the ratio of the peak and sub-peak of the auto-correlation waveform which is generated and output by the SSFBG of the prior art shown in
As
The ratio of the peak and sub-peak of the auto-correlation waveform is the signal-to-noise ratio (S/N ratio), so the greater this ratio the better. In other words, according to the SSFBG of the second embodiment, the auto-correlation waveform of which S/N ratio is larger, not only compared to a conventional SSFBG but also to the ideal value of the SSFBG of the first embodiment, can be generated. Therefore by using the optical pulse time spreader of the second embodiment as an encoder and decoder of OCDM, an optical communication system which can insure an even higher reliability can be constructed.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2006-116538 | Apr 2006 | JP | national |
