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CN114280722B - Transmission type optical filter - Google Patents

Transmission type optical filter Download PDF

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CN114280722B
CN114280722B CN202210215800.XA CN202210215800A CN114280722B CN 114280722 B CN114280722 B CN 114280722B CN 202210215800 A CN202210215800 A CN 202210215800A CN 114280722 B CN114280722 B CN 114280722B
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grating
channel
fiber grating
transmission
frequency
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CN114280722A (en
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胡胜
戴润泽
袁功进
胡凯峰
刘聪
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Hubei University of Technology
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Hubei University of Technology
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Abstract

The invention relates to an optical filter, in particular to a transmission type optical filter, which is characterized in that N-1 phase shifts are inserted into a uniform fiber grating of the transmission type optical filter to divide the grating intoNSegment(s)
Figure 496463DEST_PATH_IMAGE001
The total length of the grating isL，
Figure 243839DEST_PATH_IMAGE002
，
Figure 408235DEST_PATH_IMAGE003
，
Figure 823036DEST_PATH_IMAGE004
. The optical filter can realize the filtering of a plurality of pass bands and flat tops and narrow bands. By inserting a plurality of sampling fiber gratings
Figure 562322DEST_PATH_IMAGE005
Phase shifting, finally realizing the optical filter covering more than 100 flat-top narrow-bandwidth channels of the C + L wave band. The 3db bandwidth of the multi-channel is close to 800MHz, and the shape factor is close to 2.15.

Description

Transmission type optical filter
Technical Field
The present invention relates to an optical filter, and more particularly, to a transmission type optical filter.
Background
With the increasing demands of users, the requirements of optical networks are increasing, optical fiber communication systems require high speed, large capacity, and the like, and devices also require better functionality. Among them, in the WDM system, it is required to realize multi-path arbitrary signal processing. The fiber grating can be flexibly designed according to requirements because the spectral characteristics are easy to design and can be well compatible with a fiber system. The multi-channel fiber grating is used for multi-channel signal processing, and the general fiber grating structure with multiple channels can be realized by periodically modulating the refractive index variation of the fiber grating, and can generally sample the amplitude or phase of the refractive index variation, or simultaneously apply the two kinds of sampling to combine. In DWDM systems, the usual channel spacing is 50GHz, 100GHz according to the standard established by ITU-T, and the corresponding channel numbers are 80 and 40 in the C-band, respectively. Even in some ultra dense optical networks the channel spacing is 12.5GHz, 25 GHz. However, it is difficult to meet these performance criteria with a single sampling method.
Disclosure of Invention
The technical problem of the invention is mainly solved by the following technical scheme:
a transmission type optical filter is characterized in that N-1 phase shifts are inserted into a uniform fiber grating of the transmission type optical filter
Figure 626476DEST_PATH_IMAGE001
Dividing the grating intoNSegment(s)
Figure 605934DEST_PATH_IMAGE002
The total length of the grating isLWherein N small segments are respectively
Figure 464299DEST_PATH_IMAGE003
，
Figure 921826DEST_PATH_IMAGE004
Corresponding phase shift of
Figure 755439DEST_PATH_IMAGE005
。
In the above-described transmissive optical filter, the insertion position of the phase shift is: n-1
Figure 640219DEST_PATH_IMAGE006
Phase shifting divides the interleaved sampled fiber grating intoNAfter the small section, the total length is L,
Figure 985880DEST_PATH_IMAGE007
the reflection coefficient and the transmission coefficient of the i-th segment are respectively used
Figure 450360DEST_PATH_IMAGE008
And
Figure 181555DEST_PATH_IMAGE009
express, and satisfy
Figure 253548DEST_PATH_IMAGE010
，
Figure 273456DEST_PATH_IMAGE011
Are respectively
Figure 89097DEST_PATH_IMAGE012
And
Figure 878061DEST_PATH_IMAGE013
and (3) conjugation. Transmission coefficient of the whole gratingt andcoefficient of reflection
Figure 370222DEST_PATH_IMAGE014
Reflection coefficient of i-th segment grating
Figure 687547DEST_PATH_IMAGE015
And transmission coefficient
Figure 228250DEST_PATH_IMAGE016
Phase shift
Figure 950349DEST_PATH_IMAGE017
The relationship between them satisfies:
Figure 551095DEST_PATH_IMAGE019
(ii) a Wherein j is an imaginary number symbol,
Figure 607912DEST_PATH_IMAGE020
is a natural constant.
In the above-mentioned one transmission type optical filter, N-1 pieces based on MPS
Figure 703038DEST_PATH_IMAGE006
In phase shifted interleaved sampled fiber gratings, the structural parameters include the grating length L,
Figure 528912DEST_PATH_IMAGE021
，
Figure 113608DEST_PATH_IMAGE022
，
Figure 329826DEST_PATH_IMAGE023
duty ratio of
Figure 540227DEST_PATH_IMAGE024
The period of the sub-gratings of the interleaved sampling fiber grating is as follows:
Figure 696972DEST_PATH_IMAGE025
，
Figure 905099DEST_PATH_IMAGE026
which is the speed of light in a vacuum,
Figure 421662DEST_PATH_IMAGE021
is the equivalent refractive index of the core,
Figure 107858DEST_PATH_IMAGE023
is the amplitude of the modulation of the refractive index,
Figure 908324DEST_PATH_IMAGE027
is the total length of each of the sampled gratings,
Figure 38085DEST_PATH_IMAGE028
is the length of each segment of the uniform sub-grating,
Figure 494474DEST_PATH_IMAGE029
is the duty cycle of the pulse-width modulation,
Figure 781099DEST_PATH_IMAGE030
the central frequency of the ith sampling fiber grating; wherein the length of the grating, L,
Figure 921225DEST_PATH_IMAGE021
，
Figure 471155DEST_PATH_IMAGE022
，
Figure 414840DEST_PATH_IMAGE023
four parameters are given values.
In the above-described transmission type optical filter, a transmission type optical filter in which the channel interval is 50GHz, the number of channels is 81, the transmission spectrum covering the entire C-band is obtained, and the center frequency of each channel corresponds to the frequency of the ITU-T standard can be obtained according to the selected parameters.
Therefore, the invention has the following advantages: and filtering of multiple pass bands and flat tops and narrow bands is realized. By inserting a plurality of sampling fiber gratings
Figure 518538DEST_PATH_IMAGE006
Phase shifting, finally realizing the optical filter covering more than 100 flat-top narrow-bandwidth channels of the C + L wave band. The 3db bandwidth of the multi-channel is close to 800MHz, and the shape factor is close to 2.15.
Drawings
FIG. 1 is a schematic illustration of an interleaved sampled fiber grating structure and refractive index variation.
FIG. 2 is a diagram of the Fourier transform corresponding to a single sampled fiber grating structure.
Fig. 3a is a schematic diagram of the spectral superposition of three response spectra when M =3 (arbitrary β 1, β 2, β 3).
Fig. 3b is a schematic diagram of the spectral superposition of the three response spectra when M =3 (β 1, β 2, β 3 satisfy
Figure 965700DEST_PATH_IMAGE031
）。
FIG. 4 is a schematic diagram of a symmetric multi-phase shifted fiber grating.
FIG. 5 is a graph of scaling factors C and C
Figure 234001DEST_PATH_IMAGE032
Schematic diagram of the relationship of (1).
FIG. 6a is a graph showing the relationship between frequency and transmittance (
Figure 664982DEST_PATH_IMAGE033
)。
FIG. 6b is a graph showing the relationship between frequency and transmittance (
Figure 496672DEST_PATH_IMAGE034
)。
FIG. 7 is two
Figure 876969DEST_PATH_IMAGE006
Phase shift and three
Figure 503122DEST_PATH_IMAGE006
The phase shifted reflection channel is schematically shown with a center frequency of 193.1 THz.
Fig. 8a is a schematic diagram of a phase shift profile and a phase profile.
FIG. 8b is a schematic diagram of the transmission channel corresponding to a reference frequency 193.1 THz.
Fig. 8C is a transmission spectrum covering the C-band.
FIG. 9a is a plurality
Figure 421400DEST_PATH_IMAGE035
Schematic diagram of phase shift distribution.
Fig. 9b is a schematic diagram of the phase distribution.
Fig. 10 is a transmission spectrum covering the C-band.
FIG. 11 is a transmission spectrum with a center frequency of 193.1 THz.
FIG. 12 is a transmission spectrum covering the C + L-band, with channel spacing of 100 GHz.
FIG. 13 is a schematic diagram of the transmission channel at reference frequency 193.1 THz.
Fig. 14a is a phase shift relationship for a comb filter with a channel spacing of 12.5 GHz.
Fig. 14b is the phase relationship for a comb filter with a channel spacing of 12.5 GHz.
Figure 14c is the comb filter frequency versus reflectivity for a channel spacing of 12.5 GHz.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
Example (b):
as shown in FIG. 1, in each sampling period
Figure 869830DEST_PATH_IMAGE036
In which it is composed ofMA different period
Figure 26005DEST_PATH_IMAGE037
，
Figure 150956DEST_PATH_IMAGE038
，…，
Figure 779033DEST_PATH_IMAGE039
The length of each section of uniform sub-grating is the same as that of the section of uniform sub-grating
Figure 483684DEST_PATH_IMAGE040
。
The change in refractive index of an interleaved sampled fiber grating can be expressed as:
Figure 822261DEST_PATH_IMAGE041
(1)
wherein
Figure 806529DEST_PATH_IMAGE042
，
Figure 230557DEST_PATH_IMAGE043
，
Figure 207740DEST_PATH_IMAGE044
，
Figure 151556DEST_PATH_IMAGE045
Is a function of the truncation to be,
Figure 555993DEST_PATH_IMAGE046
。
the right hand side of the equation for (1),
Figure 218050DEST_PATH_IMAGE047
(2)
wherein,
Figure 733345DEST_PATH_IMAGE048
is the amplitude of the modulation of the refractive index,
Figure 46514DEST_PATH_IMAGE049
taking the real part of the imaginary number for the mathematical notation, i is a given integer,
Figure 369655DEST_PATH_IMAGE050
is the period of the fiber grating for a given integer i, zis a certain position on the fiber grating, j is an imaginary number symbol, and L is the grating length，
Figure 768275DEST_PATH_IMAGE028
Is the length of each segment of the uniform sub-grating,
Figure 352840DEST_PATH_IMAGE051
is the total length of one sampling period, m is a given integer,
Figure 208932DEST_PATH_IMAGE052
is the mathematical sign of the truncation function.
Therefore, the refractive index change of the interleaved sampling fiber grating can be regarded asMSuperposition of refractive index variations of sampled gratings, i.e.MThe fiber gratings of the different modulation functions are superimposed. Duty cycle of each sampled fiber gratingpThe same applies to all of them,
Figure 17488DEST_PATH_IMAGE053
。
to pair
Figure 575508DEST_PATH_IMAGE054
Fourier transform is carried out to obtain
Figure 511234DEST_PATH_IMAGE055
(3)
Figure 471100DEST_PATH_IMAGE057
Wherein,
Figure 653820DEST_PATH_IMAGE058
，
Figure 777765DEST_PATH_IMAGE059
is a dirac
Figure 438553DEST_PATH_IMAGE060
Function of channel spacing of
Figure 80623DEST_PATH_IMAGE061
，
Figure 434244DEST_PATH_IMAGE062
It is shown that the convolution of two functions,
Figure 29173DEST_PATH_IMAGE063
as a function of the refractive index after Fourier transform
Figure 244385DEST_PATH_IMAGE064
，
Figure 975581DEST_PATH_IMAGE065
I is a given integer, i is the number of orders after fourier transform,
Figure 500103DEST_PATH_IMAGE066
for a given number of angles to which i corresponds,
Figure 333061DEST_PATH_IMAGE067
is a function of the angle variable in the function,
Figure 335652DEST_PATH_IMAGE068
for a given i corresponds to the period of the uniform sub-grating.
As shown in fig. 2, forFunction of refractive index variation of single sampling fiber grating
Figure 937666DEST_PATH_IMAGE069
By Fourier transformation, the resulting discrete variation
Figure 429827DEST_PATH_IMAGE070
. Each vertical line in the graph represents a corresponding reflection channel, the frequency corresponding to the vertical line is the center frequency of the channel, and the response curve of each channel is a sinc function envelope. Because the designed interleaved sampling fiber grating has different periods and the same other parameters, the fiber grating has the same structure and the same structure
Figure 671453DEST_PATH_IMAGE071
Except for the center frequency, the response spectrum of (A) is the same as other parameters, which can be considered asMThe response spectrum is a shift in the frequency spectrum.
For simplicity of consideration, assumeM=3, the three response spectra are superimposed on the frequency domain, as shown in fig. 3a
Figure 287854DEST_PATH_IMAGE072
For any value, many frequency components in the response spectrum can be seen, some frequencies are spaced relatively close to each other and are not easy to distinguish, and the frequency coverage range corresponding to the larger response amplitude is not increased. As shown in fig. 3b, when the center frequency satisfies the special relationship:
Figure 196904DEST_PATH_IMAGE073
i.e. the spacing between the centre frequencies is an integer multiple of the channel spacing. In this case, it can be found that the superimposed response spectrum can exhibit relatively regular superimposition, and the superimposition in the upper half plane increases the response amplitude and decreases the response amplitude in the opposite direction, and as a result, a plurality of channels with the same response amplitude can be obtained. Also, linear superposition of refractive index changes is described, which may correspond to superposition of spectra. Therefore, through the analysis of a Fourier method, an interpolation sampling fiber grating with a flat envelope multi-channel reflection spectrum can be designed.
With the above analysis, in the interleaved sampling fiber grating, the channel frequency spacing
Figure 610699DEST_PATH_IMAGE074
The frequencies are equally spaced, the channel wavelengths are spaced
Figure 870779DEST_PATH_IMAGE075
，cIs the speed of light in vacuum. First, theiCenter frequency of sampled fiber grating
Figure 215173DEST_PATH_IMAGE076
Comprises the following steps:
Figure 791779DEST_PATH_IMAGE077
(4)
Figure 829005DEST_PATH_IMAGE078
(5)
Figure 107540DEST_PATH_IMAGE079
for the center frequency of the entire reflection spectrum, it should be noted thatHIt must be an integer number to satisfy the requirement that the channels are stacked in a matched manner. First, theiThe center wavelength of each sampled fiber grating is:
Figure 6357DEST_PATH_IMAGE080
。
based on the structure of the multi-phase-shift interleaved fiber grating, the phase modulation of the fiber grating is redesigned, and multi-channel transmission type filtering can be realized. The uniform grating is analyzed for phase modulation to obtain the filtering characteristic of a single channel, and then the uniform grating is sampled, so that the characteristic of the single channel can be popularized to multiple channels.
The invention relates to a symmetrical structure of fiber grating, as shown in FIG. 4, inserting (N-1) phase shift in uniform fiber grating
Figure 889999DEST_PATH_IMAGE081
By dividing the grating intoNSegment(s)
Figure 160443DEST_PATH_IMAGE082
Assuming that the total length of the grating isL，
Figure 414357DEST_PATH_IMAGE083
，
Figure 366132DEST_PATH_IMAGE084
，
Figure 104281DEST_PATH_IMAGE085
。
Each small segment can be used
Figure 234043DEST_PATH_IMAGE086
The transmission matrix is represented as:
Figure 487169DEST_PATH_IMAGE087
(6)
Figure 977057DEST_PATH_IMAGE088
and
Figure 382761DEST_PATH_IMAGE089
respectively representing the reflection coefficient and the transmission coefficient of the ith segment, can be calculated by a coupling mode theory, and satisfies
Figure 932691DEST_PATH_IMAGE090
，
Figure 876376DEST_PATH_IMAGE091
Are respectively
Figure 717425DEST_PATH_IMAGE088
And
Figure 164586DEST_PATH_IMAGE089
conjugation of (1).
By using the transmission matrix method, the transmission coefficient of the whole grating can be obtainedtReflection from small segments of the grating
Figure 695537DEST_PATH_IMAGE088
And transmission
Figure 860940DEST_PATH_IMAGE089
Phase shift
Figure 958209DEST_PATH_IMAGE092
The relationship between them.
Figure 72926DEST_PATH_IMAGE093
(7)
Finally, the transmission coefficient can be obtainedtAnd coefficient of reflectionrThe analytical formula (2).
To obtain a narrow-band "flat-topped" transmission peak, it is necessary to calculate the number of insertions
Figure 964659DEST_PATH_IMAGE035
The position of the phase shift. Consider inserting 3
Figure 679674DEST_PATH_IMAGE035
In the case of a phase shift, the phase shift,
Figure 65787DEST_PATH_IMAGE094
，
Figure 284279DEST_PATH_IMAGE095
，
Figure 346913DEST_PATH_IMAGE096
the reflection coefficient of each small section of grating is respectively near the center frequency corresponding to the Bragg wavelength
Figure 237639DEST_PATH_IMAGE097
And satisfies the following conditions:
Figure 739028DEST_PATH_IMAGE098
(8)
obtained from (7), transmittanceTThe expression of (a) is:
Figure 15289DEST_PATH_IMAGE099
(9)
wherein
Figure 787505DEST_PATH_IMAGE100
. In the vicinity of the center frequency, the condition for satisfying the complete transmission is
Figure 414795DEST_PATH_IMAGE101
Therefore, the following conditions need to be satisfied:
Figure 939449DEST_PATH_IMAGE102
(10)
wherein,
Figure 335795DEST_PATH_IMAGE103
constant equal to 0, indicating that at the center frequency,
Figure 802548DEST_PATH_IMAGE104
. In addition, the condition (10) is:
Figure 667867DEST_PATH_IMAGE105
(11)
introducing a proportionality coefficient C defined as:
Figure 183162DEST_PATH_IMAGE106
（12）
simultaneous (8), (11), (12) can be solvedC、
Figure 496332DEST_PATH_IMAGE107
、
Figure 619140DEST_PATH_IMAGE108
、
Figure 221022DEST_PATH_IMAGE109
、
Figure 540008DEST_PATH_IMAGE110
Size of (2)
Through numerical calculation, we find thatCSize and of
Figure 455487DEST_PATH_IMAGE111
Is shown in FIG. 5, following
Figure 467306DEST_PATH_IMAGE111
The size of the mixture is increased, and the mixture is,Cinstead, it is set to decrease
Figure 25326DEST_PATH_IMAGE111
Can obtain the optimumCFinally, a transmission spectrum with a flat top can be obtained, wherein,
Figure 164314DEST_PATH_IMAGE111
is the coupling strength.
When in use
Figure 186497DEST_PATH_IMAGE112
Time, calculated optimum
Figure 103637DEST_PATH_IMAGE113
. For different scale factorsCThe resulting transmission spectrum is shown in FIG. 6a when
Figure 430845DEST_PATH_IMAGE114
When is two
Figure 153950DEST_PATH_IMAGE035
Optimal scaling factor for phase shift, and in three
Figure 968322DEST_PATH_IMAGE115
Under the condition of phase shift, the top of the obtained transmission channel is not flat any more, the transmission spectrum has three transmission peaks, and the transmittance of the three peaks is 1; when C increases to an optimum value of 2.23, a "flat-top" transmission peak is obtained, with the transmittance of the top around the center frequency 193.1THz being 1; as C continues to increase, the transmission channel is no longer flat-topped, the transmission channel top becomes relatively sharp, and the peak reflectivity is 1. While the 3dB bandwidth of the transmission channel decreases as C increases. It is also understood that as C increases, the three peaks move toward the center wavelength and then add up, so the transmission channel becomes narrower. The transmittance for the center frequency 193.1THz of the transmission channel is always 1, for FIGS. 14 a-14 c, the conditions
Figure 134992DEST_PATH_IMAGE116
Is constantly equal to 0. As shown in FIG. 6b, when
Figure 667605DEST_PATH_IMAGE117
When it is not in use
Figure 132084DEST_PATH_IMAGE111
The resulting transmissive channel top is always flat, however the size of (c) varies. When in use
Figure 616942DEST_PATH_IMAGE111
At an increase, the 3dB bandwidth of the transmission channel decreases. Therefore, to design a narrow-band flat-top transmission filter, it is critical to obtain the optimal scaling factor C. When the proportionality coefficient C is an optimal value, the total length of the fiber grating is increased, and a smaller transmission channel with 3dB bandwidth can be obtained. The flat-top narrow-band transmission type optical filter plays an important role in a microwave photon signal processing system.
The optical filter of the single flat-top transmission channel is popularized to be a multi-channel flat-top transmission type optical filter. The structure of the fiber grating is shown in fig. 4.
Design three
Figure 407044DEST_PATH_IMAGE035
Phase shift interpolationOptical filter with fiber grating structure
Figure 974422DEST_PATH_IMAGE035
The phase shift divides the interleaved sampling fiber grating into four small segments with respective lengths
Figure 242593DEST_PATH_IMAGE118
，
Figure 297136DEST_PATH_IMAGE119
And
Figure 540030DEST_PATH_IMAGE120
are all integers. The reflectivity of each segment is expressed as:
Figure 47235DEST_PATH_IMAGE121
and satisfies the following relationship:
Figure 915833DEST_PATH_IMAGE122
(13)
the optimal ratio of the two components (11) and (13) can be obtainedAAndBit is noted that the best is obtainedBAndAnot necessarily in relation to integer multiples, but must be guaranteedAAndBis a positive integer.
Three are
Figure 310037DEST_PATH_IMAGE035
The form factor of the transmission channel of the phase shifted interleaved sampled fiber grating is shown in FIG. 7, with the transmission channel being chosen for a reference frequency of 193.1 THz. Amplitude of refractive index modulation of
Figure 238679DEST_PATH_IMAGE123
The length of the grating is 48mm, two
Figure 233179DEST_PATH_IMAGE124
The phase shift corresponds to a shape factor of 3.16, and three
Figure 590955DEST_PATH_IMAGE124
The phase shift corresponds to a shape factor of 2.49, indicating an increase
Figure 416829DEST_PATH_IMAGE124
The number of phase shifts may reduce the shape factor of the channel and be much smaller than that obtained by increasing the grating length or increasing the refractive index modulation amplitude. However three
Figure 454055DEST_PATH_IMAGE124
Phase shift corresponds to a 3dB bandwidth ratio of the transmission channel of two
Figure 686584DEST_PATH_IMAGE124
The phase shift is large.
Design three
Figure 896986DEST_PATH_IMAGE124
The transmission spectrum of the phase-shifted interleaved sampling fiber grating covers the C-waveband, and the channel interval is 100 GHz. The parameters are as follows:
Figure 780628DEST_PATH_IMAGE125
，
Figure 473909DEST_PATH_IMAGE126
，
Figure 239739DEST_PATH_IMAGE127
the period is 514.74nmn nm, 517.38nm, 520.04nm, 522.74nm and 525.46nm,
Figure 191515DEST_PATH_IMAGE128
duty ratio of
Figure 477134DEST_PATH_IMAGE129
Length of grating
Figure 121742DEST_PATH_IMAGE130
. As can be derived from the foregoing theoretical calculations,
Figure 312552DEST_PATH_IMAGE131
，
Figure 364557DEST_PATH_IMAGE132
insert three into
Figure 222792DEST_PATH_IMAGE124
The optimal position distribution of the phase shift and the phase variation, as shown in fig. 8a, can find that the phase distribution is centrosymmetric about the center position. FIG. 8b shows the transmission channel for a reference frequency of 193.1THz selected to have a 3dB bandwidth of 416.7MHz, a 20dB bandwidth of 900.5MHz, and a shape factor of 2.16. And the 20dB cut-off bandwidth is 12.7GHz, and the out-of-band rejection ratio exceeds 50 dB. FIG. 8C shows the transmission spectrum covering the entire C-band, with 41 transmission channels at a channel spacing of 100 GHz. We also found that the transmission spectral shape of each channel was symmetric about the channel center frequency. Since the physical structure of the fiber grating is symmetrical, and the phase distribution function is an odd function in the mathematical representation of the refractive index change, it can be found after Fourier transform that they are axisymmetric about the center frequency of the whole transmission spectrum, and each channel is symmetric about the center frequency of the channel, so the reflection spectrum has symmetry.
To increase the number of transmission channels, the MPS technique is applied to three
Figure 585771DEST_PATH_IMAGE035
In the phase-shifted interleaved sampling fiber grating, the structural parameters are as follows:
Figure 670402DEST_PATH_IMAGE125
，
Figure 963980DEST_PATH_IMAGE126
，
Figure 224191DEST_PATH_IMAGE128
duty ratio of
Figure 945022DEST_PATH_IMAGE133
The periods are 514.80nm and 51 nm respectively7.44nm, 520.11nm, 522.80nm, 525.53nm, grating length
Figure 920544DEST_PATH_IMAGE134
。
The distribution of the phase shifts and the phase distribution are shown in fig. 9a and 9 b. The main structural parameters and the first three
Figure 752234DEST_PATH_IMAGE035
The same is true for the phase shift, except that the MPS technique is applied.n=2, the distribution of the phase shift is
Figure 319482DEST_PATH_IMAGE135
While adding three
Figure 24264DEST_PATH_IMAGE035
Phase shift, and finally the superimposed phase shift distribution as shown in fig. 9a, it can be seen that the phase shift of only three positions is 0, and the three positions are exactly the positions obtained by the previous optimization calculation. Fig. 9b shows the corresponding phase distribution, and it can be seen that the phase distribution is no longer symmetric about the center position, and therefore it can be inferred that the transmission channel of the fiber grating is also no longer symmetric about the channel center frequency. Finally we have obtained a transmission spectrum with a channel spacing of 50GHz and a number of channels of 81 covering the whole C-band, the central frequency of each channel corresponding to the frequency of the ITU-T standard, as shown in fig. 10, the out-of-band rejection ratio of each transmission channel exceeding 30dB, but being greater than the three previously designed channels
Figure 411382DEST_PATH_IMAGE035
The phase shift is reduced.
Selecting a transmission channel with a reference frequency of 193.1THz as shown in fig. 11, it was found that its transmission spectrum is not symmetric about the center frequency, consistent with previous analysis guesses, but rather a high-low notch occurs, but we are mainly concerned that the out-of-band rejection ratio of the transmission spectrum of the flat-top narrow band corresponding to the center frequency is also over 30 dB. Its 3dB bandwidth is 900.5MHz, and its 20dB bandwidth is1.95GHz, shape factor 2.17. The shape factor of the polyphase-interleaved-sampled fiber grating after applying MPS technique and the first three can be found
Figure 109080DEST_PATH_IMAGE035
The phase shift is substantially uniform but the 3dB bandwidth is increased. But the number of channels is doubled and the channel spacing is halved.
Finally, in order to increase the number of channels, a multi-channel flat-top narrow-band filter covering the C + L-band is optimally designed. The structural parameters are as follows:
Figure 281567DEST_PATH_IMAGE125
，
Figure 406517DEST_PATH_IMAGE136
，
Figure 546512DEST_PATH_IMAGE137
，
Figure 470737DEST_PATH_IMAGE138
length of grating
Figure 809314DEST_PATH_IMAGE139
The periods are 512.65nm, 515.27nm, 517.91nm, 520.58nm, 523.28nm, 526.01nm, 528.76nm, 531.55nm, 534.36nm, 537.20nm, 540.08nm, 542.98nm and 545.92nm respectively. Its phase shift profile and phase profile are the same as those shown in fig. 8 a.
We obtain a transmission spectrum covering the C + L-band, as shown in FIG. 12, with a frequency range of 186 THz-196 THz, a channel number of 101, and channel spacing of 100 GHz. The out-of-band rejection ratio of the channels exceeds 30dB, and the fluctuation of the out-of-band rejection ratio of each channel is small, which indicates that the uniformity of the channels is good.
A transmission channel with a reference frequency of 193.1THz was chosen, as shown in FIG. 13, with a 3dB bandwidth of 800MHz, a shape factor of 2.15, an out-of-band rejection ratio in excess of 40dB, and a transmission spectrum that was symmetric about the center frequency.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments, or alternatives may be employed, by those skilled in the art, without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (2)

1. A multi-channel transmission-type optical filter with flat top is characterized by that N-1 phase shifts delta phi are inserted in the optical fibre raster of transmission-type optical filter1，Δφ2，Δφ3，...，ΔφN-2，ΔφN-1Dividing the grating into N small segments L1，L2，L3，...，LN-1，LNThe total length of the grating is L, L1＝LN，L2＝LN-1，…，Δφ1＝Δφ2＝...＝ΔφN-1＝π；
The insertion positions of the phase shifts are: after N-1 pi phase shifts divide the interleaved sampling fiber grating into N small segments, the reflection coefficient and the transmission coefficient of the ith small segment are respectively determined by riAnd tiExpress, and satisfy
Figure FDA0003611933500000011
ri *，
Figure FDA0003611933500000012
Are respectively riAnd tiThe transmission coefficient t of the whole grating and the reflection coefficient r of the small section of gratingiAnd a transmission coefficient tiAnd a phase shift of delta phiiThe relationship between them satisfies:
Figure FDA0003611933500000013
Figure FDA0003611933500000014
wherein j is an imaginary symbol, and e is a natural constant;
in the MPS-based N-1 pi phase shift interleaved sampling fiber grating, the structural parameters include the grating length L, Neff，Z0，Δn0Where the duty cycle p is Zg/Z0The period of the sub-gratings of the interleaved sampling fiber grating is as follows: lambdai＝c/(2nefffBi) C is the speed of light in vacuum, neffIs the core equivalent refractive index, Δ n0Is the refractive index modulation amplitude, Z0Is the total length of each sampled grating, ZgIs the length of each segment of uniform sub-grating, p is the duty cycle, fBiThe central frequency of the ith sampling fiber grating; wherein, the grating length L, neff，Z0，Δn0Four parameters are given values;
in an interleaved sampled fiber grating, the channel frequency spacing Δ f is c/(2 n)effZ0) The frequency is equally spaced, the channel wavelength spacing Δ λ ≈ λ2/(2neffZ0) And c is the speed of light in vacuum; center frequency f of ith sampling fiber gratingBiComprises the following steps:
fBi＝fc+HΔf (4)
Figure FDA0003611933500000021
fcfor the center frequency of the whole reflection spectrum, it should be noted that H must be an integer to satisfy that each channel can be overlapped in a matched manner; the center wavelength of the ith sampling fiber grating is as follows: lambda [ alpha ]Bi＝c/fBi；
Three pi phase shifts divide the interleaved sampling fiber grating into four small segments with lengths AZ0，BZ0，BZ0，AZ0A and B are both integers; the reflectivity of each segment is expressed as: r is a radical of hydrogen1，r2，r3，r4And satisfies the following relationship:
Figure FDA0003611933500000031
r1＝r4＝-j tanh(κAZ0)，r2＝r4＝-j tanh(κBZ0) (8)
the optimal ratio of A to B can be obtained by combining (7) and (8), wherein A and B are positive integers, and r isi *Is riAnd conjugation of the same.
2. The multi-channel flat-top transmissive optical filter as claimed in claim 1, wherein the channel spacing of 2 pi/Z is obtained based on selected parameters0The theoretical number of channels being the ratio of the frequency range of the band to the channel spacing
Figure FDA0003611933500000032
Wherein Δ f is a band frequency range, covering the transmission spectrum of the entire C-band, and the center frequency of each channel corresponds to the frequency of ITU-T standard.
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