CN1303446C - Tunable dispersion compensator designing and making method - Google Patents

Abstract

The design and manufacture method of a tunable dispersion compensator belongs to the technical field of optical fiber communication. The core component of the invention is an apodized sampling fiber grating with a quadratic time delay curve. The fiber grating is fabricated using a linear chirped phase template, and the grating period chirp (CGP) introduced by the template is compensated by the sampling period chirp (CSP), so that the variation range of the sampling period of the grating is relatively small, so that the fabrication process Simpler and more stable. In addition, in the design and production process of fiber grating, the change of average refractive index caused by apodization is compensated by introducing CSP, so only one exposure is required, and the production and apodization of grating can be completed at one time. Finally, the fiber grating is fixed on the precision mechanical tuning device, and the stretching of the fiber grating is realized through the control of the microcomputer, so as to control the compensation amount of dispersion.

Description

The design and fabrication method of adjustable chromatic dispersion compensator

Technical field

The design and fabrication method of adjustable chromatic dispersion compensator belongs to technical field of optical fiber communication, relates in particular to fiber grating and makes the field.

Background technology

The general indemnity fibre-optical dispersion can wait and realize as Dispersion Compensation Fiber Gratings, dispersion compensation etalon with dispersion compensating fiber or dispersion compensation device.The implementation method of this dispersion compensation is fixed, in case system design has been got well, the compensation rate of its chromatic dispersion just can not change.And the accumulation of chromatic dispersion is a time dependent process, and system can be subjected to the interference of a lot of extraneous factors, produces the chromatic dispersion of dynamic change, and this compensates in the mode of the chromatic dispersion that is changing being monitored tracking with regard to needing the dynamic-tuning dispersion compensation device.Wherein, the implementation of adjustable chromatic dispersion is the core content of dynamic-tuning dispersion compensation device.There are some modes can realize adjustable chromatic dispersion, carry out linear superposition adjustment chromatic dispersion etc. as the chromatic dispersion that changes grating of using thermal effect in fiber grating, to produce warbling of dynamic change, the variable time delay curve that utilizes a plurality of etalons to produce.Wherein the adjustable chromatic dispersion based on non-linear chirp is simple with it, effectively becomes one of noticeable method.

The time lag curve of nonlinearly chirped fiber grating is non-linear, by just can realize the change of grating time delay to the stretching of grating, wherein when the time delay of grating becomes quafric curve to change with wavelength, chromatic dispersion versus wavelength is linear, its time delay and dispersion curve as shown in Figure 1, 2, this moment, the tuning control of grating was can be more simple, stable.Therefore, the non-linear chirp grating of the different structure of design just can be realized the better compensation to system dispersion.Owing to want fabricating quality higher non-linearity chirped fiber grating to need high-quality non-linear chirp template, and the non-linear chirp template need use electron beam exposure technology to make, obtain quite difficulty of high-quality non-linear chirp template, and price is also quite expensive.And different non-linear chirp gratings needs different non-linear chirp phase masks, and this makes the design of above-mentioned tunable devices and application be subjected to certain restriction.

Owing to obtain the difficulty of high-quality non-linear chirp template, therefore occurred adopting even phase mask and sampled-grating technology to obtain the method for non-linear chirp.People such as Feng Jia, Chen Xiangfei were at " Bragg grating with new sampling structure that is used for compensation of dispersion and polarization mode disperse " Chinese invention patent (application number: 02103383.8) proposed to use the method that obtains the chirp grating cycle (CGP) of equivalence by warble the sample period (CSP) of sampled-grating in 2002.This method has used even phase mask to make grating, therefore can simplify the making of grating greatly, has very big cost advantage, and can design the grating with different delay curve easily, and do not change template.

Though this method has realized using even template to design and make the nonlinearly chirped fiber grating of equivalence, when specific design, the sample period variation range can be very big, and this brings some difficulties to making.It is to have adopted the method for re-expose to carry out the making of grating in addition, is easy to introduce in the manufacturing process of grating additional warbling.This method does not realize CSP and the conversion of CGP flexible equivalent completely.

Summary of the invention

The objective of the invention is in order to break through existing technology, and overcome the weak point of prior art, proposed the special sampling optical-fiber grating that a kind of brand-new mode designed and made the non-linear chirp effect with equivalence.This fiber grating has adopted the linear chrip stencil design, and compensates because warbling of template introducing fully realized the dirigibility of equivalent chirp design, and the sample period variation range of design is smaller, thereby manufacture craft is required more to reduce by CSP.In addition in the manufacturing process of fiber grating, we do not adopt the method for re-expose, carry out traditional method of indicating the pronunciation of a Chinese character toe by exposure for the second time, but design grating in advance, compensate owing to cut the change of the mean refractive index that toe causes by introducing CSP, therefore only need carry out single exposure, the making of grating and cut toe and just can once finish.Such design and method for making not only can be simplified the manufacturing process of grating, and have avoided re-expose to introduce additional warbling, and can greatly improve the performance of grating.At last the fiber grating that completes is fixed on the precision optical machinery tuner, the control of mechanical tuning device is realized stretching to fiber grating by microcomputer, thus the compensation rate of control chromatic dispersion.

The difference of design of the present invention, the method for making fiber grating and " Bragg grating with new sampling structure that is used for compensation of dispersion and polarization mode disperse " patent is:

The present invention is that this fiber grating has adopted the linear chrip stencil design, and compensates because warbling of introducing of template by CSP, and the variation range that makes the sampling of grating warble is smaller, thereby makes that manufacture craft is more simple, stablize.In addition in the manufacturing process of fiber grating, we be not adopt that the method for re-expose carries out grating cut toe and making, but design grating in advance, compensate owing to cut the change of the mean refractive index that toe causes by introducing CSP, therefore only need carry out single exposure, the making of grating and cut toe and just can once finish.Such design and method for making not only can be simplified the manufacturing process of grating, and have avoided re-expose to introduce additional warbling, and can greatly improve the performance of grating.The present invention more flexible Application the transformation of equivalence of CSP and CGP, and used the toe mode of cutting that CSP realizes traditional method of indicating the pronunciation of a Chinese character toe of passing through of original creation.

The principle that the present invention adopts:

We adopt the inferior group delay spectrum of the m=-1 level of sampled-grating reflection peak to be used for dispersion compensation.If the equivalent chirp grating cycle of adjustable chromatic dispersion grating is:

Λ _-1＝Λ _-1，0(1+cz ^1/2) (1)

Λ in the formula _-1The grating cycle at expression sampled-grating-1 grade reflection peak place, Λ _-1,0The initial value in the grating cycle at-1 grade of reflection peak place of expression, c represents chirp coefficient, and z is the length of optical grating axial, and the time delay that then adopts grating cycle of this form to warble becomes quafric curve to change with wavelength, and its chromatic dispersion versus wavelength is linear, so its tuning control can be simple more, stable.

We introduce in the sample period of sampled-grating and warble, and realize that thus the grating cycle of equivalence warbles.If adopted even phase mask, then once obtain the length of each sample period by following formula:

$Z_n+{\mathrm{aZ}}_n^{3/2}=n{Z}_0(a=2\mathrm{<figure-callout\; id="0"\; label="c\; Z"\; filenames="C20041000033900122.png"\; state="\{\{state\}\}">c</figure-callout>}{Z}_{}{}_0/3{\mathrm{\&Lambda;}}_{-\mathrm{1,0}})---\left(2\right)$

The ordinal number of the n representative sampling in the formula, Z ₀The expression reference length, its general and sample period order of magnitude, Z _nThe length of representing each sample period.

Owing to we have adopted linear chrip template chirp coefficient c ', therefore require the further change sample period to compensate warbling of template introducing, its computing formula is as follows:

$Z_n+b{Z}_n^2+a{Z}_n^{3/2}=n{Z}_0$ (identical in a and the formula (2), $b=c^{\&prime;}{\mathrm{<figure-callout\; id="0"\; label="Z"\; filenames="C20041000033900122.png"\; state="\{\{state\}\}">Z</figure-callout>}}_0/2{\mathrm{\&Lambda;}}_{-\mathrm{1,0}}^2$ ) (3)

Because that carries out in single exposure cuts toe the mean refraction rate coefficient of grating is changed, can in grating, introduce additional warbling, therefore we introduce once more to warble in the sample period of grating and compensate the change that the mean refraction rate coefficient takes place, thereby realized that single exposure just can realize cutting toe, and do not needed re-expose to carry out traditional method of indicating the pronunciation of a Chinese character toe.We have adopted apodizing function κ (z) to come grating is cut toe.Concrete implementation method is as follows:

$Z_n+\mathrm{gdf}\left(Z_n\right)+b{Z}_n^2+a{Z}_n^{3/2}=n{Z}_0---\left(4\right)$

F (z wherein _n)=∫ κ (z _n) dz _n, κ (z _n) be apodizing function, g is a constant, span is 0.005～0.1, by the variation decision of the maximum mean refraction rate coefficient of fiber grating.Identical in a, b and the formula (3).

Calculate by following formula we design the length of each sample period that needs.

Method for designing of the present invention is characterised in that it contains following steps successively:

(1) twice time lag curve is arranged is the time delay of warbling in the grating cycle becomes the quafric curve variation with wavelength sampling optical-fiber grating in one of design, and its equivalent chirp grating cycle is:

Λ _-1＝Λ _-1，0(1+cz ^1/2)

Wherein, Λ _-1Be the grating cycle at sampled-grating-1 grade reflection peak place,

Λ _-1,0Be the initial value in grating cycle at-1 grade of reflection peak place,

C is the equivalent chirp coefficient, setting value, and unit is (mm) ^-1/2,

Z is the optical fiber axial length;

(2) adopt the linear chrip template, and compensate warbling that template introduces by the sample period of warbling that changes sampled-grating, calculate the length of each sample period with following formula:

$Z_n+b{Z}_n^2+a{Z}_n^{3/2}=\mathrm{<figure-callout\; id="0"\; label="n\; Z"\; filenames="C20041000033900122.png"\; state="\{\{state\}\}">n</figure-callout>}{Z}_{}{}_0,$ Z _nBe the length of each sample period, n is the ordinal number of sampling, down together,

A, b are constant, are determined by following formula:

a＝2cZ ₀/3Λ _-1，0

$b=c^{\&prime;}{\mathrm{<figure-callout\; id="0"\; label="Z"\; filenames="C20041000033900122.png"\; state="\{\{state\}\}">Z</figure-callout>}}_0/2{\mathrm{\&Lambda;}}_{-\mathrm{1,0}}^2,$ C ' is the chirp coefficient of linear chrip template, setting value,

Z ₀Be the reference length of sample period, its general and sample period is got the same order of magnitude, and sets;

(3) asking above-mentioned sample period Z _nThe time, introducing once more warbles compensates owing to the variation of cutting the mean refraction rate coefficient that toe causes, at this moment, and the length Z of each sample period _nCalculate with following formula:

$Z_n+\mathrm{gf}\left(Z_n\right)+b{Z}_n^2+a{Z}_n^{3/2}=\mathrm{<figure-callout\; id="0"\; label="n\; Z"\; filenames="C20041000033900122.png"\; state="\{\{state\}\}">n</figure-callout>}{Z}_{}{}_0$

Wherein, f (z _n)=∫ κ (z _n) dz _n, κ (z _n) be apodizing function, g is a constant, span is 0.005～0.1, by the variation decision of the maximum mean refraction rate coefficient of fiber grating,

A, b are constant;

Method for making of the present invention is characterised in that it contains following steps successively:

(1) optical fiber to be processed is carried hydrogen and handle and peel off one section coat;

(2) described optical fiber is fixed on the linear chrip template that chirp coefficient is c ' after, make it;

(3) adjust the luminous power that laser instrument is output as 50mw;

(4) adjust light path, the hot spot through the scanning reflection mirror reflection is radiated on the fibre core of optical fiber;

(5) the ESP6000 system that opens microcomputer carries out initialization, and following parameter is set in input:

Z _n: the length of each sample period;

The translational speed of scanning mobile platform;

(6) start scanning platform, make it move to the reference position of grating exposure;

(7) the input grating exposed to grating in the time of every some exposure, made scanning platform move by following dutycycle, finished up to preparing grating, that is: the non-exposed area also claims the length of clear area to be:

The length of non-exposed area length=0.5 * each sample period;

(8) be fixed on the two ends of the grating that completes on the anchor clamps at precision optical machinery tuner two ends with glue;

(9) the RS232 interface of this precision optical machinery tuner is linked to each other with RS232 interface on the microcomputer, realize control to the mechanical tuning device realizing tunable dispersion compensation by the known software on the microcomputer;

The chirp coefficient c ' and the length Zn in each sampling period that it is characterized in that the linear chrip template satisfy following condition:

$Z_n+\mathrm{gf}\left(Z_n\right)+b{Z}_n^2+a{Z}_n^{3/2}=\mathrm{<figure-callout\; id="0"\; label="n\; Z"\; filenames="C20041000033900122.png"\; state="\{\{state\}\}">n</figure-callout>}{Z}_{}{}_0$

Wherein, f (z _n)=∫ κ (z _n) dz _n, κ (z _n) be apodizing function, g is a constant, span is 0.005～0.1, by the variation decision of the maximum mean refraction rate coefficient of fiber grating,

A, b are constant, are determined by following formula:

a＝2cZ ₀/3Λ _-1，0

$b=c^{\&prime;}{\mathrm{<figure-callout\; id="0"\; label="Z"\; filenames="C20041000033900122.png"\; state="\{\{state\}\}">Z</figure-callout>}}_0/2{\mathrm{\&Lambda;}}_{-\mathrm{1,0}}^2,$ C ' is the chirp coefficient of linear chrip template, setting value,

Z ₀Be the reference length of sample period, the general and sample period is got the same order of magnitude, and sets;

Design fiber grating by above method and have twice time lag curve, its chromatic dispersion versus wavelength is linear, and only needs single exposure can realize the making of grating and cut toe.This fiber grating realizes that the principle of adjustable chromatic dispersion compensation is such: fiber grating is when being in extended state, and the cycle of grating is elongated, also just is equivalent to the short wavelength direction skew of the working point of system to grating, thereby has caused the change of dispersion measure.Therefore grating is fixed on the accurate mechanical tuning device, stretching just can realize the compensation to different dispersion measures to grating.

Description of drawings

Fig. 1 is the twice time lag curve synoptic diagram of fiber grating.

Fig. 2 is the linear dispersion curve synoptic diagram of fiber grating.

Fig. 3 is the reflection spectral line of-1 grade of reflection peak of grating of the present invention.

Fig. 4 is the time lag curve (a) and the dispersion curve (b) of-1 grade of reflection peak of grating of the present invention.

Fig. 5 makes the device synoptic diagram of fiber grating for the present invention.

Fig. 6 makes the synoptic diagram of the precision optical machinery tuner of adjustable chromatic dispersion compensator use for the present invention.

Embodiment

Adjustable chromatic dispersion compensator method for making of the present invention is divided into the two large divisions: the one, and the design of cutting the toe sampling optical-fiber grating of twice time lag curve, the 2nd, the making of adjustable chromatic dispersion compensator.Concrete embodiment is described with reference to the accompanying drawings as follows:

One, the design of the fiber grating of adjustable chromatic dispersion compensator use

The equivalent chirp of the adjustable chromatic dispersion grating of designing requirement is: Λ _-1=Λ _-1,0(1+cz ^1/2), get Λ _-1,0=1545.7nm, c=3 * 10 ^-4(mm) ^-1/2

For formula (4), get Z ₀=0.28mm.Obtain a=0.037 (mm) by formula 2 ^-1/2The chirp coefficient c ' of linear chrip template is 0.048nm/mm, thereby obtains b=0.0024 (mm) ^-1, adopt Hamming to cut toe $\mathrm{\&kappa;}\left(z\right)=\frac{1+H\cos \left[\mathrm{\&pi;}(z/L-1/2)\right]}{1+H}$ (grating length wherein $L=\underset{n=1}{\overset{200}{\mathrm{\&Sigma;}}}{Z}_n$ ), H is a constant, and value is 3, and d gets 0.02, and the periodicity of sampling is 200, i.e. n=1,2,3 ..., 200, calculate the length { Z of each sample period successively _n, and to obtain the whole length of grating be 85mm.

The reflection of-1 grade of reflection peak of the grating that completes and time delay, dispersion curve are respectively shown in Fig. 3,4: its chromatic dispersion operation wavelength is 1545.2～1546.2nm, and its chromatic dispersion changes to-220ps/nm from-980ps/nm in bandwidth is the scope of 1nm.

Two, the making of adjustable chromatic dispersion compensator

The device of present embodiment preparing grating as shown in Figure 5.Wherein, light source adopts continuous 244nm frequency multiplication Argon ion laser 51 (production of U.S. coherent company).Scanning reflection mirror 52 is fixed on the ESP6000 scanning mobile platform (production of Newport company) 53, and scanning mobile platform kinematic accuracy is 0.1mm.Catoptron 52 has the function of scanner uni folded light beam, and the ultraviolet light that laser instrument 51 is exported reflexes on the linear chrip phase mask 54, this phase mask length is 60mm, and ultraviolet light is radiated at carrying on the standard single-mode fiber 55 of processing through hydrogen under it through phase mask.ESP6000 scanning mobile platform links to each other with the PIO mouth (not shown) of microcomputer.By the drive software that operation on microcomputer designs in advance, change the motion state (movement velocity, run duration, move distance) of mobile platform, it is moved according to a certain characteristics of motion, just can obtain the fiber grating that needs.

The main technique flow process of present embodiment is as follows:

1. optical fiber is carried hydrogen and handle and peel off one section coat;

2. after optical fiber being fixed on the linear chrip phase mask plate, making it to try one's best but do not stick;

3. adjust the luminous power of laser instrument to the about 50mW of output;

4. adjust light path, the hot spot through the scanning reflection mirror reflection is radiated on the fibre core of optical fiber;

5. open ESP 6000 systems of microcomputer, enter the working interface of software, and ESP 6000 is carried out initialization;

6. start the scanning mobile platform, make it can free movement;

7. side-play amount is set, makes the scanning mobile platform move to the reference position of grating exposure;

8. import the time of grating every some exposure; Grating is exposed, and order scanning mobile platform begins to move, and finishes until preparing grating;

9. the two ends of the grating that completes are used glue to be fixed on the anchor clamps at two ends of precision optical machinery tuner;

10. the RS232 interface of this precision optical machinery tuner is linked to each other with RS232 interface on the microcomputer, realize control by the software on the microcomputer, thereby realize tunable dispersion compensation the mechanical tuning device.

In the whole process of making, adopting spectrum width is that wide spectrum light source 57, circulator 56 and the precision of 25nm is that the AQ-6315B spectrometer 58 of 0.05nm carries out the test of grating performance, and the reflectance spectrum of fiber grating is analyzed, and can obtain the performance parameter of fiber grating.

The synoptic diagram of the precision optical machinery tuner that the making adjustable chromatic dispersion compensator uses as shown in Figure 6.Base 1 adopts steel plate to make, and what other parts were all direct or indirect is structured in above it.Slide rail 2 is fixed on the base, and precision electric motor 3 can be accurate mobile on slide rail under the control of computing machine by RS232 interface 6.Anchor clamps 4 are fixed on the precision electric motor, and anchor clamps 5 are fixed on the base.Use glue to be fixed on the anchor clamps 4,5 at the two ends of fiber grating 7, external optical fiber 8 is epitaxial parts of grating, realizes being connected with outside optical fiber by it in use.

Evidence: the present invention can go out high-quality fiber grating according to the needs design flexible of system, and the manufacturing process of grating is also fairly simple, reliable, and simple in structure, the stable performance of its tuner, and very big practical potentiality are arranged.

Claims (2)

1, the design method of tunable dispersion compensator, it is characterized in that it contains following steps successively: (1) Design a sampling fiber grating with a quadratic time delay curve, that is, the time delay of the grating period chirp changes quadratically with the wavelength. Its equivalent chirped grating period is: Λ _-1 ＝Λ _-1,0 (1+cz ^1/2 ) Wherein, Λ _-1 is the grating period at the sampling grating-1 reflection peak, Λ _{-1, 0} is the initial value of the grating period at the reflection peak of -1 order, c is the equivalent chirp coefficient, set value, the unit is (mm) ^-1/2 , z is the axial length of the optical fiber; (2) Using a linear chirp template and compensating the chirp introduced by the template by changing the chirp sampling period of the sampling grating, the length of each sampling period is calculated by the following formula: $Z_{\mathrm{no}}+b{Z}_{\mathrm{no}}^2+a{Z}_{\mathrm{no}}^{3/2}=\mathrm{no}{Z}_0,$ Z _n is the length of each sampling period, n is the sequence number of sampling, the same below, a, b are constants, determined by the following formula: a=2cZ ₀ /3Λ _-1,0 $b=c^{\&prime;}{Z}_0/2{\mathrm{\&Lambda;}}_{-\mathrm{1,0}}^2,$ c' is the chirp coefficient of the linear chirp template, the set value, Z ₀ is the reference length of the sampling period, which is generally of the same order of magnitude as the sampling period and is set; (3) When calculating the above sampling period, chirp is introduced again to compensate the change of the average refractive index caused by apodization. At this time, the length of each sampling period is calculated by the following formula: ${\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; gf</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; a</span>}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}$ Among them, f(z _n )=∫κ(z _n )dz _n , κ(z _n ) is an apodization function, g is a constant, the value range is 0.005～0.1, the change of the maximum average refractive index coefficient of fiber grating Decide, a, b are constants. 2. A method for making a tunable dispersion compensator, comprising the following steps: (1) Carry out hydrogen-loading treatment on the optical fiber to be processed and strip off a section of coating layer; (2) fixing the optical fiber behind the linear chirp template with chirp coefficient c', making it close to; (3) adjust the laser output to be the optical power of 50mw; (4) Adjust the optical path so that the light spot reflected by the scanning mirror is irradiated on the core of the optical fiber; (5) Turn on the ESP6000 system of the microcomputer to initialize, and input and set the following parameters: Z _n : the length of each sampling period; Scan the moving speed of the mobile platform; (6) Start the scanning platform to move it to the initial position of the raster exposure; (7) Input the exposure time of the grating at each point, and expose the grating, so that the scanning platform moves according to the following duty cycle until the grating is completed, that is, the length of the non-exposure area is also called the blank area: The length of the non-exposed area=0.5×the length of each sampling period; (8) Fix the two ends of the finished grating on the fixtures at the two ends of the precision mechanical tuning device with glue; (9) The RS232 interface of this precision mechanical tuning device is connected with the RS232 interface on the microcomputer, realizes the control of the mechanical tuning device by known software on the microcomputer, and realizes tunable dispersion compensation; It is characterized in that the chirp coefficient c' of the linear chirp template and the length Zn of each sampling period satisfy the following conditions: ${\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; gf</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; a</span>}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}$ Among them, f(z _n )=∫κ(z _n )dz _n , κ(z _n ) is an apodization function, g is a constant, the value range is 0.005～0.1, the change of the maximum average refractive index coefficient of fiber grating Decide, a, b are constants, determined by the following formula: a=2cZ ₀ /3Λ _-1,0 $b=c^{\&prime;}{Z}_0/2{\mathrm{\&Lambda;}}_{-\mathrm{1,0}}^2,$ c' is the chirp coefficient of the linear chirp template, the set value, Z ₀ is the reference length of the sampling period, which is generally of the same order of magnitude as the sampling period and is set.

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