CN103076650A - Method for designing fiber Bragg grating with arbitrary optical power distribution - Google Patents

Abstract

The invention discloses a method for designing a fiber Bragg grating with arbitrary optical power distribution. A refractive index modulation function of the fiber Bragg grating is reconstructed. The fiber Bragg grating is sectionally processed from given optical power distribution along the length of the fiber Bragg grating, and the amplitudes of a forward transmission mode and a backward transmission mode in the fiber Bragg grating at a resonant wavelength are deduced by combining boundary conditions (uN=1 and v0=0) of the fiber Bragg grating and a law of conservation of energy. Meanwhile, constant phases of the forward transmission mode and the backward transmission mode at the resonant wavelength are deduced for a uniform/apodized fiber Bragg grating according to a transmission matrix method. A reflection coefficient and a coupling coefficient are calculated by using a coupled mode matrix on the basis of the obtained amplitudes and the obtained phases of the forward transmission mode and the backward transmission mode, and the refractive index modulation function of the fiber Bragg grating is deduced from the reflection coefficient and the coupling coefficient to finish the reconstruction design of the fiber Bragg grating. The method is applied to the design of the fiber Bragg grating, and is also applied to the design of the uniform/apodized fiber Bragg grating with the arbitrary optical power distribution.

Description

A kind of fiber grating method for designing with any optical power distribution

Technical field

The present invention is mainly concerned with the fields such as fiber grating, photon filter, optical communication, Microwave photonics, light sensing, relates in particular to a kind of fiber grating method for designing with any optical power distribution.

Background technology

Fiber grating have filtering performance flexibly, easy characteristics such as, simple cheap low with fibre system fusion, insertion loss, thereby have a wide range of applications in fields such as optical communication, light signal processing, Microwave photonics, light sensings.And in the different application occasion, the characteristic requirements of fiber grating also is not quite similar.For example, in optical communication, need in the special band phase-frequency response to carry out dispersion and dispersion slope compensation, perhaps need multichannel filtering to implement wavelength-division multiplex technique; In light signal is processed, can carry out Fourier transform, difference based on the fiber grating pair light signal of particular design and differentiate and the slower rays processing; In Microwave photonics, microwave signal be controlled and be processed to the fiber grating with high-resolution phase-frequency response and super arrowband amplitude-frequency response can from precision on the light territory; At the light sensory field, dual-wavelength fiber grating or grating array are applied to sense temperature and strain, eliminate the cross sensitivity of temperature and strain.

In order to satisfy the different requirements in the above-mentioned various application, the researchist has proposed a series of restructing algorithms and design proposal both at home and abroad.Inverse scattering algorithm is wherein relatively classical a kind of: the frequency filtering response is successively calculated by inverse scattering algorithm arbitrarily, reconstructs the structural parameters (mainly being locally coupled coefficient and index modulation function) of fiber grating.Inverse scattering algorithm (sometimes being called the delamination algorithm) can Configuration design goes out to have that rectangular band is logical, complicated phase-frequency response, strong reflection rate, even multichannel/non-homogeneous multichannel optical fiber grating, and relevant paper comprises: 1) R.Feced, M.N.Zervas, and M.A.Muriel, " An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings; " IEEE Journal of Quantum Electronics, vol.35, no.8, pp.1105 – 1115,1999; 2) J.Skaar, L.Wang, and T.Erdogan, " On the synthesis of fiber Bragg gratings by layer peeling, " IEEE Journal of Quantum Electronics, vol.37, no.2, pp.165-173,2001..The joint time frequency analysis method also can be applied in the fiber grating Configuration design by expansion, such as M.A.Muriel, J.Azana, and A.Carballar, " Fiber grating synthesis by use of time-frequency representations, " Optics Letters, vol.23, no.19, pp.1526-1528,1998..In addition, pure phase position sampling technique, iterative computation, optimized algorithm also is widely used in the PHASE DISTRIBUTION of reconstruct multichannel optical fiber grating refractive index modulating function, thereby the multichannel optical fiber grating that obtains has high channel consistance and high-diffraction efficiency, such as H.Li, T.Kumagai, K.Ogusu, and Y.Sheng, " Advanced design of a multichannel fiber Bragg grating based on a layer-peeling method; " Journal of Optical Society of America-B, vol.21, no.11,1929-1938,2004.

Above restructing algorithm and method for designing concentrate on: from the customization frequency response (amplitude-frequency response and phase-frequency response), reconstruct obtains the structural parameters of fiber grating.Yet the optical power distribution of fiber grating on the grating length direction also is its another key property, can be considered as a kind of embodiment of fiber grating filtering characteristic on spatial domain.The optical power distribution of fiber grating inside has special important application in optical communication, Microwave photonics, light sensing.To the stable control of reflection spot (or time delay), the design of short fiber laser resonant cavity is based on the distributed sensing of single fiber grating etc. when processing microwave signal in the light territory.

At present, the research for the optical power distribution of fiber grating inside is confined to the optical power distribution analysis of fiber grating inside under the known structure; Be the structural parameters (mainly being the index modulation function) of known fiber optic grating, its inner optical power distribution of quantitative test, paper M.A.Muriel for example, A.Carballar, and J.Azana, " Field distributions inside fiber gratings; " IEEE Journal of Quantum Electronics, vol.35, no.4, pp.548-558,1999.And a problem demanding prompt solution is: design a fiber grating that has arbitrarily or customize optical power distribution; Be given any or customization optical power distribution, Configuration design goes out a satisfactory fiber grating.Current effective solution or the scheme of yet there are no of this problem.

Summary of the invention

In view of the existing restructing algorithm of above statement and the deficiency of method for designing, the present invention aims to provide a kind of method that can design the fiber grating with any or customization optical power distribution, thereby effectively realizes the fiber grating Configuration design based on luminous power on the spatial domain or light energy distribution.

Purpose of the present invention realizes by following process.

A kind of fiber grating method for designing with any optical power distribution is from any given optical power distribution, in conjunction with the boundary condition (u of fiber grating _N=1 and v ₀=0) and law of conservation of energy, derives and obtain the fl transmission mould of resonance wave strong point grating inside, the amplitude of backward transmission mode.Simultaneously, according to transfer matrix method, for even type, cut toe type fiber grating and derive and to obtain the constant phase of resonance wave strong point fl transmission mould, backward transmission mode.The amplitude of the fl transmission mould that is based on having obtained, backward transmission mode and phase place are used the coupled modes matrix computations to obtain reflection coefficient, coupling coefficient, and are therefrom extrapolated the index modulation function of fiber grating, finish the Configuration design of fiber grating.

Practical implementation is as follows.

At first fiber grating is divided into N section (evenly segmentation, also unequal piece-wise), in each section grating, index modulation is considered as constant; The grating section be numbered 1～N, normalization length is 0～1, shown in Fig. 1 (a).At each section at the interface, all there is fl transmission mould u _kWith backward transmission mode v _k, shown in Fig. 1 (b).Thereby the luminous power of each waypoint of fiber grating, the luminous power of difference form are:

P _k∝|u _k+v _k| ². (1)

ΔP _k=P _k-P _k-1. (2)

Define a normalized function [i.e. (3) formula], then (1) and (2) can be rewritten into (4) and (5)

$\underset{i=1}{\overset{N}{\mathrm{\Σ}}}f\left(i\right)=1---\left(3\right)$

$P_k=P_0+(P_N-P_0)\underset{i=1}{\overset{k}{\mathrm{\Σ}}}f\left(i\right)---\left(4\right)$

ΔP _k=(P _N-P ₀)f(k) (5)

Under this segmentation form, the flow process of method for designing as shown in Figure 2, from any given optical power distribution (P _k) or optical power distribution (the Δ P of difference form _k) set out.Boundary condition (u in conjunction with fiber grating _N=1 and v ₀=0) and law of conservation of energy, calculates even type, cuts the inner fl transmission mould of toe type fiber grating and backward transmission mode (comprising amplitude and phase place), i.e. u _kAnd v _k

u _N=1，v ₀=0 (6)

${\left|u_k\right|}^2-{\left|u_{k-1}\right|}^2={\left|v_k\right|}^2-{\left|v_{k-1}\right|}^2\&Proportional;\frac{P_k-P_{k-1}}{2}=\frac{{\mathrm{\&Delta;P}}_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002736341000023.png,HDA00002736341000051.png"\; state="\{\{state\}\}">k</figure-callout>}}}{2}.---\left(7\right)$

Arg (u _k)=0, arg (v _k)=pi/2. (8) wherein, phase place is got in arg () expression.The amplitude here and phase place are amplitude and the phase place of resonance wave strong point (also can be referred to as Bragg wavelength place) fl transmission mould, backward transmission mode.

The forward, backward transmission mode that is based on having obtained uses transmission matrix to obtain the reflection coefficient (ρ of each grating section _k):

$\left[\begin{array}{c}{u}_k\\ v_k\end{array}\right]={(1-{\left|{\mathrm{\&rho;}}_k\right|}^2)}^{-\frac{1}{2}}\&times;\left[\begin{array}{cc}1& {-\mathrm{\&rho;}}_k^{*}\\ {-\mathrm{\&rho;}}_k& 1\end{array}\right]\&times;\left[\begin{array}{c}{u}_{k-1}\\ v_{k-1}\end{array}\right]---\left(9\right)$

$\mathrm{Re}\left({\mathrm{\&rho;}}_k\right)=\frac{(E-C)(G+A)+(F-D)(H+B)}{(G^2-A^2)+(H^2-B^2)},---\left(10\right)$

$\mathrm{Im}\left({\mathrm{\&rho;}}_k\right)=\frac{(E-C)(H-B)+(F-D)(G-A)}{(H^2-B^2)+(G^2-A^2)},---\left(11\right)$

Wherein Re () and Im () represent respectively real part, imaginary part; A=Re (u _ku _K-1), B=Im (u _ku _K-1), C=Re (u _kv _K-1), D=Im (u _kv _K-1), E=Re (v _ku _K-1), F=Im (v _ku _K-1), G=Re (v _kv _K-1), H=Im (v _kv _K-1).

According to ρ _k, and then calculate the coupling coefficient (q of each section grating _k):

$\left|q_k\right|=\left[\mathrm{<figure-callout\; id="1"\; label="ln"\; filenames="HDA00002736341000053.png"\; state="\{\{state\}\}">ln</figure-callout>}\frac{1+\left|{\mathrm{\&rho;}}_k\right|}{1-\left|{\mathrm{\&rho;}}_k\right|}\right]/\left({2\mathrm{\&Delta;z}}_k\right)---\left(12\right)$

arg(q _k)=π-arg(ρ _k). (13)

At last, based on q _kCan calculate the index modulation (containing amplitude-phase) of fiber grating:

$\left|{\mathrm{\&Delta;n}}_k\right|=\frac{2\mathrm{n\&Lambda;}}{\mathrm{\&pi;}}\left|q_k\right|,---\left(14\right)$

$\arg \left({\mathrm{\&Delta;n}}_k\right)=\arg \left(q_k\right)-\frac{3}{2}\mathrm{\&pi;}.---\left(15\right)$

Therefore, (14), (15) are the index modulation function of the fiber grating that obtains; Optical power distribution with fiber grating inside of this index modulation function is the optical power distribution of given target.So far, finished the fiber grating reconstruct structural design with any optical power distribution.

The fiber grating with any optical power distribution and the waveguide optical grating realized based on the present invention have important application in fields such as optical communication, microwave photon, distributed sensings, when processing microwave signal in the light territory to the stable control of reflection spot (or time delay), the design of short fiber laser resonant cavity is based on distributed sensing of single fiber grating etc.

Description of drawings:

Fig. 1. (a). the segmentation synoptic diagram of fiber grating; (b). before behind the raster-segment with the optical power distribution synoptic diagram of backward transmission mode, optical power distribution and difference form.

Fig. 2. have the process flow diagram of the fiber grating method for designing of any optical power distribution.

Fig. 3. optical power distribution and the difference form thereof of even type fiber grating inside.

Fig. 4. Gauss cuts optical power distribution and the difference form thereof of toe type fiber grating.

Fig. 5. the luminous power based on even type fiber grating is reconstructed the index modulation function that design obtains.

Fig. 6. the luminous power based on even type fiber grating is reconstructed design acquisition optical power distribution and difference form thereof.

Fig. 7. the luminous power of cutting toe type fiber grating based on Gauss is reconstructed the index modulation function that design obtains.

Fig. 8. the luminous power of cutting toe type fiber grating based on Gauss is reconstructed design acquisition optical power distribution and difference form thereof.

Fig. 9. flat-head type difference form optical power distribution and corresponding optical power distribution figure.

Figure 10. be reconstructed the index modulation function of the fiber grating of design acquisition based on flat-head type difference form optical power distribution.

Figure 11. be reconstructed optical power distribution and the difference form thereof of the fiber grating of design acquisition based on flat-head type difference form optical power distribution.

Figure 12. spike type difference form optical power distribution and corresponding optical power distribution figure.

Figure 13. be reconstructed the fiber grating refractive index function that design obtains based on spike type difference form optical power distribution.

Figure 14. be reconstructed the optical power distribution of design acquisition and the distribution plan of difference form luminous power thereof based on spike type difference form optical power distribution.

Figure 15. saddle type difference form optical power distribution and corresponding optical power distribution figure.

Figure 16. be reconstructed the index modulation function that design obtains based on saddle peak type difference form optical power distribution.

Figure 17. be reconstructed the optical power distribution of design acquisition and the distribution plan of difference form luminous power thereof based on saddle peak type difference form optical power distribution.

Figure 18. multimodal difference form optical power distribution and corresponding optical power distribution figure.

Figure 19. be reconstructed the index modulation function that design obtains based on multimodal difference form optical power distribution.

Figure 20. be reconstructed the optical power distribution of design acquisition and the distribution plan of difference form luminous power thereof based on multimodal difference form optical power distribution.

Figure 21. Gauss cuts the optical power distribution of toe type waveguide optical grating and the distribution plan of difference form thereof.

Figure 22. the optical power distribution of cutting toe type waveguide optical grating based on Gauss is reconstructed index modulation function and the optical power distribution that design obtains.

Embodiment

Below in conjunction with accompanying drawing enforcement of the present invention is further described.

As shown in Figure 1, at first fiber grating is made staging treating: with even segmentation or unequal piece-wise form fiber grating is divided into the N section, the grating section be numbered 1～N, whole grating normalization length is 0～1; In each section grating, index modulation is considered as constant.

When light signal is input in the fiber grating, there is fl transmission mould and rear to transmission mode in grating inside; For N grating section, at each at the interface fl transmission mould, be expressed as respectively u to transmission mode afterwards _kAnd v _k, shown in Fig. 1 (b).Thereby the luminous power of each waypoint of fiber grating, the luminous power of difference form are:

P _k∝|E _k| ²=u _k+v _k| ², (16)

ΔP _k=P _k-P _k-1. (17)

E wherein _kThe expression optical field distribution.

For ease of expressing, define a normalized function, i.e. (18) formula; At this moment, (16) and (17) can be rewritten into (19) and (20) formula:

$\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}f\left(i\right)=1,---\left(18\right)$

$P_k=P_0+(P_N-P_0)\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right),---\left(19\right)$

ΔP _k=(P _N-P ₀)f(k). (20)

Under this segmentation form, the flow process of the method for designing that the present invention proposes as shown in Figure 2.Given any optical power distribution (P _k) or optical power distribution (the Δ P of difference form _k), with as design object.Boundary condition and law of conservation of energy according to fiber grating:

u _N=1，v ₀=0， (21)

|u _k| ²-|u _k-1| ²=|v _k| ²-|v _k-1| ²， (22)

Associating (19)～(22) formula, be not difficult to obtain:

${\left|u_k\right|}^2-{\left|u_{k-1}\right|}^2={\left|v_k\right|}^2-{\left|v_{k-1}\right|}^2\&Proportional;\frac{P_k-P_{k-1}}{2}=\frac{{\mathrm{\&Delta;P}}_k}{2}.---\left(23\right)$

Thereby, the amplitude that calculates even type, cuts the inner fl transmission mould of toe type fiber grating and backward transmission mode by (23) formula: namely | u _k| and | v _k|.Then, adopt transmission matrix, calculate to obtain u _kAnd v _kPhase place:

arg(u _k)=0,arg(v _k)=π/2. (24)

Wherein, phase place is got in arg () expression.The amplitude here and phase place are amplitude and the phase place of resonance wave strong point (also being referred to as Bragg wavelength place) fl transmission mould, backward transmission mode.

The fl transmission mould that is based on having obtained, backward transmission mode, Configuration design obtain refractive index and adjust function, and concrete steps are: v _k, u _k→ ρ _k(z) → q _k(z) → Δ n (z); ρ wherein _k(z) reflection coefficient of expression k section grating, q _k(z) coupling coefficient of expression k section grating, Δ n _kThe index modulation that represents k section grating.

By transmission matrix coupling coefficient and forward, backward transmission mode are connected:

$M_k={(1-{\left|{\mathrm{\&rho;}}_k\right|}^2)}^{-\frac{1}{2}}\&times;\left[\begin{array}{cc}1& {-\mathrm{\&rho;}}_k^{*}\\ {-\mathrm{\&rho;}}_k& 1\end{array}\right]\&times;\left[\begin{array}{cc}\exp \left(\mathrm{j\&delta;}{\mathrm{\&Delta;z}}_k\right)& 0\\ 0& \exp \left({-\mathrm{j\&delta;\&Delta;z}}_k\right)\end{array}\right]---\left(25\right)$

$\left[\begin{array}{c}{u}_k\\ v_k\end{array}\right]=M_k\&times;\left[\begin{array}{c}{u}_{k-1}\\ v_{k-1}\end{array}\right]---\left(26\right)$

Wherein δ is the off resonance amount, Δ z _kBe the length of k grating section.Off resonance amount δ is 0 in resonance wave strong point (Bragg wavelength place), thereby (25), (26) formula further are reduced to:

$\left[\begin{array}{c}{u}_k\\ v_k\end{array}\right]={(1-{\left|{\mathrm{\&rho;}}_k\right|}^2)}^{-\frac{1}{2}}\left[\begin{array}{cc}1& {-\mathrm{\&rho;}}_k^{*}\\ {-\mathrm{\&rho;}}_k& 1\end{array}\right]\&times;\left[\begin{array}{c}{u}_{k-1}\\ v_{k-1}\end{array}\right].---\left(27\right)$

U in formula (27) _k, v _k, u _K-1, v _K-1Known [detailed process is seen (21)～(24) formula]; Thereby with after the expansion of (27) formula, according to the principle that imaginary part, real part equate, find the solution and obtain ρ _k:

$\mathrm{Re}\left({\mathrm{\&rho;}}_k\right)=\frac{(C-E)(G+A)+(D-F)(H+B)}{(G^2-A^2)+(H^2-B^2)}---\left(28\right)$

$\mathrm{Im}\left({\mathrm{\&rho;}}_k\right)=\frac{(C-E)(H+B)-(D-F)(G-A)}{(H^2-B^2)+(G^2-A^2)}---\left(29\right)$

Wherein Re () and Im () represent respectively real part, imaginary part; A=Re (u _ku _K-1), B=Im (u _ku _K-1), C=Re (u _kv _K-1), D=Im (u _kv _K-1), E=Re (v _ku _K-1), F=Im (v _ku _K-1), G=Re (v _kv _K-1), H=Im (v _kv _K-1).

Because, ρ _kBetween q _kExist corresponding relation:

${\mathrm{\&rho;}}_k=\tanh \left(\right|q_k\left|{\mathrm{\&Delta;z}}_k\right)\&times;\frac{q_k^{*}}{\left|q_k\right|},---\left(30\right)$

Thereby, by the ρ that obtains _kCalculate the q of each section grating _k, namely calculate from (30) formula to obtain:

$\left|q_k\right|=\left[\mathrm{<figure-callout\; id="1"\; label="ln"\; filenames="HDA00002736341000053.png"\; state="\{\{state\}\}">ln</figure-callout>}\frac{1+\left|{\mathrm{\&rho;}}_k\right|}{1-\left|{\mathrm{\&rho;}}_k\right|}\right]/\left(2{\mathrm{\&Delta;z}}_k\right),---\left(31\right)$

arg(q _k)=π-arg(ρ _k). (32)

At last, from q _kIn calculate Δ n _kNamely according to q _k, Δ n _kCorresponding relation and definition:

$\mathrm{\&delta;n}\left(z\right)=\frac{{\mathrm{\&Delta;z}}_k\left(z\right)}{2}\exp \left\{j\right[K_{0}z+{\mathrm{\&theta;}}_k\left(z\right)]+c.c---\left(33\right)$

$q_k\left(z\right)=-j\frac{K_0}{{2n}_0}{\mathrm{\&Delta;n}}_k\left(z\right)\exp [-{\mathrm{j\&theta;}}_k\left(z\right)]---\left(34\right)$

K wherein ₀=2 π/Λ, Λ is the grating cycle, c.c represents complex conjugate.Here, in even type, cut in the toe type fiber grating θ _k(z)=0.Calculated the index modulation Δ n of each section correspondence by (33), (34) _kSuch as (35), (36), be distributed as amplitude and phase place.

${\mathrm{\&Delta;n}}_k=\frac{{2n}_0\mathrm{\&Lambda;}}{\mathrm{\&pi;}}\left|q_k\left(z\right)\right|---\left(35\right)$

$\arg \left({\mathrm{\&Delta;n}}_k\right)=\arg \left(q_k\right)-\frac{3}{2}\mathrm{\&pi;}---\left(36\right)$

At this moment, (35), (36) are the index modulation function of the fiber grating that Configuration design obtains.Fiber grating under this index modulation function is consistent with the target optical power distribution in the optical power distribution of resonance wave strong point, and so far we have finished the fiber grating reconstruct structural design with any optical power distribution.

Need to prove: the Configuration design method among the present invention is not only applicable to fiber grating, and is applicable to have the design of the waveguide optical grating of any optical power distribution, and its process is identical with principle and fiber grating, has just repeated no more.

Be the validity of the Configuration design method among displaying the present invention more directly perceived, we divide three levels to provide several design example.

In the example of the first level, respectively the optical power distribution of an even type fiber grating and the optical power distribution of difference form (Fig. 3) (any one among them is as target, and effect is the same), Gauss are cut the optical power distribution (Fig. 4) of the optical power distribution of toe type fiber grating and difference form as target.On the one hand, whether observing the index modulation that obtained by this method for designing and original even type fiber grating, Gauss, to cut toe type fiber grating consistent; On the other hand, the optical power distribution of the fiber grating that obtains of check Configuration design whether with congruence.Use this method for designing, the Configuration design take the optical power distribution of even type fiber grating as target the results are shown in Figure 5 and Fig. 6.As seen, the index modulation function of acquisition is constant: Δ n=2 * 10 ^-4, identical with former even type fiber grating; The optical power distribution that obtains (or difference form optical power distribution) is highly consistent with target optical power distribution (or difference form optical power distribution) among Fig. 3, and error is less than 10 ^-7The optical power distribution of equally, cutting toe type fiber grating take Gauss the results are shown in Figure 7 and Fig. 8 as the Configuration design of target.The index modulation function that obtains presents the Gaussian function envelope, and is identical with former Gauss's apodizing function fiber grating; And the optical power distribution that obtains (or difference form optical power distribution) is highly consistent with target optical power distribution (or difference form optical power distribution) among Fig. 4, and error is also less than 10 ^-7These two example explanations: this method for designing is very effective for the Configuration design of the fiber grating with conventional optical power distribution (or difference form optical power distribution).

In the example of the second level, for being without loss of generality, selected several special optical power distribution, be expressed as with the optical power distribution of difference form: flat-head type, spike type, saddle type, multimodal.Fig. 9 is optical power distribution and the corresponding optical power distribution of flat-head type difference form; Use this method for designing, the optical power distribution of index modulation function, optical power distribution and the difference form of acquisition is seen Figure 10 and Figure 11.Figure 12 is optical power distribution and the corresponding optical power distribution of spike type difference form; Use this method for designing, the optical power distribution of index modulation function, optical power distribution and the difference form of acquisition is seen Figure 13 and Figure 14.Figure 15 is optical power distribution and the corresponding optical power distribution of saddle type difference form; Use this method for designing, the optical power distribution of index modulation function, optical power distribution and the difference form of acquisition is seen Figure 16 and Figure 17.Figure 18 is optical power distribution and the corresponding optical power distribution of multimodal difference form; Use this method for designing, the optical power distribution of index modulation function, optical power distribution and the difference form of acquisition is seen Figure 19 and Figure 20.By these 4 examples, be not difficult to draw: for arbitrarily or the optical power distribution (the perhaps optical power distribution of difference form) of customization, adopt this method for designing to obtain result and congruence, verified this method for designing validity under general condition.

In the example of tri-layer, we stress to verify the validity of this method for designing in waveguide optical grating.Select a Gauss to cut the waveguide optical grating of toe: its cycle is 221.5nm, and dutycycle is 50%, and the grating cycle is 50, and maximum effective refractive index is poor to be 0.1; Under these parameters, waveguide optical grating is seen Figure 21 in optical power distribution and the difference form thereof of resonance wave strong point; As target, index modulation function, optical power distribution and difference form thereof that Configuration design obtains are seen respectively Figure 22 with this optical power distribution (or its difference form).Contrast Figure 21 and Figure 22, be not difficult to find: the optical power distribution of using this method for designing to obtain is consistent with the target optical power distribution; Therefore verified that this method for designing also is applicable to waveguide optical grating, and be not only fiber grating.

Comprehensive above statement, the present invention has following feature.1). this Configuration design method can realize having the fiber grating Configuration design of the optical power distribution of any optical power distribution or difference form, and the filtering characteristic of fiber grating is extended to spatial domain from frequency domain.2). this Configuration design method is not only applicable to fiber grating, also is applicable to even type, cuts toe type waveguide optical grating.

Above what state only is the present invention program's preferred implementation, should be pointed out that under the prerequisite that does not break away from the present invention program's essence, can make some changes and polishing also should be included in protection scope of the present invention in reality is implemented.

Claims (4)

1. fiber grating method for designing with any optical power distribution, the method comprises the steps:

A) at first fiber grating is divided into the N section, the grating section be numbered 1,2,3 ... k-1, k ... N, in each section grating, index modulation is considered as constant; Normalization length is 0～1, at each section at the interface, all has fl transmission mould u _kWith backward transmission mode v _k, the luminous power P of each waypoint of fiber grating then _k, difference form luminous power Δ P _kFor:

P _k∝|u _k+v _k| ² (1)

ΔP _k＝P _k-P _k-1 (2)

B) normalized function of definition:

$\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}f\left(i\right)=1---\left(3\right)$

Can draw according to formula (1)-(3):

$P_k=P_0+(P_N-P_0)\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right)---\left(4\right)$

ΔP _k＝(P _N-P ₀)f(k) (5)

C) from any given optical power distribution P _kThe perhaps optical power distribution Δ P of difference form _kSet out, in conjunction with the boundary condition u of fiber grating _N=1 and v ₀=0 and law of conservation of energy, calculate the inner fl transmission mould of fiber grating u _kWith backward transmission mode v _k:

u _N＝1，v ₀＝0 (6)

${\left|u_k\right|}^2-{\left|u_{k-1}\right|}^2={\left|v_k\right|}^2-{\left|v_{k-1}\right|}^2\&Proportional;\frac{P_k-P_{k-1}}{2}=\frac{\mathrm{\&Delta;}{P}_k}{2}---\left(7\right)$

arg(u _k)＝0，arg(v _k)＝π/2 (8)

Wherein, phase place is got in arg () expression;

D) be based on the forward, backward transmission mode that obtained, use transmission matrix:

$M_k={(1-{\left|{\mathrm{\&rho;}}_k\right|}^2)}^{-\frac{1}{2}}\&times;\left[\begin{array}{cc}1& -{\mathrm{\&rho;}}_k^{*}\\ -{\mathrm{\&rho;}}_k& 1\end{array}\right]\&times;\left[\begin{array}{cc}\exp \left(\mathrm{j\&delta;\&Delta;}{z}_k\right)& 0\\ 0& \exp (-\mathrm{j\&delta;\&Delta;}{z}_k)\end{array}\right]---\left(9\right)$

$\left[\begin{array}{c}{u}_k\\ v_k\end{array}\right]=M_k\&times;\left[\begin{array}{c}{u}_{k-1}\\ v_{k-1}\end{array}\right]---\left(10\right)$

Wherein δ is the off resonance amount, Δ z _kBe the length of k grating section, δ is 0 in resonance wave strong point off resonance amount, obtains the reflection coefficient ρ of each grating section _k:

$\left[\begin{array}{c}{u}_k\\ v_k\end{array}\right]={(1-{\left|{\mathrm{\&rho;}}_k\right|}^2)}^{-\frac{1}{2}}\&times;\left[\begin{array}{cc}1& -{\mathrm{\&rho;}}_k^{*}\\ -{\mathrm{\&rho;}}_k& 1\end{array}\right]\&times;\left[\begin{array}{c}{u}_{k-1}\\ v_{k-1}\end{array}\right]---\left(11\right)$

$\mathrm{Re}\left({\mathrm{\&rho;}}_k\right)=\frac{(E-C)(G+A)+(F-D)(H+B)}{(G^2-A^2)+(H^2-B^2)},---\left(12\right)$

$\mathrm{Im}\left({\mathrm{\&rho;}}_k\right)=\frac{(E-C)(H-B)+(F-D)(G-A)}{(H^2-B^2)+(G^2-A^2)},$

Wherein Re () and Im () represent respectively real part, imaginary part; A=Re (u _ku _K-1), B=Im (u _ku _K-1), C=Re (u _kv _K-1), D=Im (u _kv _K-1), E=Re (v _ku _K-1), F=Im (v _ku _K-1), G=Re (v _kv _K-1), H=Im (v _kv _K-1);

E) because reflection coefficient ρ _kWith coupling coefficient q _kExist following corresponding relation:

${\mathrm{\&rho;}}_k=\tanh \left(\right|q_k\left|\mathrm{\&Delta;}{z}_k\right)\&times;\frac{q_k^{*}}{\left|q_k\right|},---\left(14\right)$

And then calculate the coupling coefficient q of each section grating _k

$\left|q_k\right|=\left[\ln \frac{1+\left|{\mathrm{\&rho;}}_k\right|}{1-\left|{\mathrm{\&rho;}}_k\right|}\right]/\left(2\mathrm{\&Delta;}{z}_k\right)---\left(15\right)$

arg(q _k)＝π-arg(ρ _k). (16)

F) last, according to coupling coefficient q _k, index modulation function Δ n _kCorresponding relation:

$\mathrm{\&delta;n}\left(z\right)=\frac{\mathrm{\&Delta;}{n}_k\left(z\right)}{2}\exp \left\{j\right[K_{0}z+{\mathrm{\&theta;}}_k\left(z\right)]+c.c---\left(17\right)$

$q_k\left(z\right)=-j\frac{K_0}{2n_0}\mathrm{\&Delta;}{n}_k\left(z\right)\exp [-j{\mathrm{\&theta;}}_k\left(z\right)]---\left(18\right)$

K wherein ₀=2 π/Λ, Λ is the grating cycle, c.c represents complex conjugate, θ _k(z)=0, calculate index modulation function Δ n _kAmplitude and phase place:

$\left|{\mathrm{\&Delta;n}}_k\right|=\frac{{2n}_0\mathrm{\&Lambda;}}{\mathrm{\&pi;}}\left|q_k\left(z\right)\right|---\left(19\right)$

$\arg \left(\mathrm{\&Delta;}{n}_k\right)=\arg \left(q_k\right)-\frac{3}{2}\mathrm{\&pi;}---\left(20\right)$

E) fiber grating that has this index modulation function is the fiber grating with any optical power distribution.

2. a kind of fiber grating method for designing with any optical power distribution according to claim 1 is characterized in that the N section that described fiber grating is divided in the N section is uniform.

3. a kind of fiber grating method for designing with any optical power distribution according to claim 1 is characterized in that the N section that described fiber grating is divided in the N section is heterogeneous.

4. one of according to claim 1-3 described a kind of fiber grating method for designing with any optical power distribution also is applicable to even type, cuts toe type waveguide optical grating.

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