CN1048928A - Reflective variable period grating with sawteeth groove - Google Patents

Abstract

The present invention is a kind of reflective variable period grating with sawteeth groove, is used for integrated optics radio frequency acousto-optic spectrum analyzer and optical fiber communication wavelength division multiplexer etc.Its section is a sawteeth groove, and blazing angle is to change continuously, and grating structural parameter should satisfy relational expression: ∧ _i=(m λ)/(sinI ∴+sin θ _i) m=± 1, ± 2 .... the present invention has also proposed optimization method to the design of incident angle, angle of diffraction, blazing angle and non-central wavelength " picture point " position.Adopt the present invention diffraction efficiency can be brought up to more than 95%, and can combine in variable period grating one to collimation (convergence) and two kinds of functions of beam split, make light path compactness, reliable.

Description

Reflective variable period grating with sawteeth groove

The present invention relates to a kind of optical element, be specially a kind of reflective variable period grating, be used for integrated optics radio frequency acousto-optic spectrum analyzer and optical fiber communication wavelength division multiplexer etc.

The variable period grating is meant the grating that the grating cycle modulates according to certain rules.The blazed grating of present existing fixed cycle is all comparatively ripe from the theory to technology, for example discloses a kind of " blazed diffraction grating structure and manufacture method thereof " in the us4330175 patent.It has proposed to utilize on silicon single crystal engraving method to make the blazed grating of plane and concave surface.Though this class grating diffraction efficiency height, theoretical value can reach 100%, and it only has simple function, i.e. chromatic dispersion function (beam split function).And existing variable period grating, particularly reflective variable period grating, its section mostly is a rectangular channel, for example in the 1057th～1059 page of the 7th phase of volume " IEEE quantum electronics magazine " nineteen eighty-two 18 in the 2195th～2198 page of the employed reflective variable period grating in the integrated optics spectrum analyzer of report and U.S.'s " applied optics " (Applled Optlcs) 21 the 12nd phase of volume of nineteen eighty-two report close the reflective variable period grating that uses in ripple and the channel-splitting filter in integrated optics.This class grating diffration efficient is lower, and its maximum theoretical is 40.5%, has therefore limited application.In addition, above-mentioned variable period grating only could be worked down at designed wavelength (title centre wavelength), and at non-central wavelength, its primary characteristic can produce deviation.

The objective of the invention is to a kind of reflective variable period grating of designing for the deficiency of avoiding in the above-mentioned prior art with sawteeth groove.This grating is done on Waveguide end face or backing material, realized certain modulation by reflection (diffraction), to change the wave front of incident light to incident light.For example make plane wave become spherical wave, make ball (post) ground roll of dispersing become ball (post) ground roll of convergence, otherwise or, thereby realize collimation, focus on, change functions such as the direction of propagation.

Purpose of the present invention can reach by following measure: reflective variable period grating, its section are sawteeth groove, and blazing angle is to change continuously, and the Changing Pattern of slot pitch is defined as the Grating Modulation function, and grating structural parameter should satisfy relational expression:

∧ _i＝ (mλ)/(SinIi+Sinθi) m＝±1，±2……（1）

∧ _iBe the centre distance of i-l groove and i groove in the grating, the incident angle Ii and the diffraction angle at i grating groove place _iShould satisfy formula:

$\mathrm{SinIi}=\±\frac{\mathrm{XI}}{l_i}=\±\frac{(\mathrm{XI}-x_i)}{\sqrt{{(\mathrm{XI}-x_i)}^2+{\mathrm{YI}}^2}}\left(2\right)$ $\mathrm{Sin}{\mathrm{\θ}}_i=\±\frac{\mathrm{XO}-x_i}{r_i}=\frac{(\mathrm{XO}-x_i)}{\sqrt{{(\mathrm{XO}-x_i)}^2+{\mathrm{YO}}^2}}\left(3\right)$

Each groove of serrated slot has different blazing angle γ _i, γ _iWith incident angle I _iAnd diffraction angle _iBetween should satisfy relational expression:

γ _i＝（1/2）（Ii+θ _i）（4）

Purpose of the present invention can also reach by following other measure: have the reflective variable period grating of sawteeth groove, for non-central wavelength X _iThe coordinate F of " picture point " position should be:

Description of drawings:

Fig. 1 is that section is the variable period grating of rectangular channel.

Fig. 2 is that section is the variable period grating of sawteeth groove.

Fig. 3 is the relation between blazing angle and incident angle, the angle of diffraction.

Fig. 4 adopts channel-splitting filter embodiment of the present invention.

Below in conjunction with accompanying drawing the present invention is described in detail:

The Grating Modulation function is relevant with wavelength X, promptly has only a definite wavelength X, could satisfy phase relation between source point Q and the picture point P.And for any wavelength, the P point is not an image point, but can find the concentrated relatively facula position of an energy as " picture point " under this wavelength.The position of " picture point " is no analytic solution under general any wavelength, and the present invention proposes a kind of optimization solution, promptly in wavelength X _iUnder find 1 P _i, make P _iArrive the distance minimum of the diffracted ray of each groove of grating.

With reference to Fig. 1, if the wavelength that sends by the Q point be the incident light of λ through variable period optical grating diffraction post-concentration to the P point, grating structural parameter should satisfy relational expression (1).The incident angle I at i grating groove place _iAnd diffraction angle _iShould satisfy relational expression (2), (3) respectively, x in the formula _iBe the centre coordinate of i groove of grating, l _iAnd r _iBe respectively Q point and P point distance to x, according to Grating Modulation function (1) formula as can be known, as source point Q and picture point P during all in the infinite distance, l _i=l _o→ ∞, r _i=r _o→ ∞, at this moment incident light and diffraction light all are directional light, i.e. I _i=I _o, θ _i=θ _o, (1) formula degenerates into the grating equation of conventional grating at this moment: (SinI _o+ Sin θ _o) ∧ _o∧ in=m λ (8) formula _oBe the grating cycle.

With reference to Fig. 2, when grating has sawteeth groove, and each groove has different blazing angle (groove angle) γ _iThe diffraction central authorities principal maximum coincidence of each groove is resembled in m level (most applications is got m=1) interference, therefore improved variable period grating diffration efficient greatly, design sawteeth groove variable period blaze of grating angle obtains each groove blazing angle γ by the geometric relationship of Littrow condition and Fig. 3 _iWith incident angle Ii and diffraction angle _iBetween the pass be (4) formula.Because the restriction of actual processing, the blazing angle of each flute profile can not be accomplished continuous variation, but because γ _iVariation be very slowly, therefore can adopt the segmentation changing method, according to processing bar year and accuracy requirement, the total groove number of grating can be divided into some groups, all grooves have identical blazing angle in every group, and equal the value of the blazing angle at this class midpoint place.

The design of non-central wavelength " picture point " position is with reference to Fig. 1, and wavelength is that the angle of diffraction of incident ray diffraction light on i grating groove of λ is θ _i, diffraction light is regarded as ray how much, its slope is k _i=ctg θ _i,,, k is arranged then to the variable period grating m=l that glitters by (1) formula _i=ctg(Sin ^-1[(λ/∧ _i)-SinI _i]), because of this ray is crossed point (x on the grating planar _i, 0), can write out the equation of diffracted ray: y=k _i(x-x _i).In the ideal case, to central wavelength lambda, diffracted ray should meet at picture point P(XO, YO); To non-central wavelength X _j, then can find 1 F _j(X _j, Y _j), make itself and each diffracted ray apart from the shortest, at this moment each diffraction light wave is inevitable best in the interference situation of this point.If F _j(X _j, Y _j) to the distance L i of the 1st diffracted ray:

$\mathrm{Li}=\frac{Y-k_{i}X+k_i{x}_i}{\sqrt{1+K_1^2}}........\left(9\right)$

Make that the F point is S to the quadratic sum of the distance of each diffracted ray ²:

$S^2=\underset{i=-N}{\overset{M}{\mathrm{\Σ}}}\frac{{(Y-k_{i}X+k_i{X}_i)}^2}{1+k_1^2}.......\left(10\right)$

M in the formula, N represent grating groove ordinal number, and the total groove number of grating is M+N+l.Get S ²Minimum value, then have

(ds ²/ dx)=0 (ds ²/ dy)=0 (12) by (10) (11) (12) Shi Kede:

$Y\underset{-N}{\overset{M}{\mathrm{\Σ}}}{k}_i{K}_i-X\underset{-N}{\overset{M}{\mathrm{\Σ}}}{k}_1^2{K}_i+\underset{-N}{\overset{M}{\mathrm{\Σ}}}{k}_1^2{x}_i{K}_i=O$ $Y=\underset{-N}{\overset{M}{\mathrm{\Σ}}}{K}_i-X\underset{-N}{\overset{M}{\mathrm{\Σ}}}{k}_i{K}_i+\underset{-N}{\overset{M}{\mathrm{\Σ}}}{k}_i{x}_i{K}_i=O$

K in the formula _i=1/(1+k ² _i)

Obtain the coordinate that F orders by solution of equations and be (5) (6) (7) formula.

When design, after the coordinate of given operation wavelength and source point and picture point, can calculate the width of required each groove of variable period grating according to above-mentioned various preparing a computer program, and non-central wavelength " picture point " position.

With reference to Fig. 4, the variable period grating is positioned at the end face of waveguide, and is input with an optical fiber, and ten optical fiber are output.The optical fiber core diameter is 50 microns, and operation wavelength is ten wavelength in the 0.85-1.3 micron, and the wavelength interval is 0.05 micron, and centre wavelength is 1.05 microns.The input optical fibre end face is as source point, and its coordinate is the XI=10 millimeter, the YI=17.32 millimeter.The output optical fibre end face is " picture point ", and the picpointed coordinate of centre wavelength is XO=0, the YO=20 millimeter.The poor wide of the variable period grating of designing is 1.40～3.66 microns, midpoint groove width ∧ _o=2.0 microns, " picture point " of other each wavelength is as following table:

(micron)

5 millimeters of grating length overalls, blazing angle are divided ten sections variations, can get γ by (6) formula _iBetween 8 degree～19 degree.

Because the present invention has adopted the groove structure of (segmentation) variation blazing angle continuously, has improved diffraction efficiency greatly.Calculate through theory, ideally efficient can reach more than 95%.Adopt non-central wavelength " picture point " position of the present invention's design, then might combine in variable period grating one to collimation (convergence) and two kinds of functions of beam split, make light path compactness, reliable.Through further improving and the development manufacture craft, will in various spectral instruments, be used widely.Description of drawings: 1-waveguide, 2-grating (chirped), 3-input optical fibre, 4-output optical fibre.

Claims (2)

1, have the reflective variable period grating of sawteeth groove, its section is a sawteeth groove, it is characterized in that blazing angle is continuous variation, and the Changing Pattern of slot pitch is defined as the Grating Modulation function, and grating structural parameter should satisfy relational expression:

∧ _i= (mλ)/(SinIi+Sinθi) m=±1，±2……(1)

∧ _iBe the centre distance of l-1 groove and the 1st groove in the grating, the incident angle I1 and the diffraction angle at the 1st grating groove place _iShould satisfy formula:

$\mathrm{SinIi}=\±\frac{\mathrm{XI}-x_i}{l_i}=\±\frac{(\mathrm{XI}-x_i)}{\sqrt{{(\mathrm{XI}-x_i)}^2+{\mathrm{YI}}^2}}.....\left(2\right)$ $\sin {\mathrm{\θ}}_i=\±\frac{\mathrm{XO}-x_i}{r_i}=\±\frac{(\mathrm{XO}-\mathrm{xi})}{\sqrt{{(\mathrm{XO}-x_i)}^2+{\mathrm{YO}}^2}}.....\left(3\right)$

Each groove of serrated slot has different blazing angle γ ₁, γ ₁Diffraction angle with incident angle I1 _iBetween should satisfy relational expression:

γ _i=(1/2)(Ii+θ _i)

2, the reflective variable period grating with sawteeth groove as claimed in claim 1 is characterized in that for non-central wavelength X _iThe coordinate F of " picture point " position should be:

In the formula:

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