CN101021595A - Optical fiber sampling optical grating and planar optical wave guide sumpling grating - Google Patents

Abstract

The invention relates to an optical fiber sampling grating and a plane light waveguide sampling grating, where the refractivity variation of the gratings along the fiber core/waveguide axis is periodical and expressed by product of refractivity function and sampling function of a mother grating, where the refractivity function of the mother grating is deltan(z)=delta n0 Sin (4 pi n0 z/lambda B), wherein delta n0 is refractivity variation amplitude of grating, ne is effective refractivity of fiber core/waveguide, and lambdaB is Prague wavelength of grating; Fourier transform of the sampling function has a property that its two sides are symmetrical and change linearly or approximately linearly, adopting Sinc2, second-order rational function or Sinc-Sinc2 combined function; and the Sinc2 sampling optical fiber grating and Sinc2 sampling plane waveguide grating have linear or approximately linear delay spectrum envelopes and paths of each wavelength are symmetrical, able to generate large numbers of constant delay steps less than 1ps and allow wideband operation of signal.

Description

A kind of sampling by optical fiber grating and planar optical waveguide sampled-grating

Technical field

The present invention relates to photonic element, relate in particular to a kind of sampling by optical fiber grating and planar optical waveguide sampled-grating that is used as high-resolution and high-speed digital signal processor.

Background technology

Under many situations of communication, signal transmits in different passage mediums needs the different time, demonstrates different delay (delay is a kind of relativeness in time) when arriving next receptacle or processor.Ps (10 ^-12Second) there are many important use short delay of magnitude, for example carries out the high-resolution inhibit signal and handle in microwave phased array wave beam forms.Produce the sampling of THz light by means of multi wave length illuminating source, thereby realize the signal processing function in many high speeds and broadband.Traditional electronic delay line is merely able to produce ns (10 ^-9Second) the short of level postpone, and because of frequency dependence can not wideband operation.The general optical fiber lag line has overcome the difficulty of wideband operation, still because of the restriction (1ps is corresponding to 0.2mm optical fiber) of fiber cut precision, is difficult to technically realize that with many optical fiber a large amount of and constant ps postpones.Adopt the lag line of optical fiber grid to demonstrate more advantage.

The optical fiber grid are to select element by a kind of wavelength that forms periodic index of refraction variation in fibre core, and dissimilar optical fiber grid all have ripe manufacturing technology and have been used widely in fields such as communications.For example, the chirped fiber grid can produce continuous short the delay on different wavelength, but because the lag characteristic of chirped fiber grid has shown that it is a continuous curve for the linearity with certain slope of wavelength, shown in curve among Fig. 11, therefore, when the electric signal with certain bandwidth is modulated on a certain optical wavelength and imports such grating, the delay that different frequency signals will produce monotone increasing or subtract, thereby the bandwidth problem that has chromatic dispersion to bring.Many optical fiber grid of discrete cascade can not be obtained 1ps time step because of the restriction of the space length that is subjected to adjacent gratings.Though stack optical fiber grid have been broken away from above all restrictions, can realize the short delay of 1ps, but the method for making of stack grating determines that it is to have write that previous grating is write next grating in identical place again and a kind of special grating that forms, because the grating of being write will have different operation wavelengths at every turn, obtain a different laser beam fringe period in optical waveguide thereby therefore need adjusting to write mounting for grating.Because 1ps is corresponding to the 0.2mm fiber lengths, write grating at every turn and may bring the error that causes because of adjusting, so when the raster count that will write into is big, this problem is just more serious, and the manufacture characteristic that the grating that therefore superposes is repeatedly write grating has determined to obtain in this way that a large amount of and constant 1ps postpones is difficult.

Summary of the invention

The objective of the invention is to: a kind of sampling by optical fiber grating and planar optical waveguide sampled-grating are provided, and this grating can produce a large amount of and constant in 1ps (10 by means of multi wave length illuminating source ^-12Second) time step.

The present invention solves the problems of the technologies described above the technical scheme that is adopted to be:

A kind of slab guide sampled-grating, described grating along waveguide axis to variations in refractive index be periodic distribution, described grating is represented by the refractive index function and the sampling function product of master grating to change of refractive along waveguide axis; The refractive index function of described master grating is

δn(z)＝δn ₀Sin〔4πn _ez/λ _B〕

Wherein: δ n ₀Be the grating index amplitude of variation, n _eBe the effective refractive index of waveguide, λ _BIt is the bragg wavelength of grating; The fourier transform of described sampling function has symmetria bilateralis and is linearity or the characteristic of approximately linear variation.

Described slab guide sampled-grating, wherein: described sampling function is Sinc ²Sampling function.

Described slab guide sampled-grating, wherein: described Sinc ²The expression formula of sampling function is:

$S\left(z\right)$ $\underset{n=1}{\overset{s}{\mathrm{\Σ}}}\left\{\mathrm{Rect}\right[z-$ $(n-1/2)L_s,L_s/2\left]\right\}{\left\{\frac{\mathrm{Sin}\left[2N_s\mathrm{\π}(z/L_s-n+1/2)\right]}{2N_s\mathrm{\π}(z/L_s-n+1/2)}\right\}}^2$

Wherein: L _sBe the length of each sampling, be defined as L/s, L is a master grating length, and s is a sampling number;

Z: waveguide axis to;

N _s: Sinc ²The one-sided secondary lobe number of function;

Rect: be used to control the rectangular function of the brachymemma of secondary lobe number, wherein: z-(n-1/2) L _sBe its center, L _s/ 2 is its width.

Described slab guide sampled-grating wherein is characterised in that: described sampling function adopts second order rational function or Sinc-Sinc ²Composite function.

A kind of sampling by optical fiber grating, described grating is periodic distribution along the axial variations in refractive index of fibre core, and described fiber grating is represented by the refractive index function and the sampling function product of master grating along fibre core axle change of refractive; The refractive index function of described master grating is

δn(z)＝δn ₀Sin〔4πn _ez/λ _B〕

Wherein: δ n ₀Be the grating index amplitude of variation, n _eBe the effective refractive index of fiber cores, λ _BIt is the bragg wavelength of grating; The fourier transform of described sampling function has symmetria bilateralis and is linearity or the characteristic of approximately linear variation.

Described sampling by optical fiber grating, wherein: described sampling function is Sinc ²Sampling function.

Described sampling by optical fiber grating, wherein: described Sinc ²The expression formula of sampling function is:

$S\left(z\right)=\underset{n=1}{\overset{s}{\mathrm{\Σ}}}\left\{\mathrm{Rect}\right[z-(n-1/2)L_s,L_s/2\left]\right\}{\left\{\frac{\mathrm{Sin}\left[2N_s\mathrm{\π}(z/L_s-n+1/2)\right]}{{2N}_s\mathrm{\π}(z/L_s-n+1/2)}\right\}}^2$

Wherein: L _sBe the length of each sampling, be defined as L/s, L is a master grating length, and s is a sampling number;

Z: fiber axis to;

N _s: Sinc ²The one-sided secondary lobe number of function;

Rect: be used to control the rectangular function of the brachymemma of secondary lobe number, wherein: z-(n-1/2) L _sBe its center, L _s/ 2 is its width.

Described sampling by optical fiber grating, wherein: described sampling function adopts second order rational function or Sinc-Sinc ²Composite function.

Beneficial effect of the present invention is: because the sampling function of sampled-grating of the present invention adopts Sinc ²(annotate: Sinc ²Z=Sin ²Z/z ²), second order rational function or Sinc-Sinc ²Functions such as composite function calculate as can be known Sinc from fourier transform ²Conversion Deng function has symmetria bilateralis and is linearity or the characteristic of approximately linear variation, and the delay of grating and grating reflection spectral intensity have the relation of approximately linear, and adjacent reflectance spectrum intensity has less difference.Therefore the hyperchannel delay spectrum envelope that adopts such function to have linearity or approximately linear as the fiber grating and the waveguide grating of sampling function, and each wavelength channel all is symmetrical, thereby can produce a large amount of constant delays, and allow the signal wideband operation less than 1ps.Again because planar optical waveguide can produce the relative index of refraction variation bigger than fiber cores, the such sampled-grating that forms on planar optical waveguide can obtain to satisfy more high reflectance wavelength channels that special delay spectrum envelope requires, and can carry out integrating of planar lightwave circuit with other device, thereby satisfy requirement integrated in the modern Application technology.

Description of drawings

Fig. 1 is the lag characteristic of a passage of the retardation characteristic and the sampled-grating of chirped fiber grid or the grating that superposes;

Fig. 2 is Sinc ²Sampled-grating waveguide index change curve in one-period;

Fig. 3 is Sinc ²Function and its transforming function transformation function;

Fig. 4 a, b are respectively Sinc ²The delay spectrum of 16 wavelength channels with linear characteristic of sampled-grating and the distribution plan of these 16 channel delay minimum value;

Fig. 5 makes Sinc for adopting the Sagnac interferometer ²The principle of sampled-grating;

Fig. 6 is for utilizing Sinc ²The slab guide sampled-grating obtains the principle schematic less than the delay of 1ps.

Embodiment

With embodiment the present invention is described in further detail with reference to the accompanying drawings below:

The sampled-grating that can produce constant time delay less than 1ps of the present invention, can on optical fiber, form, also can on planar optical waveguide, form, because can producing bigger relative index of refraction, the relative fiber cores of planar optical waveguide changes, thereby can obtain to satisfy more high reflectance wavelength channels of special delay spectrum envelope requirement, and, the Sinc that on planar optical waveguide, forms ²Sampled-grating can carry out integrating of planar lightwave circuit with other device.Because identical with the principle that forms sampled-grating in slab guide on the optical fiber, method is close, therefore, below be that example is analyzed only with the sampled-grating that in slab guide, produces.

The optical fiber grid are to select element by a kind of optical wavelength that forms periodic index of refraction variation in fibre core or waveguide, and its index distribution can be used on index modulation Δ n (z) expression on the waveguide length direction.A sampled-grating can be expressed as the refractive index function of master grating and multiplying each other of sampling function mathematics, promptly

Δn(z)＝s(z)δn(z)

Expressed the variations in refractive index of the sampled-grating of generation along grating length direction z.Wherein δ n (z) is the refractive index function of master grating, and s (z) is a sampling function.And master grating refractive index function δ n (z) is described by grating length and variations in refractive index, is the master grating of L for length, and its refractive index can be write as along the sine function that is changed to of Z direction:

δn(z)＝δn ₀Sin〔4πn _ez/λ _B〕

Wherein: δ n ₀Be the grating index amplitude of variation, n _eBe the effective refractive index of waveguide, λ _BIt is the bragg wavelength of grating.And sampling function is equivalent to a kind of modulation to master grating, and the envelope of master grating refractive index is changed according to the sampling function rule.Sampling function employing Sinc when sampled-grating ²During function, Sinc ²Sampling function can be counted N by its one-sided secondary lobe _sDescribe.Because actual grating can not be an endless, so adopt the brachymemma of rectangular function to control the secondary lobe number.Whole sampling forms by connecting a plurality of single samplings.Therefore, such sampling function can be write as:

$S\left(z\right)=\underset{n=1}{\overset{s}{\mathrm{\Σ}}}\left\{\mathrm{Rect}\right[z-(n-1/2)L_s,L_s/2\left]\right\}{\left\{\frac{\mathrm{Sin}\left[2N_s\mathrm{\π}(z/L_s-n+1/2)\right]}{{2N}_s\mathrm{\π}(z/L_s-n+1/2)}\right\}}^2$

Wherein: L _sBe the length of each sampling, be defined as L/s, s is a sampling number, and the rectangular function Rect that is used for brachymemma is described by its center and width, z-(n-1/2) L _sBe its center, L _s/ 2 is its width; Z be waveguide or fiber axis to, n is the summation sequence number.Change of refractive is as shown in Figure 2 in one-period for periodic waveguide of Xing Chenging or optical fiber like this.

Based on the fourier transform theory as can be known, Sinc ²Function (Sin ²Z/z ²) fourier transform be [(pi/2) ^1/2/ 4] [(f-2) Sign[f-2]-2fSign[f]+(f+2) Sign[f+2]], Sinc ²(z) and transforming function transformation function as shown in Figure 3, have the characteristic of monosymmetric linear change, can find the solution the reflectance spectrum of such sampled-grating with coupling mode equations.In case obtained the complex amplitude reflectivity of this grating, its phase function θ _ρ(λ) can be derived, delay spectrum can pass through then

τ(λ)＝-(λ ²/2πc)[dθ _ρ(λ)/dλ]

Calculated, wherein c is a light speed in a vacuum.In other words, Sinc ²Sampled-grating has determined grating can produce discrete a plurality of wavelength channels, and reflectance spectrum has the characteristic of monosymmetric channel strength linear change.And the linear spectrum envelope of the delay that we need is to be produced by the phase function of the amplitude reflectivity derivative to wavelength.This shows that set up the sampling function of sampled-grating and the corresponding relation of grating reflection spectrum and then delay spectrum envelope based on the fourier transform theory, promptly the linear delay spectrum envelope of grating can be by Sinc ²Sampled-grating realizes, can produce a large amount of constant delay steps, and each wavelength channel all is symmetrical, shown in curve among Fig. 12, allows the signal wideband operation.In addition, high light grid (requiring reflectivity＞99% of each passage) and two factors of sampling brachymemma also exert an influence to delay spectrum.In practical study, a sampling silicon waveguide optical grating is designed, and the result has shown the triangle delay spectrum envelope of a near symmetrical, and the both sides envelope has presented higher linearity.The hyperchannel that we select one section envelope to comprise is arbitrarily observed its details, shown in Fig. 4 a, Fig. 4 b, 16 wavelength channels that shown the delay spectrum with linear envelope have the reflectivity greater than 99%, all 16 postpone minimum value standard deviation 4.2% with respect to linear characteristic are arranged, and the average retardation step is 0.25ps.

By above analysis as can be known, Sinc ²The slab guide sampled-grating is one can obtain the short solution that postpones of a large amount of＜1ps.And Sinc ²All of slab guide sampled-grating postpone passages can disposable formation in manufacture process, its need not to superpose refractive index control one by one that grating needs and regulating.The previous existing report of making about the high precision of Sinc sampling optical fiber grid with arbitrary refractive index section, it has also shown makes such Sinc ²The feasibility of sampled-grating.Sinc ²The manufacturing of sampled-grating can be adopted the roughly the same method of making Sinc sampled-grating (annotate: what the Sinc sampled-grating required is the multi-wavelength reflection channel of uniformity), promptly uses " the Fiber Bragg Grating FBG manufacturing technology of arbitrary refractive index section continuously ".The principle of making grating with the Sagnac interferometer as shown in Figure 5, among the figure, mark 3 be a shadow mask, 4 be optical waveguide, 5 is the grating mask, 6 is to control mobile system, 7 is Sagnac face mirror.In the Sagnac optical devices two are restrainted from the laser of controlling mobile system 6 through grating mask 5, Sagnac face mirror 7 and shadow mask 3 form interference fringe in optical waveguide 4, be the variations in refractive index that laser field that this striped distributes causes waveguide material, promptly formed grating.Has Sinc ²The laser field striped of function feature is carried out by control computer and relevant procedures.Consequent wavelength channel resembles mutual isolation the Sinc sampling optical fiber grid.Each postpones, and passage presents and superpose grating similarly symmetry and wideband operation characteristic.Recently, a kind of at As based on the Chalcogenide material ₂S ₃The technology of making sampled-grating in the ridge waveguide has also shown a very practical methods, and it can obtain the typical variations in refractive index up to 0.04.Its dirigibility makes this technology be applicable to this sampled-grating and photoelectricity planar circuit is integrated.

By means of a multi-wavelength or wideband light source, Sinc ²The slab guide sampled-grating can be used as＜short delay line of 1ps or＞the 1THz high-speed sampler, produce a large amount of constant delays less than 1ps.Acquisition less than the principle of the delay of 1ps as shown in Figure 6.After the light wave of different wave length arrives the optical circulator inlet simultaneously, incide Sinc through optical circulator first output terminal ²The slab guide sampled-grating, the light wave of different wave length is at Sinc ²(equivalence) diverse location in the slab guide sampled-grating is reflected, and returns circulator, and through the output of optical circulator second output terminal, forms constant time delay.In modern technologies, produce a large amount of constant delays and have very high practical value less than 1ps.At the multi-beam phased array antenna system, the delay step of needed minimum along with the wave beam frequency of operation or (with) increase of numbers of beams and reducing.For example, 512 wave beams that are operated in the 2GHz frequency need the delay compensation of 1ps step.Therefore, higher frequency of operation will need＜the delay step of 1ps.In the waveform generator technology, in order to obtain high speed high-resolution waveform, the interval that is used for the sampling of structure waveform must be much smaller than the cycle of waveform.For example, remove each periodic waveform of structure for the broadband waveform of realizing the 10GHz repetition frequency with 100 samplings, like this, the sample interval of＜1ps is a minimum requirement.If the waveform repetition frequency is higher or require more sampling for higher resolving power, then the sample interval must be littler.These requirements are can be Sinc with this technology still with (for example, the sampling rate of Tektronix AWG710 has only 4Gb/s) of traditional electronic technology or digital and electronic sampling realization ²The sampling waveguide optical grating is realized.Sinc particularly ²Planar optical waveguide can produce bigger relative index of refraction than fiber cores and change, and the result can obtain to satisfy the more high reflectance wavelength channel of special delay spectrum envelope requirement.In addition, the Sinc that on planar optical waveguide, forms ²Sampled-grating can carry out integrating of planar lightwave circuit with other device.Therefore such sampled-grating is used for overall performance and the efficient that high speed and high-resolution signal processing function module will improve system significantly.

From the fourier transform relation as can be known, second order rational function and Sinc-Sinc ²Composite function etc., its conversion also has monosymmetric linearity or the characteristic that changes of approximately linear as shown in Figure 3, therefore also can be used as the sampled-grating that sampling function removes to realize having linearity or approximately linear delay spectrum envelope, the short of acquisition＜1ps postpones.

Be understandable that, for a person skilled in the art, can be equal to replacement or change according to technical scheme of the present invention and inventive concept thereof, and all these changes or replacement all should belong to the protection domain of the appended claim of the present invention.

Claims (8)

1, a kind of slab guide sampled-grating, described grating is periodic distribution along waveguide axis to the variations in refractive index of z, it is characterized in that: described grating is represented by the refractive index function and the sampling function product of master grating to change of refractive along waveguide axis; The refractive index function of described master grating is

δn(z)＝δn ₀Sin〔4πn _ez/λ _B〕

Wherein: δ n ₀Be the grating index amplitude of variation, n _eBe the effective refractive index of waveguide, λ _BIt is the bragg wavelength of grating; The fourier transform of described sampling function has symmetria bilateralis and is linearity or the characteristic of approximately linear variation.

2, slab guide sampled-grating according to claim 1 is characterized in that: described sampling function is Sinc ²Sampling function.

3, slab guide sampled-grating according to claim 2 is characterized in that: described Sinc ²The expression formula of sampling function is:

$S\left(z\right)=\underset{n=1}{\overset{s}{\mathrm{\Σ}}}\left\{\mathrm{Rect}\right[z-(n-1/2)L_s,L_s/2\left]\right\}{\left\{\frac{\mathrm{Sin}\left[{2N}_s\mathrm{\π}(z/L_s-n+1/2)\right]}{{2N}_s\mathrm{\π}(z/L_s-n+1/2)}\right\}}^2$

Wherein: L _sBe the length of each sampling, be defined as L/s, L is a master grating length, and s is a sampling number;

Z: waveguide axis to;

N _s: Sinc ²The one-sided secondary lobe number of function;

Rect: be used to control the rectangular function of the brachymemma of secondary lobe number, wherein: z-(n-1/2) L _sBe its center, L _s/ 2 is its width.

4, slab guide sampled-grating according to claim 1 is characterized in that: described sampling function adopts second order rational function or Sinc-Sinc ²Composite function.

5, a kind of sampling by optical fiber grating, described grating is periodic distribution along the axial variations in refractive index of fibre core, it is characterized in that: described fiber grating is represented by the refractive index function and the sampling function product of master grating along fibre core axle change of refractive; The refractive index function of described master grating is

δn(z)＝δn ₀Sin〔4πn _ez/λ _B〕

Wherein: δ n ₀Be the grating index amplitude of variation, n _eBe the effective refractive index of fiber cores, λ _BIt is the bragg wavelength of grating; The fourier transform of described sampling function has symmetria bilateralis and is linearity or the characteristic of approximately linear variation.

6, sampling by optical fiber grating according to claim 5 is characterized in that: described sampling function is Sinc ²Sampling function.

7, sampling by optical fiber grating according to claim 6 is characterized in that: described Sinc ²The expression formula of sampling function is:

$S\left(z\right)=\underset{n=1}{\overset{s}{\mathrm{\Σ}}}\left\{\mathrm{Rect}\right[z-(n-1/2)L_s,L_s/2\left]\right\}{\left\{\frac{\mathrm{Sin}\left[{2N}_s\mathrm{\π}(z/L_s-n+1/2)\right]}{{2N}_s\mathrm{\π}(z/L_s-n+1/2)}\right\}}^2$

Wherein: L _sBe the length of each sampling, be defined as L/s, L is a master grating length, and s is a sampling number;

Z: fiber axis to;

N _s: Sinc ²The one-sided secondary lobe number of function;

Rect: be used to control the rectangular function of the brachymemma of secondary lobe number, wherein: z-(n-1/2) L _sBe its center, L _s/ 2 is its width.

8, sampling by optical fiber grating according to claim 5 is characterized in that: described sampling function adopts second order rational function or Sinc-Sinc ²Composite function.

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