CN101345588B - Method for implementing optical bullet propagation without time-space stretching by using photon crystal - Google Patents

Abstract

The invention relates to a photo bomb transmission method without time-space widening using photon crystal, which comprises following steps: determining aperture size, the aperture is needed which can superpose self-collimation area of equifrequency graph and zero group velocity dispersion area of group velocity dispersion graph according to photon crystal dispersion relation equifrequency graph and group velocity dispersion graph; perforation, adopting monocrystalline silicon material, perforating the monocrystalline silicon using electron beam exposure and ICP etching technology, to form periodically arranged air round aperture array of square crystal lattice or triangular crystal lattice, the aperture being above-mentioned size. The invention provides a convenient, energy-saving and brand-new means for accomplishing photon bomb transmission, also provides a basic medium material for optical signal transmission and processing, which will be widely used in field of optical integration, optical transmission and optical chip and signal processing.

Description

Utilize photonic crystal to realize the method for the photon bullet propagation of no time-space stretching

Technical field

The invention belongs to the optical communication technique field, particularly relate to a kind of method of utilizing photonic crystal to realize the photon bullet propagation of no time-space stretching.

Background technology

The development of calculating along with all optical communication and full photometry grows with each passing day based on the information transmission of optical chip and the signal processing demand to the light stable pulse ^[1G.P.Agrawal, Nonlinear Fiber Optics, Academic Press, Singapore, 2005. ' ²H.A.Haus and W.S.Wong, Solitons in optical communications, Rev.Mod.Phys.684231996 ^]Stable+light pulse not only can directly be used as the carrier of binary number, and because it in space indiffusion matter, satisfies the requirement of signal processing in the full photosystem.The conventional method that obtains the light stable pulse is to utilize nonlinear material ^[3Y.Silberberg, Collapse ofoptical pulses, Opt.Lett.15,1,282 1990. ' ⁴B.A.Malomed, D.Mihalache, F.Wise, and L.Torner, Spatiotemporal optical solitons, J.Opt.B:Quantum Semiclassical Opt.7, R53 2005. ^]This is a kind of method based on compensation principle, by the nonlinear interaction of light and material, utilizes Nonlinear Self-Focusing compensation space diffraction effect, utilizes non-linear self-alignment to regulate compensation of dispersion mutually, thus realize light wave in the space, temporal local.Because therefore its indiffusion in the space, on the time is known as the time orphan, spatial soliton, space-time orphan (photon bullet).

Although utilize and non-linearly can realize stable optical transmission, non-linear but is that energy relies on, and has an energy threshold, is lower than this threshold value, and orphan's propagation will be dispersed.And Nonlinear Mechanism depends on nonlinear material strongly, and the actual nonlinear material that can use and few, this dependence has greatly limited the material that can use.Photonic crystal can control effectively to the mobile of light, therefore is subjected to broad research ^[5E.Yablonovitch, Phys.Rev.Lett.58,2,059 1987; S.John, Phys.Rev.Lett..58,2,486 1987. ⁶J.D.Joannopoulos, R.D.Meade, and J.N.Winn, Photonic Crystals:Molding the Flow of Light, Princeton University Press, Princeton, NJ, 1995; C.M.Soukoulis, Photonic Crystals and Light Localization in the21stCentury, edited by C.M.Soukoulis Kluwer, Dordrecht, 2001 ^]By adjusting photon crystal structure, can handle dispersion relation.This just means the diffraction and the chromatic dispersion that can utilize the structural design acquisition to want.Especially, use suitable structure, can eliminate diffraction and GVD (Group Velocity Dispersion), thereby in linear structure, realize the stable propagation of similar optical soliton.This is a kind of based on the brand-new control method of eliminating principle, and different with above-mentioned nonlinear method is: pulse stability and pulse energy are irrelevant, also do not rely on the non-linear nature of material simultaneously.

Summary of the invention

Technical problem to be solved by this invention provides a kind of method of not having time-space stretching when realizing light pulse propagation, the time-space stretching of light pulse is meant: light pulse has the general aspects of diffusion when propagating, broadening in time is called chromatic dispersion, and the broadening on the space is called diffraction.The present invention utilizes photonic crystal, has eliminated the factor that causes diffraction and chromatic dispersion from principle, thereby the realization light pulse does not have the stable propagation of space-time broadening.

The technical solution adopted for the present invention to solve the technical problems is: a kind of method of utilizing photonic crystal to realize the photon bullet propagation of no time-space stretching is provided, comprises the following steps:

(1) determine pore size: according to the dispersion relation isofrequency map and the GVD (Group Velocity Dispersion) graph of a relation of photonic crystal, can make the aperture of zero GVD (Group Velocity Dispersion) area coincidence on auto-collimation zone and the GVD (Group Velocity Dispersion) figure on the isofrequency map is required aperture;

(2) punching: adopt single crystal silicon material, utilize electron beam exposure and ICP lithographic technique, punch on monocrystalline silicon piece, form tetragonal or positive triangular crystal lattice and be the air array of circular apertures of periodic arrangement, its aperture is the determined aperture of step (1).

Described photonic crystal adopts linear material to make, and has complete bandgap structure, and work photonic band gap and other can be with not have and overlap.

There is the auto-collimation zone in the work photonic band gap of described photonic crystal, has zero GVD (Group Velocity Dispersion) zone.

There is overlapping in the auto-collimation zone of the work photonic band gap of described photonic crystal with zero GVD (Group Velocity Dispersion) zone.

Described photonic band gap can reduce third-order dispersion to a great extent by reducing dielectric material contrast of refractive index or duty ratio, thereby increases photon bullet propagation scope, reduces the requirement to light impulse length.

The present invention adopts silica-base material, utilizes electron beam exposure and ICP lithographic technique, and punching forms two dimension on silicon wafer, three-dimensional air array of circular apertures.Because the nonlinear effect of silicon materials own is more weak, under non-high light condition, material can be thought linear.

The dissemination of light wave in photonic crystal determined by dispersion relation.Suppose to be respectively k vertically with the wave vector component that is parallel to the direction of propagation _‖With k _⊥, then intracrystalline dispersion relation is ω (k _‖, k _⊥).If incident light frequencies omega ₀=ω (k ₀, 0), so at k ₀=(k ₀, 0) near, ω (k _‖, k _⊥) can be expressed as:

$\mathrm{\ω}(k_{\left|\right|},k_{\⊥})={\mathrm{\ω}}_0+\frac{1}{2}{\left(\frac{{\∂}^2\mathrm{\ω}}{{\∂k}_{\⊥}^2}\right)}_{k_0}{k}_{\⊥}^2+{\left(\frac{\∂\mathrm{\ω}}{{\∂k}_{\left|\right|}}\right)}_{k_0}(k_{\left|\right|}-k_0)+\·\·\·$

In the equation (1),

Because the mirror image symmetry has disappeared;

Indicating the size of diffraction, and working as ${({\&PartialD;}^2\mathrm{\&omega;}/{\&PartialD;k}_{\&perp;}^2)}_{{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="H2008100420750E00011.png"\; state="\{\{state\}\}">k</figure-callout>}}_0}=0$ The time do not have a diffraction.Especially, satisfy when a certain k ⊥ scope $({\&PartialD;}^2\mathrm{\&omega;}/{\&PartialD;k}_{\&perp;}^2{)}_{{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="H2008100420750E00011.png"\; state="\{\{state\}\}">k</figure-callout>}}_0}=0,$ Represent that then the finite width light beam can not have diffraction, auto-collimation ground is propagated. ${(\&PartialD;\mathrm{\&omega;}/{\&PartialD;k}_{\left|\right|})}_{{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="H2008100420750E00011.png"\; state="\{\{state\}\}">k</figure-callout>}}_0}=v_g$ Be group velocity, have different group velocitys, caused the broadening on the optical pulse time just because of light pulse different frequency component.Time dispersive for convenience of description is k _‖(ω) be launched into about ω ₀Taylor series,

k _‖(ω)＝k ₀+(ω-ω ₀)β ₁+(ω-ω ₀) ²β ₂+… (2)

Wherein

${\mathrm{\&beta;}}_m={\left(\frac{d^m{k}_{\left|\right|}}{d{\mathrm{\&omega;}}^m}\right)}_{\mathrm{\&omega;}={\mathrm{\&omega;}}_0},(m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;)---\left(3\right)$

Because

(2) to have omitted the higher order term more than three times be appropriate to formula.Parameter beta ₁=1/v _gThe indicating impulse envelope is by group velocity vg motion; Parameter beta ₂Be GVD (Group Velocity Dispersion), corresponding to the time explanation of pulse.Especially, work as β ₂=0 indicating impulse broadening that has no time.So, when dispersion relation satisfies auto-collimation and zero GVD (Group Velocity Dispersion) simultaneously, can realize that space-time does not have the photon bullet propagation of broadening.

For the photonic crystal of tetragonal and positive triangular crystal lattice, all there is the auto-collimation zone in first and second photonic band gaps, therefore first and second can be with and can be with as work.In addition, because first can be with the point that does not have zero GVD (Group Velocity Dispersion), and second can have zero GVD (Group Velocity Dispersion) point, so adopt second photonic band gap can be with as working.By structure optimization, regulate the air aperture, zero GVD (Group Velocity Dispersion) frequency is overlapped with the auto-collimation scope, thereby obtain to support the medium material of photon bullet propagation.The present invention is full optical transmission, full photometry is calculated and signal processing provides the foundation material.

Beneficial effect

The invention provides the means that a kind of easy, energy-conservation and brand-new means realize the photon bullet propagation, for optical signal transmission and processing provide a kind of media base material, integrated at light, optical transmission and optical chip and signal processing field will be widely used.

Description of drawings

Fig. 1. second photonic band gap is along the GVD (Group Velocity Dispersion) curve chart of ky=0 direction in the two-dimension square grid photonic crystal.Illustration for mutually should be able to the equifrequency line chart, wherein thick line is represented auto-collimation equifrequency line.

Fig. 2. pulse is with the transverse width change curve of propagating.Illustration is a pulse shape.

Fig. 3. (a) temporal evolution of pulse in photonic crystal, spread length is respectively: L=8.5a, 86.5a, 150.5a, 214.5a, 287.5a, and 342.5a.(b) the vibration details of the pulse tail that third-order dispersion causes is arranged.

Fig. 4. the transmission spectrum of different monitoring points, solid line wherein, line segment, chain-dotted line represent that respectively spread length is respectively L=150.5a, the transmission spectrum of 278.5a and 342.5a.

Fig. 5. second photonic band gap is along the GVD (Group Velocity Dispersion) curve chart of ky=0 direction in the two-dimension square grid photonic crystal.Illustration for mutually should be able to the equifrequency line chart.

Embodiment

Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiment only to be used to the present invention is described and be not used in and limit the scope of the invention.Should be understood that in addition those skilled in the art can make various changes or modifications the present invention after the content of having read the present invention's instruction, these equivalent form of values fall within the application's appended claims institute restricted portion equally.

As shown in Figure 1, in dielectric material, make the airport array formation photonic crystal of two-dimension square grid periodic arrangement.Dielectric material is a monocrystalline silicon, refractive index n=3.46.Airport radius r=0.35a, a are lattice constant.Considering the incident of TE ripple, is the isofrequency map of second photonic band gap shown in Fig. 1 illustration, and as seen in frequency range ω=0.286～0.302 (2 π c/a), along [10] direction, photonic crystal supports the auto-collimation of wide-angle to propagate.There are one zero GVD (Group Velocity Dispersion) point ω in corresponding therewith GVD (Group Velocity Dispersion) curve such as Fig. 1 ₀=0.2915 (2 π c/a), and at ω ₀Near curvilinear motion is mild.Because 1 GVD (Group Velocity Dispersion) point is positioned at the auto-collimation frequency range, reach a conclusion: the photonic crystal support does not have the photon bullet propagation of space-time broadening.

For confirming above-mentioned photon bullet propagation, utilize FDTD to carry out the numerical simulation experiment.If incident light is a space-time Gaussian TE pulsed light, central wavelength lambda ₀=1.55 μ m are along photonic crystal [10] direction incident.Pulse FWHM width h=16a, pulse FWHM duration w=0.3ps, respective frequencies scope v=1.922～1.950 * 10 ¹⁴Hz.The requirement of auto-collimation and zero GVD (Group Velocity Dispersion) is satisfied in the selection of pulse.Fig. 2 has provided pulse duration h with the variation relation of propagating, and visible pulsewidth h does not have obvious variation in very long spread scope, and pulse keeps the shape identical with Fig. 2 illustration substantially.The temporal evolution of pulse has also been done investigation, and Fig. 3 a is that magnetic flux density is at different monitoring points evolution curve in time.Significantly, in related monitoring range, pulse envelope keeps identical shape substantially.Figure 4 shows that the transmission spectrum of different monitoring points, at the frequency range Δ _v=1.89～1.99 * 10 ¹⁴Hz, transmissivity this means that all greater than 95% the duration pulse shorter than 0.3ps still can keep stablizing indiffusion in this spread scope.

Although the propagation of above-mentioned photon bullet can be owing to the auto-collimation and the zero group velocity effect of second order, the diffraction of high-order and chromatic dispersion are influential to the stable of it.With the third-order dispersion is the example explanation: at first define the third-order dispersion length L _d=W ³/ β ₃, when the pulse propagation distance less than L _d, can think that then it is stable propagating.For above-mentioned photonic crystal, β ₃(ω ₀The 1528a of)=- ²/ 4 π ²c ³, L then _d=6.25 * 10 ⁴A, for the all-optical chip system, this is a very large length.Although third-order dispersion is little, also can in evolution, observe, it can cause the vibration of pulse tail, shown in Fig. 3 a.Be clear meter, Fig. 3 b has provided the details of pulse tail field vibration, and monitoring site is in spread length L=85.5a place.Because the size of third-order dispersion has determined the length of stable propagation, therefore always wish β ₃The smaller the better.

Be compacting third-order dispersion, β ₃The smaller the better, promptly the GVD (Group Velocity Dispersion) curve is smooth more good more.Because the variation of GVD (Group Velocity Dispersion) curve derives from the Bragg scattering, reduce scattering and just can reduce its dependence frequency, reduce scattering so can reach by reduction contrast of refractive index and pore size, and then the β that reduces ₃Purpose.As an example, the refractive index and the aperture of above-mentioned photonic crystal change into: n=2.83, r=0.32a.The GVD (Group Velocity Dispersion) curve as shown in Figure 5, it is more smooth to compare curve with Fig. 1, and zero group velocity scattering point is positioned at the auto-collimation frequency range, ω=0.323～0.34 (2 π c/a).Significantly, the photon bullet propagation can be supported by this crystal, and third-order dispersion obtains bigger compacting.

Claims (2)

1. a method of utilizing photonic crystal to realize the photon bullet propagation of no time-space stretching comprises the following steps:

(1) determine pore size: according to the dispersion relation isofrequency map and the GVD (Group Velocity Dispersion) graph of a relation of photonic crystal, can make the aperture of zero GVD (Group Velocity Dispersion) area coincidence on auto-collimation zone and the GVD (Group Velocity Dispersion) graph of a relation on the isofrequency map is required aperture;

(2) punching: adopt single crystal silicon material, utilize electron beam exposure and ICP lithographic technique, punch on monocrystalline silicon piece, form tetragonal or positive triangular crystal lattice and be the air array of circular apertures of periodic arrangement, its aperture is the determined aperture of step (1);

Described photonic crystal adopts linear material to make, and has complete bandgap structure, and work photonic band gap and other can be with not have and overlap; There is the auto-collimation zone in the work photonic band gap of described photonic crystal, has zero GVD (Group Velocity Dispersion) zone; There is overlapping in the auto-collimation zone of the work photonic band gap of described photonic crystal with zero GVD (Group Velocity Dispersion) zone.

2. a kind of method of utilizing photonic crystal to realize the photon bullet propagation of no time-space stretching according to claim 1, it is characterized in that: described photonic band gap can be by reducing dielectric material contrast of refractive index or duty ratio, can reduce third-order dispersion, thereby increase photon bullet propagation scope, reduce requirement light impulse length.

Images