CN102621605A - Phase diaphragm for measuring material optical nonlinearity - Google Patents

Abstract

The invention discloses a phase diaphragm for measuring material optical nonlinearity, which changes the circular phase object with the uniform phase retardance Pi/2 into the annular phase object with the phase retardance Pi/2. The numerical simulation proves that when the non-linear phase shift PhiNL is more than 0 and less than Pi and the widths of the phase objects are the same, the improved annular phase diaphragm has slightly higher measuring precision than that of the circular phase object in measuring the third-order nonlinearity and is the ideal measuring range of the optical nonlinearity. When the non-linear phase shift PhiNL is more than 0 and less than Pi, the annular phase diaphragm not only can measure and distinguish the size and the sign of the third-order nonlinearity refractivity, but also doesn't influence the sensitivity of the system measurement.

Description

A kind of phase diaphragm of measuring the material optical nonlinearity

Technical field

The present invention relates to a kind of phase diaphragm that can measure material three rank optical nonlinear refractions.

Background technology

Along with the develop rapidly of art such as optical communication and optical information processing, non-linear photon is learned investigation of materials and is become more and more important.The realization of functions such as light logic, optical storage, optical transistor, photoswitch mainly depends on the progress that non-linear photon is learned material.The measuring technique of Medium Optics nonlinear parameter is the gordian technique of research nonlinear optical material.4f phase coherence imaging system (G.Boudebs and S.Cherukulappurath; " Nonlinear optical measurements using a 4f coherent imaging system with phase object "; Phys.Rev.A; 69,053813 (1996)) be exactly a kind of new method of measuring nonlinear refraction coefficient of materials and absorption that proposes in recent years.

4f phase coherent imaging method is a kind of measuring method of beam aberration; This method is on 4f system object plane, to place a phase diaphragm; Non-linear object to be measured is placed on the Fourier plane, and on exit facet, receives the method for shoot laser pulse diagram picture with the CCD camera.This method can utilize monopulse to measure the size and the symbol of nonlinear refraction coefficient simultaneously.Phase diaphragm is to make the more phase object of small circular of an area at the center of a circular iris, and the phase delay of a pi/2 is arranged through other local light of light ratio of phase object.When the nonlinear refractive index of measured material when being positive, the nonlinear images that CCD receives since positive phase contrast strengthen around the strength ratio in the position of phase object.Opposite, when non-linear this refractive index of measured material for negative the time, a little less than wanting around the strength ratio of the position of the phase object of nonlinear images.

4f phase coherent imaging method utilizes phase diaphragm to realize the size of nonlinear refractive index and the measurement of symbol dexterously.

Summary of the invention

The size and the symbol of the third-order non-linear refraction coefficient of medium also can effectively measured and distinguish to a kind of phase diaphragm provided by the invention, this phase diaphragm, and can not influence the sensitivity of measurement.

For achieving the above object, the technical scheme that the present invention adopts is:

A kind of phase diaphragm of measuring the material optical nonlinearity is characterized in that, the phase object that is in the diaphragm center in the said phase diaphragm is annular phase object.

Phase diaphragm is to constitute through the annular phase object that forms at a diaphragm center plating transparent dielectric film.The bit phase delay of the annular phase object at phase diaphragm center is 2m π+pi/2, and wherein m is an integer.

Be modified into the annular phase object of symmetry through phase object, make the zone at annular phase object place also produce pi/2 phase and postpone the unified phase delay pi/2 of original circle.Same is positive sample for nonlinear refractive index, and phase delay is that the zone of pi/2 is because positive phase contrast intensity enhancing in nonlinear images.Opposite, when non-linear this refractive index of measured material for negative the time, in nonlinear images phase delay be pi/2 the zone since negative phase-contrast intensity reduce.

Utilize diaphragm of the present invention to divide two parts to carry out, i.e. nonlinear measurement and energy calibration in the measurement that the 4f phase coherence imaging system carries out nonlinear refractive index.The concrete steps of nonlinear measurement are:

(1) takes testing sample away, gather a pulse diagram picture, be called image without image with the CCD camera.

(2) testing sample is placed on the Fourier plane, neutral attenuator is placed on before the nonlinear sample, make the light intensity that shines on the sample be reduced to the range of linearity,, be called linear image with pulse diagram picture of CCD camera collection.

(3) testing sample is placed on the Fourier plane, moved on to after the sample, gather a pulse diagram picture, be called nonlinear images with the CCD camera with before gathering neutral attenuator that linear image is to use.

Energy calibration is that nonlinear sample is taken away, and a certain position that energy meter is placed between two convex lens of 4f system makes laser facula can all get on the energy meter probe.Launch a laser pulse, measure the energy of pulse, gather the reference hot spot of reference path simultaneously with the CCD camera with energy meter.Because all devices all are linear units in the light path at this moment, so according to the size that just can know the incident pulse energy with reference to the power of hot spot.The energy that incides the pulse on the testing sample in the nonlinear measurement process just can calculate through the reference hot spot that same laser pulse produces like this.

After measurement finishes, obtain the value of nonlinear refractive index through the non-linear hot spot of numerical fitting as input with linear beam spot.The sensitivity of experiment is that the strength difference by non-linear diaphragm decides.For the common phase diaphragm that has circular object, the mean intensity in phase object zone and phase object are Δ T with the difference of the mean intensity of exterior domain in the later nonlinear images of definition normalization.For annular phase diaphragm, the mean intensity that in like manner can define the annular region of phase delay pi/2 in the later nonlinear images of normalization is Δ T ' with the regional in addition mean intensity difference of the annular object of no phase delay.

Numerical simulation shows; Under the situation of identical incident intensity; In the nonlinear images of phase diaphragm of annular phase object, because the mean intensity of the square region of phase delay pi/2 is with almost equal with the mean intensity in phase object zone in the nonlinear images of the phase diaphragm of circular phase object.So in the present phase diaphragm, can be not influential for the sensitivity of systematic survey.

The raising of the sensitivity of annular phase diaphragm is different along with the variation of sample nonlinear phase shift.The variation of sensitivity is defined as 1-Δ T '/Δ T, the nonlinear phase shift that then in sample, produces | Φ _NL| under the situation of＜π, so new phase diaphragm can be not influential for measuring accuracy.

Theoretical model of the present invention is following.

Two-dimensional bodies are by the normalized linear polarization monochrome plane wave (E=E by the pulse laser emission on the plane of incidence of 4f system ₀(t) exp [j (ω t-kz)]+c.c.) irradiation.If the phase object transmitance be t (x, y), then behind phase object the surface be: O (x, y, t)=E (x, y, t) t (x, y), so sample front-surface field amplitude be O (x, y, spatial fourier transform t):

$S(u,v,t)=\frac{1}{\mathrm{\λf}}\mathrm{FT}\left[O(x,y,t)\right]=\frac{1}{\mathrm{\λf}}\∫\∫O(x,y,t)\exp [-2\mathrm{\πj}(\mathrm{ux}+\mathrm{vy})]\mathrm{dxdy}---\left(1\right)$

The symbol of FT in the following formula---Fourier transform; U is confocal spatial frequency of locating the x direction of 4f system, u=x/ λ f; V is confocal spatial frequency of locating the y direction of 4f system, v=y/ λ f; F is the focal length of lens L1 and L2; λ is the excitation wavelength of incoming laser beam.

Only consider third-order non-linear, and sample thickness is far smaller than the beams focusing degree of depth, then sample can be thought to approach, the amplitude of pulse laser and phase change communication satisfaction in sample:

$\frac{\∂I}{{\∂z}^{\′}}=-({\mathrm{\α}}_0+\mathrm{\βI})I$

$\frac{\mathrm{d\Δ\φ}}{{\mathrm{dz}}^{\′}}={\mathrm{kn}}_{2}I---\left(2\right)$

Q in the formula (u v) represents empty nonlinear phase shift, and q (u, v, t)=α ₂L _EffI (u, v, t); L _EffBe effective length, L _Eff=[1-exp (α L)]/α; L is the thickness of medium; I (u, v, t) be the intensity of light beam in sample (be proportional to | S (u, v, t) | ²), α is linear absorption coefficient (m ^-1); β is two-photon absorption coefficient (m/W); n ₂Be nonlinear refractive index (m ²/ W).

So complicated light field amplitude can be written as on the thick surface of nonlinear medium:

$S_L(u,v,t)=S(u,v,t)\exp [-\frac{\mathrm{\&alpha;L}}{2}]{[1+q(u,v,t)]}^{\frac{\mathrm{<figure-callout\; id="2"\; label="jk\; n"\; filenames="HDA0000148634770000011.png,HDA0000148634770000021.png"\; state="\{\{state\}\}">jk</figure-callout>}{n}_{}{}_2}{\mathrm{\&beta;}}-1/2}---\left(3\right)$

T (u v) by the complex amplitudes response of non-linear generation, can be defined as:

$T(u,v)=\frac{S_L(u,v,t)}{S(u,v,t)}={\left\{\exp \right[\mathrm{\&alpha;L}\left]\right[1+q(u,v,t)\left]\right\}}^{-1/2}\exp \left[j{\mathrm{\&Phi;}}_{\mathrm{NL}}(u,v,t)\right]---\left(4\right)$

Φ wherein _NL(u v) is the nonlinear phase shift that nonlinear medium causes, its expression formula is:

Φ _NL(u，v，t)＝ln[1+q(u，v，t)]kn ₂/β (5)

For a kind of special situation, when medium is that α and β can ignore when can't harm kerr medium.Then equation (5) can abbreviation be Φ _NL(u, v, t)=kn ₂(t), similar (4) are reduced to S to LI for u, v _L(u, v, t)=S (u, v, t) exp [j Φ _NL(u, v, t)].

Exit facet in the 4f system, can write as intensity becomes:

I _im(x，y，t)＝|U(x，y，t)| ²＝|F ^-1[S _L(u，v，t)T(u，v，t)H(u，v)]| ² (6)

FT in the formula ^-1Be contrary Fourier transform symbol; H (μ is undistorted or the coherent optics transport function of free lens ν), NA is lens L ₁Numerical aperture; G is the enlargement factor of total system.

Because CCD is the response to the ability distributions of incident laser, can be calculated as by integration so can flow:

$F={\&Integral;}_{-\&infin;}^{+\&infin;}{I}_{\mathrm{im}}(x,y,t)\mathrm{dt}={\&Integral;}_{-\&infin;}^{+\&infin;}{\left|U(x,y,t)\right|}^2\mathrm{dt}---\left(7\right)$

If consider that incident light is flat-top light (top-hat), place the transmitance of the circular iris of the 4f system plane of incidence to be defined as:

$t(x,y)=\mathrm{circ}(\sqrt{x^2+y^2}/R_a)---\left(8\right)$

The prerequisite of this hypothesis is that the radius of circular aperture diaphragm is R _aComparing with the spatial spread (waist radius of Gauss light) of incident light and to want much little, is to pass through diaphragm for the monochromatic plane wave energy of incident like this.Add that at the diaphragm center half width is L _P(L _P＜R _a) square PO, so have φ at the center of flat-top light _LPhase delay, the transmitance of square phase diaphragm is written as:

t _P(x，y)＝t _α(x，y)exp{jφ _Lrect(x/2L _p)rect(y/2L _p))} (9)

We can simulate the picture intensity that CCD detects on the 4f system exit facet by formula (1)-(9).

Under the situation that the phase object width equates, it is a little bigger to utilize improved annular phase diaphragm measurement material optics third-order non-linear of the present invention and the phase object measuring accuracy of utilizing circle to compare outline, is desirable optical nonlinearity measurement range.Annular phase diaphragm of the present invention is at nonlinear phase shift 0＜Φ _NLDuring＜π, can not only measure and distinguish the size and the symbol of third-order non-linear refractive index, and can not have influence on the sensitivity of systematic survey.

Description of drawings

Fig. 1 is a 4f phase coherence imaging system schematic diagram of the present invention.Wherein: 1, laser instrument; 2, phase diaphragm; 3, convex lens; 4, testing sample; 5, convex lens; 6, neutral attenuator; 7, CCD camera; 8, beam splitter; 9, catoptron; 10, convex lens; 11, catoptron; 12, beam splitter; 13, circular phase object; 14, annular phase object.

Fig. 2 is with the phase diaphragm synoptic diagram of circular phase object in the embodiment of the invention.

Fig. 3 is the phase diaphragm synoptic diagram of annular phase object in the embodiment of the invention.

Fig. 4 in the embodiment of the invention with the nonlinear images and the sectional view thereof of the phase diaphragm numerical simulation of circular phase object.

Fig. 5 is the nonlinear images and the sectional view thereof of the phase diaphragm numerical simulation of band shape phase object in the embodiment of the invention.

Fig. 6 is the graph of a relation of Δ T ' and nonlinear phase shift of the phase diaphragm of annular phase object in the embodiment of the invention.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is further described:

Fig. 1 is the Experimental equipment of 4f phase coherence imaging system.Experimental provision can be divided into measuring system and energy frame of reference two parts.Measuring system is made up of laser instrument 1, phase diaphragm 2, convex lens 3, testing sample 4, convex lens 5, neutral attenuator 6 and CCD camera 7.Wherein convex lens 3 constitute the 4f system with convex lens 5, and phase diaphragm 2 is placed on the object plane of 4f system, and testing sample 4 is on the Fourier plane, and CCD camera 7 received pulse image on the picture plane of 4f system.At first restraint (this part has omitted) among Fig. 1 from the laser that laser instrument 1 sends through expanding; The laser pulse that expands after restrainting forms nearly top-hat light through phase diaphragm 2; The Fourier transform of light beam planoconvex lens 3 converges on the testing sample 4 that is placed on the Fourier plane, because the nonlinear refraction character of testing sample 4 makes the phase place of pulse of incident change.The pulse of surperficial outgoing is received by CCD camera 7 through the inverse Fourier transform of convex lens 5 behind the sample, is called main spot.

The energy frame of reference is made up of beam splitter 8, catoptron 9, convex lens 10, catoptron 11 and beam splitter 12.The laser that comes out from phase diaphragm 2 is divided into two bundles by beam splitter 8, is wherein a branch ofly received by CCD camera 7 at last through catoptron 9, convex lens 10, catoptron 11 and beam splitter 12, is called with reference to hot spot.

Shown in Figure 2 is exactly the common form of phase diaphragm 2, and phase object 13 is circular, the light beam bit phase delay pi/2 of other part of optical beam ratio through phase object 13.Shown in the accompanying drawing 3 is annular phase diaphragm, is made up of the phase diaphragm of an annular jointly annular phase object 14 and its interior zone.Wherein annular phase object 14 produces the phase delay pi/2.

The measurement that utilizes the 4f phase coherence imaging system to carry out nonlinear refractive index divides two parts to carry out, i.e. nonlinear measurement and energy calibration.The concrete steps of nonlinear measurement are:

The first step: take testing sample 4 away, gather a pulse diagram picture, be called image without image with CCD camera 7.

Second step: testing sample 4 is placed on the Fourier plane, neutral attenuator 6 is placed on before the testing sample 4, make the light intensity that shines on the testing sample 4 be reduced to the range of linearity,, be called linear image with pulse diagram picture of CCD camera 7 collections.

The 3rd step: testing sample 4 is placed on the Fourier plane, moved on to after the testing sample 4,, be called nonlinear images with pulse diagram picture of CCD camera 7 collections with before gathering neutral attenuator 6 that linear image is to use.

Energy calibration is that nonlinear sample 4 is taken away, and a certain position that energy meter is placed between convex lens 3 and the convex lens 5 makes laser facula can all get on the energy meter probe.Launch a laser pulse, measure the energy of pulse, gather the reference hot spot of reference path with CCD camera 7 simultaneously with energy meter.Because all devices all are linear units in the light path at this moment, so according to the size that just can know the incident pulse energy with reference to the power of hot spot.The energy that incides the pulse on the testing sample 4 in the nonlinear measurement process just can calculate through the reference hot spot that same laser pulse produces like this.

Fig. 4 (a) is the nonlinear images that the phase diaphragm by common circular phase object obtains, and accompanying drawing 4 (b) then is the sectional view of accompanying drawing 4 (a) along y=0.The used major parameter of numerical simulation is the phase object radius and the ratio ρ=L of diaphragm radius _p/ R ' _a=0.5mm/1.5mm ≈ 0.33, testing sample nonlinear phase shift Φ _NL=0.3716.Accompanying drawing 5 (a) is that the phase diaphragm with annular phase object obtains nonlinear images, and accompanying drawing 5 (b) then is the sectional view of accompanying drawing 5 (a) along y=0.The used annular phase object length of side is ρ '=L ' with the ratio of diaphragm radius in the simulation _p/ R _a=0.5/1.5 ≈ 0.33 makes the area of annular region equate with the width of border circular areas, and its nonlinear phase shift is Φ _NL=0.3743.Definition is Δ T with the mean intensity of phase diaphragm position and the difference of the mean intensity outside the phase object in the nonlinear images of the phase diaphragm generation of circular phase object.And the nonlinear images that produces for the phase diaphragm of annular phase object; In like manner we define the average intensity of phase diaphragm position in the nonlinear images that annular phase place zone produces and the difference of the mean intensity outside the phase object is defined as Δ T '; Because the width in the circular phase place of hypothesis zone equates with the width in annular phase place zone in accompanying drawing 4 (b) and accompanying drawing 5 (b) simulation process; It is bigger to see that bit phase delay in Δ T and the accompanying drawing 5 (b) in the accompanying drawing 4 (b) is that the difference of the mean intensity outside mean intensity and the phase object of position of annular phase object of pi/2 is compared the latter, and promptly annular phase diaphragm can be not influential to the measurement sensitivity of system.

Numerical simulation shown in Figure 6 shows the sensitivity Δ T ' and nonlinear phase shift Φ that improves the back system _NLRelation.Can find out among the figure when considering 0＜Φ _NLDuring＜π; Both are a kind of almost linear relations; Again according to the third-order non-linear refraction coefficient of nonlinear phase shift and the medium relation under thin sample is approximate; Thereby can draw also energy measurement third-order non-linear refractive index of annular phase diaphragm, this and circular phase diaphragm are basically identical in theory.

Claims (3)

1. a phase diaphragm of measuring the material optical nonlinearity is characterized in that, the phase object that is in the diaphragm center in the said phase diaphragm is annular phase object.

2. a kind of phase diaphragm of measuring the material optical nonlinearity according to claim 1, it is characterized in that: said phase object is made up of transparent dielectric film.

3. a kind of phase diaphragm of measuring the material optical nonlinearity according to claim 1 and 2 is characterized in that: the bit phase delay of the annular phase object at said phase diaphragm center is 2m π+pi/2, and wherein m is an integer.

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