CN104596958B - The analysis method of the biochemical sensor based on series connection LPWG - Google Patents

The analysis method of the biochemical sensor based on series connection LPWG Download PDF

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CN104596958B
CN104596958B CN201510024712.1A CN201510024712A CN104596958B CN 104596958 B CN104596958 B CN 104596958B CN 201510024712 A CN201510024712 A CN 201510024712A CN 104596958 B CN104596958 B CN 104596958B
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lpwg
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sandwich layer
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waveguide grating
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CN104596958A (en
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王玲芳
陈开鑫
张梦若
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University of Electronic Science and Technology of China
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Abstract

The present invention discloses a kind of analysis method of the biochemical sensor based on series connection LPWG, by using the coupled characteristic of LPWG, by the light of the certain bandwidth range in incident light wave centered on resonance wavelength, by LPWG1Tested covering is coupled into, by LPWG2This part is optically coupled into waveguide core layer again, the basic mode with symport in waveguide core layer interferes output.When measured matter changes, the resonance wavelength in output spectra can shift, by detecting that side-play amount can calculate measured matter concentration.The absorption spectrum signal of liquid, realizes the qualitative of measured matter in analysis output spectra.On the one hand solve conventional biochemical sensor carrys out qualitatively problem to the method for the present invention by the single certain sensitive film of expensive and Testing index;On the other hand the bandwidth limitation problems for needing the absorption bands for avoiding water to be brought in liquid, aqueous quantitative determination are solved.

Description

The analysis method of the biochemical sensor based on series connection LPWG
Technical field
The invention belongs to integrated optics field, bio-photon field and spectrum analysis field, and in particular to long period The Mode Coupling and transmission characteristic of waveguide optical grating, and quantification and qualification model and method in biochemical sensitive mechanism.
Background technology
At present, for the domestic and international biochemical sensor developed, either based on electrochemical principle, microflow control technique or base In the biochemical sensor that optical principle is detected, generally in the biochemical sensitive membrane of contact surface deposit of device and measured matter, root The selection of measured matter is completed according to there is physicochemical change to the absorption of predetermined substance or with it by sensitive membrane and is distinguished, And need volume larger prism and optical circulator.This design, not only increased the design complexity of device, can also Increase the size and cost of sensor, and each sensitive membrane generally is only capable of carrying out qualitative, sensitive membrane to a kind of respective substance Can be deteriorated as selectivity occurs in the increase of use time and frequency of use, and produce cross-sensitivity, can so reduce sensing The sensitivity of device and detection efficiency, cause qualitative inaccurate.
Accurate refractive index (RI) sensing is extremely important for scientific research and commercial Application.Because essentially all of The quantitative determination of biological and chemical material can realize by detecting its refractive index, so, it is accurate for biochemical sensitive Really the refractive index of parsing measured matter is a prerequisite.It is generally detected as material demand and solvent is used as and as load by water Body is admitted to detection zone, if selected absorption information of the detection light source wave band comprising water, can not complete quantitative or can be right Quantitative result produces considerable influence.The detection light source of specific band like this can only be just selected, which limits detection range. Particularly in mid and far infrared wave band, the fundamental frequency absorption information of basic all substances (comprising biochemical gas, liquid) is remote red all in Wave section, the absorption coefficient of material than in big 1~2 order of magnitude of near infrared band, detection sensitivity can be greatly improved, but In mid and far infrared wave band, the absorption of water is very strong, and the appearance of this challenge brings greatly puzzlement to biochemistry detection.It can be seen that, During hydrous matter is to biochemical sensitive in the research process of biochemical sensor the adverse effect of quantitative problem carry out further investigation will It is very important.
The content of the invention
The present invention is the above-mentioned technical problem for solving, and proposes a kind of analysis side of the biochemical sensor based on series connection LPWG Method.
The technical solution adopted by the present invention is:The analysis method of the biochemical sensor based on series connection LPWG, the sensor Including sandwich layer and tested covering, in be in contact with tested covering, laterally LPWG is extended in tested covering direction to sandwich layer1With LPWG2, methods described specifically includes following steps:
S1:Incident light enters through sandwich layer first end, and part light is through LPWG1Tested covering is coupled into, part light is along sandwich layer Transmission;
S2:Along the part light of tested covering transmission through LPWG2It is coupled into sandwich layer;
S3:The part interference of light of co-propagate is exported in sandwich layer of the part light with step S1 obtained by step S2, is obtained Output spectra, calculates the side-play amount and the wherein absorption spectrum information of material of resonance wavelength in analysis output spectra.
Further, in step S1, can be through LPWG1The part light for being coupled into tested covering is in being with resonance wavelength The light of certain bandwidth range of the heart.
Further, the sandwich layer is rectangular waveguide, and the tested covering is rectangular waveguide.
Further, it is characterised in that the step S1 is specially:Incident light enters from waveguide first end, by length It is L1LPWG1Afterwards, sandwich layer mould is respectively A with the output amplitude of tested cladding modeco(L1) and Acl(L1),
Wherein, Λ is LPWG1Cycle, L1It is LPWG1Length,It is LPWG1Constant, It is LPWG1The amplitude of the tested cladding mode in place, κ1Represent LPWG1The coefficient of coup,It is LPWG1Locate the width of sandwich layer mould Degree,In s1It is and LPWG1Relevant constant,It is light through long It is L to spend1LPWG1Phase shift afterwards,It is the effective refractive index of sandwich layer mould,To be tested the effective refractive index of cladding mode,It is LPWG1The phase mismatch factor, λ represents resonance centre wavelength.
Further, the step S2 also includes step S20:It is the waveguide of d, sandwich layer mould and tested cladding mode by length Output amplitude be respectively Aco(L1+ d) and Acl(L1+d);
Wherein, d is LPWG1With LPWG2Connection waveguide length.
Further, the step S2 is specially:It is L by length2LPWG2Afterwards, sandwich layer mould is defeated with tested cladding mode Go out amplitude respectively Aco(L1+d+L2) and Acl(L1+d+L2);
Wherein, Λ is LPWG2Cycle, L2It is LPWG2Length,It is LPWG2Constant, It is LPWG2The amplitude of the tested cladding mode in place, κ2Represent LPWG2The coefficient of coup,It is LPWG2Locate the width of sandwich layer mould Degree,In s2It is and LPWG2Relevant constant,For light passes through Length is L2LPWG2Phase shift afterwards,It is LPWG2The phase mismatch factor, λ Represent resonance centre wavelength.
Further, the step S3 is specially:The output of sandwich layer mould with the output of tested cladding mode interfere and obtains defeated Go out spectrum, the side-play amount and the wherein absorption spectrum information of material of resonance wavelength in analysis output spectra are calculated, while calculating sandwich layer Mould output is respectively T (L with the power output of tested cladding mode1+d+L2) and R (L1+d+L2),
Wherein, | | | |2" determinant " computing is first done in expression to matrix, then carries out the computing of " mould ".
Further, the waveguide parameter is determined by following methods step;
S01:The square wave of single mode operation in the range of the incident wavelength for determining for resonance wavelength with Marcatili methods Lead the parameter of sandwich layer physical dimension and sandwich layer;
The rectangular waveguide sandwich layer physical dimension is specifically included:The width a of sandwich layer mould, the height h of sandwich layer mould, the depth of grating Degree Δ h;
The parameter of the sandwich layer mould is specifically included:Transmission βco, along the transmission K in x, y directionx、Ky, and calculate In resonance central wavelength lambdaRUnder sandwich layer Effective index
S02:The physical dimension of the tested covering of rectangular waveguide and the ginseng of tested cladding mode are determined with Marcatili methods Number;
The tested covering physical dimension of the rectangular waveguide is specifically included:The width b of tested cladding mode, is tested the height of cladding mode Degree h;
The parameter of the tested cladding mode is specifically included:Transmission βcl, along the transmission K in x, y directionx、Ky, and count Calculate in resonance central wavelength lambdaRUnder tested covering Effective index
S03:According to the effective refractive index of sandwich layer mouldAnd the effective refractive index of tested cladding modeUsing LPWG Phase-matching conditionDetermine the periods lambda of LPWG.
Beneficial effects of the present invention:The analysis method of the biochemical sensor based on series connection LPWG proposed by the present invention, passes through Using the coupled characteristic of LPWG, by the light of the certain bandwidth range in incident light wave centered on resonance wavelength, by LPWG1Coupling Close and enter tested covering, by LPWG2This part is optically coupled into waveguide core layer again, the base with symport in waveguide core layer Mode interference is exported.When liquid changes, the resonance wavelength in output spectra can shift, by detecting that side-play amount can calculate liquid Concentration.The absorption spectrum signal of liquid, realizes the qualitative of fluid to be measured in analysis output spectra.On the one hand the method for the present invention solves Conventional biochemical sensor by the single certain sensitive film of expensive and Testing index carrys out qualitatively problem;On the other hand solve The bandwidth limitation problems for needing the absorption bands for avoiding water to be brought in liquid, aqueous quantitative determination of having determined.To realize being more than The high sensitivity of 2000nm/RIU, small size, the LPWG biochemical sensitive technical research of low cost, will detect in military biochemical war agent Aspect possesses wide application background, can be in people such as the increasingly severe now food for concerning national economy, drug safeties With important technical support is provided in the solution of field question, with important scientific meaning and far-reaching realistic meaning.
Brief description of the drawings
Fig. 1 is the three-dimensional structure diagram of new polymers LPWG biochemical sensors provided in an embodiment of the present invention;
Wherein, 1 is LPWG1, 2 is the cascade waveguide between two LPWG, and 3 is LPWG2, 4 is liquid cladding, and 5 is polymer Waveguide core layer, 6 is SiO2Covering, 7 is Si substrates, and 8 is liquid turnover micropore.
Fig. 2 is the Mode Coupling and transmission characteristic schematic diagram of sensor mechanism provided in an embodiment of the present invention;
Wherein, (a) is top view, and (b) is cross-sectional view.
Fig. 3 is the calculated results output spectra of biochemical sensor provided in an embodiment of the present invention.
Fig. 4 is the solution of the present invention flow chart.
Specific embodiment
For ease of skilled artisan understands that technology contents of the invention, enter one to present invention below in conjunction with the accompanying drawings Step explaination.
It is as shown in Figure 1 the three-dimensional structure diagram of new polymers LPWG biochemical sensors of the invention, referring to the solid of Fig. 1 Structure chart, sensor of the invention is by two series connection long-period waveguide grating, i.e. LPWG1 and LPWG2, and fluid to be measured is used as side Bread crumb is constituted.Part optical signals are coupled into tested covering 4 by incident light through waveguide first end into LPWG1, in sandwich layer Light enters LPWG by one section of straight wave guide 22.Sandwich layer uses polymeric material, and other coverings in addition to tested covering 4 use dioxy SiClx.Whole sensor is by sandwich layer 5, SiO2Covering 6, substrate 7 and micropore 8 are constituted.
The Mode Coupling and transmission characteristic schematic diagram of the sensor mechanism of invention are illustrated in figure 2, as shown with LPWG Coupled characteristic, by the light of the certain bandwidth range in incident light centered on resonance wavelength, certain bandwidth range passes through Specific grating sets and determines, its method for solving refers to document《The lithium niobate long-period waveguide grating of electro-optical tuning is old to be opened It is prosperous, the intelligent .2012 of Li Jun》, by LPWG1Tested covering is coupled into, by LPWG2This part is optically coupled into sandwich layer again, with The sandwich layer Mode interference output of symport in sandwich layer.When measured matter changes, the resonance wavelength in output spectra can shift, For example, when measured matter is liquid, by detecting that side-play amount calculates strength of fluid, the absorption spectrum of liquid in analysis output spectra Signal, realizes the qualitative of fluid to be measured.
The analysis method of the biochemical sensor based on series connection LPWG of the invention, specifically includes following steps:
Carry out key parameter calculating first, the key parameter calculate include it is following step by step:
S01:The square wave of single mode operation in the range of the incident wavelength for determining for resonance wavelength with Marcatili methods Lead the parameter of sandwich layer physical dimension and sandwich layer mould;
The rectangular waveguide sandwich layer physical dimension is specifically included:The width a of sandwich layer, the height h of sandwich layer, the tooth Δ high of grating h;
The parameter of the sandwich layer mould is specifically included:Transmission β, along the transmission K in x, y directionx、Ky, and calculate Sandwich layer Effective index under resonance central wavelength lambdaSpecific computational methods are the common method of this area, herein not Elaborate again.
S02:The physical dimension and tested covering of the tested covering of rectangular waveguide in step 1a are determined with Marcatili methods The parameter of mould;
The tested covering physical dimension of the rectangular waveguide is specifically included:The width b of tested covering, is tested the height h of covering;
The parameter of the tested cladding mode is specifically included:Transmission β, along the transmission K in x, y directionx、Ky, and calculate The tested bag Effective index gone out under resonance central wavelength lambda
S03:According to the effective refractive index of sandwich layer mouldAnd the effective refractive index of tested cladding modeUsing LPWG Phase-matching conditionThereby determine that the periods lambda of LPWG.
Secondly, according to the key parameter for drawing, output spectra calculating is carried out, is illustrated in figure 4 the solution of the present invention flow chart, Specifically include it is following step by step:
S1:As shown in the top view (a) and cross-sectional view (b) of Fig. 2, the cycle of LPWG is Λ, i.e. LPWG1And LPWG2Week Phase is Λ, LPWG1And LPWG2Length be respectively L1And L2, L in the present embodiment1=L2=L, LPWG1And LPWG2Connection ripple The length led is d, and the width of fiber waveguide is a, is highly h, and the depth of grating is Δ h, and the refractive index of sandwich layer is nco, it is tested covering Refractive index be ncl1, the refractive index of under-clad layer is n in waveguidecl2
Light from waveguide first end, i.e. A ends, by LPWG1Sandwich layer mould is respectively A with the output amplitude of tested cladding mode afterwardsco (L1) and Acl(L1), by coupled mode theory and transfer matrix method.Draw shown in both values such as formula (1),
Wherein, Λ is LPWG1Cycle, L1It is LPWG1Length,It is LPWG1Constant, It is LPWG1The amplitude of the tested cladding mode in place, κ1Represent LPWG1The coefficient of coup,It is LPWG1Locate the width of sandwich layer mould Degree,In s1It is and LPWG1Relevant constant,It is light through long It is L to spend1LPWG1Phase shift afterwards,It is the effective refractive index of sandwich layer mould,To be tested the effective refractive index of cladding mode,It is LPWG1The phase mismatch factor, λ represents resonance centre wavelength.
S20:It is the waveguide of d by length, sandwich layer mould is respectively A with the output amplitude of tested cladding modeco(L1+ d) and Acl (L1+d);
Wherein, d is LPWG1And LPWG2Connection waveguide length.
S2:It is again L by length2LPWG2Sandwich layer mould is with the amplitude of cladding mode afterwards,
Wherein, Λ is LPWG2Cycle, L2It is LPWG2Length,It is LPWG2Constant, It is LPWG2The amplitude of the tested cladding mode in place, κ2Represent LPWG2The coefficient of coup,It is LPWG2Locate the width of sandwich layer mould Degree,In s2It is and LPWG2Relevant constant,For light passes through Length is L2LPWG2Phase shift afterwards,It is LPWG2The phase mismatch factor, λ Represent resonance centre wavelength.
S3:By sandwich layer mould output and tested cladding mode output interfere obtain output spectra as shown in figure 3, in figure respectively to Go out 3 kinds of different refractivities, i.e. refractive index is respectively:nc1-1、nc1-2、nc1-3, measured matter output spectra, by calculate analyze The side-play amount of resonance wavelength and the wherein absorption spectrum information of material in output spectra, realize material it is quantitative with it is qualitative, while meter Calculate the power output respectively T (L of the output of sandwich layer mould and tested cladding mode1+d+L2) and R (L1+d+L2),
Wherein, | | | |2" determinant " computing is first done in expression to matrix, then carries out the computing of " mould ".
Biochemical sensor of the invention uses polymeric material as waveguide core layer in silicon substrate, and in waveguide core side wall system Make two LPWG of series connection, using measured matter as waveguide covering.Above-mentioned measured matter can for biochemical liquid, biochemical gas or Person is qualified solid matter etc..The part that will be transmitted in waveguide by two LPWG is optically coupled into liquid cladding, Sandwich layer is coupled light into through LPWG again after transmitting a segment distance, is finally obtained containing caused by because of measured matter refraction index changing The side-play amount and measured matter of resonance wavelength absorb the spectral signal of information.
The analysis method of the biochemical sensor based on series connection LPWG proposed by the present invention, the coupling by using LPWG is special Property, by the light of the certain bandwidth range in incident light wave centered on resonance wavelength, by LPWG1Tested covering is coupled into, By LPWG2This part is optically coupled into sandwich layer again, the basic mode with symport in sandwich layer interferes output.When measured object qualitative change During change, the resonance wavelength in output spectra can shift, by detecting that side-play amount can calculate strength of fluid.Quilt in analysis output spectra The absorption spectrum signal of material is surveyed, the qualitative of measured matter is realized.On the one hand the method for the present invention solves conventional biochemical sensing Device carrys out qualitatively problem by the single certain sensitive film of expensive and Testing index;On the other hand it is liquid, aqueous fixed to solve The bandwidth limitation problems for needing the absorption bands for avoiding water to be brought in amount detection.It is highly sensitive more than 2000nm/RIU to realize Degree, small size, the LPWG biochemical sensitive technical research of low cost, will possess wide application in military biochemical war agent context of detection Background, can be in the solution of the civil area problems such as the increasingly severe now food for concerning national economy, drug safety Important technical support is provided, with important scientific meaning and far-reaching realistic meaning.
One of ordinary skill in the art will be appreciated that embodiment described here is to aid in reader and understands this hair Bright principle, it should be understood that protection scope of the present invention is not limited to such especially statement and embodiment.For ability For the technical staff in domain, the present invention can have various modifications and variations.It is all within the spirit and principles in the present invention, made Any modification, equivalent substitution and improvements etc., should be included within scope of the presently claimed invention.

Claims (8)

1. the analysis method of the biochemical sensor based on series connection LPWG, it is characterised in that the sensor includes sandwich layer and is tested Covering, in be in contact with tested covering, laterally the first long-period waveguide grating LPWG is extended in tested covering direction to sandwich layer1 With the second long-period waveguide grating LPWG2, methods described specifically includes following steps:
S1:Incident light enters through sandwich layer first end, and part light is through the first long-period waveguide grating LPWG1Tested covering is coupled into, Part light is transmitted along sandwich layer;
S2:Along the part light of tested covering transmission through the second long-period waveguide grating LPWG2It is coupled into sandwich layer;
S3:The part interference of light of co-propagate is exported in sandwich layer of the part light with step S1 obtained by step S2, is exported Spectrum, calculates the side-play amount and the wherein absorption spectrum information of material of resonance wavelength in analysis output spectra.
2. method according to claim 1, it is characterised in that in step S1, can be through the first long-period waveguide grating LPWG1The part light for being coupled into tested covering is the light of the certain bandwidth range centered on resonance wavelength.
3. method according to claim 2, it is characterised in that the sandwich layer is rectangular waveguide, the tested covering is square Shape waveguide.
4. method according to claim 3, it is characterised in that the step S1 is specially:Incident light is from waveguide first end Into, by length be L1The first long-period waveguide grating LPWG1Afterwards, sandwich layer mould is distinguished with the output amplitude of tested cladding mode It is Aco(L1) and Acl(L1),
A c o ( L 1 ) A c l ( L 1 ) = e j β c o + β c l 2 L 1 e j KL 1 2 0 0 e - j KL 1 2 · t 1 e j θ 1 2 jr 1 jr 1 * t 1 e - j θ 1 2 · A c o ( 0 ) A c l ( 0 ) ;
Wherein, j represents imaginary unit, βcoRepresent the transmission of sandwich layer mould, βclThe transmission of tested cladding mode is represented,It is the first long-period waveguide grating LPWG1Constant, Λ is the first long-period waveguide grating LPWG1Cycle, L1It is One long-period waveguide grating LPWG1Length,It is the first long-period waveguide grating LPWG1The tested cladding mode in place Amplitude, κ1Represent the first long-period waveguide grating LPWG1The coefficient of coup,It is the first long-period waveguide grating LPWG1Locate the amplitude of sandwich layer mould,In s1It is and the first long-period waveguide grating LPWG1Relevant is normal Number, κ1 *Represent κ1Conjugate complex number, r1 *Represent r1Conjugate complex number, δ be the first long-period waveguide grating LPWG1From the coefficient of coup,For light by length be L1The first long-period waveguide grating LPWG1Phase shift afterwards,It is core The effective refractive index of layer mould,To be tested the effective refractive index of cladding mode, It is the first long-period waveguide grating LPWG1The phase mismatch factor, β1It is the first long-period waveguide grating LPWG1Phase mismatch The parameter of the factor, λ represents resonance wavelength, Aco(0) amplitude of sandwich layer mould initial position, A are representedcl(0) at the beginning of representing tested cladding mode Beginning position amplitude.
5. method according to claim 3, it is characterised in that the step S2 also includes step S20:It is d by length Waveguide, sandwich layer mould is respectively A with the output amplitude of tested cladding modeco(L1+ d) and Acl(L1+d);
A c o ( L 1 + d ) A c l ( L 1 + d ) = e jβ c o d 0 0 e jβ c l d · A c o ( L 1 ) A c l ( L 1 ) ;
Wherein, j represents imaginary unit, βcoRepresent the transmission of core film layer, βclRepresent the transmission of tested claddingmode, Aco (L1) represent that incident light is L by length1LPWG1Sandwich layer mould output amplitude afterwards, Acl(L1) incident light by length be L1's LPWG1The output amplitude of cladding mode is tested afterwards, and d is the first long-period waveguide grating LPWG1With the second long-period waveguide grating LPWG2Connection waveguide length.
6. method according to claim 3, it is characterised in that the step S2 is specially:It is L by length2Second length Period waveguide grating LPWG2Afterwards, sandwich layer mould is respectively A with the output amplitude of tested cladding modeco(L1+d+L2) and Acl(L1+d+ L2);
A c o ( L 1 + d + L 2 ) A c l ( L 1 + d + L 2 ) = e j β c o + β c l 2 L 2 e j KL 2 2 0 0 e - j KL 2 2 · t 2 e j θ 2 2 jr 2 jr 2 * t 2 e - j θ 2 2 · A c o ( L 1 + d ) A c l ( L 1 + d ) ;
Wherein, j represents imaginary unit, βcoRepresent the transmission of core film layer, βclThe transmission of tested claddingmode is represented,It is the second long-period waveguide grating LPWG2Constant, Λ is the second long-period waveguide grating LPWG2Cycle, L2It is Two long-period waveguide grating LPWG2Length,It is the second long-period waveguide grating LPWG2The tested covering in place The amplitude of mould, κ2Represent the second long-period waveguide grating LPWG2The coefficient of coup,For the second long-period wave is guide-lighting Grid LPWG2Locate the amplitude of sandwich layer mould,In s2It is and LPWG2Relevant constant, κ2* κ is represented2Conjugation Plural number, r2* r is represented2Conjugate complex number,For light by length be L2The second long-period wave Guide grating LPWG2Phase shift afterwards,It is the second long-period waveguide grating LPWG2's The phase mismatch factor, β2It is the second long-period waveguide grating LPWG2The phase mismatch factor parameter, λ represents resonance wavelength.
7. method according to claim 3, it is characterised in that the step S3 is specially:Sandwich layer mould is exported and is tested Cladding mode output interfere and obtains output spectra, calculates the side-play amount of resonance wavelength in analysis output spectra and the wherein absorption of material Spectral information, while calculating the power output respectively T (L of the output of sandwich layer mould and tested cladding mode1+d+L2) and R (L1+d+ L2),
T ( L 1 + d + L 2 ) R ( L 1 + d + L 2 ) = | | A c o ( L 1 + d + L 2 ) | | 2 | | A c l ( L 1 + d + L 2 ) | | 2 ;
Wherein, Aco(L1+d+L2) represent that incident light is L by length1LPWG1, length for d waveguide, and length be L2's LPWG2The output amplitude of sandwich layer mould, A afterwardscl(L1+d+L2) incident light by length be L1LPWG1, length for d waveguide, with And length is L2LPWG2The output amplitude of cladding mode is tested afterwards, | | | |2" determinant " computing is first done in expression to matrix, then Carry out the computing of " mould ".
8. the method according to claim 4 to 7 any one, it is characterised in that the sensor parameters are by following methods Step determines:
S01:The rectangular waveguide core of single mode operation in the range of the incident wavelength for determining for resonance wavelength with Marcatili methods The parameter of layer physical dimension and sandwich layer;
The rectangular waveguide sandwich layer physical dimension is specifically included:The width a of sandwich layer, the height h of sandwich layerco, the depth delta h of grating;
The parameter of the sandwich layer mould is specifically included:Transmission βco, along the transmission K in x, y directionxco、Kyco, and calculate Sandwich layer Effective index under resonance wavelength
S02:The physical dimension of the tested covering of rectangular waveguide and the parameter of tested cladding mode are determined with Marcatili methods;
The tested covering physical dimension of the rectangular waveguide is specifically included:The width b of tested covering, is tested the height h of coveringcl
The parameter of the tested cladding mode is specifically included:Transmission βcl, along the transmission K in x, y directionxcl、Kycl, and calculate The tested covering Effective index gone out under resonance wavelength
S03:According to the effective refractive index of sandwich layer mouldAnd the effective refractive index of tested cladding modeUsing the phase of LPWG Matching conditionDetermine the periods lambda of LPWG.
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