CN103076647A - Surface plasmon polariton type flat channel filter based on metal-insulator-metal structure - Google Patents

Abstract

The invention discloses a surface plasmon polariton type flat channel filter based on a metal-insulator-metal structure. The surface plasmon polariton type flat channel filter is composed of two metal interlayers and an insulator layer between the two metal interlayers, the insulator layer comprises alternately-arranged insulators in two kinds of refractive indexes, which form N cycles; the N cycles are same in the structure and are composed of K subcycles, each of the subcycles contains one insulator 1 with high index of refraction and one insulator 2 with low high index of refraction, and the Kth subcycle n the Nth cycle is lack of one insulator with low high index of refraction. For the N cycles, the lengths of the K insulators with high index of refraction in each cycle are increased progressively and linearly in the same rule, the consistency of dispersionloss in multiple filtering channels is improved, and the multichannel flat filtering is achieved. The surface plasmon polariton type flat channel filter based on the metal-insulator-metal structure, disclosed by the invention has important application on photo-communication and photoelectric signal processing, and miniaturization integrated photoelectronic devices and modules.

Description

The smooth multi-channel filter of surface plasma build of metal-dielectric-metal construction

Technical field

The present invention is mainly concerned with the fields such as surface plasma bulk effect, photoelectric device, optical communication and Photoelectric Signal Processing, relates in particular to a kind of smooth multi-channel filter of surface plasma effect type of metal-dielectric-metal construction.

Background technology

Surface plasma (surface plasmons, SPs) or surface plasma excimer (surface plasmon polaritions, SPPs) be that local is at a kind of special electromagnetic format of field at metal-dielectric (can be referred to as dielectric, insulator again) interface, it is propagated along the metal surface, and perpendicular to the interface to the both sides exponential damping.Because the surperficial propagation characteristic of its uniqueness, light can be confined in the sub-wavelength yardstick based on the metal Nano structure of SPP, therefore in following nanometer integrated optical circuit, have significant application value.Wherein, metal-dielectric-metal (metal-insulator-metal, MIM, can be referred to as metal-dielectric-metal or metal-insulator-metal type again) waveguide is a kind of typical SPP waveguide or device architecture, it can be strapped in surface plasma wave in the less scope, is conducive to realize more photonic device and the loop of high integration; In addition, its structure is very simple, is convenient to make processing.

Type based on the mim structure device is more, common wave filter, coupling mechanism, beam splitter, the lens etc. of comprising, and relevant paper comprises: 1) W.L.Barnes, A.Dereux, T.W.Ebbesen.Surface Plasmon Subwavelength Optics[J] .Nature, 2003,424,824 – 830; 2) Z.Sun, H.K.Kim.Refractive Transmission of Light and Beam Shaping with Metallic Nano-optic Lenses[J] .Applied Physics Letters, 2004,85 (4), 642; 3) B.Wang, G.P.Wang.Plasmon Bragg Reflectors and Nanocavities on Flat Metallic Surfaces[J] .Applied Physics Letters, 2005,87,013107.Specific to device indispensable in this communication of wave filter and the signal processing, have both at home and abroad at present much about the report based on the SPP mode filter of MIM waveguide, comprise the annular resonance cavity filter, zigzag filter, Bragg grating filter, wavelength-division multiplex (WDM) filter construction etc., such as: 1) Sanshui Xiao, Liu Liu, and Min Qiu.Resonator channel drop filters in a plasmon-polaritons metal[J] .Optics Express, 2006, Vol.14, No.7,2932-2937; 2) Xianshi Lin, Xuguang Huang.Tooth-shaped plasmonic waveguide filters with nanometeric sizes[J] .Optics Letters, 2008, Vol.33, No.23,2877-2879; 3) Bing Wang, Guoping Wang.Plasmon Bragg reflectors and nanocavities on flat metallic surface[J] .Applied Physics Letters, 2005,87,013107; 4)Xian Mei, Xuguang Huang, Jin Tao, Jiahu Zhu, Yunjin Zhu, and Xiaopin Jin, A wavelength demultiplexing structure based on plasmonic MDM side-coupled cavities[J] .Journal of the Optical Society of America B, 2008, Vol.27, No.12,2707-2713.Above-mentioned wave filter belongs to single channel filtering in single channel filtering or the single port; With respect to the single channel wave filter, multichannel comb filter (or single port multi-channel filter) also is communication and the very crucial device of signal process field.But also fewer about research and the report of SPP type multi-channel filter at present.For example, the people such as Y.Gong have designed a kind of multi-channel filter of the quasi-periodic sequence optical grating construction based on the MIM waveguide, and Numerical Simulation Results shows: obtain 10 reflected channel in 1.2～1.8 mum wavelength scopes; Because this document is not considered the wavelength dependence loss in the MIM waveguide, can't quantitative measurement interchannel flatness (Yongkang Gong, Xueming Liu, and Leiran Wang.High-channel-count plasmonic filter with the metal – insulator – metal Fibonacci-sequence gratings[J], Optics Letters, 2010, Vol.35, No.3,285-287.).The people such as H.Lu have introduced dish type nanometer micro-cavity structure in the MIM waveguide, emulation has obtained 4 reflection peaks in 0.5～0.7 mum wavelength scope, although considered loss in simulation process, its channel flatness is about 7dB, thereby channel flatness performance is inadequate.(Hua Lu,Xueming Liu,Yongkang Gong,Leiran Wang,Dong Mao.Multi-channel plasmonic waveguide filters with disk-shaped nanocavities[J],Optics Communications,2011,Vol.284,No.10-11,2613-2617）

According to above analysis as can be known, not yet be well solved based on the flatness problem of the SPP type multi-channel filter of MIM waveguide at present or demand significant improvement urgently; And flatness is to weigh multichannel to a key index of wave filter, and it directly affects the consistance, power equalization etc. of multichannel parallel processing.

Therefore, in order to realize excellent channel flatness, the present invention proposes a kind of smooth multi-channel filter of surface plasma bulk effect (SPP) type based on the MIM waveguide.

Summary of the invention

In view of the poor problem of flatness based on the SPP type multi-channel filter of MIM waveguide of above statement, the present invention aims to provide a kind of smooth multi-channel filter of SPP type based on the MIM waveguide, obtains excellent flatness at interchannel.

The present invention has announced a kind of surface plasma build multi-channel filter based on metal-dielectric-metal construction, is comprised of dielectric layer between two metal sandwichs and the metal sandwich; It is characterized in that: described dielectric layer comprises medium one and the medium two of a plurality of alternative arrangements, form N the consistent cycle of structure, each cycle is made of K subcycle, each subcycle comprises a medium one and a medium two, K default medium two of subcycle in N cycle, wherein N, K are positive integer; In each periodic structure, the refractive index of K medium one all is n ₁, its length increases progressively by linear rule, and the length of medium two is fixed as L _b, refractive index is n ₂, the length of its medium one is much smaller than the length of medium two.

The concrete structure of described wave filter as shown in Figure 1.Between two metal sandwichs, insert N cycle that is consisted of by two kinds of different refractivity media (or being referred to as dielectric, insulator) alternative arrangement, its height (on the z direction) is 45nm; A described N periodic structure is consistent, consisted of by K subcycle, each subcycle comprises a high refractive index medium (medium one) and a low refractive index dielectric (medium two), K default low refractive index dielectric of subcycle in N cycle, and wherein N, K are positive integer; In each periodic structure, the refractive index of K medium one all is n ₁, the length on its x direction increases progressively by linear rule, is expressed as respectively L ₁, L ₂... .L _K-1, L _KThe length of medium two is fixed as L _b, refractive index is n ₂Here, n ₁＞n ₂, and the length (L of medium one ₁, L ₂... .L _K-1, L _K) much smaller than the length (L of medium two _b).L ₁, L ₂... .L _K-1, L _KThe linear increment rule be:

L ₁＝d ₁

L _k＝d ₁+(k-1)d ₂ (1)

Wherein, d ₁Be fundamental length, d ₂Be gradual change step-length or incremental steps.

Because the length of medium one is all much smaller than the length of medium two, so we can be with L ₁, L _b, L ₂See a Fabry-Perot (F-P) resonator cavity as; The like, the whole wave filter that is made of dielectric layer can be considered the F-P resonator cavity of a plurality of cascades, and its total transmission matrix can be abbreviated as:

$S=\frac{1}{{(t_1{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">t</figure-callout>}}_2.....t_K)}^{N-1}(t_1{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">t</figure-callout>}}_2.....t_{K-1})}\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]---\left(2\right)$

Thereby this wave filter overall transmission filter response (T) can be expressed as:

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HDA00002736335000012.png"\; state="\{\{state\}\}">E</figure-callout>}}_0^{+}\\ E_0^{-}\end{array}\right]=S\&times;\left[\begin{array}{c}{E}_N^{+}\\ E_N^{-}\end{array}\right]---\left(3\right)$

$T=\frac{E_N^{+}}{{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HDA00002736335000012.png"\; state="\{\{state\}\}">E</figure-callout>}}_0^{+}}=\frac{{(t_1{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">t</figure-callout>}}_2.....t_K)}^{N-1}(t_1{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">t</figure-callout>}}_2.....t_{K-1})}{A-r_{K}B}---\left(4\right)$

Wherein,

With The incident field and the reflection light field that represent respectively filter input end,

With

The incident field and the reflection light field that represent respectively filter output; t ₁, t ₂, t ₃... ..t _KAnd r ₁, r ₂, r ₃... ..r _KBe respectively transmission coefficient, the reflection coefficient of the medium one of reference numeral in each cycle, φ ₁, φ ₂... .. φ _KRepresent the phase shift of each F-P resonator cavity; A, B, C, D are the element in total transmission matrix, by t ₁, t ₂, t ₃... ..t _K, r ₁, r ₂, r ₃... ..r _K, φ ₁, φ ₂... .. φ _KThe common decision; A, B, the detailed expression-form of C, D are seen the embodiment part.Thereby the phase shift of the transmission coefficient of the response of this wave filter and a plurality of medium one, reflection coefficient, a plurality of F-P resonator cavitys is closely related.

Be the definite performance of weighing multi-channel filter, investigate emphatically two important indexs here: flatness and contrast all represent with dB.Flatness is defined as the ratio of maximum filtering channel peak power and minimum filtering channel peak power, such as (5) formula; Contrast (peak-to-notch contrast ratio) is defined as the ratio of channel peak power and trough power, such as (6) formula.

F=10lg(T _max/T _min) (5)

R=10lg(T _peak/T _notch) (6)

Wherein F and R represent respectively flatness and contrast, T _MaxAnd T _MinRepresent respectively maximum channel peak power and minimum channel peak power, T _PeakAnd T _NotchRepresent respectively channel peak power and trough power.

The novel part of this filter construction mainly is: linearity increases the length of K medium one (large index medium) in each cycle successively, namely linear increase L ₁, L ₂... .L _K-1, L _kLength [being formula (1)], thereby the effective length of each F-P resonator cavity and mean refractive index are changed.These changes will significantly improve the interchannel flatness.Inherent physical mechanism is described below.

The total losses of the F-P resonator cavity in the MIM waveguide are jointly to be determined by resonator cavity equivalent length and dispersion loss coefficient, and they are corresponding metal absorption loss and dispersion loss respectively.The general variation in the filter wavelength scope of the absorption loss of metal is very little; The dispersion loss coefficient can be expressed as: α=4 * π * Im (n _Eff)/λ, wherein Im (n _Eff) be the imaginary part of average effective refractive index in the MIM waveguide.Fig. 2 has provided the variation relation of dispersion loss coefficient along with wavelength, and can know and see: the dispersion loss coefficient is very large in the shortwave strong point, reduce along with the increase of wavelength, especially have to go to the toilet less than the wavelength region may of 1 μ m reduce sharply little; After wavelength was greater than 1 μ m, decline rate slowed down, and tended to be steady in the long wave strong point.

Because the dispersion loss coefficient is very large in the value of shortwave strong point, and reduce along with the increase of wavelength.So when there was not the length gradual change in K medium one in each cycle, whole filter response was large at the dispersion loss longer wavelength place that the shortwave strong point is subject to, and change violent.Thereby in a plurality of channels that form, shortwave strong point channel peak power is low, and long wave strong point channel peak power is high, and the peak power of interchannel is also uneven.When the length at K medium one of each intraperiod line increase, the mean refractive index of each F-P resonator cavity can increase gradually, and the equivalent length of F-P resonator cavity also can increase; According to F-P resonator cavity phase-matching condition, transmission peaks can integral body red shift occur; Again owing to the increase of dispersion loss coefficient along with wavelength reduces, the more important thing is that its variation tendency tends towards stability, therefore the transmission filtering channel has obtained effectively evading in the large dispersion loss coefficient of shortwave strong point, the fast change trend of dispersion loss, has significantly improved the consistance of a plurality of filtering channel place dispersion loss.Based on this physical mechanism, choose and Optimal Parameters, obtain more smooth a plurality of filtering channel.It is to be noted: because L ₁, L ₂... .L _K-1, L _KLinear the increasing of length, the transmission filter factor of whole wave filter can reduce along with the increase of device length, thereby there is a decline on the whole in the peak power of all channels, but can not affect the flatness of interchannel.

Therefore, because the length gradual change of high refractive index medium (medium one) has improved the consistance of a plurality of filtering channel place dispersion loss, increase substantially the flatness of interchannel, realized smooth multichannel filtering function.This multichannel flat filter has important application in integrated optoelectronic device and module, Parallel Optical Communication and signal processing.

Description of drawings:

Fig. 1. the structural drawing of smooth multi-channel filter

Fig. 2. the dispersion loss coefficient is along with the variation relation figure of wavelength

(n ₁＝2.2,n ₂＝2,d ₁＝10nm,d ₂＝5nm,L _b＝300nm)。

Fig. 3. the gradual change step-length is d ₂Multichannel filtering response during=5nm

(n ₁＝2.2,n ₂＝2,d ₁＝10nm,d ₂＝5nm,L _b＝300nm)。

Fig. 4. the multichannel filtering response during without gradual change

(n ₁＝2.2,n ₂＝2,d ₁＝10nm,d ₂＝0nm,L _b＝300nm)

Fig. 5. gradual change step-length d ₂=5nm, L _bMultichannel filtering response during=500nm

(n ₁＝2.2,n ₂＝2,d ₁＝10nm,d ₂＝5nm,L _b＝500nm)

Fig. 6. gradual change step-length d ₂=5nm, L _bMultichannel filtering response during=200nm

(n ₁＝2.2,n ₂＝2,d ₁＝10nm,d ₂＝5nm,L _b＝200nm)

Embodiment

Below in conjunction with accompanying drawing enforcement of the present invention is further described.

The structure of the smooth multi-channel filter that the present invention proposes as shown in Figure 1.Between two metal sandwichs, insert N cycle that is consisted of by two kinds of different refractivity medium alternative arrangements, its height (on the z direction) is 45nm; A described N periodic structure is consistent, consisted of by K subcycle, each subcycle comprises a high refractive index medium layer (medium one) and a low refractive index dielectric layer (medium two), K default low refractive index dielectric of subcycle in N cycle, and wherein N, K are positive integer; In each periodic structure, the refractive index of medium one all is n ₁, its length (on the x direction) linear increment is expressed as respectively L ₁, L ₂... .L _K-1, L _KThe length of medium two is fixed as L _b, refractive index is n ₂Here, n ₁＞n ₂, and the length (L of medium one ₁, L ₂... .L _K-1, L _K) much smaller than the length (L of medium two _b).L ₁, L ₂... .L _K-1, L _KThe linear increment rule be:

L ₁＝d ₁

L _k＝d ₁+(k-1)d ₂ (7)

Wherein, d ₁Be fundamental length, d ₂Be gradual change step-length or incremental steps.

Because the length of medium one is all much smaller than the length of medium two, so we can be with L ₁, L _b, L ₂See a Fabry-Perot (F-P) resonator cavity as; The like, the whole wave filter that is made of dielectric layer can be considered the F-P resonator cavity by a plurality of cascades, and the transmission matrix in each cycle is expressed as:

${\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_1={\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">S</figure-callout>}}_2=......=S_{N-1}=\frac{1}{t_1{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">t</figure-callout>}}_2.....t_K}\left[\begin{array}{cc}\exp (-{\mathrm{i\&phi;}}_1)& {-\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_1\exp \left({\mathrm{i\&phi;}}_1\right)\\ -{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_1\exp \left({-\mathrm{i\&phi;}}_1\right)& \exp \left({\mathrm{i\&phi;}}_1\right)\end{array}\right]$

$\&times;\left[\begin{array}{cc}\exp \left({-\mathrm{i\&phi;}}_2\right)& {-\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\exp \left({\mathrm{i\&phi;}}_2\right)\\ {-\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\exp \left({-\mathrm{i\&phi;}}_2\right)& \exp \left({\mathrm{i\&phi;}}_2\right)\end{array}\right]\&times;....---\left(8\right)$

$\&times;\left[\begin{array}{cc}\exp \left({-\mathrm{i\&phi;}}_K\right)& {-r}_K\exp \left({\mathrm{i\&phi;}}_K\right)\\ {-r}_K\exp \left({-\mathrm{i\&phi;}}_K\right)& \exp \left({\mathrm{i\&phi;}}_K\right)\end{array}\right]$

$S_N=\frac{1}{t_1{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">t</figure-callout>}}_2.....t_{K-1}}\left[\begin{array}{cc}\exp (-{\mathrm{i\&phi;}}_1)& {-\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_1\exp \left({\mathrm{i\&phi;}}_1\right)\\ -{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_1\exp \left({-\mathrm{i\&phi;}}_1\right)& \exp \left({\mathrm{i\&phi;}}_1\right)\end{array}\right]$

$\&times;\left[\begin{array}{cc}\exp \left({-\mathrm{i\&phi;}}_2\right)& {-\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\exp \left({\mathrm{i\&phi;}}_2\right)\\ {-\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\exp \left({-\mathrm{i\&phi;}}_2\right)& \exp \left({\mathrm{i\&phi;}}_2\right)\end{array}\right]\&times;....---\left(9\right)$

$\&times;\left[\begin{array}{cc}\exp \left({-\mathrm{i\&phi;}}_{K-1}\right)& {-r}_{K-1}\exp \left({\mathrm{i\&phi;}}_{K-1}\right)\\ {-r}_{K-1}\exp \left({-\mathrm{i\&phi;}}_{K-1}\right)& \exp \left({\mathrm{i\&phi;}}_{K-1}\right)\end{array}\right]$

Total transmission matrix further is reduced to:

$\&times;\left[\begin{array}{cc}\exp \left({-\mathrm{i\&phi;}}_2\right)& {-\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\exp \left({\mathrm{i\&phi;}}_2\right)\\ {-\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\exp \left({-\mathrm{i\&phi;}}_2\right)& \exp \left({\mathrm{i\&phi;}}_2\right)\end{array}\right]\&times;....---\left(8\right)$

Wherein, t ₁, t ₂, t ₃... ..t _KAnd r ₁, r ₂, r ₃... ..r _KBe respectively transmission coefficient, the reflection coefficient of the medium one of each reference numeral in the cycle; φ ₁, φ ₂... .. φ _KRepresent the phase shift of each F-P resonator cavity.A, B, C, D are the element in total transmission matrix; By (8)～(10) formula as can be known: A, B, C, D are t ₁, t ₂, t ₃... ..t _K, r ₁, r ₂, r ₃... ..r _K, φ ₁, φ ₂... .. φ _KComposite function.Thereby the phase shift of the transmission coefficient of the response of this wave filter and a plurality of medium one, reflection coefficient, a plurality of F-P resonator cavitys is closely related.Here, front N-1 is in the cycle, and each cycle can be considered K equivalent F-P resonator cavity; N cycle can be considered K-1 equivalent F-P resonator cavity; Within each cycle, the phase shift of i F-P resonator cavity can be expressed as:

${\mathrm{\&phi;}}_i=\frac{{2\mathrm{\&pi;n}}_i{l}_i}{\mathrm{\&lambda;}},i=\mathrm{1,2,3},......---\left(11\right)$

N wherein _iThe mean refractive index that represents i F-P resonator cavity:

$n_i=\frac{L_i{n}_1+{\mathrm{<figure-callout\; id="2"\; label="L\; b\; n"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">L</figure-callout>}}_b{n}_{}{}_2+L_{i+1}{n}_1}{L_i+L_b+L_{i+1}},---\left(12\right)$

L wherein _i, L _I+1Be the length of adjacent two media one in i the F-P chamber.

It is the equivalent length of i F-P resonator cavity.

Based on (8)～(12) formula, calculate to obtain wave filter overall transmission filter response (T), be expressed as:

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HDA00002736335000012.png"\; state="\{\{state\}\}">E</figure-callout>}}_0^{+}\\ E_0^{-}\end{array}\right]=S\&times;\left[\begin{array}{c}{E}_N^{+}\\ E_N^{-}\end{array}\right]---\left(13\right)$

$T=\frac{E_N^{+}}{{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="HDA00002736335000012.png"\; state="\{\{state\}\}">E</figure-callout>}}_0^{+}}=\frac{{(t_1{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">t</figure-callout>}}_2.....)}^{N-1}(t_1{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">t</figure-callout>}}_2.....t_{K-1})}{A-r_{K}B}---\left(14\right)$

Wherein,

With

The incident field and the reflection light field that represent respectively filter input end,

With

The incident field and the reflection light field that represent respectively filter output.So far, obtained the filter response (T) by (13), (14) formula, it presents each transmission filtering channel feature.

The novel part of this filter construction mainly is: linearity increases the length of K medium one in each cycle successively, namely sets L ₁, L ₂... .L _K-1, L _KBe linear increment relation [being formula (7)], thereby the effective length of each F-P resonator cavity and mean refractive index are changed.These changes will significantly improve the interchannel flatness.Inherent physical mechanism is described below.

The total losses of the F-P resonator cavity in the MIM waveguide are jointly to be determined by resonator cavity equivalent length and dispersion loss coefficient, and they are corresponding metal absorption loss and dispersion loss respectively.The general variation in the filter wavelength scope of the absorption loss of metal is very little; The dispersion loss coefficient can be expressed as: α=4 * π * Im (n _Eff)/λ, wherein Im (n _Eff) be the imaginary part of average effective refractive index in the MIM waveguide.Fig. 2 has provided the variation relation of dispersion loss coefficient along with wavelength, and can know and see: the dispersion loss coefficient is very large in the shortwave strong point, reduce along with the increase of wavelength, especially have to go to the toilet less than the wavelength region may of 1 μ m reduce sharply little; After wavelength was greater than 1 μ m, decline rate slowed down, and tended to be steady in the long wave strong point.

Because the dispersion loss coefficient is very large in the value of shortwave strong point, and reduce along with the increase of wavelength.So when there was not the length gradual change in K medium one in each cycle, whole filter construction was large at the loss longer wavelength place that the shortwave strong point is subject to, and change violent.Thereby in a plurality of channels that form, shortwave strong point channel peak power is low, and long wave strong point channel peak power is high, and the peak power of interchannel is also uneven.When the length at K medium one of each intraperiod line increase, the mean refractive index of each F-P resonator cavity can increase gradually, and the equivalent length of F-P resonator cavity also can increase; According to F-P resonator cavity phase-matching condition, transmission peaks can integral body red shift occur; Again owing to the increase of dispersion loss coefficient along with wavelength reduces, the more important thing is that its variation tendency tends towards stability, therefore the transmission filtering channel has obtained effectively evading in the large dispersion loss coefficient of shortwave strong point, the fast change trend of dispersion loss, has significantly improved the consistance of a plurality of filtering channel place dispersion loss.Based on this physical mechanism, choose and Optimal Parameters, obtain more smooth a plurality of filtering channel.It is to be noted: at this moment because L ₁, L ₂... .L _K-1, L _KLinear the increasing of length, the transmission filter factor of whole wave filter can reduce along with the increase of device length, thereby there is a decline on the whole in the peak power of all channels, but can not affect the flatness of interchannel.

For structural design and the theoretical model of verifying wave filter, we adopt two-dimensional finite time-domain difference method (FDTD, Solutions) that its performance is studied, and are further described by reference to the accompanying drawings.Here, select silver as metal level, its specific inductive capacity adopts the drude model to describe:

${\mathrm{\&epsiv;}}_m={\mathrm{\&epsiv;}}_{\&infin;}-{\mathrm{<figure-callout\; id="2"\; label="w\; p"\; filenames="HDA00002736335000012.png,HDA00002736335000021.png"\; state="\{\{state\}\}">w</figure-callout>}}_p^{}/({\mathrm{<figure-callout\; id="0"\; label="w"\; filenames="HDA00002736335000012.png"\; state="\{\{state\}\}">w</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="0"\; label="iw"\; filenames="HDA00002736335000012.png"\; state="\{\{state\}\}">iw</figure-callout>}}_0\mathrm{\&gamma;})---\left(15\right)$

Wherein, ε _∞=3.7, w _p=1.38 * 10 ¹⁶Hz, γ=2.73 * 10 ¹³Hz, w ₀Be incident light frequency.As an example of this flat filter performance specification, structural parameters are chosen for n ₁=2.2, n ₁=2, d ₁=10nm, d ₂=5nm, L _b=300nm, N=3, K=6.At this moment, the filter response of acquisition as shown in Figure 3.We can find out from Fig. 3, and channel number is 14 in 1～2 mum wavelength scope, and the channel flatness is 0.4dB, and flatness index is very excellent; Simultaneously, the contrast of filtering channel is in 14.8dB～20dB scope.

For embodying the advantage of this wave filter on flatness, the length that we have contrasted medium one is the filtering performance of constant (when increasing progressively without linearity) evenly.Work as L ₁, L ₂... .L _K-1, L _KLength when constant (being 10nm), Fig. 4 has provided corresponding filter response: the flatness of a plurality of channels in 0.6～1.5 mum wavelength scope is about 6.8dB.Simultaneously, can find out that filtering channel peak power and contrast change larger in whole wavelength coverage, and the shortwave strong point along with wavelength reduce sharply reduce, thereby the flatness index of channel is relatively poor.Comparison diagram 3 and Fig. 4 announce wave filter in the present invention: as the length (L of medium one ₁, L ₂... .L _K-1, L _K) gradual change occurs, can obtain smooth a plurality of pectination channels, it is 6.8dB-0.4dB that flatness has been improved 6.4dB().

For further studying other performance index of this wave filter, such as flexibly the free spectrum region of filtering channel number and filtering (FSR), when respectively the length of medium two being increased to 500nm or being reduced to 200nm by 300nm, obtain Fig. 5 and filter response shown in Figure 6.

Comparison diagram 3, Fig. 5 and Fig. 6, can clearly find: when the length of medium two increased, the length of each F-P resonator cavity enlarged markedly, and according to F-P resonator cavity phase-matching condition, the filtering channel number increases to 27 by 14; But because the length of whole dielectric structure increases, absorption loss also can increase, and therefore the peak value integral body of a plurality of filtering channel decreases.When the length of medium two reduced, the length of each F-P resonator cavity significantly reduced, and the FSR of multichannel filtering increases; Because the length of whole dielectric layer reduces, absorption loss also can reduce, and therefore the peak value integral body of a plurality of filtering channel raises to some extent.Therefore, for the smooth filter response of multichannel, filtering channel number and FSR can flexible.

Comprehensive above statement, the present invention has following feature.1). as SPP type device, this multi-channel filter has compact conformation, is convenient to highly integrated and advantage miniaturization; 2). high refractive index medium length presents linear increment trend in a plurality of subcycles, has improved the consistance of dispersion loss, has significantly improved the flatness of interchannel.

Above what state only is the present invention program's preferred implementation, should be pointed out that under the prerequisite that does not break away from the present invention program's essence, can make some changes and polishing also should be included in protection scope of the present invention in reality is implemented.

Claims (2)

1. the surface plasma build multi-channel filter based on metal-dielectric-metal construction is comprised of dielectric layer between two metal sandwichs and the metal sandwich; It is characterized in that: described dielectric layer comprises medium one and the medium two of a plurality of alternative arrangements, form N the consistent cycle of structure, each cycle is made of K subcycle, each subcycle comprises a medium one and a medium two, K default medium two of subcycle in N cycle, wherein N, K are positive integer; In each periodic structure, the refractive index of K medium one all is n ₁, its length increases progressively by linear rule, and the length of medium two is fixed as L _b, refractive index is n ₂, the length of its medium one is much smaller than the length of medium two.

2. the multi-channel filter based on metal-dielectric-metal construction as claimed in claim 1, the index of refraction relationship of wherein said medium one and medium two is: n ₁＞n ₂

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