CN101515044A - Optimal design method of subwavelength metal polarization beam splitting grating - Google Patents

Abstract

The present invention provides an optimal design method of subwavelength metal polarization beam splitting grating, which can effectively settles the parameter confirming problem of subwavelength metal polarization beam splitting grating. Firstly the splitter period lambada is confirmed according to the period condition of subwavelength beam splitting grating. Then the variation relationship of effective refractive index and duty cycle of grating of TE polarization and TM polarization are confirmed with an effective medium theory, and the duty cycle f of grating is confirmed according to the required effective refractive index. Finally, the groove depth h of grating is confirmed according to the 1/4 wavelength matching principle of film optical anti-reflection. The optimal design method of subwavelength metal polarization beam splitting grating provided by the invention settles the problem for optimizing multi-grating parameter combination in designing, and increases the scientificity, reliability and timeliness of designing.

Description

The Optimization Design of sub-wavelength metal polarization beam splitting grating

Technical field

The invention belongs to the grating design field, the optimal design that relates to a kind of polarization beam-splitting grating, be particularly related to a kind of sub-wavelength metal polarization beam splitting grating Optimization Design, this method is to simplifying the method for designing of sub-wavelength metal polarization beam splitting grating, and the polarization beam splitting performance that improves grating has great importance.

Background technology

Along with the continuous progress of micro-processing technology, but present fabrication cycle is less than the sub-wave length metal grating of 100nm.Only there is 0 order diffraction in sub-wave length metal grating, diffraction efficiency is stable, has good polarization beam splitting characteristic, and volume is little, efficient is high, easy of integration, be the core component in the optical modules such as polarising beam splitter, optical memory, optical circulator, optoisolator, be with a wide range of applications in fields such as optical communication, optical measurement, optical information processing, liquid crystal displays.The common required angle wide accommodation of sub-wavelength metal beam-splitting optical grating, spectral width, extinction ratio height, to insert loss low, and also requirement can provide enough making tolerances simultaneously.Therefore, make sub-wavelength metal polarization beam splitting grating, must carry out optimal design earlier,, make grating reach best beam splitting performance to determine best grating parameter.

At present, usually adopt strict electromagnetic vector diffraction theory (the Cormier G that combines with genetic algorithm, Boudreau R, Theriault is J Opt Soc Am B 18 1771 S.2001) method sub-wavelength metal polarization beam splitting grating is optimized design, (grating accounts for the wide f of ratio to choose the grating parameter that needs optimization before this method is calculated earlier, groove depth h and periods lambda), and be expressed as " chromosome ", providing one group of hypothesis separates, calculate by strict electromagnetic vector diffraction theory then,, therefrom select " chromosome " (local optimum is separated) that conforms and duplicate by the principle of the survival of the fittest, again by intersecting, mutation process produces the group of a new generation's " chromosome " who more conforms, and constantly evolves, and will converge at last on one " chromosome " that conforms most, obtain the optimum solution of problem, promptly the overall situation is separated.This method algorithm complexity, counting yield is low even can not get global optimization sometimes separates.

For the optimization of sub-wavelength metal polarization beam splitting grating, also there is not a kind of scientific and reliable method for designing at present.Traditional empirical analysis method is mainly calculated grating diffration efficient under the different parameters based on strict vector electromagnetic theory, and determine the grating optimal design parameters by artificial method, this method can't solve the grating cycle, account for the optimization problem of Multi-parameter Combined Tool such as wide ratio, groove depth, what often obtain is locally optimal solution, and because human factor may cause parameter to select mistake.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, propose a kind of new Optimization Design that is used for sub-wavelength metal polarization beam splitting grating.

Because sub-wave length grating has the form birefringent effect, can equivalence be the positive hyaline layer of even single shaft (Brundrett DL, Glytsis EN, Gaylord TK 1994Appl.Opt.332695), account for wide ratio by adjusting grating, can make grating layer obtain the effective refractive index of any size between incident layer and basalis.

Method of the present invention specifically comprises following step:

1. determine the grating periods lambda.Periodic condition (Λ≤λ according to sub-wave length grating ₀/ 10), determine operation wavelength λ ₀The time the grating periods lambda.

2. required effective refractive index when adopting Film Optics antireflection method for designing to calculate TM polarization max transmissive.

3. adopt effective MEDIUM THEORY to determine that TE polarization and TM polarization effective refractive index and grating account for the variation relation of wide ratio, and determine the wide f of ratio of accounting for of grating according to the effective refractive index that the 2nd step was determined.

4. determine grating groove depth h according to Film Optics antireflecting 1/4 Wavelength matched principle.

The present invention utilizes the antireflection principle of effective MEDIUM THEORY and Film Optics to solve definite problem of grating optimal parameter, realizes the beam splitting of TE polarization and TM polarization, can improve science, reliability, the agility of design.

Description of drawings

Fig. 1 is the sub-wavelength metal polarization beam splitting grating structural representation

Fig. 2 is grating layer metal effective refractive index and the relation that accounts for wide ratio variation

Fig. 3 is the relation of TE polarized light and TM polarized light diffraction efficiency and incident angle variation

Fig. 4 is the relation that extinction ratio and incident angle change

Fig. 5 is for inserting the relation that loss and incident angle change

Fig. 6 is the relation of TE polarized light and TM polarized light diffraction efficiency and lambda1-wavelength (operation wavelength) variation

Fig. 7 is the relation that extinction ratio and lambda1-wavelength (operation wavelength) change

Fig. 8 is for inserting the relation that loss and lambda1-wavelength (operation wavelength) change

Embodiment

At 1550 nanometer operation wavelengths design sub-wavelength metal polarization beam splitting grating, concrete optimal design process of the present invention is described in detail below, required sub-wavelength metal polarization beam splitting grating structure as shown in Figure 1.

The first step: determine the grating periods lambda.Periodic condition (Λ≤λ according to sub-wave length grating ₀/ 10), determine operation wavelength λ ₀Grating periods lambda during=1550 nanometers≤155 nanometers in order to reduce difficulty of processing, is got higher limit Λ=150 nanometers in grating cycle usually, and this moment, only there was 0 order diffraction in grating.

Second step: required effective refractive index when determining TM polarization max transmissive.Equivalence is a metal film to sub-wave length metal grating to the TE polarized light, has reflection characteristic, and equivalence is a deielectric-coating to the TM polarized light, concrete transmissison characteristic.According to the antireflection method for designing of Film Optics, when the refractive index of deielectric-coating satisfies $n=\sqrt{n_1{n}_2}$ (n ₁Be incident layer refractive index, n ₂Be grating basalis refractive index) time, can realize the max transmissive of TM polarization.When the incident layer is air n ₁=1.0, the grating basalis is quartzy n ₂=1.45, and during vertical incidence (incident angle θ=0 degree), then realize the required effective refractive index of TM polarization max transmissive $n=\sqrt{1.0\×1.45}\≈1.20.$

The 3rd step: determine that grating accounts for the wide f of ratio

According to effective MEDIUM THEORY, TE polarized light and TM polarized light are expressed as respectively at the effective refractive index of grating layer:

$n_{\left|\right|}=\sqrt{{\mathrm{fn}}_r^2+(1-f)n_g^2}---\left(1\right)$

$n_{\⊥}=\frac{1}{\sqrt{{\mathrm{fn}}_r^{-2}+(1-f)n_g^{-2}}}---\left(2\right)$

Wherein f is that grating accounts for wide ratio, i.e. the ratio in live width and cycle, n _r=n ' _r+ k ' _rI and n _g=n ' _g+ k ' _gI is respectively the complex index of refraction of grating ridge and grating groove, n ' and k ' are respectively the real part and the imaginary part of complex index of refraction, utilize (1) formula and (2) formula can true objective TE polarization and TM polarization effective refractive index and grating account for the variation relation collection of illustrative plates (the grating ridge is a metallic aluminium) of wide ratio, as shown in Figure 2, n ' among the figure _||(n ' _⊥), k ' _||(k ' _⊥) be respectively the real part and the imaginary part of TE (TM) polarized light effective refractive index.According to definite effective refractive index n ' of second step _⊥=n, and from Fig. 2, draw the wide f=0.3 of ratio of accounting for of grating.

The 4th step: determine the grating groove depth.According to Film Optics antireflecting 1/4 Wavelength matched principle, when the grating layer optical thickness satisfies λ ₀/ 4, promptly

nh＝λ ₀/4(3)

In the formula: h is the grating groove depth, and n is the TM polarized light at the effective refractive index of grating layer (being determined by step 2), can calculate TM polarized light required grating groove depth h=1550/ (4 * 1.20)=323 nanometer when realizing max transmissive.

The optimal design parameter that can determine the sub-wavelength aluminum metal polarization beam-splitting grating of this example 1550 nanometer operation wavelengths by above four steps is: periods lambda=150 nanometers, account for wide than f=0.3, groove depth h=323 nanometer.

By rigorous coupled wave theory (Moharam MG, Pommet DA, the polarization beam splitting performance of grating when Grann EB and Gaylord TK 1995J.Opt.Soc.Am.A 12 1077) calculating above-mentioned optimal design parameter, as seen in the big ranges of incidence angles of-28 °＜θ＜28 °, the transmissivity of the reflectivity of TE polarized light and TM polarized light is higher than 96.3% and 97.5% (Fig. 3) respectively, extinction ratio is higher than 64dB and 25dB (Fig. 4) respectively, inserts loss and is lower than 0.13dB and 0.16dB (Fig. 5) respectively.At 1200 nanometers＜λ ₀In the wide incident light spectrum scope of＜1800 nanometers, the transmissivity of the reflectivity of TE polarized light and TM polarized light all is higher than 96% (Fig. 6), extinction ratio is higher than 61dB and 23dB (Fig. 7) respectively, inserts loss and all is lower than 0.16dB (Fig. 8), has best polarization beam splitting characteristic.

Claims (1)

1, the Optimization Design of sub-wavelength metal polarization beam splitting grating, the antireflection principle of effective MEDIUM THEORY of described method utilization and Film Optics solves definite problem of grating optimal parameter, realize the beam splitting of TE polarization and TM polarization, method specifically may further comprise the steps:

(1) determines the grating periods lambda: according to the periodic condition A≤λ of sub-wave length grating ₀/ 10, determine operation wavelength λ ₀The time the grating periods lambda;

Required effective refractive index when (2) adopting Film Optics antireflection method for designing to calculate TM polarization max transmissive:

The effective refractive index that TM polarization max transmissive is required $n=\sqrt{n_1{n}_2},$ N wherein ₁Be incident layer refractive index, n ₂Be grating basalis refractive index;

(3) adopt effective MEDIUM THEORY to determine that TE polarization and TM polarization effective refractive index and grating account for the variation relation of wide ratio, and determine that according to the effective refractive index that (2) step was determined accounting for of grating is wide than f:

According to effective MEDIUM THEORY, TE polarized light and TM polarized light are expressed as respectively at the effective refractive index of grating layer:

$n_{\left|\right|}=\sqrt{f{n}_r^2+(1-f)n_g^2}---\left(1\right)$

$n_{\⊥}=\frac{1}{\sqrt{{\mathrm{fn}}_r^{-2}+(1-f)n_g^{-2}}}---\left(2\right)$

Wherein f is that grating accounts for wide ratio, i.e. the ratio in live width and cycle, n _r=n ' _r+ k ' _rI and n _g=n ' _g+ k ' _gI is respectively the complex index of refraction of grating ridge and grating groove, n ' and k ' are respectively the real part and the imaginary part of complex index of refraction, utilize (1) formula and (2) formula can determine that TE polarization and TM polarization effective refractive index and grating account for the variation relation collection of illustrative plates of wide ratio, and the effective refractive index n ' that determines according to (2) step _⊥=n draws the wide f of ratio of accounting for of grating from concern collection of illustrative plates;

(4) determine grating groove depth h according to Film Optics antireflecting 1/4 Wavelength matched principle:

nh＝λ ₀/4 (3)

In the formula: h is the grating groove depth, and n is the effective refractive index of TM polarized light at grating layer, is determined λ by step (2) ₀Be operation wavelength.

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