1287648 · 九、發明說明： 【發明所屬之技術領域】 光子晶體(photonic crystals)係折射率週期性變化之 料，利用光子晶體可以設計與製作性能優異的光電元件， 高速光子開關、高效率發光二極體、低功率雷射等。本發明之 B 型抗谐振反射光波導（B-type Antiresonant Reflecting1287648 · IX. Description of the invention: [Technical field of invention] Photonic crystals are materials whose refractive index changes periodically. Photonic crystals can be used to design and fabricate photovoltaic elements with high performance. High-speed photonic switches and high-efficiency light-emitting diodes Polar body, low power laser, etc. B-type antiresonant reflecting waveguide of the invention
Optical Waveguide,纖OW-B)結構之光子晶體波 型抗邊振反射光波導結構和光子晶體結構設計之光路傳導元 件，具有縱模和橫模的基模傳輸能力，可運用在光通訊、光資 訊等領域，同時元件有較大的波導核心尺寸，可以解決光子晶 體波導與光纖在垂直方向上耦合的問題，也是積體光電元件的 設計平台。 【先前技術】， 光子晶體是一種折射係數週期性變化的結構，特定波長的 光在光子晶體中因布拉格繞射(Bragg，s diffracti〇n)的影響 而無法穿越，形成光子能隙（ph〇t〇nic bandgap，PBG)，光子 月b隙了以類比成半導體材料的電子能隙。Eli Yabl〇n〇vitch 在1987年首先提出光子晶體和光子能隙的概念⑴，s.Optical Waveguide, fiber OW-B) structure photonic crystal wave type anti-edge vibration reflection optical waveguide structure and photonic crystal structure design optical path conduction element, with longitudinal mode and transverse mode fundamental mode transmission capability, can be used in optical communication, light In the field of information and other fields, the component has a large waveguide core size, which can solve the problem of coupling the photonic crystal waveguide and the optical fiber in the vertical direction, and is also a design platform for the integrated photovoltaic element. [Prior Art] A photonic crystal is a structure in which a refractive index changes periodically. Light of a specific wavelength cannot be traversed by a Bragg diffraction (Bragg, s diffracti〇n) in a photonic crystal to form a photonic energy gap (ph〇 T〇nic bandgap, PBG), photon monthly b-slot is analogized to the electron energy gap of semiconductor materials. Eli Yabl〇n〇vitch first proposed the concept of photonic crystal and photonic energy gap in 1987 (1), s.
John 同 時也提出光子晶體中光侷限性的理論m。 在能隙範圍内的光波無法在光子晶體内傳播，如果在光 子晶體中設計線缺陷（linedefects)，則能隙中特定波長的光 就可以在光子晶體結構中傳輸。這種外加的缺陷能有效地引導 光線經過指定的路徑，此種元件即稱為光子晶體波導 (photonic crystal waveguides)。光子晶體波導的導光機制 有別於傳統光波導：傳統光波導是利用内部全反射的原理導 光，=以在大角度轉彎處，光波會有很大的損耗；而光子晶體 波導是以光子能隙作為侷限光線的機制，所以能做出大角度彎 5 !287648 折的高傳輸效率光波導⑶。 、現有的光子晶體波導元件，雖然水平方向以二 作為侷限光的機制，但是垂直方向上仍然沿用内部全 ^ 理。為了要讓波導維持在單模態的傳輸條件，波導核心的尺^ 必須小於1微米，相較於光纖的核心直徑約6〜1〇微米，、子 晶，波導與光纖之尺寸及光場不匹配會造成相互耦^效率 低落，限制了光子晶體元件的量測及後續的應用。為了解決馬 合的問題，有多個研究團隊提出改善的方式/例如光'拇 (grating)、鏡面聚焦（prism or mirror)、漸進式结構 (tapered structure)等[4-7]，但是上述方法只能解決水$方 向耦合的問題，垂直方向的耦合仍然沒有具體可行的方案。因 此本發明以B型抗諧振反射光波導結構設計來解決朵早'曰駚 波導與光纖之垂直方向耦合問題[8]。 ' - 【先前技術檢索資料】John also proposed the theory m of optical limitations in photonic crystals. Light waves in the energy gap cannot propagate in the photonic crystal. If linedefects are designed in the photonic crystal, light of a specific wavelength in the energy gap can be transmitted in the photonic crystal structure. This added defect effectively directs light through a specified path. These components are called photonic crystal waveguides. The light guiding mechanism of the photonic crystal waveguide is different from the traditional optical waveguide: the traditional optical waveguide uses the principle of internal total reflection to guide light, = at a large angle, the light wave will have a large loss; and the photonic crystal waveguide is a photon. The energy gap acts as a mechanism for limiting the light, so it can make a high transmission efficiency optical waveguide (3) with a large angle bend of 5,287,648. In the existing photonic crystal waveguide element, although the horizontal direction is two as a mechanism for limiting light, the internal total is still used in the vertical direction. In order to maintain the waveguide in single mode transmission conditions, the size of the waveguide core must be less than 1 micron, compared to the core diameter of the fiber by about 6 to 1 micron, the size of the subcrystal, the waveguide and the fiber, and the optical field. Matching results in low coupling efficiency, limiting the measurement of photonic crystal components and subsequent applications. In order to solve the problem of Ma He, there are several research teams suggesting ways to improve / such as light 'grating, prism or mirror, tapered structure, etc. [4-7], but the above method It can only solve the problem of water-direction coupling, and there is still no concrete feasible solution for the coupling in the vertical direction. Therefore, the invention designs a B-type anti-resonant reflective optical waveguide structure to solve the vertical coupling problem between the early waveguide and the optical fiber [8]. ' - 【Prior Art Search Data】
1. E. Yablonovitch, ^Inhibited spontaneous emission in solid-state physics and electronics,ff Phys. Rev. Lett., vol. 58, no. 20, pp. 2059-2062,1987. 2· S. John，"Strong localization of photons on certain disordered dielectric superlattices，” Phys· Rev. Lett” Vol. 58, pp· 2486-2488, 1987. 3. Attila Mekis? J. C. Chen, I. Kurland, Shanhui Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, "High Transmission through Sharp Bends in Photonic Crystal Waveguides/* Phys. Rev. Lett., vol. 11, pp. 3787-3790, 1996. 4· Attila Mekis and J· D· Joannopoulos，’’Tapered Couplers for Efficient Interfacing Between Dielectric and Photonic Crystal 6 12876481. E. Yablonovitch, ^Inhibited spontaneous emission in solid-state physics and electronics, ff Phys. Rev. Lett., vol. 58, no. 20, pp. 2059-2062, 1987. 2· S. John," Strong localization of photons on certain disordered dielectric superlattices,” Phys· Rev. Lett” Vol. 58, pp· 2486-2488, 1987. 3. Attila Mekis? JC Chen, I. Kurland, Shanhui Fan, Pierre R. Villeneuve, and JD Joannopoulos, "High Transmission through Sharp Bends in Photonic Crystal Waveguides/* Phys. Rev. Lett., vol. 11, pp. 3787-3790, 1996. 4· Attila Mekis and J· D· Joannopoulos, ''Tapered Couplers For Efficient Interfacing Between Dielectric and Photonic Crystal 6 1287648
Waveguides,” J. Lightwave Technol·，vol· 19, ρρ· 211-217， 2001. 5 · Yong Xu，Reginald K. Lee，and Amnon Yariv，"Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry，” Opt. Lett·， vol. 25, pp.755-757? 2000.Waveguides," J. Lightwave Technol·, vol. 19, ρρ· 211-217, 2001. 5 · Yong Xu, Reginald K. Lee, and Amnon Yariv, "Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry, Opt. Lett·, vol. 25, pp.755-757? 2000.
6· Wan Kuang，Cheolwoo Kim，Andrew Stapleton，and John D. O’Brien，"Grating-assisted coupling of optical fibers and photonic crystal waveguides/1 Opt. Lett., vol. 21, pp. 1604-1606,2002· 7. Dennis W. Prather, Janusz Murakowski, Shouyuan Shi, Sriram Veiikataraman，Ahmed Sharkawy，Caihua Chen，and David Pustai? MHigh-efficiency coupling structure for a single-line-defect photonic-crystal waveguide,,f Optics Letters, vol. 21, no. 18，ρρ·160Μ603,2002· 8· Μ· A· Duguay，Υ· Kokubun，Τ· L. Koch，and L· Pfeiffer, f,Antiresonant reflecting optical waveguides in Si02-Si multilayer structures,ff Appl Phys, Lett, vol. 495 no. 1, pp. 13-15,1986. 【發明内容】 ，本發明提出「B型抗諧振反射光波導結構之光子晶體波 導」，其結構如圖一所示，元件的垂直方向如圖二所示係由Β 型抗諧振反射光波導結構構成。抗諧振反射光波導的第一覆層 反射率高於核心層與第二覆層之反射率；而Β型抗諧振反射光 波導的第一覆層反射率則略低於核心層與第二覆層之反射 率。利用抗諧振反射將基模反射至核心層，高階模態散逸 折射率的基板，以義單模高效率傳輸的目的。鱗的 向係由圓形空氣孔洞在介電材料上週期性排列成三角形晶格 1287648. 冓成光子晶體結構’在光子B日日體結構上移去— 机 ^線缺陷’等效為基模傳輸的光波導。因此本“ J以光子能隙作為侷限光線的機制，垂直方向 以能做出大角度騎的高傳皮内^全反射機制，所 抗譜振反射光波導結構具有下列優點：⑴ (2)單模傳輸；（3)可彈性地選擇光波. -^扣耗， 率，以配合輸出、入光纖的厚折射 增效率;及⑷可製作於高折射率基片士== r 反射光㈣結齡了具有上述的伽之外 ^t% (transverse electric field, TE ) tr_erse magI^tlc field，顶）兩種模態 $ «undamental inodes)都有低傳輸損耗的特性，因此呈 ， ^橫模的傳輸能力。並可彈性選擇波導各層的厚度^折$ ，率材料，解決光子晶體波導與光纖在垂直方向上 4 ’並可供作積體光電元狀設計平台。 揭口的問 ^#_光波導概，本發_具的優 =Ϊΐ:Ϊ f 寸削侧題。水平方向採用光子 3:構光子能隙侷限光、線’而非傳統波導的内部全ί 射機制，所以能做出高傳輸效率的大角度彎折。 的，f晶體波導相比，本發明獨具的優點為.·垂直 °採用B型抗諧振反射光波導結構，而非内部全反 3尺寸與材料折射率的選擇具有相t彈性，可以依 t光纖㈣陳大波導私尺寸與對應折射率材料，^ 子曰a體波導與光纖在垂直方向上耦合的問題。 ’、 8 1287648 【實施方式】 本發明之「B型抗諧振反射光波導結構之光子晶體波導」 的設計分為兩個部份。 第一部份在元件的垂直方向上為一 β型抗諧振反射光波導 結構’包含-波導核心層（core)、一折射率低於核心層之第 了覆層（firstcladding)、一折射率與核心層相等或較低之 第二覆層（second cladding)，以及一高折射率的美姑 (substrate);首先，依應用需求選定所用光波之工作波^ , ^本發明實施例之工作波長λ為1. 55卿，接著蚊搭配的波 V材料系統，亦即β型抗諧振反射光波導之各層的折射率與厚 度。 ’、 為了將來積體光學整合的目的，元件的設計配合半 製程，選用Si材料作為基板，基板的折射率w =3 5 · 一 ^以^人驗^折射率^心為了與單模光纖能支 波導核"層的厚度設計成‘8叩。當滿 ^粕振條件（antiresonacecondition)時，第二覆層的厚 Λ2 •(2户+ 1)，Ρ = 〇，ι，2,3，.6· Wan Kuang, Cheolwoo Kim, Andrew Stapleton, and John D. O'Brien, "Grating-assisted coupling of optical fibers and photonic crystal waveguides/1 Opt. Lett., vol. 21, pp. 1604-1606, 2002 · 7. Dennis W. Prather, Janusz Murakowski, Shouyuan Shi, Sriram Veiikataraman, Ahmed Sharkawy, Caihua Chen, and David Pustai? MHigh-efficiency coupling structure for a single-line-defect photonic-crystal waveguide,, f Optics Letters, vol 21, no. 18, ρρ·160Μ 603, 2002· 8· Μ· A· Duguay, Υ· Kokubun, Τ· L. Koch, and L· Pfeiffer, f, Antiresonant reflecting optical waveguides in Si02-Si multilayer structures, ff Appl Phys, Lett, vol. 495 no. 1, pp. 13-15, 1986. SUMMARY OF THE INVENTION The present invention proposes a "photonic crystal waveguide of a B-type anti-resonant reflective optical waveguide structure", the structure of which is shown in FIG. The vertical direction of the element is shown in Fig. 2 by a Β-type anti-resonant reflective optical waveguide structure. The first cladding reflectance of the anti-resonant reflective optical waveguide is higher than the reflectivity of the core layer and the second cladding layer; and the first cladding reflectance of the Β-type anti-resonant reflective optical waveguide is slightly lower than the core layer and the second cladding The reflectivity of the layer. The anti-resonant reflection is used to reflect the fundamental mode to the core layer, and the high-order mode dissipates the refractive index of the substrate for the purpose of high-efficiency single-mode transmission. The orientation of the scale is periodically arranged into a triangular lattice on the dielectric material by a circular air hole 1287648. The photonic crystal structure of the photonic crystal is removed on the photon B-day structure - the machine defect is equivalent to the fundamental mode. The optical waveguide that is transmitted. Therefore, the "J is a photon energy gap as a mechanism for limiting the light, and the vertical direction is a high-transmission internal reflection mechanism that can make a large angle ride. The anti-spectral reflection optical waveguide structure has the following advantages: (1) (2) Mode transmission; (3) elastically selectable light wave. -^ deducting, rate, to match the output and into the fiber, thick refractive efficiency; and (4) can be made in high refractive index substrate == r reflected light (four) age The above two modalities (transverse electric field, TE) tr_erse magI^tlc field, top) two modalities $«undamental inodes have low transmission loss characteristics, so the transmission of transverse mode Capability, and can flexibly select the thickness of each layer of the waveguide, and the rate material can solve the photonic crystal waveguide and the optical fiber in the vertical direction 4' and can be used as an integrated photocell design platform. In general, the hair of the hair _ has the advantage = Ϊΐ: Ϊ f inch side problem. The horizontal direction uses photon 3: the photon energy gap limits the light, the line 'is not the internal full-grain mechanism of the traditional waveguide, so it can make high transmission The efficiency of the large angle bend. The f crystal waveguide compared to the hair The unique advantages are: vertical. B-type anti-resonant reflective optical waveguide structure, instead of internal full-reverse 3 size and material refractive index selection has phase t elasticity, can be based on t fiber (four) Chen Da waveguide private size and corresponding refraction Rate material, the problem that the sub-body waveguide and the optical fiber are coupled in the vertical direction. ', 8 1287648 [Embodiment] The design of the "B-type anti-resonant reflective optical waveguide structure photonic crystal waveguide" of the present invention is divided into two Part. The first part is a β-type anti-resonant reflective optical waveguide structure in the vertical direction of the element, including a waveguide core, a first cladding, a refractive index lower than the core layer. a second cladding with equal or lower core layers, and a high refractive index of the substrate; first, the operating wave of the used light wave is selected according to the application requirements, and the operating wavelength λ of the embodiment of the present invention It is 1. 55 qing, followed by the wave-V material system of the mosquito, that is, the refractive index and thickness of each layer of the β-type anti-resonant reflected optical waveguide. 'For the purpose of future optical integration of components, the design of the component is matched with the half process, and the Si material is selected as the substrate. The refractive index of the substrate is w = 3 5 · · ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ The thickness of the waveguide core & layer is designed to be '8 叩. When the condition of the antiresonacecondition is exceeded, the thickness of the second coating is •2 • (2 households + 1), Ρ = 〇, ι, 2, 3,.
、一 X ,v n\ \n\d]; … 波導核心層的折射率與厚度，〜為第二覆層之折 射率p為大於或等於〇之整數；若第二覆声盘椤心爲夕批 相等，則第二覆層的厚度何簡化^:覆層與核〜層之折射率 ^2 = · {2P +1) 上述兩個公式中，通常p設為 0即可，如此第一盘第一霜屏 不至，因此第二覆層的厚度—0.5:心7覆層都 層與核心層選用之材料其折射率必須能 H 場兩種模態的交疊光子能隙(j〇int b 广 圖-為先子晶體不同折射率的能，可以觀察到折射率必須 9, X, vn\ \n\d]; ... the refractive index and thickness of the waveguide core layer, ~ is the refractive index p of the second cladding layer is greater than or equal to the integer of 〇; if the second sounding disk is 椤If the batch is equal, how is the thickness of the second cladding simplified? ^Refractive index of the cladding layer and the core to the layer ^2 = · {2P +1) In the above two formulas, usually p is set to 0, so the first disk The first frost screen is not available, so the thickness of the second cladding layer is 0.5: the core 7 coating layer and the core layer are selected from materials whose refractive index must be capable of H field two modes of overlapping photon energy gaps (j〇int b broad map - for the energy of different refractive indices of the precursor crystal, it can be observed that the refractive index must be 9
^287648 大於3· 〇才會有交疊能隙，因此 的折射率，所以w =3 •為第一覆層與核心層 雜的石夕。圖四和圖五j性或高濃度摻 損耗與第-覆層厚度賴係圖電本=^^各個模態傳輸 可以獲得低損耗顶和TMq模態的 選擇/7= 〇. η μπι ’ 的目的。據此決定_W_B、的元# J 1到長距離傳輸 1· 00/3.20/, 45 /, 20/, 50 = 料上週期性排曰rtf二維空氣孔洞在介電材 必頌:向電％和橫向磁場兩觀態交疊的光子能隙， 士、須文.②計制的半徑『以及晶格常數《同到 角：is’ 體的對稱性必須越高越好，因此採用三 tit播Hi中橫向ΐ場和橫向磁場兩種模態之光波 子曰二墓洞引入線缺陷模態，形成光 子Β曰波導。本發明實施例翻的波導核心材料折射率是 ί管艮據平面波展開法（Plane贿 子、曰1體波導能隙圖看出在空氣孔洞半徑與晶格常數 至〜為0.47的時候，有最大的能隙值。對應的能隙頻 率從 0.46 到 〇.51 (3/λ)’中心頻率為（〇 46 + 〇 51)/2 = 〇二485。據此求得晶格常數a = 〇. 485 λ = 〇. 752 μηι，孔洞直 徑 ί/ = 〇· 94a = 〇· 707 μιη。 士、在分別設計水平及垂直方向結構之後，以三維有限差分 日守域法(Finite Difference Time Domain, FDTD)計算 β 型抗 。白振反射光波導結構之光子晶體波導的傳輸效率。此波導利用 一維光子晶體及抗諧振反射層，分別將水平及垂直方向基模的 光波侷限在波導核心層，高階模態則大部份散逸至下方的基 板。圖七為空氣孔洞蝕刻深度對傳輸效率的關係圖，得知空氣 孔洞被餘刻到8· ΟΟμπι也就是核心層的厚度時，傳輸效率可以 達到最大值；其原因是因為垂直方向的光波由抗諧振反射層反 7648 2核心相’所以空氣蘭只需要_至核^ 樺Hit型抗譜振反射光波導結構之光子晶體波導兼且 只向電％和檢向磁場模態的高效率傳輸能力。 八 本發贿出新的B型抗諧振反射光波導結構 fi:水平方向採用光子晶體結構提供光的侷限能力，垂g °罪B型抗雜反射提供光的舰能力，在核心層的厚度達到 的匕仍麟供基模的傳輸能力’橫向電場和橫向磁場模 可達到哪以上。因為核心層的厚度與光纖匹配， 光ΐ晶體波導與光纖在垂直方向的搞合_，並提供 檟體光電兀件設計的平台。 【圖式簡單說明】 ，為Β型抗拍振反射光波導結構之光子晶體波導的結構示 思圖； 圖^為Β型抗諧振反射光波導結構圖； 圖二為光子晶體不同折射率的能隙圖； 圖四為橫向電場模態傳輸損耗與第一覆層厚度沁關係圖； 圖五為橫向磁場模態傳輸損耗與第一覆層厚度沁關係圖； 圖六為光子晶體波導能隙圖； 圖七為空氣孔洞蝕刻深度對傳輸效率的關係圖； 圖八為不同頻率橫向電場及橫向磁場的傳輸效率圖。 【主要元件符號說明】 1:空氣孔洞 1287648 2:核心層 3:第一覆層 第二覆層 基板^287648 is greater than 3· 〇 will have overlapping energy gap, so the refractive index, so w = 3 • is the first cladding and the core layer of the stone. Figure 4 and Figure 5 of the j- or high-concentration doping loss and the thickness of the first-clad layer. The modal transmission of each mode can obtain the choice of low-loss top and TMq mode /7= 〇. η μπι ' purpose. According to this decision _W_B, Yuan # J 1 to long distance transmission 1· 00/3.20/, 45 /, 20/, 50 = periodic discharge rtf two-dimensional air holes in the dielectric must be: The photon energy gap between the % and the transverse magnetic field, the radius of the measurement, and the lattice constant "the same angle: the symmetry of the is' must be higher, so the three tits are used. The two modes of the horizontal ΐ field and the transverse magnetic field in Hi are introduced into the line defect mode to form a photonic Β曰 waveguide. In the embodiment of the present invention, the refractive index of the waveguide core material is ί 艮 according to the plane wave expansion method (Plane bribe, 曰1 body waveguide energy gap diagram shows that the air hole radius and the lattice constant to ~ 0.47, the maximum The energy gap value. The corresponding bandgap frequency is from 0.46 to 〇.51 (3/λ)' center frequency is (〇46 + 〇51)/2 = 〇2485. The lattice constant a = 〇 is obtained accordingly. 485 λ = 〇. 752 μηι, hole diameter ί/ = 〇· 94a = 〇· 707 μιη. After designing the horizontal and vertical structures separately, the three-dimensional finite difference time domain method (FDTD) Calculate the transmission efficiency of the photonic crystal waveguide of the white-reflected optical waveguide structure. The waveguide utilizes a one-dimensional photonic crystal and an anti-resonant reflective layer to respectively limit the light waves of the horizontal and vertical fundamental modes to the waveguide core layer, the high-order mode. Most of the state is dissipated to the underlying substrate. Figure 7 shows the relationship between the etching depth of the air hole and the transmission efficiency. It can be seen that the air hole is engraved to the thickness of the core layer. The reason is because the vertical direction of the light wave is reversed by the anti-resonant reflective layer 7648 2 core phase 'so the air blue only needs _ to the core ^ birch type-type anti-spectral reflection optical waveguide structure of the photonic crystal waveguide and only the electricity % and High-efficiency transmission capability for detecting magnetic field modes. Eight new british B-type anti-resonant reflective optical waveguide structures: the use of photonic crystal structures in the horizontal direction to provide limited optical capabilities, and the use of B-type anti-aliasing provides The ship's ability to light, the thickness of the core layer is still the transmission capacity of the basic mode. The transverse electric field and the transverse magnetic field mode can reach more than. Because the thickness of the core layer matches the fiber, the optical waveguide and the fiber are perpendicular. The orientation of the _, and provide a platform for the design of the 兀 body photoelectric element. [Simple diagram of the diagram], the structure of the photonic crystal waveguide of the Β-type anti-beat reflection optical waveguide structure; Figure ^ is the Β type resistance Figure 2 is the energy gap diagram of the different refractive index of the photonic crystal; Figure 4 is the relationship between the transverse electric field mode transmission loss and the first cladding thickness ;; Figure 5 is the transverse magnetic field mode Figure 6 shows the energy gap of the photonic crystal waveguide; Figure 7 shows the relationship between the etching depth of the air hole and the transmission efficiency; Figure 8 shows the transmission efficiency of the transverse electric field and the transverse magnetic field at different frequencies. [Main component symbol description] 1: Air hole 1287648 2: Core layer 3: First cladding second cladding substrate