波谱学杂志, 2024, 41(4): 393-404 doi: 10.11938/cjmr20243111

研究论文

基于法布里-珀罗谐振腔的W波段电子顺磁共振探头研制

罗文尤, 荣星,*

中国科学院微观磁共振重点实验室,中国科学技术大学,安徽 合肥 230026

A W-Band Electron Paramagnetic Resonance Probe Based on Fabry-Perot Cavity

LUO Wenyou, RONG Xing,*

CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China

通讯作者: * Tel: 0551-63606664, E-mail:xrong@ustc.edu.cn.

收稿日期: 2024-04-19   网络出版日期: 2024-06-07

基金资助: 国家自然科学基金资助项目(12150010)

Corresponding authors: * Tel: 0551-63606664, E-mail:xrong@ustc.edu.cn.

Received: 2024-04-19   Online: 2024-06-07

摘要

本文研制了一种基于法布里-珀罗谐振腔的W波段电子顺磁共振探头.利用法布里-珀罗谐振腔所具备的大体积和开放腔等特点,本文将法布里-珀罗谐振腔用作谱仪探头的谐振器部分,并且设计了波纹波导来实现微波桥与法布里-珀罗谐振腔之间的低损耗微波信号传输.所研制的探头工作在W波段,空载品质因数为1 542.最终将该探头集成于W波段电子顺磁共振谱仪,通过测量Mn(II)掺杂的CaO粉末样品的谱线,展示了该探头在常温下用于W波段连续波电子顺磁共振实验的能力.探头的调制场频率设置为100 kHz,实验结果显示探头的最大调制场幅度可达8.9 G(1 G=10-4 T),谱仪绝对自旋数灵敏度为6.6×108 spins/(G•$\sqrt{Hz}$)

关键词: 电子顺磁共振; 法布里-珀罗谐振腔; 波纹波导; 灵敏度

Abstract

This paper presents a new W-band electron paramagnetic resonance (EPR) probe design based on Fabry-Perot cavity. In this probe, a Fabry-Perot cavity with open structure and large effective volume is used as a resonator. Corrugated waveguides are designed to achieve low-loss microwave signal transmission between the W-band microwave bridge and the Fabry-Perot cavity. The probe works in W-band, and the unloaded quality factor is 1 542. A room-temperature continuous wave EPR experiment with Mn(II) in CaO powder was conducted after assembling the probe into a W-band EPR spectrometer. The results show that the modulation field amplitude is 8.9 G (1 G=10-4 T) when the modulation field frequency is set to 100 kHz, and the absolute spin sensitivity is estimated to be 6.6×108 spins/(G•$\sqrt{Hz}$), which verifies the feasibility of utilizing Fabry-Perot cavity as a high sensitivity W-band EPR probe.

Keywords: electron paramagnetic resonance (EPR); Fabry-Perot cavity; corrugated waveguide; sensitivity

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本文引用格式

罗文尤, 荣星. 基于法布里-珀罗谐振腔的W波段电子顺磁共振探头研制[J]. 波谱学杂志, 2024, 41(4): 393-404 doi:10.11938/cjmr20243111

LUO Wenyou, RONG Xing. A W-Band Electron Paramagnetic Resonance Probe Based on Fabry-Perot Cavity[J]. Chinese Journal of Magnetic Resonance, 2024, 41(4): 393-404 doi:10.11938/cjmr20243111

引言

电子顺磁共振(Electron Paramagnetic Resonance,EPR)谱仪可以对含有未成对电子的物质进行检测,是一种重要的物质结构分析仪器.EPR谱仪被广泛用于化学反应机理研究、生物分子结构分析、材料缺陷和掺杂物的检测等[1-6].近年来太赫兹微波技术[7]与超导磁体技术[8]的进步为高频高场EPR谱仪的发展提供了技术基础.高频高场EPR谱仪相比于传统X波段谱仪具有更高灵敏度、更高谱线分辨率、更大激发能量等优势[9,10],例如利用高频高场EPR谱仪对粉末状酶氨酸缺失的铜蓝蛋白Azurin突变体(AzC-W48)中色氨酸自由基[11]或辅酶Q10阴离子自由基[12]进行探测,可分析自由基的朗德因子张量取向,而这在分辨率较低的X波段谱仪上是难以开展的.

探头是EPR谱仪的核心部件之一,其性能对谱仪的灵敏度、分辨率等指标具有重要影响.待测样品被装载于探头中,磁体系统在探头处产生特定强度的外磁场,微波信号在探头的样品区域被转换为垂直于外磁场的交变磁场,样品中的自旋与外磁场和交变磁场产生相互作用.当满足磁共振条件时,样品会吸收或者辐射出电磁波信号,该信号经由探头传输至微波接收机,再经由一系列信号处理过程转换为最终的谱线.EPR探头有谐振型和非谐振型两类.一种常见的非谐振型探头结构是共面波导[13].相比于谐振型探头,非谐振探头具有更大的工作带宽,但是其探测灵敏度不足.为了提高探测灵敏度,通常选用谐振型探头.常见的谐振型探头包括矩形谐振腔[14]、圆柱形谐振腔[15]、裂环式谐振腔[16]等,其中圆柱形谐振腔在X波段到W波段等谱仪上均有应用.然而当EPR谱仪工作频率达到几十GHz乃至百GHz量级时,圆柱形谐振腔这类封闭式腔体的尺寸会迅速减小,导致腔体的加工难度变大,有效装载样品空间变小,且封闭腔内的样品难以与射频场、光、电场等外部激励耦合,这制约了高频高场EPR谱仪的性能.法布里-珀罗谐振腔(Fabry-Perot Cavity)是一类开放式谐振腔,相比于圆柱形谐振腔更容易与外部场实现耦合[17,18],且其谐振结构和较大的样品装载空间保证了高灵敏度.在1985年,Haindl等人[19]开发出首台基于法布里-珀罗谐振腔的W波段EPR谱仪.接着在2005年Earle等人[20]利用基于法布里-珀罗谐振腔的EPR谱仪实现了对生物溶液样品的测试.2010年,Neugebauer研发了基于法布里-珀罗谐振腔的宽带EPR谱仪[21].目前国内尚缺少基于法布里-珀罗谐振腔的高频高场EPR设备的研制.

本文利用法布里-珀罗谐振腔设计并实现了一款W波段(94.04 GHz)EPR谱仪探头,使用波纹波导来实现微波桥和谐振腔之间的低损耗微波信号传输,相较于已经发表的法布里-珀罗谐振腔设计[19,22],本文改进了腔体谐振频率调节装置,实现了基于电动位移台的精细调节,且探头可以在低温下工作.通过一系列实验测试了法布里-珀罗谐振腔的性能,包括谐振频率、品质因数、调制场幅度等关键参数,并使用Mn(II)掺杂的CaO粉末样品(下文简称为Mn标样品)进行了常温下的W波段连续波EPR实验,标定了谱仪的绝对自旋数灵敏度.

1 探头设计

法布里-珀罗谐振腔的典型结构如图1所示,法布里-珀罗谐振腔由两片球面反射镜组成,是一种开放式的谐振腔,球面镜能汇聚微波达到减少衍射损耗的目的.腔体长度为${{L}_{c}}$,腔体的两个镜片孔径分别为${{a}_{1}}$${{a}_{2}}$,曲率半径分别为${{R}_{1}}$${{R}_{2}}$,曲率半径趋近于无穷大时对应镜片为平面镜.两镜片的振幅反射率为${{r}_{1}}$${{r}_{2}}$,振幅透射率为${{t}_{1}}$${{t}_{2}}$.忽略镜片引入的微波相位变化,只考虑微波的低阶模式,当入射微波频率为腔体谐振频率时,微波在腔内多次反射后形成的微波模式为基模高斯光束.可以用几何光学的方法理解法布里-珀罗谐振腔的谐振现象.令入射微波的振幅为${{U}_{0}}$,波矢为${{k}_{c}}$,则法布里-珀罗谐振腔的反射振幅${{U}_{ref}}$满足(1)式[23]

$\frac{{{U}_{\text{ref}}}}{{{U}_{0}}}\propto \frac{1}{1-{{r}_{\text{1}}}{{r}_{\text{2}}}exp(2i{{k}_{c}}{{L}_{c}})}$

图1

图1   法布里-珀罗谐振腔的结构示意图

Fig. 1   Schematic diagram of Fabry-Perot cavity


从法布里-珀罗谐振腔反射出的信号功率${{I}_{ref}}$与输入信号功率${{I}_{inc}}$满足(2)式:

$\frac{{{I}_{ref}}}{{{I}_{inc}}}=\frac{|{{U}_{\text{ref}}}{{|}^{2}}}{|{{U}_{\text{0}}}{{|}^{2}}}\propto \frac{1}{1+\frac{4{{r}_{1}}{{r}_{2}}}{{{\text{(1-}{{r}_{1}}{{r}_{2}})}^{2}}}si{{n}^{2}}({{k}_{c}}{{L}_{c}})}$

法布里-珀罗谐振腔的空载品质因数为${{Q}_{U}}=\text{ }\!\!\pi\!\!\text{ }{{q}_{0}}\sqrt{{{r}_{\text{1}}}{{r}_{\text{2}}}}/(1-{{r}_{\text{1}}}{{r}_{\text{2}}})$,其中${{q}_{0}}$为模序数,满足${{k}_{c}}{{L}_{c}}=2{{q}_{0}}\text{ }\!\!\pi\!\!\text{ }$,可通过提升镜片的反射率以及谐振腔腔长来提高谐振腔的空载品质因数.通过金属镀膜的方法可增加镜片的反射率.由于谐振腔中存在衍射损耗,腔体不能过长,否则大量的微波能量会从谐振腔侧壁辐射到外部反而造成品质因数降低,因此需要选择合适的${{L}_{c}}$.实际设计时,为了实现外部微波传输线与法布里-珀罗谐振腔的耦合,会将其中一个球面镜替换为金属栅结构.

本文所设计探头的整体结构示意图如图2(a)所示,探头主要由法布里-珀罗谐振腔和波纹波导组成.法布里-珀罗谐振腔用于装载样品,波纹波导用于转化微波模式以及实现微波桥与法布里-珀罗谐振腔之间的低损耗微波信号传输.从圆波导入射到波纹波导的微波信号模式为TE11,经波纹波导转化为HE11模式.从波纹波导中发射的HE11模式微波约98%的能量集中在高斯模式,而谐振状态下法布里-珀罗谐振腔内电磁场驻波服从高斯模式分布,因此HE11模式微波耦合入法布里-珀罗谐振腔时具有较少的能量损耗[24,25].

图2

图2   (a)探头的结构示意图, 探头主要由法布里-珀罗谐振腔与波纹波导构成, 波纹波导将入射的TE11模式的微波转化为HE11模式,①~④表示波导的各分段;(b)波纹波导②的剖面图;(c)法布里-珀罗谐振腔的结构示意图,⑤金属网格和⑥球面镜构成谐振腔结构;(d)探头实物图,核心部件包括:⑦金属网格、⑧样品台、⑨调制场线圈、⑩球面镜、⑪⑫⑬压电位移台

Fig. 2   (a) Schematic diagram of the probe, mainly composed of two parts, Fabry-Perot cavity and corrugated waveguides. The corrugated waveguides work as a mode converter for generating the HE11 mode from the TE11 mode. ①~④ are four segments of corrugated waveguides; (b) Cross-sectional diagram of the corrugated waveguide②; (c) Schematic diagram of the probe, ⑤ is the metallic mesh and ⑥ is the spherical mirror; (d) Photograph of the Fabry-Perot cavity, ⑦ is the metallic mesh, ⑧ is the sample holder, ⑨ is the modulation coil, ⑩ is the spherical mirror, and ⑪⑫⑬ are piezoelectric positioners


图2(b)所示,波纹波导的内壁上分布有周期性的波纹.波纹的参数包括波纹深度d、波纹周期p、波纹宽度${{\omega }_{t}}$以及倾角α.波纹波导具有带宽大、传输损耗小、交叉极化低,以及传输的微波模式高度对称的特点,这些特点使得波纹波导常被用于高频线路中[21,26].本文设计的波纹波导主要分为4个部分.如图2(a)①所示的第一段波导为圆波导到波纹波导的过渡波导,波纹波导的整体倾角为2.0˚,波导的波纹深度从${{\lambda }_{0}}/2$渐变到${{\lambda }_{0}}/4$${{\lambda }_{0}}$ 为入射微波的波长.之后其它段的波导波纹深度维持${{\lambda }_{0}}/4$,所有波导的波纹周期为${{\lambda }_{0}}/3$.图2(a)②所示的第二段波导整体倾角为2.6˚,用于扩大波纹波导内径,图2(b)所示波导为第二段波导的部分结构的剖面图.如图2(a)③所示的第三个波导倾角为0˚,第三个波导为大尺寸波导,其内径为$6{{\lambda }_{0}}$.这种大尺寸波导可用来减小高频下波导的传输损耗[21].如图2(a)④所示的第四段波导倾角为2.4˚,用于将发射的微波耦合入法布里-珀罗谐振腔.可通过测试波纹波导的反射系数${{S}_{11}}$来评估其损耗,在波纹波导末端安装反射镜,用矢量网络分析仪测得整套波纹波导在94.04 GHz处的反射系数为-6.8 dB,则波纹波导在94.04 GHz处的传输系数${{S}_{12}}$约为-3.4 dB.

图2(c)所示,法布里-珀罗谐振腔主要由金属网格和一个球面镜组成.入射微波激发了金属网格表面等离子激元,表面等离子激元部分能量耦合到网格结构的另一面再耦合成微波出射,部分能量从入射面反射,因此金属网格的设计能耦合一部分入射的微波到法布里-珀罗谐振腔内,同时能够将谐振腔的功率耦合一部分到外部的微波传输线.可以通过调节金属网格的参数来调节金属网格对特定频段微波的透射率和反射率[27].当微波频率与谐振腔谐振频率相同时,入射微波在金属网格和球面镜之间多次反射,形成高斯模式的驻波.金属网格可以减少由于模式不匹配、模式转化或空间辐射导致的能量损耗[28],我们选择如图3所示的正方形金属网格作为耦合结构,金属条纹的宽度2a=40 μm,网格周期g=200 μm.金属网格对微波的反射与透射能力受金属网格尺寸参数的控制:2a=g时,金属网格为全封闭结构,入射微波近乎完全反射;当2a=0时,金属网格为全开放结构,此时入射微波近乎完全透射;当0<2a<g时,金属网格具有一定的反射和透射能力.本文设计的金属网格是在中国科学技术大学微纳研究与制造中心制成的,在直径为28 mm、厚度为0.26 mm的圆柱形双抛石英片上通过金属电镀工艺先镀一层200 nm的钛膜以增加金属的附着能力,再镀一层2 000 nm的铜膜,然后通过掩模版方法剥去金属膜中不需要的部分,最终得到目标金属网格.

图3

图3   金属网格示意图. 黑色条纹为金属条纹

Fig. 3   Scheme of the metallic mesh. The black areas are metallic strips


金属网格的反射与透射能力取决于网格的参数,反射率$|\Gamma {{|}^{2}}$与透射率$|\tau {{|}^{2}}$满足(3)式[29]

$\left\{ \begin{matrix} & |\Gamma {{|}^{2}}=1/({{(1+R)}^{2}}+{{\left( \frac{{{Z}_{0}}}{{{\omega }_{m}}} \right)}^{2}}) \\ & |\tau {{|}^{2}}=({{R}^{2}}+{{\left( \frac{{{Z}_{0}}}{{{\omega }_{m}}} \right)}^{2}})/({{(1+R)}^{2}}+{{\left( \frac{{{Z}_{0}}}{{{\omega }_{m}}} \right)}^{2}}) \\ \end{matrix} \right.$

其中归一化阻值$R=\sqrt{4\pi \in {{f}_{\text{m}}}{{\rho }_{\text{R}}}}(g/2a)$$\in $为真空介电常数,${{f}_{\text{m}}}$为入射到金属网格的微波频率,${{\rho }_{\text{R}}}$为常温下金属的电阻率,铜的${{\rho }_{\text{R}}}=1.712\times {{10}^{-8}}\text{ }\Omega \text{m}$;归一化阻抗${{Z}_{\text{0}}}=1.5\ln (\csc ((\text{ }\!\!\pi\!\!\text{ /2)}\cdot \text{(}a\text{/}g\text{)))}$;归一化频率${{\omega }_{\text{m}}}=\omega /{{\omega }_{0}}-{{\omega }_{0}}/\omega $$\omega =g/{{\lambda }_{\text{m}}}$${{\omega }_{\text{0}}}=1-0.27a/g$,其中${{\lambda }_{\text{m}}}$为入射微波波长.对于94.04 GHz的微波信号,${{\lambda }_{\text{m}}}=3.19\text{ mm}$,计算得该金属网格对于94.04 GHz的微波有98.31%的反射率和1.276%的透射率,与文献[22]数据相符.通过计算评估了不同金属材料对探头性能的影响,常温下银的${{\rho }_{\text{R}}}=1.587\times {{10}^{-8}}\text{ }\Omega \text{m}$,对应制成的金属网格反射率与透射率分别为$|\Gamma {{|}^{2}}=$98.32%与$|\tau {{|}^{2}}=$1.276%;金的${{\rho }_{\text{R}}}=2.214\times {{10}^{-8}}\text{ }\Omega \text{m}$,对应制成的金属网格反射率与透射率分别为$|\Gamma {{|}^{2}}=$98.25%与$|\tau {{|}^{2}}=$1.276%.评估结果显示相同尺寸参数的金、银、铜网格具有相近的反射率与透射率.曲率半径${{R}_{2}}=$57.6 mm的球面金属镜被用作法布里-珀罗谐振腔的反射镜,球面金属镜有助于减少微波的散射损失并提高谐振腔模式的稳定性.在镜面上镀一层10 μm厚的金膜用于提高反射率,并且金膜可以作为保护膜防止镜片氧化.图2(d)⑨为一对赫姆霍兹线圈构成的调制场线圈,其位于法布里-珀罗谐振腔两侧.通过外部驱动器向调制场线圈施加交变电流,可在腔内样品处生成交变的调制场磁场.调制场磁场的方向平行于超导磁体产生的外磁场,垂直于由入射微波在样品处产生的磁场.法布里-珀罗谐振腔是一种开放腔,因此在支撑探头的笼式结构长杆上可以方便的安装设备来实现外部场与腔内样品的耦合.位移台系统主要由两个直线位移台和一个旋转位移台组成,图2(d)⑪、⑫所示直线位移台型号为Linear25-z-LR.HV,总行程达16 mm,步进为150 nm,图2(d)所示旋转位移台型号为Rotator25.HV,总行程达320˚,步进为0.01˚.图2(d)⑪所示直线电动位移台用于电动控制球面镜的位置从而调节法布里-珀罗谐振腔的腔长.图2(d)和所示的直线位移台和旋转位移台用于控制样品位置和旋转样品.

按照图2(d)所示结构组装探头,在探头顶部连接矢量网络分析仪的微波端口,通过直线位移台调节法布里-珀罗谐振腔的腔长度来控制法布里-珀罗谐振腔的谐振状态,记录法布里-珀罗谐振腔谐振时的反射曲线与非谐振时的反射曲线,将两次记录的反射曲线作差得到探头的反射曲线.实验测得探头的反射曲线如图4(a)实测值所示,使用公式${{S}_{11}}={{s}_{0}}+\sqrt{2/\text{ }\!\!\pi\!\!\text{ }}\cdot A/w\cdot \exp (-2{{(f-{{f}_{0}})}^{2}}/{{w}^{2}})$对探头的反射曲线进行拟合,其中f为入射的微波频率,${{s}_{0}}$Aw${{f}_{0}}$都是待拟合的常数.拟合曲线如图4(a)虚线所示,拟合结果显示探头的谐振频率${{f}_{0}}=$94.04 GHz,$w=$0.052 GHz,半高宽$\Delta {{f}_{0}}=\sqrt{2\ln 2w}=$0.061 GHz,因此探头的空载品质因数$Q={{f}_{0}}/\Delta {{f}_{0}}=$1 542.如图4(b)所示通过调节直线位移台改变法布里-珀罗谐振腔的腔体长度,记录法布里-珀罗谐振腔谐振频率随位移台移动长度的变化情况,图4(b)中测量所得到的谐振点的横坐标值为${{b}_{0}}-{{d}_{\text{c}}}$${{d}_{\text{c}}}$为位移台移动长度,${{b}_{0}}$为由游标卡尺测量得到的位移台的移动长度与实际腔体长度之间的差距.法布里-珀罗谐振腔的谐振频率拟合式为${{f}_{\text{c}}}=({{q}_{0}}+(2{{p}_{0}}+{{m}_{0}}+1)\text{arccos}\sqrt{{{g}_{\text{1}}}{{g}_{\text{2}}}}/\text{ }\!\!\pi\!\!\text{ )}c/\text{(2}{{L}_{\text{c}}})$,其中腔体长度${{L}_{\text{c}}}={{b}_{0}}-{{d}_{\text{c}}}$,谐振时模序数${{q}_{0}}$满足${{L}_{\text{c}}}={{q}_{0}}\lambda /2$,其中$\lambda $为入射微波波长,不考虑高阶模式(${{p}_{0}}={{m}_{0}}=0$),金属网格的共振共焦参数${{g}_{1}}=1$,球面镜的共振共焦参数${{g}_{\text{2}}}=1-{{L}_{\text{c}}}/{{R}_{\text{2}}}$,拟合结果显示图4(b)中模序数${{q}_{0}}$取值为16到27,拟合曲线与实验记录的谐振点分布相符合.通过直线位移台电动控制法布里-珀罗谐振腔的腔体长度,使得法布里-珀罗谐振腔的谐振频率遍历75~110 GHz.受限于矢量网络分析仪75~110 GHz的工作频率范围,法布里-珀罗谐振腔可遍历的谐振频率无法在更宽的频带测试.直线位移台步进为150 nm,因此对于${{q}_{0}}=$19${{L}_{\text{c}}}=$30.4 mm的法布里-珀罗谐振腔其谐振频率调节步进为0.47 MHz.位移台为钛合金制成,标称的工作温度范围为1.6~400 K,可以兼容低温实验;位移台可以在高达18 T的环境磁场下工作,可以兼容更高频高场的EPR实验,因此本文设计的探头有广泛的可扩展性.

图4

图4   (a)探头反射曲线的测试结果和拟合结果. 其中黑色点为实测数据,虚线为拟合结果. (b)不同直线位移台移动长度下法布里-珀罗谐振腔谐振频率的测试结果和拟合结果. 其中黑色点为实测数据,虚线为拟合结果

Fig. 4   (a) Reflection coefficient of the probe. Black dots are experimental data, and the dashed line stands for the fitting result. (b) Resonance frequency of the Fabry-Perot cavity versus the moving distance of the piezoelectric positioner. Black dots are experimental data, and the dashed lines stand for the fitting result


2 装载法布里-珀罗谐振腔探头的EPR谱仪性能测试

将法布里-珀罗谐振腔探头安装到W波段EPR谱仪,进行连续波EPR实验.谱仪结构如图5所示,主要包括超导磁体(Magnet)、X波段微波桥(X-band microwave bridge)、W波段发射机(W-band microwave transmitter)、W波段接收机(W-band microwave receiver)、探头(Probe)、控制与读出系统(PC).超导磁体在样品处产生的磁场为水平方向,场强范围是0~6 T,可处于静磁场模式或者线性扫描模式.微波桥系统主要用于生成激励信号并接收从谐振腔反射回来的信号,可分为发射机(图5中1框所示)与接收机(图5中2框所示)两部分.其中,发射机主要包括微波源(MW source)、混频器(Mixer)、带通滤波器(Band-Pass Filter,BPF)、放大器(Amplifier)、可调衰减器(Attenuator),用于处理微波信号的合成、滤波、放大、功率调节等,并将产生的激励信号通过环行器(Circulator)馈入探头.接收机主要包括低噪声放大器(Low-Noise Amplifier,LNA)、混频器等,对从谐振腔反射回来的信号进行低噪声放大、混频等处理,将微波信号下变频至X波段,经由X波段微波桥提取出最终的EPR信号.控制与读出系统包括调制场驱动器(Modulation Field Driver)、锁相放大器(Lock-in Amplifier)和必备的电源与通信模块,其中调制场驱动器用于产生调制场磁场,锁相放大器用于实现对连续波EPR信号的相敏检测,并转换EPR信号为数字信号传输至软件端.

图5

图5   W波段顺磁共振谱仪结构图[30]. 超导磁体生成B0场. 矩形框1为W波段发射机. 线路中84.5 GHz的本振微波信号与9~10 GHz的信号混频,生成93.5~94.5 GHz的W波段微波. 矩形框2为W波段接收机,探头出射的信号经过低噪声放大器后与84.5 GHz的本振信号混频,得到X波段信号进入X波段微波桥,经锁相放大器检测转换为数字信号

Fig. 5   Schematic diagram of the W-band EPR spectrometer. The superconducting magnet generates B0. Box 1 stands for the W-band microwave(MW) transmitter. An 84.5 GHz Local Oscillator(LO) microwave signal is mixed with the 9~10 GHz signal to generate a 93.5~94.5 GHz W-band microwave. Box 2 stands for the W-band microwave receiver. The output signal from the probe is amplified by a low-noise amplifier (LNA) and mixed with the 84.5 GHz LO signal. The output signal from the down converter mixer is fed into the X-band microwave bridge. The EPR signal is collected by the lock-in amplifier and converted to the digital signal


2.1 探头调制场幅度标定实验

连续波EPR谱仪使用调制场技术来提高谱线信噪比(Signal-to-Noise Ratio,SNR),调制场幅度的准确性对于谱线分析至关重要,因此需要对调制场幅度进行标定.通过分析不同调制场驱动电压下谱线的线宽来对调制场幅度进行标定.连续波EPR谱线一阶微分谱的实测线宽${{L}_{w}}$与调制场幅度${{B}_{\bmod }}$满足(4)式[31]

${{L}_{w}}=-\frac{2}{\sqrt{3}}{{B}_{pp}}+\sqrt{{{\left( \frac{4}{\sqrt{3}}{{B}_{pp}} \right)}^{2}}+B_{\text{mod}}^{\text{2}}}$

其中${{B}_{pp}}=\sqrt{1+{{\gamma }^{2}}B_{\text{1}}^{\text{2}}{{T}_{1}}{{T}_{2}}}/{{T}_{2}}$γ为电子自旋旋磁比,${{B}_{1}}$为样品处的微波磁场强度,${{T}_{1}}$${{T}_{2}}$为电子自旋的纵向和横向弛豫时间.${{B}_{1}}$主要受微波功率和谐振腔性质影响,${{T}_{1}}$主要受样品性质和温度的影响,${{T}_{2}}$主要受样品性质、温度以及外磁场均匀性的影响.在特定样品、微波功率、谐振腔、温度以及磁场均匀性的情况下,${{B}_{pp}}$为常数.调制场幅度${{B}_{mod}}$与调制线圈的驱动电压${{V}_{mod}}$满足线性关系:${{B}_{mod}}=k{{V}_{\bmod }}$,其中$k$为调制场线圈的磁场转换效率.对于特定的调制场系统,$k$为常数.测试一阶微分谱的实测线宽${{L}_{w}}$与调制线圈驱动电压${{V}_{mod}}$的变化曲线,使用(4)式进行拟合,可以得到${{B}_{pp}}$$k$的拟合值,即可实现对调制场幅度的标定.

实验中使用Mn标样品测试其常温下的W波段连续波EPR谱线,使用上述方法进行调制场幅度的标定.微波功率设定为2.8 mW,调制场线圈驱动电压在0.25~5.00 V区间内取11个点,所得一阶微分谱实测线宽${{L}_{w}}$随驱动电压${{V}_{mod}}$的变化曲线如图6所示.通过拟合得${{B}_{pp}}$为(1 G=10-4 T),电压到调制场磁场幅度转化系数$k$为1.8 G/V.实验中驱动电压最大加至5.00 V,此时调制场幅度为8.9 G.

图6

图6   不同调制场幅度下Mn标样品的W波段EPR谱线一阶微分谱线宽测试结果,其中黑色点为实测数据,虚线为拟合结果

Fig. 6   W-band continuous wave EPR linewidth of Mn(II) measured at different modulation voltage. Black dots are experimental data, and the dashed line stands for the fitting result


2.2 灵敏度评估

使用上述Mn标样品测试谱仪绝对自旋数灵敏度.谱仪绝对自旋数灵敏度通过最小可测量自旋数来评估,最小可测量自旋数代表谱线信噪比为1时对应的样品自旋数目,该值越小谱仪性能越好.对于占据特定空间大小的Mn标样品,连续波EPR一阶微分谱线的信噪比表达式如(5)式所示[32]

$\text{SNR}=\sigma \frac{{{N}_{\text{S}}}}{{{n}_{\text{L}}}}\frac{{{B}_{0}}}{\Delta B}\frac{\sqrt{P}}{{{(1+P/{{P}_{\text{half}}})}^{b/2}}}{{Q}_{\text{L}}}\frac{1}{\sqrt{{{k}_{\text{B}}}T{{f}_{\text{d}}}F}}=\frac{{{N}_{\text{S}}}}{{{n}_{\text{L}}}\Delta B\sqrt{{{f}_{\text{d}}}}}\frac{1}{{{N}_{\min }}}$

其中$\sigma $是由谱仪性能决定的常数,${{N}_{\text{S}}}$是电子自旋数目,${{B}_{0}}$是共振峰对应的磁场强度,$\Delta B$是谱线线宽,P是微波功率大小,${{P}_{\text{half}}}$是半饱和功率,b是与样品线型有关的常数,${{Q}_{\text{L}}}$是探头的有载品质因数,${{k}_{\text{B}}}$是玻尔兹曼常数,T是温度,${{f}_{\text{d}}}$表示接收机的等效噪声带宽,F表示接收机的噪声因子,${{n}_{\text{L}}}=$6(近似认为由于超精细分裂形成6个峰幅度相同),谱仪绝对自旋数灵敏度${{N}_{\min }}$满足(6)式:

$\frac{1}{{{N}_{\min }}}=\sigma {{B}_{0}}\frac{\sqrt{P}}{{{(1+P/{{P}_{\text{half}}})}^{b/2}}}{{Q}_{\text{L}}}\frac{1}{\sqrt{{{k}_{\text{B}}}T{{f}_{\text{d}}}F}}$

对于占据特定空间大小的样品,${{N}_{\min }}$表征了谱仪能够测试到的最小自旋数目,是对谱仪微波桥系统、探头、信号采集系统较为综合的表征.通常选用自旋数已知的样品,测试其连续波谱线,通过(7)式计算谱仪绝对自旋数灵敏度:

${{N}_{\min }}=\frac{{{N}_{\text{S}}}}{{{n}_{\text{L}}}\cdot \text{SNR}\cdot \Delta B\cdot \sqrt{{{f}_{\text{d}}}}}$

选用Mn标样品进行连续波信号测试.Mn标样品的等效哈密顿量为[33]

$H={{g}_{\text{e}}}{{\mu }_{\text{e}}}B{{S}_{\text{z}}}-{{g}_{\text{n}}}{{\mu }_{\text{n}}}B{{I}_{\text{z}}}+IAS$

(8)式中${{g}_{\text{e}}}$表示电子自旋的朗德因子,${{\mu }_{\text{e}}}$表示波尔磁子, ${{g}_{\text{n}}}$表示Mn(II)核自旋的朗德因子, ${{\mu }_{\text{n}}}$表示核磁子,B表示外磁场大小, S表示电子自旋,I表示核自旋, A表示超精细耦合常数.Mn标样品占据主导的跃迁谱线为$|+\frac{1}{2}$, ${{m}_{I}}\rangle \leftrightarrow |-\frac{1}{2}$, ${{m}_{I}}\rangle $, ${{m}_{I}}=\pm \frac{1}{2}$, $\pm \frac{3}{2}$,$\pm \frac{5}{2}$, 跃迁能量为$\Delta E(|+\frac{1}{2}, {{m}_{I}}\rangle \leftrightarrow |-\frac{1}{2},{{m}_{I}}\rangle )={{g}_{\text{e}}}{{\mu }_{\text{e}}}B+A{{m}_{I}}$. ${{m}_{I}}$的不同取值分别对应不同EPR吸收峰,总共六个峰.Mn标样品装载于内径为0.5 mm的样品管内,样品高度为7.12 mm, 总体积为${{V}_{\text{Mn}}}=1.4\text{ m}{{\text{m}}^{\text{3}}}$, 该样品的自旋浓度为$1.1\times {{10}^{12}}\text{ m}{{\text{m}}^{-3}}$, 得总自旋数为${{N}_{\text{S}}}=1.6\times {{10}^{12}}$.

进行Mn标样品连续波信号测试时实验参数如表1所示,得到常温下Mn标样品的W波段连续波EPR谱线如图7(a)所示.Mn标样品共有六个EPR吸收峰,实验扫描得到的EPR谱线符合预期.测量得图7(a)中虚线框内的吸收峰峰值为$67\text{ }\!\!\mu\!\!\text{ V}$,线宽为4.6 G.同表1条件下测得磁场偏共振时的噪声信号如图7(b)所示,测得噪声信号强度的标准差为$0.68\text{ }\!\!\mu\!\!\text{ V}$.

表1   EPR实验参数

Table 1  Parameters of the EPR experiment

名称参数
样品Mn标样品
温度室温
微波功率2.8 mW
时间常数100 ms$({{f}_{\text{d}}}=0.78\text{ Hz)}$
调制场频率100 kHz
调制场幅度4.4 G
扫场范围3.31~3.38 T
扫描点数1750

新窗口打开| 下载CSV


图7

图7   (a)常温下Mn标样品的W波段连续波EPR谱线. 测试虚线框内信号的峰峰值作为信号强度. (b)磁场偏共振下的噪声谱. 微波频率为94.04 GHz,微波功率为2.8 mW,调制场幅度为4.4 G@100 kHz,时间常数为100 ms

Fig. 7   (a) W-band continuous wave EPR spectra of Mn(II) in GaO powder at room temperature. The peak to peak amplitude of the signal within the dashed box is measured as the signal strength. (b) Noise signal measured at off resonance. The MW frequency is 94.04 GHz with an input power of 2.8 mW. The modulation amplitude is 4.4 G@100 kHz. The time constant is 100 ms


通过改变微波功率(0.067~15 mW),其他测试参数同表1,测试了一系列不同微波功率下Mn标样品EPR谱红色虚线框内对应峰的信号强度和磁场偏共振时的噪声信号大小,测试结果如图8所示.从图8中可见,微波功率小于2.8 mW时信号强度与信噪比都随微波功率的增加而增加,当微波功率大于2.8 mW时信号强度随微波功率的增加而增加,但是信噪比随微波功率的增加而减小,微波功率为2.8 mW时信噪比达到最大值(99),通过(7)式得常温下谱仪绝对自旋数灵敏度为6.6×108 spins/(G•$\sqrt{Hz}$).由于当前微波系统所使用的微波源具有一定的相位噪声,当入腔功率大于2.8 mW时,波源相位噪声会随着微波功率的增加而增加,成为限制谱仪信噪比的主要因素,后期会优化微波源相位噪声来进一步提高谱仪灵敏度.

图8

图8   不同样品微波功率下Mn标样品的W波段EPR谱线一阶微分谱峰峰值与信噪比的测试结果

Fig. 8   W-band continuous wave EPR signal intensity and SNR of Mn(II) measured at different microwave power


将国际上已发表的代表性高频EPR谱仪灵敏度与本工作进行比较,结果见表2.序号1、2和3的谱仪分别使用了圆柱形谐振腔、法布里-珀罗谐振腔和非谐振型探头.由于仪器的灵敏度数据在不同温度下测得,为了合理比较需将灵敏度修正为室温灵敏度.根据电子自旋的极化度来修正信号强度,电子自旋的极化度${{\rho }_{\text{e}}}=(1-\exp (-{{g}_{\text{e}}}{{\mu }_{\text{e}}}{{B}_{0}}/{{k}_{\text{B}}}T))/(1+\exp (-{{g}_{\text{e}}}{{\mu }_{\text{e}}}{{B}_{0}}/{{k}_{\text{B}}}T))$,极化的电子自旋数目${{N}_{\text{T}}}={{\rho }_{\text{e}}}{{N}_{\min }}$,以此为标准将灵敏度修正为室温灵敏度,修正后结果见表2第6列,其中室温灵敏度代指理论上该谱仪在室温条件下的绝对自旋数灵敏度,而绝对自旋数灵敏度是通过最小可测量自旋数来评估的,室温灵敏度数值越小谱仪越灵敏.

表2   本文工作与现有EPR谱仪对比

Table 2  Comparison of this work with the existing work

序号频率/GHz探头种类灵敏度/
(spins/(G•$\sqrt{Hz}$)
极化度室温灵敏度/
(spins/(G•$\sqrt{Hz}$)
1[34]94圆柱形谐振腔$2.0\times 1{{0}^{7}}$@300 K0.7515%$2.0\times 1{{0}^{7}}$
2[22]95法布里-珀罗谐振腔$3.0\times 1{{0}^{8}}$@130 K1.753%$7.0\times 1{{0}^{8}}$
3[35]94非谐振$1.0\times 1{{0}^{9}}$@1.5 K90.57%$1.2\times 1{{0}^{11}}$
4(本工作)94法布里-珀罗谐振腔$6.6\times 1{{0}^{8}}$@300 K0.7515%$6.6\times 1{{0}^{8}}$

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谱仪1使用了具有高品质因数和高填充系数的圆柱形谐振腔,其灵敏度是这四台谱仪中的最优灵敏度.本工作与使用了法布里-珀罗谐振腔的谱仪2灵敏度相当,远优于使用了非谐振结构探头的谱仪3的灵敏度.通过典型尺寸评估谐振腔的体积,对于谱仪1的TE011模式的圆柱形谐振腔,圆柱底面半径为${{a}_{\text{cy}}}$,圆柱形谐振腔腔长为$2{{a}_{\text{cy}}}$,则谐振时入射微波波长$\lambda =1.52{{a}_{\text{cy}}}$,因此整个圆柱形谐振腔体积${{V}_{\text{cy1}}}=1.88{{\lambda }^{3}}$;对于谱仪2的TEM008模式的法布里-珀罗谐振腔,腔内基模高斯光束光斑半径近似为$2\lambda $,法布里-珀罗谐振腔腔长为$4\lambda $,因此法布里-珀罗谐振腔体积${{V}_{\text{FP2}}}=50.3{{\lambda }^{3}}$;对于谱仪4(本文工作)的TEM0019模式的法布里-珀罗谐振腔,法布里-珀罗谐振腔腔长为$9.5\lambda $,因此法布里-珀罗谐振腔体积${{V}_{\text{FP4}}}=119{{\lambda }^{3}}$.本工作的谐振腔体积大于谱仪2的谐振腔体积,且远大于谱仪1的谐振腔体积,因此本工作的谐振腔探头可装样空间更大,这对低自旋密度样品的测试是有利的.

3 结论

本文设计了一款基于法布里-珀罗谐振腔的W波段EPR谱仪探头,探头主要包括法布里-珀罗谐振腔及波纹波导.该探头能够在W波段工作,空载品质因数为1 542,由于在样品台附近的笼式结构支撑长杆上预留了空间,可以方便的实现与外部场的耦合.使用Mn标样品进行常温下W波段连续波EPR实验,标定得到装载该探头的EPR谱仪绝对自旋数灵敏度为6.6×108 spins/(G•$\sqrt{Hz}$),与国际上基于法布里-珀罗谐振腔探头的EPR谱仪相当.且本工作创新设计了电动调谐装置,实现了对谐振频率在75 GHz到110 GHz范围内按照0.47 MHz步进进行精度调节的功能,相比于传统的机械调节方案,具有稳定高、可重复性强、数字化控制程度高等优势.

装载该探头的EPR谱仪所测得的EPR谱线线宽偏大,这源于黄铜材料的波纹波导退火处理后剩磁仍然过大导致磁场均匀性有限,这在一定程度限制了EPR谱仪性能.下一步工作将对腔体附近的机械结构和材料进行优化,利用紫铜材料制作波导并减少波导侧壁厚度以减少波导的剩磁,来提高磁场的均匀性.同时基于该探头开展脉冲EPR实验,并集成电子-核双共振功能、光照功能等,发挥法布里-珀罗腔的优势,将W波段EPR谱仪应用于金属蛋白分析、生物分子结构解析、量子计算等研究方向.

利益冲突

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