2. The susceptibility matrix

#### 2.1 Magnetic dipole precesses around the applied magnetic field

The properties of ferrites are very intriguing. Without a DC bias magnetic field H0, the magnetic dipoles of ferrites are randomly orientated. They exhibit dielectric properties only. The dielectric loss can be high or low depending on the loss tangent of the soft ferrites. Interestingly, when the DC bias magnetic field is strong enough, and the ferrite is magnetically saturated, the magnetic dipole will precess around the DC bias field at a frequency called the Larmor frequency (ω0∝H0). Waves with different circular polarizations will corotate or counter-rotate with the precession of the magnetic dipoles.

Figure 2 shows the Larmor precession with the circularly polarized fields [7]. Circular polarization may be referred to as right handed or left handed, depending on the direction in which the electric (magnetic) field vector rotates. For a

Ferrite Materials and Applications DOI: http://dx.doi.org/10.5772/intechopen.84623

#### Figure 2.

are ceramic-like materials with specific resistivities that may be as much as 10<sup>14</sup> greater than that of metals and with dielectric constants around 10 to 16 or greater. Ferrites are made by sintering a mixture of metal oxides and have the general chemical composition MOFe2O3, where M is a divalent metal such as Mn, Mg, Fe, Zn, Ni, Cd, etc. Relative permeabilities of several thousands are common [5, 6]. The magnetic properties of ferrites arise mainly from the magnetic dipole moment

The hysteresis (B-H) curves for (a) hard ferrimagnetism and (b) soft ferrimagnetism. The remnant polarization (Br) and the coercive field (Hc) for the hard ferrites should be as large as possible. On the other hand, for the soft ferrites, the remnant polarization (Br) and the coercive field (Hc) are very small or even close

The magnetic dipole moment precesses around the applied DC magnetic field by treating the spinning electron as a gyroscopic top, which is a classical picture of the magnetization process. This picture also explains the anisotropic magnetic properties of ferrites, where the permeability of the ferrite is not a single scalar quantity, but instead is a generally a second-rank tensor or can be represented as a matrix. The left and right circularly polarized waves have different propagation constant along the direction of the external magnetic field, resulting in the nonreciprocity of a propagating wave. Since the permeability should be treated as a tensor (matrix), not a scalar permeability, it is generally much difficult to understand and to have

The properties of ferrites are very intriguing. Without a DC bias magnetic field H0, the magnetic dipoles of ferrites are randomly orientated. They exhibit dielectric properties only. The dielectric loss can be high or low depending on the loss tangent of the soft ferrites. Interestingly, when the DC bias magnetic field is strong enough, and the ferrite is magnetically saturated, the magnetic dipole will precess around the DC bias field at a frequency called the Larmor frequency (ω0∝H0). Waves with different circular polarizations will corotate or counter-rotate with the precession of

Figure 2 shows the Larmor precession with the circularly polarized fields [7]. Circular polarization may be referred to as right handed or left handed, depending

on the direction in which the electric (magnetic) field vector rotates. For a

2.1 Magnetic dipole precesses around the applied magnetic field

associated with the electron spin [2].

Electromagnetic Materials and Devices

Figure 1.

to zero.

intuition, even for the researchers.

2. The susceptibility matrix

the magnetic dipoles.

138

Larmor precession of a magnetic moment m around the applied DC bias field H<sup>0</sup> (¼ H0z^) with (a) a righthand circularly polarized (RHCP) wave and (b) a left-hand circularly polarized (LHCP) wave. The frequency of the Larmor precession in both cases are the same, i.e., the Larmor frequency ω<sup>0</sup> ¼ μ<sup>0</sup> ð Þ γH<sup>0</sup> . H<sup>þ</sup> t and H� <sup>t</sup> are the transverse components of the incident waves which rotate clockwise (RHCP) and counterclockwise (LHCP) from the source viewpoint looking in the direction of propagation. The thumb points the direction of the wave propagation, and the fingers give the rotation of the transverse components [7].

right-hand circularly polarized (RHCP) wave, the fields rotate clockwise at a given position from the source looking in the direction of propagation. The magnetic dipole moment m processes around the H0 field vector, like a top spinning precess around the z-axis at the Larmor frequency ω0. The spinning property depends on the applied DC bias magnetic field. Figures 2(a) and (b) shows the RHCP and LHCP waves with the gyrating frequency of ω. When the RHCP wave is propagating along the direction of the DC bias field, it corotates with the precession of the magnetic dipole moments. On the other hand, the left-hand circularly polarized (LHCP) wave will counter-rotate with the precession of the dipole moments.

A linearly polarized incident wave can be decomposed into RHCP and LHCP waves of equal amplitude. The orientation of the linearly polarized wave changes after the wave propagates a certain distance because of the distinct propagation constants. The phenomenon is the famous Faraday's rotation [5, 6]. This unique property has various applications, such as phase shifters, isolators, and circulators. However, it is difficult to follow for students and even researchers in that the permeability is a tensor, not just a simple proportional constant.

Here we consider the simplest case for the pedagogic purpose—a circularly polarized plane wave is normally incident upon a semi-infinite medium. The wave characteristics such as the propagation constant k and the wave impedance Z are associated with the permeability μ, which is a tensor for the ferrite medium [5]. By finding the preferred eigenvalues, it will be shown that the properties of μ depend on the DC bias field H0, the saturated magnetization Ms, and the operating frequency ω. By adjusting the frequency of the incident wave, i.e., ω, the permeability μ changes, especially close to the Larmor frequency (ω0). Such an effect is called the ferrite magnetic resonance (FMR) or gyromagnetic resonance [7].

### 2.2 Derivation of the susceptibility matrix

The permeability μrð Þ ω is a tensor. Note that the permittivity εrð Þ ω can be expressed in a tensor as well, but in the region of interest around 10 GHz, it can be treated as a complex proportional constant for many ceramics. Many microwave textbooks and literature have elaborated the derivation of the permeability tensor [5–7]. In this paper, a more accessible interpretation of the permeability tensor is provided. The magnetic properties of a material are due to the existence of magnetic dipole moment m, which arise primarily from its (spin) angular momentum s. The magnetic dipole moment and angular momentum have a simple relation, m ¼ �γs, where <sup>γ</sup> is the gyromagnetic ratio (<sup>γ</sup> <sup>¼</sup> <sup>e</sup>=<sup>m</sup> <sup>¼</sup> <sup>1</sup>:<sup>759</sup> � <sup>10</sup><sup>11</sup> <sup>C</sup>=kg). When a DC bias magnetic field B0 (¼ μ0H0) is present, the torque τ exerted on the magnetic dipole moment is

$$
\boldsymbol{\pi} = \mathbf{m} \times \mathbf{B}\_0 = \mu\_0 \mathbf{m} \times \mathbf{H}\_0. \tag{1}
$$

M ¼ ½ � χ H ¼

The permeabilities of the RHCP and LHCP waves are

Therefore, this study will mainly focus on the RHCP wave.

ΔHμ0γ 2ω<sup>0</sup>

<sup>r</sup> ¼ 1 þ

0 @

the permeability for the RHCP wave now reads

μ<sup>þ</sup>

3. Characterization of ferrite materials

where <sup>χ</sup>xx <sup>¼</sup> <sup>χ</sup>yy <sup>¼</sup> <sup>ω</sup>0ωm<sup>=</sup> <sup>ω</sup><sup>2</sup>

Ferrite Materials and Applications

a much more dramatic response.

[2, 3]. Since

141

eigenvalues of the susceptibility matrix are

DOI: http://dx.doi.org/10.5772/intechopen.84623

χxx χxy 0 χyx χyy 0 0 00

<sup>0</sup> � <sup>ω</sup><sup>2</sup> � � and <sup>χ</sup>xy ¼ �χyx <sup>¼</sup> <sup>j</sup>ωωm<sup>=</sup> <sup>ω</sup><sup>2</sup>

3 7 5

H, (9)

<sup>ω</sup><sup>0</sup> � <sup>ω</sup>, (10)

<sup>ω</sup><sup>0</sup> <sup>þ</sup> <sup>ω</sup>: (11)

� �, (12)

� �: (13)

, (14)

A: (15)

<sup>0</sup> � <sup>ω</sup><sup>2</sup> � �. The

2 6 4

<sup>χ</sup><sup>þ</sup> <sup>¼</sup> <sup>ω</sup><sup>m</sup>

<sup>χ</sup>� <sup>¼</sup> <sup>ω</sup><sup>m</sup>

The eigenvectors corresponding to these two eigenvalues are the right-hand circularly polarized wave (RHCP, denoted as +) and the left-hand circularly polarized wave (LHCP, denoted as -), respectively. The symbols, + and -, represent positive helicity and negative helicity, respectively. The LHCP wave has a relatively mild response over the entire frequency range. On the contrary, the RHCP wave has

<sup>μ</sup><sup>þ</sup> <sup>¼</sup> <sup>μ</sup><sup>0</sup> <sup>1</sup> <sup>þ</sup> <sup>ω</sup><sup>m</sup>

<sup>μ</sup>� <sup>¼</sup> <sup>μ</sup><sup>0</sup> <sup>1</sup> <sup>þ</sup> <sup>ω</sup><sup>m</sup>

Eq. (12) has a singularity when the wave frequency ω is equal to the Larmor frequency ω0. This phenomenon is called the ferri-magnetic resonance (FMR, or called gyromagnetic resonance) [6]. On the contrary, Eq. (13) is relatively mild.

For a resonant cavity with a quality factor (Q), the loss effect can be introduced by using the complex resonant frequency ω0ð Þ 1 � i=2Q . By analogy with the resonant cavity, the loss part can be calculated by using the complex frequency ω<sup>0</sup> ! ω<sup>0</sup> 1 � iΔHμ<sup>0</sup> ð Þ γ=2ω<sup>0</sup> , where ΔH is the ferrimagnetic resonance linewidth

<sup>¼</sup> <sup>Δ</sup>Hμ0<sup>γ</sup>

<sup>2</sup>H0μ0<sup>γ</sup> <sup>¼</sup> <sup>Δ</sup><sup>H</sup>

ω<sup>m</sup> ω0

<sup>1</sup> � <sup>ω</sup> ω0 � � <sup>þ</sup> <sup>i</sup> <sup>Δ</sup><sup>H</sup>

To conduct a complete simulation of a ferrite device, we need to know its complex permittivity, the saturation magnetization, and the resonance linewidth. We will discuss how to characterize the ferrite's properties in the next section.

Here we will discuss the measurement of the most important properties of ferrites, including the dielectric properties (ε<sup>r</sup> þ iεi), the saturation magnetization

2H<sup>0</sup>

2H<sup>0</sup>

1

ω<sup>0</sup> � ω

ω<sup>0</sup> þ ω

Since the torque is equal to the time change rate of the angular momentum, we have

$$
\mathbf{r} = \frac{d\mathbf{s}}{dt} = \frac{-\mathbf{1}}{\chi} \frac{d\mathbf{m}}{dt} \,. \tag{2}
$$

By comparing Eqs. (1) and (2), we obtain

$$\frac{d\mathbf{m}}{dt} = -\mu\_0 \gamma \mathbf{m} \times \mathbf{H}\_0. \tag{3}$$

A large number of the magnetic dipole moment m per unit volume give rise to an average macroscopic magnetic dipole moment density M. The torque exerting on the magnetization per unit volume M due to the magnetic flux H has the same form as Eq. (3):

$$\frac{d\mathbf{M}}{dt} = -\mu\_0 \gamma \mathbf{M} \times \mathbf{H}.\tag{4}$$

M and H in Eq. (4) differ slightly from m and H<sup>0</sup> in Eq. (3) in that M and H can further be divided into two parts: the DC term and the high-frequency AC term. The DC term is, in general, much larger than the AC term. The applied DC bias magnetic field H<sup>0</sup> is assumed to be in the z-direction. When H<sup>0</sup> is strong enough, the magnetization will be saturated, denoted as Ms which aligns with the direction of H0. If the AC term just polarizes in the transverse direction (i.e., the xy plane), the external magnetic bias field and the magnetization can be written as,

$$\mathbf{H} = H\_{\mathbf{x}}\hat{\mathbf{x}} + H\_{\mathbf{y}}\hat{\mathbf{y}} + H\_0\hat{\mathbf{z}},\tag{5}$$

$$\mathbf{M} = M\_{\mathbf{x}} \hat{\mathbf{x}} + M\_{\mathbf{y}} \hat{\mathbf{y}} + M\_{\mathbf{s}} \hat{\mathbf{z}}.\tag{6}$$

Since the AC terms have an exp(�iωt) dependence, by substituting Eq. (5) and (6) into Eq. (4) the transverse component terms read

$$(\alpha\_0^2 - \alpha^2)\mathbf{M}\_{\mathbf{x}} = \alpha\_0 \alpha\_m H\_{\mathbf{x}} + j\alpha \alpha\_m H\_{\mathbf{y}};\tag{7}$$

$$(\alpha\_0^2 - \alpha^2)\mathcal{M}\_\mathcal{Y} = -j\alpha\alpha\_m H\_\mathcal{x} + \alpha\iota\_0\alpha\_m H\_\mathcal{Y} \tag{8}$$

where ω<sup>0</sup> ¼ μ0γH<sup>0</sup> and ω<sup>m</sup> ¼ μ0γMs. In matrix representation, Eq. (7) and (8) can be rewritten as

Ferrite Materials and Applications DOI: http://dx.doi.org/10.5772/intechopen.84623

2.2 Derivation of the susceptibility matrix

Electromagnetic Materials and Devices

moment is

have

as Eq. (3):

The permeability μrð Þ ω is a tensor. Note that the permittivity εrð Þ ω can be expressed in a tensor as well, but in the region of interest around 10 GHz, it can be treated as a complex proportional constant for many ceramics. Many microwave textbooks and literature have elaborated the derivation of the permeability tensor [5–7]. In this paper, a more accessible interpretation of the permeability tensor is provided. The magnetic properties of a material are due to the existence of magnetic dipole moment m, which arise primarily from its (spin) angular momentum s. The magnetic dipole moment and angular momentum have a simple relation, m ¼ �γs, where <sup>γ</sup> is the gyromagnetic ratio (<sup>γ</sup> <sup>¼</sup> <sup>e</sup>=<sup>m</sup> <sup>¼</sup> <sup>1</sup>:<sup>759</sup> � <sup>10</sup><sup>11</sup> <sup>C</sup>=kg). When a DC bias magnetic field B0 (¼ μ0H0) is present, the torque τ exerted on the magnetic dipole

Since the torque is equal to the time change rate of the angular momentum, we

dt <sup>¼</sup> �<sup>1</sup> γ dm

A large number of the magnetic dipole moment m per unit volume give rise to an average macroscopic magnetic dipole moment density M. The torque exerting on the magnetization per unit volume M due to the magnetic flux H has the same form

M and H in Eq. (4) differ slightly from m and H<sup>0</sup> in Eq. (3) in that M and H can further be divided into two parts: the DC term and the high-frequency AC term. The DC term is, in general, much larger than the AC term. The applied DC bias magnetic field H<sup>0</sup> is assumed to be in the z-direction. When H<sup>0</sup> is strong enough, the magnetization will be saturated, denoted as Ms which aligns with the direction of H0. If the AC term just polarizes in the transverse direction (i.e., the xy plane),

Since the AC terms have an exp(�iωt) dependence, by substituting Eq. (5) and

where ω<sup>0</sup> ¼ μ0γH<sup>0</sup> and ω<sup>m</sup> ¼ μ0γMs. In matrix representation, Eq. (7) and (8)

<sup>τ</sup> <sup>¼</sup> <sup>d</sup><sup>s</sup>

dm

dM

the external magnetic bias field and the magnetization can be written as,

(6) into Eq. (4) the transverse component terms read

ω2

ω2

can be rewritten as

140

By comparing Eqs. (1) and (2), we obtain

τ ¼ m � B0 ¼ μ0m � H0: (1)

dt ¼ �μ0γ<sup>m</sup> � H0: (3)

dt ¼ �μ0γ<sup>M</sup> � <sup>H</sup>: (4)

H ¼ Hxx^ þ Hyy^ þ H0z^, (5) M ¼ Mxx^ þ Myy^ þ Msz^: (6)

<sup>0</sup> � <sup>ω</sup><sup>2</sup> Mx <sup>¼</sup> <sup>ω</sup>0ωmHx <sup>þ</sup> <sup>j</sup>ωωmHy; (7)

<sup>0</sup> � <sup>ω</sup><sup>2</sup> My ¼ �jωωmHx <sup>þ</sup> <sup>ω</sup>0ωmHy, (8)

dt : (2)

$$\mathbf{M} = [\boldsymbol{\chi}] \mathbf{H} = \begin{bmatrix} \boldsymbol{\chi}\_{xx} & \boldsymbol{\chi}\_{xy} & \mathbf{0} \\ \boldsymbol{\chi}\_{yx} & \boldsymbol{\chi}\_{yy} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{0} \end{bmatrix} \mathbf{H}, \tag{9}$$

where <sup>χ</sup>xx <sup>¼</sup> <sup>χ</sup>yy <sup>¼</sup> <sup>ω</sup>0ωm<sup>=</sup> <sup>ω</sup><sup>2</sup> <sup>0</sup> � <sup>ω</sup><sup>2</sup> � � and <sup>χ</sup>xy ¼ �χyx <sup>¼</sup> <sup>j</sup>ωωm<sup>=</sup> <sup>ω</sup><sup>2</sup> <sup>0</sup> � <sup>ω</sup><sup>2</sup> � �. The eigenvalues of the susceptibility matrix are

$$\chi^{+} = \frac{\alpha\_m}{\alpha\_0 - \alpha},\tag{10}$$

$$\chi^- = \frac{a\_m}{a\_0 + a}.\tag{11}$$

The eigenvectors corresponding to these two eigenvalues are the right-hand circularly polarized wave (RHCP, denoted as +) and the left-hand circularly polarized wave (LHCP, denoted as -), respectively. The symbols, + and -, represent positive helicity and negative helicity, respectively. The LHCP wave has a relatively mild response over the entire frequency range. On the contrary, the RHCP wave has a much more dramatic response.

The permeabilities of the RHCP and LHCP waves are

$$
\mu^{+} = \mu\_0 \left( \mathbf{1} + \frac{a\_m}{a\_0 - a} \right),
\tag{12}
$$

$$
\mu^- = \mu\_0 \left( 1 + \frac{\alpha\_m}{\alpha\_0 + \alpha} \right). \tag{13}
$$

Eq. (12) has a singularity when the wave frequency ω is equal to the Larmor frequency ω0. This phenomenon is called the ferri-magnetic resonance (FMR, or called gyromagnetic resonance) [6]. On the contrary, Eq. (13) is relatively mild. Therefore, this study will mainly focus on the RHCP wave.

For a resonant cavity with a quality factor (Q), the loss effect can be introduced by using the complex resonant frequency ω0ð Þ 1 � i=2Q . By analogy with the resonant cavity, the loss part can be calculated by using the complex frequency ω<sup>0</sup> ! ω<sup>0</sup> 1 � iΔHμ<sup>0</sup> ð Þ γ=2ω<sup>0</sup> , where ΔH is the ferrimagnetic resonance linewidth [2, 3]. Since

$$\frac{\Delta H\mu\_0\chi}{2\alpha\_0} = \frac{\Delta H\mu\_0\chi}{2H\_0\mu\_0\chi} = \frac{\Delta H}{2H\_0},\tag{14}$$

the permeability for the RHCP wave now reads

$$\mu\_r^+ = \left( \mathbf{1} + \frac{\frac{\alpha\_0}{a\alpha\_0}}{\left(\mathbf{1} - \frac{\alpha}{a\alpha\_0}\right) + i\frac{\Delta H}{2H\_0}} \right). \tag{15}$$

To conduct a complete simulation of a ferrite device, we need to know its complex permittivity, the saturation magnetization, and the resonance linewidth. We will discuss how to characterize the ferrite's properties in the next section.

### 3. Characterization of ferrite materials

Here we will discuss the measurement of the most important properties of ferrites, including the dielectric properties (ε<sup>r</sup> þ iεi), the saturation magnetization (Ms or 4πMs), and the resonance linewidth (ΔH). The behavior of the spin wave linewidth should be considered when the field strength of an electromagnetic wave exceeds a threshold value, that is, the high-power condition. For the general purpose, only the first three properties will be used in the ferrite simulation.

3.2 Saturation magnetization

Ferrite Materials and Applications

DOI: http://dx.doi.org/10.5772/intechopen.84623

3.3 Resonance linewidth

However, obtaining the relation of χ″

commonly used technique [9, 12].

H0, where χ″

Figure 4.

143

Ferrites have a strong response to the applied magnetic field. The magnetic properties of ferrites arise mainly from the magnetic dipole moment associated with the electron spin. Relative permeabilities of several thousands are common. The saturation magnetization (Ms or 4πMs) of a ferrite plays a key role as shown in Section 2. Researchers or engineers use the saturation magnetization as a design parameter that enters into the initial selection of a ferrimagnetic material for microwave device applications. Typical ferrimagnets exhibit values of 4πMs between 300 gauss (G) and 5000 G. Static or low-frequency methods are generally

used to measure 4πMs [12]. From the measured hysteresis loop as shown in

Note that the saturation magnetization is denoted as Ms in the SI unit, but since the values are generally displayed in Gaussian unit (gauss, G), 4πMs is commonly used. Also, the internal bias H<sup>0</sup> is different from the applied H-field (Ha). Demagnetization factor should be considered [5, 6]. The demagnetization factor allows us to calculate the H-field inside the sample denoted as H0. In all, measurement of the saturation magnetization from the dynamic hysteresis loop characteristics can be

The loss of ferrite material is related to the linewidth, ΔH, of the susceptibility

xx has decreased to half of its peak value. For a fixed microwave

xx versus

xx versus H0, where χ″

xx versus H<sup>0</sup> is not easy. Here we adopt another

xx versus

xx

curve near resonance. Consider the imaginary part of the susceptibility χ″

The linewidth, ΔH, is defined as the width of the curve of χ″

the bias field H0. The linewidth ΔH is defined as the width of the curve of χ″

frequency ω, resonance occurs when ω<sup>0</sup> ¼ μ0γHr, such that ω ¼ ω<sup>0</sup> ¼ μ<sup>0</sup> ð Þ γHr .

has decreased to half its peak value. This is the idea that is introduced in [5].

The hysteresis curve regarding the magnetization M and the internal bias H0. When the applied internal magnetic field H<sup>0</sup> is large enough, the magnetization will be saturated, denoted as (Ms or 4πMs). When H<sup>0</sup> decreases to zero, the remnant polarization is denoted as Mr. The polarization will change sign (from positive to

negative) when H<sup>0</sup> is greater than �Hc which is called the coercive field.

Figure 4, one can determine the saturation magnetization Ms.

used for the design and simulation of ferrite devices.

### 3.1 Dielectric properties

Ferrites are ceramic-like materials with relative dielectric constants around 10 to 16 or greater. The resistivities of ferrites may be as high as 1014 greater than that of metals. Since ferrites are dielectric materials. The dielectric properties (ε<sup>r</sup> þ iεi) always play an important role with or without the influence of the magnetic field. The perturbation method is the most commonly employed resonant technique [8, 9]. The perturbation method is very good for small-size and low-dielectric samples. When measuring the high-dielectric samples, however, the fields and the resonant frequency change drastically. The perturbation technique may lead to a reduced accuracy. Recently, the field enhancement method was proposed [10, 11]. The field enhancement method operates at a condition opposite to the perturbation method. The resonant frequency and quality factor alter significantly and depend on not only the geometry of the cavity but the sample's size and complex permittivity as well. Luckily, both the perturbation method and the field enhancement method agree well for samples with the dielectric constant below 50, which is suitable for most of the ferrites.

Figure 3 shows the ideal of the field enhancement method. Figure 3(a) shows the resonant frequency as functions of the dielectric constant (εr) using a simulation setup as in Figure 3(b). The ingot-shaped sample has a diameter of 16.00 mm and thickness of 5.00 mm. The solid blue line depicts the simulation result for the field enhancement method. From the measured resonant frequency, we can derive the corresponding dielectric constant. On the other hand, the dashed black line is obtained using a sample with the same diameter but much thinner in thickness of 1.0 mm. The response of the 1-mm-thick sample quite resembles the perturbation method. The imaginary part of the permittivity (εi) or the loss tangent ( tan δ ¼ εi=εr) can then be determined from the measured resonant frequency and the quality factor. The field enhancement method has very wide measuring range from unity to high-κ dielectrics and from lossless to lossy materials [10, 11].

#### Figure 3.

(a) Resonant frequency versus dielectric constant based on full-wave simulations. The solid curve can be divided into three regions: low, transition, and ultrahigh. The dashed line is simulated with a much thinner sample of 1.00 mm in thickness, which exhibits the properties similar to those of perturbation. (b) Schematic diagram of the field enhancement method. It consists of a cylindrical resonant cavity and a metal rod. The sample is placed on the top of the metal rod. The metal rod focuses and enhances the electric field significantly. An SubMiniature version A (SMA) 3.5-mm adapter couples the wave from the top of the cavity [11].
