## 1 Introduction  
Complementary metaresonator-based microwave sensors have high sensitivity, fast response time, broad sensing range, inexpensive fabrication, and high accuracy and are appropriate for diverse climates; therefore, these sensors are very popular in research and industrial applications. These sensors can be employed for the identification of electromagnetic properties of gases [1, 2], liquids [3, 4], and solids [5, 6] in various frequency band-Metamaterials were theoretically predicted by [PERSON] in 1968 [7] and experimentally verified by [PERSON] in 2000 [8]. The main components of metamaterials are split-ring resonators (SRRs) [9] and complementary split-ring resonators (CSRRs) [10]. Recently, the development of theoretical and experimental models within the scope of microwave sensing using SRR and CSRR has led to the potential applications for biomedical [11, 12], chemical [13, 14], and electronic sector [15, 16].  
SRR was a superconducting resonator [17] before its introduction as a microstructure with imaginary magnetic permeability components. Initially, it was used to demonstrate left-handed behavior [18], negative refraction [19], backward wave radiation [20], negative group velocity [21], stopband [22], and passband filters [23]. Later on it was used to design alignment sensor [24], biosensor [25], displacement sensor [26], microfluidic sensor [27], rotation sensor [28], strain sensor [29], thin-film sensor [30], and velocity sensor [31]. SRR based sensors have a very narrow region for the electric field concentration between the splits at the resonance, which interacts with the material under test (MUT). Thesesensors are not suitable for testing large samples due to the small sensing area; CSRR solves this problem. By applying the babinet principle on SSR [32], its dual counterpart was introduced as CSRR. Initially, CSRR was used to design metamaterial transmission lines [33], passband [34] and stopband filters [35]. Later on, it was used to measure dielectric loss tangent [36], liquid characterization [37], thickness measurement [38], and evaluation of permittivity [39].  
In the recent past, several techniques have been proposed to calculate the dielectric properties of oil samples [40; 41; 42; 43]. In [40], a single port sensor based on CSRR is presented to detect adulteration of edible oils with a minimum frequency shift of 14 MHz in the X band. An analytical method is proposed in [41] to calculate the dielectric constant and loss tangent of oils based on a CSRR sensor with a resonant frequency of 2.5 GHz and an average sensitivity of 3.58%. In [42], a metamaterial sensor operating at millimeter-wave is designed to evaluate the oils and their chemical characteristics with a frequency shift of 1.12 GHz. A submersible single-port microwave sensor is presented in [43] to evaluate the complex permittivity of oils based on multiple complementary SRR with a resonant frequency of 8.49 GHz and an average sensitivity 7.25%. However, the aforementioned sensors have sensitivity limitations due to noncompact structure design and minor interaction of electromagnetic fields with the OUT. Furthermore, most of the proposed sensors for oil testing are based on single resonance frequency, which causes low precision and less accuracy in measurement.  
This paper proposes a dual notch meteresonator sensor with high sensitivity, compact size, low cost, and convenient operation. The proposed complementary mirror-symmetric S resonator (CMSSR) shows dual notch resonance in the C and X bands. The CMSSR is coupled electrically with the microstrip transmission line for excitation, and a Teflon container is attached to the CMSSR, which makes it suitable for oil characterization. The unique design of the proposed meteresonator sensor and simulation analysis is explained in Section 2. Measurement setup and characterization of oil samples are accomplished in Section 3. Mathematical modeling of the measured data is performed in Section 4. Finally, the main results and technical contributions are summarized in Section 5.