1. INTRODUCTION
All-optical fiber based-sensors, due to their intrinsic characteristic of simple, compact size, cost-effective, resistance to electromagnetic interference, good hostility to corrosion, durability, flexibility, accuracy and so on  [1] have interested considerable attention in many applications such as medical applications  [2–4], chemical  [5], and environmental  [6]. They have been effectively applied as refractive index (RI)  [7,8], temperature  [9], displacement  [10], environmental monitoring  [11], humidity  [12,13], strain  [14], acoustic  [15], force  [16] sensors and so on. Optical fiber based-refractive-index (RI) sensors or refractometers are actually beneficial in a diversity of industrial applications like chemical or biological sensors [8]. In comparison to conventional refractive index sensors like optical path measurement method, Optical fiber based-RI sensors have drawn distinct concentration owing to the compact size, high sensitivity and the appropriateness for remote sensing  [17,18].
To date, a series of RI sensors have been fabricated based on the long-period fiber grating (LPFG)  [19], fiber Bragg grating (FBG)  [20], Fabry-Perot interferometer (FPI) [12], Mach-Zehnder interferometer (MZI)  [21], photonic crystal fiber (PCF)  [1], and single-mode fiber-coreless fiber-single mode fiber (SCS)  [22].
But, most of these fiber structures are exposed to damage that causes the fabrication process more complex and costly. Single-mode–multimode–single-mode (SMS) fiber configuration which is usually constructed by splicing a multimode fiber (MMF) or PCF section between two single-mode fiber (SMF) section  [1,23,24]. The conventional method to enhance the sensitivity of an in-line MZI sensor is by enlarging its cavity length  [20]. However, the long cavity leads to more difficult to package the sensor. Herein, CLF which is operational analogous to MMF has won more attraction of RI sensing application, in which the sensitivity can be improved by reducing the diameter of the CLF  [12]. The RI-SCS configuration depends on the principle of multimode interference (MMI). As the core mode of the propagated in single-mode fiber section, a number of high-order modes are excited and guided through the CLF. Then, at the other splicing point, the high-order modes are coupled and backward to the core fiber of the single-mode fiber  [25]. Additionally, when the light passes via the CLF which functions as the sensing area, the evanescent wave absorption varies with the variation in the surrounding environmental medium. This causes to the varies into the RI of the outer medium (which acts as a cladding layer) and subsequently the output transmission signal will be modified  [26].
In this work, the RI sensing structure comprises of single-mode fiber-coreless fiber-single mode fiber (SCS) configuration and the encirclement refractive index behaves as the cladding of the CLF. The sensor performance of SCS configuration with different CLF diameters and lengths has been investigated. The CLF diameter is decreased by the chemical etching method. The better sensor sensitivity was attained when the CLF diameter was 50 μm.
SENSING PRINCIPLE
The SCS sensor structure comprises of two segment of single-mode fiber (SMF) and one segment of CLS in between. The three segment are spliced together. The schematic diagram of the SCS sensor configuration is depicted in the Fig.1 (A-B). As the light injected into the first section of SMF, the redoubled high-order linear polarization (LP) modes have been excited. Then the light travels through SMF-CLF at the first splicing point, high-order modes will be propagated via the CLF with diverse propagation constants. After that, as the light propagated through the second splicing point of CLF-SMF, these modes will be reconnected to create the modal interference. Consequently, the characteristic of the output spectrum is varied with contrast to the input spectrum. The modal field shapes for these modes (normalized with regard to the all cross-section of the fiber) can excellently be estimated by that of an infinitely total parabolic media.
For a standard multi-mode fiber including CLF, the propagation constants of the m and n symmetric modes can be given as  [23]:
β m ̵̶ βn =\(\frac{u_{m\ -}^{2}\ u_{n}^{2}}{2\ k_{\text{o\ \ }}a^{2}\ n_{\text{core}}}\)(1)
Where βm and βn are the longitudinal propagation constants for the order modes m, n. um and un are the normalized transverse propagation constants, while the \(a\) is the core radius of the CF, \(n_{\text{core}}\) is the core refractive index of the CF.
As the phase difference between the two modes is the integer multiple of 2Л, constructive interference can occur in condition:
(β m ̵̶ βn )L = 2Л N (2)
Then, the wavelength of the constructive interference can be given as  [23]:
λ =\(\frac{8\left(2N+1\right)n_{\text{core\ \ \ }}a^{2}}{\left(m+n\right)\left[2\left(m+n\right)-1\right]L}\ \)(3)
where the L is the CLF length and N is the natural number.
While, the wavelength difference is  [23]:
Δλ = λN – λN-1=\(\ \frac{16\ n_{\text{core}}a^{2}}{\left(m-n\right)\left[2\left(m+n\right)-1\right]L}\)(4)
From these relations, it worthy known that the dips and peaks are related to L which peaks have the tendency to be intensive as L varied. The boundary condition for the light propagated in the CLF is altered when the surrounding RI is changed. The mode field and propagation constant are fixed. From equation (2), the phase condition of the destructive or constructive interference is varied and N is also varied as the propagation constants are altered. Moreover, it can be observed that the constructive or destructive interference wavelength shift. The wavelength shift variations depend on the changing values of the surrounding RI  [23].