1. Introduction

Fiber index profiling is important and required in many applications. Many different techniques implementing such a measurement have been developed. Reflection-type scanning optical microscopy is widely used for measuring the reflectance distribution on the fiber cross-section and then determining the refractive index profile [1–5]. Nevertheless, this approach often expends a lot of scanning time and needs complicated data acquisition and analysis processes. Therefore, capturing the reflective fiber cross-sectional image at one time, without the need for scanning point to point, seems a faster and more convenient method. In addition, if we adopt the broadband white light from a tungsten lamp as the test light source in a conventional optical microscope, the refractive index determined from the reflectance by the Fresnel equation will cause significant problems because the refractive index and the camera sensitivity are different for various wavelengths. Alternatively, using coherent laser light of a single wavelength as the test light source instead will easily produce unclear and non-uniform fiber images, and the resulting focused spot of light will be too small to provide a locally constant intensity profile over the fiber end-face. As a consequence, in this report, we propose and demonstrate a novel fiber index profiling technique that captures the high-quality reflective fiber cross-sectional image with a partially coherent laser light source, a technique that is easy to perform on multimode optical fibers and which yields easily analyzed results. The partially coherent laser light source has better directionality than a broadband light source that is temporally and spatially incoherent, so it is more convenient to achieve the focusing and imaging processes. Meanwhile, the captured reflective fiber cross-sectional image using the partially coherent laser light has relatively higher optical intensity and lower noise. Besides, without the necessity of utilizing a band pass filter, the monochromaticity of the partially coherent laser light promises more accuracy when using the Fresnel equation to calculate the refractive-index difference from the detected reflectance distribution. This creative approach demonstrates another significant and novel application of reduced-coherence laser light, in addition to observing high-quality transmission-type cross-sectional images of various optical fibers [6,7], performing high-precision in-plane vibration characterization of microelectromechanical systems [8], improving the fabrication quality of microstructures by ultraviolet laser photolithography [9], and capturing the various near-field averaged optical mode patterns of photonic crystal fibers [10]. The techniques used in this approach and the optics concepts required in the analysis are well known, yet the integration is a work of great originality.

2. Experimental system and analysis methods

The experimental setup for capturing the reflective fiber cross-sectional image with partially coherent laser light is shown in Fig. 1 . The output beam (optical power ~90 mW) of a 532-nm green diode-pumped solid-state (DPSS) laser (GLM-L3IF-100, Unice E-O Services Inc.) was sent through a half-wave plate and a polarizing beam splitter to adjust the optical power of the reflected beam to be ~6 mW, to which the CCD camera (Newport LBP-3-USB) could adapt more easily. To obtain clearer and more uniform fiber cross-sectional images [6,7], the laser beam reflected by the polarizing beam splitter was first sent through a high-speed rotating diffuser (frequency ~70 Hz) to transform the coherent laser light into a low-coherence light source composed of many scattered fluctuating tiny light spots. After the diffuser, we utilized a 10× microscope objective (MO) to collect and collimate the diffracted laser light. The partially coherent laser light was further reflected by another non-polarizing beam splitter and coupled onto the test fiber by another 10× MO focusing lens. Then we projected the light reflected by the fiber end-face onto the CCD camera placed behind the non-polarizing beam splitter by using the same 10× MO as the imaging lens. Because we launched the coherent laser beam directly into the rotating diffuser without focusing in advance [7], the transformed light beam was highly spatially incoherent, such that the beam size focused onto the fiber end-face was large enough to give a nearly constant intensity distribution over the fiber end-face, simplifying the determination of the fiber index profile from the captured reflective fiber cross-sectional image. The test fiber was a step-index multimode optical fiber (Thorlabs AFS50/125Y, core ~50 μm, cladding ~125 μm, and length ~25 cm), which had a homogeneous refractive index distribution within its core. The specified numerical aperture (NA) value of the test fiber is approximately equal to 0.22 [11]. By using the Sellmeier dispersion equation [12], the refractive index of the fiber cladding composed of pure silica glass at an optical wavelength of 532 nm can be calculated to be n_cladding = 1.4607. Since NA =_{$\sqrt{n_{core}^2-n_{cladding}^2}$}, the predicted refractive-index difference between the core and cladding of the test fiber is approximately equal to Δn = n_core − n_cladding = 0.01647.

 

Fig. 1 Experimental setup for capturing the reflective fiber cross-sectional image with partially coherent laser light. MO, microscope objective; PC, personal computer; CCD, charge-coupled device; and DPSS, diode-pumped solid-state.

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Here we interpret the calculation procedure for analyzing the reflected light intensity distribution of the captured reflective fiber cross-sectional image. As stated above, since the refractive index of the fiber cladding is n_cladding = 1.4607, we can compute its reflectance R_cladding = 0.03505 from the Fresnel equation [1–4] by assuming normal incidence of the focused light onto the fiber end-face:

3. Experimental results

Based on the aforementioned experimental configuration and calculation procedure, we tried to determine the refractive index profile of a step-index multimode optical fiber from the reflective fiber cross-sectional image captured with partially coherent laser light. Figure 2(a) shows the reflective fiber image captured in the initial test. The calculated overall two-dimensional refractive index distribution on the fiber cross-section is shown in Fig. 2(b), and the transverse one-dimensional refractive index profile across the fiber center in the horizontal direction is plotted in Fig. 2(c) as a representative profile, from which the averaged refractive-index difference Δn between the core and cladding of the test fiber is found to be 0.04609. The chosen boundaries for the two parts to retrieve the mean values of the refractive indices are marked by the dotted lines indicated in the Fig. 2(c). Hence, the percentage error of the initial Δn measurement is 179.8%. We attributed the severe measurement error to the additional reflected light from the rear fiber face positioned in air, because the fiber core intensity in Fig. 2(a) seemed too high.

 

Fig. 2 (a) The captured reflective fiber cross-sectional image in the initial test. (b) The calculated overall two-dimensional refractive index distribution on the fiber cross-section. The corresponding length per pixel is 0.258 μm. (c) The transverse one-dimensional refractive index profile across the fiber center in the horizontal direction. The dotted lines indicate the chosen boundaries for the two parts to retrieve the mean values of the refractive indices.

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In the revised setup, we inserted the other fiber end-face into water [5], the refractive index of which is much closer to that of the optical fiber than that of the air. Thus, we were able to decrease the reflected light from the rear fiber face. The new measurement and analysis results are shown in Fig. 3 . The optical intensity in the secondary reflective cross-sectional image of the fiber was composed mainly of the reflected light from the front fiber face. The fiber core intensity in Fig. 3(a) appeared to be much lower than that in Fig. 2(a), further approaching the fiber cladding intensity. From the amended transverse one-dimensional refractive index profile across the fiber center in the horizontal direction in Fig. 3(c), the averaged refractive-index difference Δn between the core and cladding of the test fiber is then found to be 0.01688. The chosen boundaries for the two parts to retrieve the mean values of the refractive indices are also marked by the dotted lines indicated in the Fig. 3(c). Hence, the percentage error of the secondary Δn measurement is reduced to 2.49%, demonstrating the advantage and reliability of the proposed fiber index profiling method using partially coherent laser light.

 

Fig. 3 (a) The newly captured reflective cross-sectional image of the fiber in the revised setup. (b) The newly calculated overall two-dimensional refractive index distribution on the fiber cross-section. The corresponding length per pixel is 0.258 μm. (c) The amended transverse one-dimensional refractive index profile across the fiber center in the horizontal direction. The dotted lines indicate the chosen boundaries for the two parts to retrieve the mean values of the refractive indices.

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The proposed technique requires that the optical signal in the fiber image is normalized to the empirically computed refractive index value of the fiber cladding at an optical wavelength of 532 nm using the Sellmeier dispersion equation [12], and thus it is not self calibrated. In the case the fiber cladding is doped with a few possible network modifiers and thus has a refractive index slightly different from that of a pure silica glass, the calculated refractive index of the fiber core by the presented approach will slightly deviate from the proper value. Nevertheless, the measured refractive-index difference between the core and cladding of the test fiber will not have deviation nearly, and it still can provide some useful information for specific systems.

Most initially, the optical fiber under test was bent naturally from the fiber holder down to the optical table fortuitously with the other end of the fiber nearly vertically pointing to the steel plate. In this case, the fiber core in the captured reflective fiber cross-sectional image appeared to be very bright and the percentage error of the measured refractive-index difference was about 521%. We attribute it to the reason that the light originally guided in the fiber core after emanating from the other fiber end-face was highly reflected by the steel plate of the optical table. Therefore, in the following tests, either in the air or in the water, the other end of the test fiber was briefly fixed by an elevated baseplate and kept from being directed vertically again to the optical table or to the bottom of the beaker filled with water.

The fiber end-face was produced by cutting the optical fiber with a simple diamond scribing pen (54468, Ted Pella Inc.), instead of a precision fiber cleaver, and breaking it into two parts. It resulted an obvious crack at the boundary (width ~30% of the fiber diameter), as shown in Figs. 2(a) and 3(a) (see the bottoms of the fiber images). As a consequence, the captured reflective fiber cross-sectional images look not fully circular. Meanwhile, due to the fiber cracking at the boundary, the surface of the fiber end-face was not fully flat. The fiber images in Figs. 2(a) and 3(a) show that in the fiber core there are spots that are red while the backgrounds are yellow. A similar situation also occurs in the fiber cladding. Hence, there is a belt of slight bulge zone induced by the fiber cracking on the surface of the fiber end-face. As a result, the transverse one-dimensional refractive index profiles across the fiber center [Figs. 2(c) and 3(c)] should be taken in the horizontal direction (approximately along the crack direction) rather than in the vertical direction (approximately perpendicular to the crack direction), which will lead to greater measurement error. From another point of view, this reflection-type partially coherent fiber imaging system can also be used to inspect the degree of flatness of the fiber end-face, since the incident partially coherent laser light has a nearly constant intensity distribution over the fiber end-face.

The spatial resolution of the refractive index profiling in our system is mainly decided by the pixel size of the CCD chip, which corresponds to the length per pixel in the captured fiber image, 0.258 μm, because we don’t need to use a strongly focused optical beam of very small waist size to scan the fiber endface as with the other methods [1–4]. The resolution of the refractive-index difference, δn [1–4], is approximately 0.0051, by calculating the standard deviation of the refractive index profile across the fiber core segment in Fig. 3(c). Hence, the accuracy (or the relative error) of the refractive-index difference, δn/n [1–4], is measured to be 0.352%, from dividing the resolution of the refractive-index difference by the refractive index of the fiber cladding (n_cladding = 1.4607), which can be improved by further lowering the optical coherence of the partially coherent laser light [6]. The resolution or accuracy of the refractive-index difference in our present system is not sufficient to determine the refractive index profile of a single-mode optical fiber, compared with the other scanning methods [1–5]. Nevertheless, it is small enough to determine the refractive index profiles of various multimode optical fibers.

The measurement error of the refractive-index difference Δn between the fiber core and cladding can be further improved if we make the front fiber face smoother with a fiber polisher or a precision fiber cleaver. Increasing the speed of the rotating diffuser can make the captured fiber image appear clearer and more uniform. Replacing the water with an index-matching oil [1] with a refractive index that is nearly the same as that of the optical fiber can further reduce the reflected light from the rear fiber face. Further, polishing the rear fiber face at an inclined angle can direct the reflected light in another direction and can effectively hinder the CCD camera from receiving the reflected light from the rear fiber face. Increasing the distance between the CCD camera and the focusing/imaging lens can enlarge the captured fiber image and can reveal with greater clarity the tiny structure of the fiber index profile. If all these treatments were used, the refractive index profiling of even a single-mode optical fiber with its much smaller core diameter (normally ~8 μm) and much lower refractive-index difference (normally ~0.005) could also be realized by capturing the reflective cross-sectional image of the fiber with partially coherent laser light. Notice that the focusing/imaging lens cannot be replaced by a 20× or higher amplifying ratio MO because the beam size of the partially coherent laser light focused onto the fiber end-face must be large enough to give a nearly constant intensity distribution over the fiber end-face, otherwise a reflection mirror needs to be used to calibrate the transverse intensity distribution of the incident light at the fiber end-face, or unless a single-mode optical fiber with much smaller core size is under test. The fact the reduced-coherence laser light can be easily projected onto the fiber end-face without the need for the beam profile calibration and the capturing of the reflective fiber cross-sectional image without the need for the probe-tip feedback control is less cumbersome than with the other scanning methods [1–5] makes it an attractive alternative. The further exploration of the refractive index profiling of a single-mode optical fiber with this reflection-type partially coherent fiber imaging system is under investigation and full of challenges.

4. Conclusion

We have successfully achieved the refractive index profiling of a step-index multimode optical fiber by directing partially coherent laser light onto the fiber end-face and by analyzing the captured high-quality reflective cross-sectional image of the fiber. The reflected light from the other fiber end-face positioned in air can increase the fiber core intensity in the captured reflective fiber image, which can be greatly improved by inserting that end of the fiber into water. This novel and creative technique for fiber index profiling by analyzing the reflective fiber cross-sectional image captured with partially coherent laser light is simple and easy to perform. It is also useful in determining the refractive index profiles of other types of multimode optical fibers. If more improvements could be made, the refractive index profiling of a single-mode optical fiber could also be achieved.