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This paper presents a method for the efficient production of all-fiber semi reflective mirrors suitable for fiber sensors and other all-fiber device applications. The mirrors are obtained by the short duration etching of a standard single mode fiber in hydrofluoric acid, followed by an on-line feedback-assisted fusion splicing process. Fiber mirror reflectance up to 9.5% with excess losses below 0.25 dB were produced in practice, which is in good agreement with provided theoretical and modeling analyses. Control over the etching time and fusion splicing process allows for balancing between reflectance and transmittance, while maintaining low excess loss of experimentally produced mirrors.
©2010 Optical Society of America
1. Introduction
In-fiber mirrors have various applications in optical sensors [1–4] and other photonics devices. Broadband operational spectrum, high or adjustable reflectance, small (fiber diameter) size, simple, fast and low-cost production process, high tensile strength and low insertion loss are desired fiber mirror properties that are difficult to achieve simultaneously, in practice.
Several techniques for fiber mirror production have been studied in the past [1,2,4–6]. Currently, the common method for in-fiber mirror production is based on the deposition of TiO2 on the cleaved fiber endface [1,5], followed by fusion splicing to another flat cleaved fiber end. Such fiber mirrors provide broadband spectral characteristics and low insertion losses, however, they are difficult and, in many instances, impractical to produce (for example in the case of cabled fibers) as they require the vacuum deposition (sputtering or electron beam deposition) of TiO2.
Significant, and even adjustable reflections, can also be obtained from in-fiber Fabry-Perot cavities that can be produced without a vacuum deposition process. Successful creations of in-fiber Fabry-Perot (FP) cavities have been demonstrated in the past by several authors [2–4,7,8]. Particularly interesting is the etch and splice procedure [2–4,8,9] that allows for simple and quick fiber cavity production. This paper presents the detailed investigation of a process for making Fabry-Perot cavity-based, low-loss, adjustable reflectance all-fiber mirrors, based on an etch and splice procedure.
2. Description of a Fabry-Perot cavity mirror
A fiber mirror based on an in-fiber FP cavity is shown Fig. 1 . The field in the air cavity is not guided and, therefore, expands in a transversal plane as it propagates along the cavity.
If we assume Gaussian modal field distribution, the field expansion can be described as:
where w(L) is the field radius at the second cavity surface, w0 is the initial Gaussian field radius at the first cavity surface that is approximated by the half of the fiber mode field diameter (MFD), λ is the wavelength and L is cavity length. The expansion of the modal field in the cavity reduces overlapping between the field in the cavity and the modal field of the fiber at the second cavity surface, which leads to a reduction in transmittance. However when the cavity length L is shorter than the MFD, this field expansion and associated overlapping/transmittance reduction can be practically neglected. For example, for L = λ = 1310 nm and w0 = 4.2 µm, Eq. (1) equals the value of 1.0005, which represents insignificant field diameter expansion.Exact solution of the Fabry-Perot cavity reflectance can be then described by:
where R is the reflectance of both cavity surfaces. If R is approximated by R = ((ncore-1)/ (ncore + 1))2 = 0.034 (assuming ncore = 1.45) the mirror reflectance Rc can be set by the cavity length L adjustment within the range that corresponds to:orThe above expressions are valid for an infinite cavity diameter and for flat and parallel cavity surfaces.The cavity can, however, be effectively produced by selective etching of the fiber’s core, as discussed in detail later in the paper. In such a case, the produced in-fiber cavity diameter always has dimensions comparable to the fiber’s MFD. For example, in our typical design, the cavity diameter corresponded to fiber’s core diameter and is thus smaller than MFD. This means that further reduction of the reflectance R can be expected, due to the partial overlapping of the propagating modal field and cavity cross-section.
In order to estimate a practically achievable reflectance, transmittance and excess loss of a Fabry-Perot air-cavity mirror, a series of simulations were performed using the FDTD method, with commercial OptiFDTD simulation software from Optiwave Systems Inc. When considering radial symmetry, the simulations were simplified to the 2D model of the mirror to obtain a manageable simulation case.
The reflectance, transmittance and excess loss versus cavity length were calculated for two different cavity diameters at λ = 1310 nm. The excess loss presents a useless loss of the optical power that is neither transmitted nor reflected at the splice. Excess loss is, therefore, a direct measure of fiber mirror quality, defined as:
In the first simulation case, the real mirror was modeled by setting the cavity diameter equal to the diameter of SM fiber’s core (dcav = dcore = 8.4 µm). Another simulation was performed for a large cavity diameter (dcav = 30 µm >> dcore), in order to verify the agreement between simulation results and description given by Eq. (2). The simulation results for both cavity diameters are shown in Fig. 2 .
Fig. 2 (a) reflectance, (b) transmittance and (c) excess loss vs. cavity length, for two different cavity diameters: dcav = dcore = 8.4 µm (red line) and dcav = 30 µm >>dcore (blue line)
The simulation results show that the maximum expected reflectance of the real cavity is about 11.2% at 1310 nm, which indicates a reduction of about 12% in respect to the simulation results for the large cavity diameter (the simulation results for the large cavity diameter are otherwise in good agreement with Eq. (2). This corresponds roughly to the fraction of the power propagating outside the core of the standard SM fiber at 1310 nm. In contrast to the large diameter cavity that is nearly lossless, the excess loss of the simulated real cavity versus cavity length exhibits periodic oscillation, superimposed on a slow rising function – Fig. 2c. Therefore, the optimal range of cavity lengths is within range 0 to λ/4, where the entire range of possible reflectances and simultaneously lowest excess loss can be achieved.
The real cavity additional excess loss and it’s oscillatory behavior versus cavity length can be explained by the transversal discontinuity of the propagation medium impedance within the real cavity region, which leads to excess scattering losses. Using a simplified heuristic explanation, the initial fiber modal field can be decomposed into two components that propagate within the cavity: the major field component that propagates through the air cavity, and in a minor field component that propagates within the fiber cladding region surrounding the same cavity. The difference in propagation constants for both propagating field components causes their phase mismatch at the second cavity interface, which results in an imperfect mode field reconstruction and, thus, additional excess losses. This heuristic explanation predicts an oscillatory behavior of excess loss as the minor and major field components go in-and-out of phase with increasing cavity length. The period Λ of excess loss versus cavity length can be estimated by Λ = λ/(nair- ncladding) or Λ = 2.92 µm for the case of λ = 1310 and ncladding = 1.45, complying well with the FDTD simulation shown in Fig. 2c.
Finally, Fig. 3 shows typical large-diameter cavity (Fig. 3a) and real cavity (Fig. 3b) simulations. The simulated cavity length was L≈1.5 µm in both simulation cases (this length corresponding to the first maximum in excess loss characteristics to best demonstrate the difference). The scattered field of real cavity is clearly visible in Fig. 3b.
Fig. 3 FDTD simulation of an in-fiber cavity: (a) large-diameter cavity (dcav = 30 µm >>dcore) and (b) real cavity model (dcav≈dcore)
Another important parameter that should be considered in mirror design is the spectral width of the Fabry-Perot cavity. The spectral characteristics of the mirror can be estimated directly from Eq. (2). In order to provide the largest spectral width, the cavity length should be kept as short as possible. Figure 4 shows calculated normalized reflectance versus wavelength for a practical case, where the cavity length equals λ/4 (as discussed above, the optimum real cavity length due to excess losses should be kept between 0 and λ/4, λ/4 is thus the worst expected case). Using −1 dB criterion, the calculated spectral width from Eq. (3) is Δλ = 869 nm (between λ = 994 nm and λ = 1938 nm, as shown on Fig. 4.
3. Fabrication of the FP-mirror by the etch and splice process
Silica doped with GeO2 etches at a higher rate than pure silica when exposed to hydrofluoric acid (HF) [10,11]. Consequently, when a flat cleaved standard single-mode fiber tip is exposed to HF, the germanium doped core will etch at a higher rate than the pure silica cladding. For a germanium doped core with an index difference of 0.5x10−3 (or 0.35%), the core etches at an approximately 1.85 higher rate than pure silica using 40% HF at 25 C. A relatively short exposure of the fiber tip to the HF therefore allows for the controlled formation of a micro cavity at the tip of the fiber. It should, however, be mentioned that modern standard single mode fibers can also employ different combinations or distributions of dopants in the core, resulting in different etching properties. For example Corning’s SMF-28e + core etches almost twice as fast as the core of SMF28e.
When etched fiber was properly spliced to another flat cleaved fiber, a FP mirror as shown in Fig. 1 was created.
The general impact of the etching time on the mirror reflectance was investigated at first to obtain initial data necessary for full development of the splicing procedure as described later in the text. We used 40% HF at 25 C in all experiments. In this examination a standard fusion process was used by applying the same set of fusion parameters that gave consistent splicing results across all investigated cavity lengths. A substantial number of mirrors were experimentally produced, in order to determine the relation between the etching time and the achievable properties of the spliced mirror. Figure 5 shows the average value and standard deviation of reflectance and excess losses of at least five produced samples over different etching times between 40 s and 170 s. The presented results were obtained from five produced samples for each etching time, thus over 70 mirror samples were produced altogether in this experiment.
Since a longer etching time results in a larger cavity length of the spliced mirror, a periodic variation in reflectance versus etching time, shown in Fig. 5a, is expected when considering the description and simulation results presented in the previous section. However, the etching time can only be roughly correlated with actual cavity depth, due to the overlap of fibers encountered during the splicing process. Figure 5b confirms that only a cavity length within the range 0 to λ/4 can provide very low excess loss fiber mirrors, as predicted in the previous section (a cavity length of λ/4 corresponds to an etching time of approximately 70 s, where the first reflectance peak occurs). There is, however, a practical limitation when making arbitrary short cavities. It was impossible to create repeatable and good tensile strength splices with fibers that were etched for less than 40 s, while using the conventional fusion process. This limited the minimum achievable reflectance to about 5% within the range of cavity lengths that provide small excess losses. A shorter etching time and, consequently smaller cavity depth, resulted in a total fusion of the fibers without leaving an air-gap in between fiber cores, even after performing extensive search of the fusion parameters.
An experimental setup for mirror fabrication, shown in Fig. 6 , was utilized in order to achieve good mirror production repeatability and be able to use the optimum cavity length range (0 to λ/4).
Splicing was performed using a Vytran FFS-2000 filament splicer. The broadband radiation from LED source (λ = 1310 nm, Δλ = 50 nm) was delivered through a coupler to the spliced mirror. A personal computer (PC) received the values for the reflected and transmitted optical powers measured by power meters PM1 and PM2 through a GPIB bus, and thus controlled the entire fusion splicing process.
The splicing process was then divided into two subsequent processes. In the first subsequence, the fibers were fused together by using short-duration high-temperature splicing. This assured good fiber bonding and provided simultaneous fire-polishing of the cavity’s end surface, being uneven after etching due to germanium concentration fluctuations (fiber profile ripple) present in the fiber core.
In the second subsequence, the splicing temperature was reduced to the level allowed for the long-term preservation of the splice region’s geometrical integrity, and simultaneous manipulation of the heated region’s length. In this step on-line monitoring of the reflectance was used to control the splicer’s linear motors. The linear motors were used to perform slow contraction (or expansion) of the heated splice region, which allowed for fine tuning of the cavity length and, consequently, mirror reflectance. The motor movement and the splicing process were terminated when the measured reflectance reached the preset target value.
An example of the fiber mirror production process using the above-described on-line feedback, is shown in Fig. 7 . This figure shows the typical reflectance change during splicing. The production of a 2% reflectance mirror was targeted during this experiment. The fiber in the presented experiment was etched for 70 s, which resulted in an initial cavity length that was considerably longer that required to achieve 2% reflectance. The cavity was then formed during the first splicing subsequence (the first peak in the graph). In the second subsequence, the splice region was compressed by the movements of the splicer’s longitudinal linear motors. Consequently, the reflectance first reached maximum value and then gradually reduced while pushing the fibers together. Splicing was terminated when the measured reflectance of the mirror reached approximately 0.3% higher value than the target value of 2%. This offset was necessary since reflectance continues to fall for a short time after the splicer filament is turned off. The offset value of 0.3% was obtained experimentally and corresponded to the mean value of the reflectance drop range, of typically between 0.1 and 0.5%.
Causes for such variable offset behavior can probably be found in the structural deformation (contraction) of the splice region when cooling down to room temperature, and the residual compression of the region around the splice, which is caused by the slow-filament cooling process and residual tension applied to the fiber during the fiber pulling or compression phase.
When required, further fine adjustment of mirror reflectance was applied in a separate fine-tuning process performed by the same experimental setup, as in the case of the initial splicing procedure. Tuning was performed by short-pulsed heating of the spliced region (heating filament ON-time = 0.5 s, OFF-time = 0.5 s) and slight stretching or compressing of the fiber region around the cavity, until achieving the desired reflectance. The typical reflectance change during the mirror fine-tuning process, is presented in Fig. 8 . Using this additional tuning step, the reflectance of the produced mirrors can be set at a precision better than 0.1%.
Fig. 8 Reflectance fine-tuning: example of fine-tuning mirror reflectance from initial 6.7% to a target of 7%
Figure 9 shows photography of a typically-produced mirror obtained by oil immersion microscopy.
A short mirror cavity is visible in the center of the fiber. Figure 9 reveals almost parallel surfaces of the cavity, with rounded edges. The cavity length was λ/4 (or about 330 nm). This particular mirror cavity length was tuned to achieve a maximum possible reflectance, which corresponded to 9.5%. A maximum reflectance of 9.5% was obtainable in a repeatable way, and was lower than estimated by earlier computer simulations which predicted 11.2% maximum reflectance. Additional FTDT simulation was therefore performed in order to determine whether the curvatures of the cavity edges impact maximum-obtainable reflectance of the mirror. The geometrical shape for the cavity simulation layout was obtained from Fig. 9, as shown in Fig. 10 . Simulation of the cavity with curved surfaces yielded a maximum reflectance of 10.3%, which confirmed the conclusion that the rounded edges of a cavity reduce maximum mirror reflectance.
4. Experimental evaluation of mirror fabrication method
An extensive experimental investigation was performed regarding the achievable fiber mirror performance and repeatability of the fabrication method. A large number of mirror samples were produced using different etching times and different target reflectances, in order to find the optimal fabrication conditions for achieving maximum transmittance or lowest excess loss, respectively.
Four batches of fibers were prepared with different etching durations. The etching times were 40 s, 50 s, 60 s and 70 s. With each batch the mirrors with different reflectances within the entire range of achievable values were produced. The target reflectances were <0.1%, 1%, 3%, 5%, 8% and 9.5%. Excess losses for each target reflectance are presented in Fig. 11 .
Fig. 11 (a) average values with standard deviation and (b) the minimum achieved values of excess loss for different target mirror reflectances
The diagrams in Fig. 11 show the average and lowest excess losses for each targeted reflectance that were obtained from at least five samples, produced with fibers from the same batch (prepared using identical etching times). Therefore, over 120 samples were produced within this experimental investigation.
Within the range of the target mirror reflectances up to 5%, the lowest excess loss was achieved by utilizing 40 s etching time. An etching time of 60 s proved to be the most appropriate for a target reflectance of 8%, and 70 s for mirrors with maximum achievable reflectance. These results correlated well with experimentally-evaluated dependence between etching time and mirror reflectance, as presented in Fig. 5. The excess loss probably increases during adjustment of the desired mirror’s reflectance by over-compression of fibers and a fine-tuning process that likely causes deformation of cavity surfaces and core misalignments. Consequently, to achieve optimum results regarding excess loss, a rough adjustment of the cavity length should be performed using etching time control, while the active splicing feedback control should only be used for fine cavity length adjustments. Increased excess loss is evident when adjusting cavity length, particularly at minimum reflectance which requires a large compression of the splice region. Finally, it should be stressed here, that the above experiment was performed for Corning’s SMF28e. Different single-mode fibers produced by the same or different producers might give different results. For example, significantly different etching times were obtained with SMF28e + , having a different core composition than SMF28e.
The tensile strength of the produced mirrors was periodically measured. The average tensile strength for 60 produced and tested mirrors was 1.8 N with standard deviation of 0.21 N. The reduced tensile strength limits the minimum bend radius of the fiber that contains the mirror due to the mechanical failure issues, however, we did not observe any significant influence on mirror optical performances upon bending of the fiber.”
Repeatability of the mirror fabrication method was experimentally evaluated by producing 30 mirror samples with target reflectance of 5%. The fibers were etched in the same batch for 40 s. Statistical evaluation of achieved reflectances and excess losses presented in the histograms of Fig. 12 , shows good repeatability and control over the fabrication process, which can provide high production yield during potential practical mirror production.
5. Conclusion
This paper investigated a design and method for the production of adjustable reflectance, low-loss, broadband, all-fiber mirrors, based on a miniature, in-fiber Fabry-Perot cavity. Cavities at the tip of optical fibers were produced by etching standard single-mode fibers in 40% HF for a short time (about 1 minute). High production repeatability was achieved by the introduction of active feedback control into the fusion splicing process, thus allowed for tuning of the desired reflectance whilst providing low excess losses. Maximum reflectances of 9.5% with excess losses below 0.3 dB were achieved on a repeatable scale. Very low excess losses (below 0.1 dB) were achieved for mirrors with reflectances within range 1 to 4%. Theoretical and FDTD modeling was in good agreement with experimental results. FDTD simulations also revealed the difference between finite and large (or infinite) diameter mirror cavities. The finite diameter cavity mirrors exhibited higher excess losses than the infinite diameter cavity mirrors, however, these losses can be minimized if the cavity length is maintained within a 0-λ/4 span.
Control over etching time and the splicing process allowed for balancing between desired reflectance and transmittance of the produced mirrors, which is particularly useful in cases when mirrors are used in power-budged sensitive applications, such as quasi distributed sensor arrays.
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