Long-period cascaded fiber taper filters A. Martinez-Rios,* G. Salceda-Delgado, and J. A. Guerrero-Viramontes Grupo de Sensores Opticos y Microdispositivos, Centro de Investigaciones en Optica, Loma del Bosque 115, Col. Lomas del Campestre, Leon, Gto 37150, Mexico *Corresponding author:
[email protected] Received 11 October 2013; revised 3 January 2014; accepted 7 January 2014; posted 13 January 2014 (Doc. ID 199321); published 7 February 2014
Fiber filters based on periodic cascaded tapered fiber sections are demonstrated. The filters consist of up to seven tapered sections separated periodically by more than 3 mm from center to center, with nominal tapered sections of 1 mm × 1 mm × 1 mm longitudinal dimensions. The transmission spectrum consists of discrete notches, resembling those observed in long-period fiber gratings, which differs from the observed spectrum in Mach–Zender interferometers based on cascaded tapers. Its sensitivity to external perturbations, such as refractive index or mechanical stress, made the device potentially very useful as a sensor or tunable filter. © 2014 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2340) Fiber optics components; (060.2360) Fiber optics links and subsystems. http://dx.doi.org/10.1364/AO.53.000944
1. Introduction
Tapering optical fibers is a popular technique used to modify their light-guiding characteristics and to create simple and sophisticated all-fiber devices [1–4]. In particular, cascading two tapered sections has been used to fabricate all-fiber Mach–Zender interferometers. On the other hand, the fabrication of long-period fiber gratings (LPFGs) by electric arc [5], and CO2 laser irradiation [6], is in most cases based on the tapering induced by the process. In this case, the taper geometry and dimensions are approximately the same, with a fixed periodic separation between them, and they constitute an example of an all-fiber device based on concatenating similar tapers. Another well-known fiber device that relies on the concatenation of two tapered fiber sections is the fiber Mach–Zender interferometer (FMZI) [7]. The output transmission spectrum of a FMZI consists in most cases of well-defined periodic notches, where the period decreases as the separation between them augments. Recently, a series of asymmetric abrupt tapers has been used to create 1559-128X/14/050944-07$15.00/0 © 2014 Optical Society of America 944
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fiber comb filters [8]. In this case, the device performance relies on the concatenation of a series of abrupt tapers in two different types of fibers, i.e., a single-mode fiber (SMF) and an erbium-doped fiber. Spectral filters have also been fabricated by concatenating nonidentical tapered fiber sections [9]. In this particular case, a single transmission band can be obtained if the phase shift experienced at each taper differs by a factor of 2. The filters presented in this work are more related to the last case; however, there are significant differences. First, in our case the tapered fiber sections are selected to be geometrically equal; in some cases they are separated by a fixed periodic distance, and in other cases the separation may not be periodic. Furthermore, the tapers are short—longitudinal dimensions of 1 mm × 1 mm ×1 mm (transition–waist–transition)— but not as short as those used for the fabrication of standard LPFGs. In the case of periodical separation, for the cases analyzed here, the separation or spatial period of the concatenated tapers in greater than 3 mm. For the nonperiodical case, the higher separation from center to center may be higher than 6 mm. In addition, in all cases the minimum diameter reduction at the taper waist was in the order of 60 μm, which is still far from the transition point
from core to cladding guiding for the fundamental mode, considering a standard telecommunications fiber (i.e., SMF-28). The device operation relies on the interaction between the core fundamental mode and the cladding modes excited at each taper transition. The core and cladding modes experience a differential phase shift along the taper waist and in the sections that separates each taper. The sensitivity to external refractive index and bending stress translates into significant changes in the depth and spectral position of the notches. As we will show, slight bending allows the tuning of the notches in a 100 nm range (1420–1520 nm), and the notch depth may be as high as 34 dB, while the out-of-band loss may as low as 1.8 dB. 2. Operating Principle
A tapered fiber section may be seen as a single interferometer, where at the first or input taper transition some of the core light is coupled to cladding modes, in a degree that depends on the strength and slope of the diameter change. On the other hand, at the waist zone the core mode and excited cladding modes experience a differential phase shift that determines the degree of interference at the second or output taper transition. If the taper transition slopes are fast enough, there is no complete recoupling from the cladding to the core mode at the second transition, and some light remains propagating through the cladding. For this particular case, we may see the single taper as a device that couples light from the core mode to the cladding modes, so that, if a taper with the same characteristics is concatenated, a typical Mach–Zender interferometer spectrum may be observed. This spectrum consists of notches separated periodically, where the period depends inversely on the separation length between tapers. Here, the separation lengths are for all cases below 7 mm and the tapers are quasi-adiabatic, so that, for a single taper, only a slight spectral modulation is observed. Thus, the transmission spectrum is a result of the accumulated effect and the interaction between the concatenated tapers. Figure 1 shows a section of a concatenated taper filter device described in this work. This figure was obtained by taking photographs of each taper section and joining them using commercial software Mathematica. In order to evaluate numerically the concatenated taper performance, the effective indices of the core and cladding modes are first calculated using the Erdogan [10] formulas for the characteristic equations, and the Sellmeier coefficients for a 3 mol. % GeO2 doped core fiber [11]. A database of effective indices of core and cladding modes at several core/cladding radii and wavelengths was created, and the generated data were fitted to an interpolating function
Fig. 1. Photography of a section of the concatenated taper filter device.
Fig. 2. Effective index difference between the fundamental core mode and the HE12 cladding mode decreases with the cladding radius and wavelength. (The vertical scale is the effective refractive index difference between both modes.)
to simplify the analysis [12]. Since axial symmetry is assumed, only HE1m cladding modes are considered. Figure 2 shows a surface plot of the effective index difference between the fundamental core mode and the HE12 cladding mode as a function of wavelength and cladding radius. In the top of Fig. 3 the real profile of a concatenated taper device is shown. This graph was obtained by taking successive images along the taper sections, which later on were assembled, and the cladding dimensions were extracted by image processing. For this real profile, the coupling coefficient was calculated from effective index functions of the core mode and the first cladding mode, as a function of wavelength and cladding radius. In the bottom of Fig. 3 a density plot of the calculated coupling coefficient is shown, where it can be observed that the highest coupling takes place at the taper section, particularly at the transition zones. For this calculation we have used the normalization formulas and field expressions of the Erdogan work [10], and the coupling coefficient expression (7.33) of the Bures textbook [13]. Despite the device length being in the order of 2.3 mm, the numerical solution of the coupled mode equations is an intensive problem, since, for higher accuracy, a large number of steps should be realized even for a single wavelength. In order to illustrate the wavelength selectivity of the n-concatenated taper device, the coupled mode equations were solved through the Rung—Kutta algorithm assuming coupling between the fundamental core mode and the HE12 cladding mode. For a single wavelength, this calculation required us to divide the domain (i.e., the length of the device) in length increments as high as 1 × 106. Figure 4 shows the results obtained at two distinct wavelengths, 1.55 μm (solid curve) and 1.6 μm (dashed curve). Clearly, it can be observed that the output intensity is a result of the accumulated effect of each concatenated taper, and there is a strong spectral selectivity. In what follows we 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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processing system and to accommodate the desired series of tapers. Each taper was fabricated successively, and the transmitted power was monitored during fabrication. Nominally, each tapered section was fabricated by selecting the downtaper–waist– uptaper longitudinal dimensions to 1 mm each in the Vytran interface, while the cladding diameter at the waist was selected to be in most cases 60 μm. In general, all fabricated tapers have approximately the target waist diameter; however, the longitudinal dimensions have slight variations mainly due to the differences in the initial tension applied before tapering. In all cases presented here, after the concatenated tapers were fabricated, images of each section of the whole device were taken and processed to obtain a better picture of the real taper profile. Figure 5 shows the geometrical profile of two distinct cascaded taper devices. Their main difference with respect to the taper profile of Fig. 3 is in the average separation between the tapers from center to center, which in the last case was around 3964.7 μm. In the case of the first (top) profile, the waist diameter was selected to be around 55 μm. For comparison purposes, from now on we refer to the cascaded taper devices as the first, second, and third according to the value of the period, i.e., the separation from center to center of the tapered section, the “first” being the one with the lowest value.
Fig. 3. Top: real measured profile of the concatenated taper device. Bottom: density plot of the corresponding calculated coupling coefficient (squared absolute).
will concentrate on the experimental realization and some of the device characteristics. 3. Device Fabrication and Characteristics
The devices presented in this work were fabricated on standard SMF-28 using a Vytran glass processing system GP-3400. Prior to fabrication, the protective polymer of a section of fiber was removed, and this section was cleaned by an ultrasonic bath of acetone. This section was long enough to fit into the glass
Fig. 4. Evolution of the intensity of the fundamental mode along the device assuming 1.55 μm (solid curve) and 1.6 μm (dashed curve) wavelengths. 946
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Fig. 5. Measured taper profiles of the first (top) and third (bottom) cascaded taper devices obtained through image processing.
practical purposes identical, the change in the differential phase shift is the main factor that should determine the position and strength of the attenuation bands. Thus, it is possible to control the position of the attenuation bands, in a repeatable form, by controlling the separation between tapers, although the taper profile also gives additional degrees of freedom to select the wavelength position of the attenuation bands. 4. Sensitivity to External Refractive Index
Fig. 6. Evolution of the transmission spectrum during the fabrication process of cascaded taper devices with average period of 3708.59 μm (solid curves), 3964.7 μm (dashed curves), and 4603.78 μm. In the case of the second cascaded taper device, after the third taper was fabricated a single broad and deep band is obtained at 1502 nm; by adding more tapers this band disappears, and after the sixth taper a single band at 1338 nm is obtained.
It is worth mentioning the criteria used to select the waist diameters in the proposed device. As is well known, when a pair of tapers are concatenated, a Mach–Zender fiber interferometer (MZFI) is formed. The strength, period, and spectral position of the MZFI spectral interference pattern depend on the geometry of the tapers, the fiber type, and the separation between tapers. In particular, for standard step-index SMF, the waist diameter is the main factor that determines the spectral position of the interference pattern [7], while the separation between tapers determines the bandwidth and separation between the loss notches. Figure 6 shows the evolution of the transmission spectrum as the tapers are added. As can be observed, after two tapers are added there are broad attenuation bands, which are separated by 209 nm (first, Λave 3708.59 nm), 189 nm (second, Λave 3964.7 nm), and 195.66 nm (third, Λave 4603.78 nm), and the deeper bands are positioned in the 1500–1600 nm range. We have found that by selecting the waist diameter between 55 and 60 μm [7], a spectral interference pattern is formed with deeper notch bands in the 1400–1700 nm range. This was the main criteria to select 60 μm as the waist diameter in most cases. As more tapers are added, the spectral interference pattern is strongly modified, and after several concatenated tapers well-defined notch bands are formed, resembling the spectra observed in standard LPFGs. In contrast with standard LPFGs, there is not an evident correlation between the change in the period and the position of the notch bands. Instead, the notch bands experience a discrete shift with a change in the period, which for the longer wavelength bands results in an apparent shift toward shorter wavelengths when only three tapers are cascaded, and a shift toward longer wavelengths when six tapers are cascaded. Since the tapered sections are for
Although the spectra of the cascaded taper devices shown in Fig. 6 are in fact deep and broad, they are in some sense ugly. On the other hand, as was mentioned previously, the changes in the periodic separation between tapers seem to be not correlated directly with the position of the notch or attenuation bands. This is caused by the ultra-long period of the device, compared with the periodic separations observed in standard LPFGs, which causes the phase shift experienced by the interacting modes to evolve through several beat lengths. Thus, we do not expect that changes in the external refractive index result in a continuous shift of the relevant notch bands. As a matter of fact, as will be shown below, immersion of the cascaded taper filter in a liquid with calibrated refractive index has a significant effect in the spectral transmission. In order to get a higher dynamic range, the spectral transmission of the cascaded taper filters was measured by using a fiber coupled LED source with 100 nm bandwidth, and 1550 nm center wavelength. Figure 7 shows the result of the immersion of the first cascaded taper device in liquids with distinct refractive index. In air (see Fig. 6) practically there is no loss band at the 1450–1650 nm spectral range. As we can see, the bands do not disappear even when the external refractive index is higher than the cladding refractive index, and at refractive indices of 1.36 (solid curve in Fig. 7) and 1.45 (dot-dashed curve in Fig. 7), the loss bands are deep and narrow. In fact we
Fig. 7. When the first cascaded taper filter device is immersed in liquid with different refractive indices, the notch bands switch to other wavelengths and its depth also varies. 10 February 2014 / Vol. 53, No. 5 / APPLIED OPTICS
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cascaded tapers may be used to fabricate. In the next section a nonperiodic cascaded taper device fabricated on the waist of a long tapered section is presented. As will be shown, the resultant device has an enhanced sensitivity to slight bending allowing us to tune the position of the notch band in a range as large as 100 nm. 5. Nonperiodic Cascaded Taper Filter Fabricated on a Long Tapered Section
Fig. 8. For external refractive index values lower than the cladding index no loss band is observed in the case of the second cascaded taper device; however, for refractive index values higher than the cladding index a loss band around 1516 nm is observed. Eventually, for a external refractive index of 1.54 this band reach is maximum depth.
may observe that for other refractive indices the depths of the loss bands observed for refractive index values of 1.36 and 1.45 merge, which is particularly evident when the external refractive index has values of 1.43 and 1.47. On the other hand, Fig. 8 shows the effect of the immersion of the second cascaded taper device on liquids with different refractive indices. We must note from Fig. 6 (dashed curve) that, at the measurement range from 1480 to 1580 nm, there is not any loss band after the device is fabricated. However, it is clear that for refractive indices higher than the cladding index a loss band is observed. This loss band reaches its maximum depth for an external refractive index value of 1.54, where a narrow and deep band at 1516 nm appears. From the results of the external refractive index sensitivity shown above, it is clear that the cascaded taper filters presented here are not suitable to use as refractive index sensors. This is mainly due to the fact that the external changes, as in the case of the period change, result in a switch in the position of the notch bands. However, for example, whenever water is contaminated with another material liquid or solid there is an increase in the refractive index, which depends on the concentration. Thus, we may optimize the device so that a deep band loss will appear when the refractive index of the liquid under analysis reaches a value indicating the presence of the pollutant. This effect may be useful in the detection or monitoring of specific high refractive index liquids such as carbon disulfide, cynnamaldehyde, and bromoform. For example, if a fluid of interest reaches a high refractive index value due to some excessive concentration of the “pollutant” fluid, there will be a sudden and noticeable change in the spectrum of the transmitted light by the fiber. The fact that the changes in the period of the cascaded taper filter only result in the switching of the loss band position tells us that even nonperiodic 948
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Figure 9 shows the geometrical profile of a cascaded taper device fabricated on a tapered section obtained by processing the images taken along the whole device. In this case the fabrication involves two steps. In the first step, a fiber taper with longitudinal dimensions of 3 mm × 30 mm × 3 mm (uptaper– waist–downtaper) and 80 μm waist diameter was fabricated. Once this taper was fabricated, a series of tapers with longitudinal dimensions of 1 mm × 1 mm × 1 mm (uptaper–waist–downtaper) were cascaded along the waist zone to form the filter device. As can be observed, in this case the separation between the cascaded tapers is in some sense arbitrary, particularly between the first and the second taper, and between the fifth and the sixth taper. Even in this case a well-defined loss band is formed in the 1450–1650 nm range. Notice that at the sixth taper the waist diameter and the section between tapers are smaller; this was due to an additional pulling and heating that occurred when the seventh taper was made, since in this case the sixth taper was still inside the heating region. Once the cascaded taper device was fabricated, it was fixed between two translation stages separated by approximately 10 mm. When the fiber was kept straight, a single notch band around 1522 nm with 25 dB depth is observed (top left graph in Fig. 10). By applying slight bending, i.e., by reducing the separation between the translation stages by 32 μm (top
Fig. 9. Cascaded taper device can also be fabricated by using nonperiodical separations from taper to taper. Here, the device was made on a relatively long tapered section along the waist zone with 80 μm diameter. As in the other cases the waist diameter of the cascaded sections was selected to be of 60 μm.
Fig. 10. Position of the loss band may be tuned or switched in a range of 100 nm by slightly bending the cascaded taper device. In most cases the depth of the loss band may exceed 20 dB.
right graph in Fig. 10), the deep of the notch band increases to 32 dB. Further bending switches the position of the loss band, being possible to obtain a deep band around 1420 nm (25 dB depth), by reducing the separation between the translation stages by 218 μm (bottom left graph in Fig. 10). In between these values the other notch bands appear, and in some cases multiple bands may be observed. An examination of the changes in the transmission spectrum with bending reveals that up to four loss bands or resonances may be observed. By labeling the four most significant resonances as (1), (2), (3), and (4), starting from the lower wavelength band, it is possible to detect that in fact there is a continuous shift in the notch wavelength with bending (see Fig. 11). These bands experience changes in their depth and bandwidth, so that there are some points where one or several of them are more noticeable than the others. Apparently, the overall effect of bending is the switching or tuning of the loss bands, which independently continuously
shift their wavelength, and at the same time their depth is changing. The characteristics of this filter may be of interest, for example, in tunable fiber lasers. It is common to insert wavelength tunable or switchable filters, based, for example, on long-period gratings or tapers, inside the fiber laser cavities to obtain a corresponding wavelength tuning or switching. The apparent advantage of the cascaded taper fiber filter is the possibility to tune, by switching the notch wavelength, the resonances in a long wavelength range—in the present case in a 100 nm range. In addition the notch bands may have depths higher than 20 dB, allowing us to suppress undesirable signals by more than 99%. The reason for fabricating the concatenated taper device on a tapered section was to apply it in the wavelength switching of fiber lasers. In particular, it is easier to excite a tapered section (due to the reduced diameter) with acoustic vibrations that may switch dynamically the wavelength of the loss band, and hence the gain spectrum of a fiber laser cavity. Currently we are directing our efforts toward developing such an acoustically driven fiber filter, which would be very useful in the development of a low-cost, all-fiber sweep fiber laser source. Further and extensive experimental and theoretical work is needed to optimize the performance of the cascaded taper filters, in particular, to reduce the insertion loss. This requires a fine tuning of the whole fabrication process, starting with the preparation of the fiber and ending with the fabrication parameters, such as filament power, tension, and pull velocity. Another important factor that affects any optical fiber device is the temperature, and in fact its effect is very similar in most fiber devices based on SMF. Once the target wavelength operational range of the filter is obtained, schemes for temperature compensation may be used, which in general will require knowledge of the environmental condition under which the device is going to be used. It is worthwhile to mention that the proposed device requires a reduced number of tapers, in contrast with most of the LPFGs, which may require as much as 100 periods to obtain a reasonable depth in the notch band (usually no more than 15 dB). 6. Conclusions
Fig. 11. Four most noticeable resonances that appear as the fiber is bent are labeled as (1), (2), (3), and (4), starting from the lowest wavelength band. In this case, the bending results in a continuous shift of the notch wavelengths, and at the same time their depth, and hence the 3 dB bandwidth, are modified.
In conclusion, the characteristics of optical fiber filters based on cascaded tapers have been presented. The cascaded tapers are separated by a periodic distance in excess of 3 mm, with a total length
