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Chirped fiber Bragg gratings can straightforwardly and efficiently be fabricated onto microfibers with a uniform phase mask. Due to the variation of the propagating constant, which depends on the fiber diameter, the broadband spectrum of the grating can be formed. Depending on the different responses to the ambient refractive index in different parts of the grating, the bandwidth of the grating can be tuned by changing the surrounding solution. In addition, by being partly immersed in a liquid, the diameter-chirped Bragg grating can act as a broadband Fabry-Perot interferometer, whose spectrum can be tuned by means of controlling the liquid level and ambient refractive index.
© 2016 Optical Society of America
1. Introduction
Chirped fiber Bragg gratings (CFBG) play an important role in dispersion compensation [1] and broadband Fabry-Perot filters [2–4] for optical fiber communication applications. Normally, chirped gratings are inscribed onto optical fibers by changing the grating period along the axial length, such as linear, quadratic, jumping, or random, building the correspondence between the Bragg wavelength and the axial dimension.
Currently, the transverse dimension of the optical fiber is taken into consideration. Reduced to micron or sub-micron size, micro/nanofibers bridge the fields of micro/nanophotonics and fiber optics, showing a promising prospect in optical interconnection [5,6], particle trapping [7,8], and bio-molecule detection [9–11]. Owing to the change of the propagating constant, which is diameter-dependent, broadband Bragg gratings can be formed in microfibers with a chirp diameter instead of a grating period. This alternative method not only provides the diversity in the CFBG fabrication but also the flexibility in spectral tuning that is highly required by the dynamic network reconfiguration and dispersion management. Several efforts have been proposed to control the spectra of those diameter chirped FBG by means of adjusting the axial strain onto the gratings [12–16]. In addition, the ambient refractive index (RI) also has an influence on tailoring the spectrum once the fiber diameter is thin enough to allow the evanescent wave to spread outside the fiber structure. Etching a uniform FBG is one method to gain that goal [17] at the expense of time consumption, the inflexibility in diameter selection, and the initial spectrum setting.
Due to the highly efficient microfiber Bragg grating inscription technique that we had reported before [18–20], the broadband FBG can be straightforwardly obtained by directly imprinting uniform photorefractive pitches onto microfibers with chirped diameters. The initial spectrum is flexibly shaped through the fiber structure, exposing time and grating length. In response to the change in RI of the outer environment, the bandwidth of the grating can effectively be tuned. Furthermore, the wide-band Fabry-Perot interference spectrum is formed by partly immersing the grating into liquid. Moreover, the interference pattern can be tuned through the contrast liquid level and ambient RI.
2. Theory and principle
The propagating constant β for the HE11 mode of the microfiber can be calculated by combining with the dispersion relation of the three-layer-step-structure given by [21,22]. The ncore and nclad are set to 1.47 and 1.44404, respectively, at a wavelength of 1550 nm, in terms of the parameters of the 62.5/125 multimode telecom fiber. Assuming the core diameter is reduced proportionally with the fiber diameter (cladding diameter), the relationship between β and the fiber diameter is shown in Fig. 1, when the fiber is surrounded by air.
Fig. 1 Variation of the propagating constant with the diameter of fiber. Inset: the detailed view focusing on the fiber diameter below 5 μm.
As β for the HE11 mode decreases to less than the ncladk0 value, the propagating light can no longer be confined by the fiber core structure. It can be seen in Fig. 1 that the fiber, which has a diameter below 5 μm, can present the characteristic of a microfiber [18]. A sharp decrease of β exists along with further miniaturization of the fiber. Therefore, the difference of the propagating constants results in the contrast between the fiber diameters d, which can be expressed as:
While propagating in the microfiber, even the light following the HE11 mode is capable of reaching the ambient environment via the evanescent field. Therefore, as the ambient RI increases, the propagating constant would be enhanced. Moreover, due to the stronger evanescent field, light transmitting in the thinner fiber poses a higher ability to experience an RI increase, enabling a higher response in the propagating constant, which can be observed in Fig. 2.
Fig. 2 Changes in the propagating constant in different diameter fibers as the environment’s RI varies.
Thus, Eq. (1) can be adjusted to:
where nen is the ambient RI. Accordingly, the non-uniformity of the modulating region in the fiber determines the original bandwidth of the grating, which can be tuned by the surrounding environment.3. Experiments and results
The microfiber was tapered from a Corning 62.5/125 multimode fiber by the flame-heated drawing technique. The fiber was stretched by using two linear stages when it was heated by the flame. The heat source did not move during the taper process. The moving speed of each linear stage was 1 mm/s and the moving range was 10 mm. After several seconds, a microfiber with a diameter less than 10 μm and a length of 2–3 cm could be obtained.
We tested the insertion loss of the microfibers with the diameter range from 3 μm to 10.5 μm. The deionized water and the sucrose solution with RI of 1.365 were used to provide the liquid environment. The result was shown in Fig. 3. The microfibers presented low insertion loss within 0.3 dB while they were placed in the air, depending on the adiabatic tapers and the high RI contrast between the silica and the air. Therefore, the light transmitting in the microfiber could be tightly confined by the fiber structure, enabling the low insertion loss. But, as if the tapers were immersed into the liquid with higher RI, the light energy would spread out of the silica/liquid margin through the evanescent wave. The insertion loss grew sharply as the diameter decreased below 3.5 μm. In the water and solution, the 3 μm microfiber presented the insertion loss of as large as 25 dB and 30 dB respectively. As a consequence, the optimal ranges of the fiber diameters were between 3.5 to 4 μm, considering both the response to the RI and the insertion loss in the higher RI environment.
Fig. 3 (a) The insertion loss of different microfibers in different environments. Inset: the microscopic images of the microfibers; (b) the transmission of the 3.5 μm microfiber; (c) the transmission of the 3 μm microfiber.
As shown in Fig. 4, a 193-nm excimer laser and a phase mask with a uniform pitch of 1072.15 nm were used. The laser repetition rate was maintained as 200 Hz. Focused by a cylindrical lens, 120 mJ/cm2 of UV energy density per pulse was incident upon the microfiber. We used an aperture slot to shape the incident beam to a more perfect rectangle with a width of 2.5 mm. A broadband source with a wavelength range of 1250–1650 nm and an average power density of −30 dBm/nm was connected to a circulator for providing the baseline. A Yokogawa 6370C optical spectrum analyzer (OSA) with a resolution of 0.02 nm was used to monitor the transmission and reflection spectra of the fiber Bragg grating through the different ports of the circulator. A microscope was aligned vertically with the microfiber for detecting the proper region. By UV-scanning the uneven part of the microfiber with a 5 μm/s velocity in-axis, a 3.5 mm length chirped Bragg grating could be achieved with a reflectivity of 50% within 3 min due to the higher inscription efficiency we had demonstrated [19,20].
Fig. 4 Schematic of the chirped Bragg grating inscription in the non-uniform region of the microfiber.
Initially, we chose the transition part of the microfiber with a diameter range from 3.4 to 3.7 μm. As shown in Fig. 5, the transmission spectrum of the microfiber chirped Bragg grating (labeled as mCBG1) shows that the reflectivity of the grating reaches ~3 dB with the center wavelength of 1534 nm. Provided by the intrinsic reflection of the Bragg grating structure, the spectrum of the mCBG could be monitored just by the reflection port of the circulator. An initial 10 dB-bandwidth of 5.5 nm in the reflection spectrum can be explained by Eq. (1). The center wavelength of reflection is 1529.1 nm, shorter than transmission because the release of the loading in the inscription. The waveguide of the microfiber allowed higher order modes propagating in the fiber, although, the effective-index difference was significantly enlarged between the fundamental mode and the higher order modes. Therefore, the resonances contributed to the higher order modes were located in far shorter wavelengths, hardly influencing the fundamental mode resonance [19]. So, only the HE11 mode resonance was taken into account in the following study.
Fig. 5 (a) Spectrum of mCBG1: up: the transmission; down: the reflection in different RI; (b) relationship between the bandwidth and the outer RI.
The grating was subsequently immersed into the sucrose solution, whose RI could be adjusted by the solution density. As the ambient RI increases, the reflection spectrum moves to a longer wavelength and the spectral shape changes. By extracting the data from Fig. 5 (a), we can find that the bandwidth is gradually compressed in this process due to the fact that the thicker part of the microfiber is less impacted by the environment, demonstrated in Eq. (2). Finally, at RI = 1.378, the bandwidth is ~4.4 nm, which implies that up to 20% of the original bandwidth can be tuned through the outer environment. The continuous bandwidth-tuning is ~0.3 nm as the mCBG1was surrounded only by liquid. The deviated point at RI = 1.333 was probably caused by the process of immersing the grating in the water, which would introduce a little axial strain that impacts the grating.
The second grating was inscribed in the fiber with a sharper transition, which is labeled as mCBG2. The diameters in the modulating region are within the range 3.4 to 3.9 μm. Thus, a wider band of reflection can be achieved with 10.5 nm in air, as illustrated in Fig. 6. The ledge at the shorter wavelength may be caused by a region of uniformity in the microfiber that was involved. The reflection spectrum is also red-shifted and shrunk as the ambient RI increases. In the higher density solution, 2.1 nm of bandwidth could be tuned. The continuous bandwidth-tuning is ~0.6 nm. The loss is slightly larger than the previous one attributed to the sharper transition leading to the somewhat deviation of the adiabatic taper, although, the increased loss didn’t prevent us from analyzing the characteristics of the grating.
Fig. 6 (a) Spectrum of mCBG2; up: the transmission; down: the reflection in different RI; (b) relationship between the bandwidth and the outer RI.
Next, to further investigate the characteristics of the responses to the environment in different positions, mCBG2 was partially immersed into the liquid in the beaker as shown in Fig. 7. The grating region was separated by two different environments - the air and the liquid. Driven by the liquid level, which denotes the relative position of the grating in contrast to the boundary, the spectrum evolution of mCBG2 is studied. At the beginning, by precisely controlling the position, the thinner part of the grating is next to the surface of the liquid, which is defined as the original position (level = 0).
As the grating region was gradually immersed into the water, the bandwidth of the spectrum could also be tuned. According to the Fig. 8 extracted from the Fig. 7, at first, the bandwidth shrunk during the increasing of the water level. The minimal bandwidth was 7.5 nm at 2 mm level. The tuning was more significant than the aforementioned experiment since the thicker part of the grating remained in the air maintaining the margin of the spectrum at longer wavelength. Then, by further raising the water level, the spectrum broadened again mainly because the resonant wavelengths in thicker segments took parts in the wavelength-shifting, crossing over the longer wavelength margin. Finally, as the water level increased to surround the whole grating region, the bandwidth was ~9 nm, which agreed with Fig. 6(b).
Apart from that, it is notable that an interference spectrum is observed in this process, whose features change with the rise of the liquid level.
4. Discussion
Further consideration should be carried out on this type of broad spectral device. Unlike the traditional chirped Bragg grating that has only been mapped between the Bragg wavelength and axial position, the mCBG brings in an additional dimension, the fiber diameter, leading to the different RI responses in different positions.
If the thinner part of the grating is inserted into the liquid, the resonances at shorter wavelength will red-shift correspondingly to the increase of the ambient RI, matching the longer wavelengths as the thicker part is still in the air. The matching relation can be expressed in Eq. (3) as:
where the nliquid and nair represent the refractive indices in the liquid and the air, respectively.Obviously, a Fabry-Perot interference structure is formed including two matched grating regions with a non-matched area between them, which can be observed in Fig. 7. Corresponding to the lifting of the water level, the interference pattern presents variations in a range of characteristics. At first, the interference dips generally move to longer wavelengths. Meanwhile, combining with the interference bandwidth broadening and the dip bandwidths, the intervals of the resonant dips are enlarged from 0.6 nm (at the 0.5 mm level) to 2.5 nm (at the 2.5 mm level). Finally, the interference disappears at 3 mm.
Simulations of the non-uniform microfiber and its response to the liquid level are proposed to analyze the phenomenon quantitatively, as shown in Fig. 9. Here, the effective index (Neff) of the microfiber is taken into consideration, which is an alternative to the propagating constant.
The relationship between the fiber diameter and Neff is shown in left and right of Fig. 9. A segment of non-uniform microfiber can be estimated as a collection on those Neff. Assuming the diameter is proportional to the axial position, the level changes can be reflected by the diameter. As the liquid rises to level 1, which is illustrated in the left of Fig. 9, the part immersed follows the curves in the liquid while the rest still follows the curve in the air. Thus, a matched condition is achieved between the immersed part and a certain part of the rest. The blank region between them is the cavity length.
When the liquid level rises to level 2, as shown on the right of Fig. 9, a larger span of the Neff, which denotes the length of the immersed part, participates in the interference, leading to the broadening of the total interference bandwidth and the dip bandwidths. At the same time, the cavity is shortened accordingly, expanding the longitude mode spacing of the F-P structure that reflects the free spectrum range of the interference spectrum.
Furthermore, it can be deduced that the parts inside and outside the liquid overlap without any cavity as if the liquid was lifted to a certain level, offering the elimination of the interference pattern. In this case, only the bandwidth of the grating can be tuned after further lifting the liquid beyond that threshold level, in accordance with the spectrum in Fig. 7 at the 3 mm level.
Furthermore, it is found that the cavity structure is highly dependent on the RI of the liquid. The higher the RI of the liquid, the longer the cavity will be obtained. What is more, the visibility of the interference fringes is influenced by the RI of the liquid as well. Owing to the energy exchange via the evanescent field, the guiding mode energy in the microfiber structure would be reduced if the outer RI increases, which impacts the coupling coefficient. As shown in Fig. 10, assuming the index modulation is 1 × 10−4, the coupling coefficient κ can be calculated with the change of the ambient RI.
Fig. 10 Calculation of the coupling coefficient along with the RI in different diameter microfiber Bragg gratings.
According to the figure, κ presents a negative trend with the increase of RI. In addition, the reflectivity at the resonance wavelength will be reduced accordingly. Considering the fact that mCBG2 has a higher reflectivity at shorter wavelengths, two gratings in different regions can be matched not only for the wavelengths but also the reflectivity. This can be achieved by immersing a certain length of the thinner part into the liquid with a specific RI, providing an F-P interference pattern with a considerable large fringe contrast.
We have simulated the reflection spectrum of mCBG2 in response to the different levels of the liquid with an RI of 1.36 at 590 nm (estimated to ~1.345 at 1550 nm). The uniform region length of mCBG2 is set to 0.7 mm with a diameter of 3.4 μm for presenting the ledge at shorter wavelengths. It is assumed that the diameter of the fiber linearly increases to 3.9 μm in the rest of the grating region. According to Fig. 11, along with the shrinkage of the spectral bandwidth, the longitude mode interval of the F-P structure is enlarged from 0.4 nm (at 0.5 mm) to 0.6 nm (at 1.5 mm). Moreover, the high contrast of the interference is also obtained when 1.5 mm of grating length is immersed into the liquid due to the reflectivity matching the two grating segments.
Accordingly, we test the spectral change of mCBG2 by immersing the grating slowly into the solution liquid with RI = 1.36 at 590 nm. The optimization of the F-P interference spectrum can be caught at the 1 mm level, as shown in Fig. 12. The 10 dB bandwidth of the spectrum is compressed to 7 nm. The interval between the dips is measured as ~1.24 nm. The contrast is over 27 dB of the dip, which is adjusted to near the center of the reflection spectrum. The Q value of the corresponding dip and the finesse of the cavity can be calculated to ~2100 and ~4.5, respectively. The discrepancy between the simulation and the experiment result is mainly caused by the parameters of the uniform region length and the relationship between the diameter and axis position.
5. Conclusion
In this study, broadband Bragg gratings were formed in microfibers with chirped diameters using the high-efficiency microfiber inscription method. The principle of the chirped grating was demonstrated. By changing the surrounding liquid, the bandwidth of the spectrum can effectively be tuned depending on the inconsistency of the ambient RI responses at different diameters. Furthermore, a deeper discussion was proposed to those diameter-position-wavelength mapping devices. Provided by a boundary of two distinct surrounding environments within the grating region, the shorter wavelengths of the resonances in the liquid jump and match to the longer wavelengths, which are invariable in air. Therefore, the Fabry-Perot structure can be formed by leaving a space between the matching regions, whose spectrum can be tuned by the liquid RI and the boundary position. The devices proposed can be applied as tunable dispersion compensators as well as broadband filters.
Funding
National Science Fund for Distinguished Young Scholars of China (61225023); National Natural Science Foundation of China (61405074, 61307100); Guangdong Natural Science Foundation (2015A030313324); Pearl River S and T Nova Program of Guangzhou and Guangdong college student S and T innovation program.
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