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Abstract
We present an innovative concept of a semi-aperiodic phase mask design that enables the realization of multi-notch fiber Bragg gratings (FBG). This design utilizes the overlap and interference of near-infrared ultrashort laser pulses diffracted by short sequenced phase mask sections, which not only allows for a highly stable and reproducible inscription of a large number of wavelength filters but also paves the way towards full aperiodic phase masks. The semi-aperiodic FBG inscribed by this phase mask enables versatile notch filters showing multiple non-equidistant resonances. Those filters target applications, for instance in ground-based telescopes, where a large number of hydroxyl emission lines emitted in the upper atmosphere at near-infrared wavelengths restrict the observation of faint extraterrestrial objects.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The demand of compact and efficient fiber based spectral filter devices strongly drives the investigation of various filter designs by means of fiber Bragg gratings (FBG). FBG consist of a periodic refractive index change inside the fiber core which functions as a narrowband in-fiber reflector. They have proven to be excellent in-fiber filters due to their outstanding properties for the precise filtering of specific wavelengths [1,2]. For instance, in Raman spectroscopy the scattering of the excitation laser wavelength is usually orders of magnitude stronger in comparison to the Raman signal. Therefore, filtering out the laser wavelength drastically reduces scattering effects inside the spectrometer which significantly improves signal-to-noise ratio [3,4]. The same is true for near infrared spectroscopy in astronomy where observations are limited due to a large number ($\ge 100$) of hydroxyl emission lines coming from the earth’s upper atmosphere [5,6]. Those emission lines are strong in intensity which causes scattered light inside the spectrograph and hence shadow the signal of faint extraterrestrial objects. The light collected by the telescope is coupled into fibers to transport it to the spectrograph. Therefore, precise fiber-based filters are required filtering out those lines prior to the spectrograph and thus allowing for utilizing the remaining extraterrestrial light passing in-between [7]. The hydroxyl emission lines have typical linewidths of about $10$ pm [7]. The filters therefore should not only address the wavelengths very accurate but also have narrow bandwidths of a few hundred picometer maximum [7]. It is important to highlight, that a large number of narrowbanded notch filters are essential for sufficient operation [8]. This requires efficient filters with low insertion losses to maximize the light throughput. In summary, a high number of narrowbanded filters which precisely address the desired wavelengths and have low insertion losses are required.
Here, we will focus on the inscription of FBG using ultrashort laser pulses. The application of ultrashort pulsed lasers enables the modification of different kinds of glasses without the requirement of any photosensitivity as result of the nonlinear absorption and the subsequently material reorganization [9–12]. This allows for the inscription of FBG into various types of fibers operating in different wavelength ranges exceeding the H band (around $1450 - 1800$ nm), for instance beyond 2 µm where fused silica is no longer transparent [13]. In addition, those ultrashort pulse-induced modifications inside silica can have very low insertion loss [14]. Consequently, the inscription with ultrashort laser pulses has a great potential to provide those highly desired filter elements [15].
Using ultrashort laser pulses and the point-by-point inscription enables single modifications inside the core with flexible periods [16–18]. Each modification is induced with a single laser pulse; thus, the period is determined by the relative velocity of the fiber movement with respect to the laser beam and the repetition rate of the laser. However, as these modifications are small voids inside the fiber core, they induce strong scattering losses [19]. The scattering can be strongly reduced by using the line-by-line technique where the laser beam scans perpendicular over the fiber core inducing a homogeneous refractive index change [20,21]. While this technique gives maximum design freedom in the grating profile it is relatively slow and critical to alignment issues including the positioning systems accuracy limiting reproducibility [22,23]. These drawbacks can be overcome by the phase mask technique [24–27]. The working principle is depicted in Fig. 1. Here, the phase mask functions as a diffraction grating that is optimized to diffract the incoming laser beam into the $\pm 1$st orders. The resulting two beam interference behind the phase mask generates a periodic interference pattern that is imprinted into the fiber core by a cylindrical lens [26]. Therefore, this technique provides high stability and reproducibility, however, while having the limitation that the inscribed period is fixed by the phase masks period.
Fig. 1. Schematic of the phase mask technique where ultrashort laser pulses are focused with a cylindrical lens through a phase mask into the fiber core for the permanent periodic modification of the refractive index.
For the realization of a compact and fiber-integrated multi-notch filter aperiodic FBG have been presented [23,28]. They offer the advantage that a large number of filters can be realized in a relatively short section of the fiber. This compactness is an important aspect as the fiber has to be stabilized thermally and kept strain-free in order to avoid any shift of the resonances. The aforementioned line-by-line technique is one option for inscribing such aperiodic gratings into the fiber core. However, the fabrication of aperiodic FBG is very demanding and reproducibility is critical. While the use of a phase mask approach would significantly increase the reproducibility and throughput, a direct transfer of complex aperiodic FBG profiles into the phase mask seems almost impossible.
Here, we present a novel design of a semi-aperiodic fiber Bragg grating (saFBG) by applying a semi-aperiodic phase mask inscribing multiple resonances located spatially very close to each other along the fiber axis. Proving the functionality of this scheme can lead to more complex phase mask designs based on the same approach for finally realizing full aperiodic FBGs. In the following, we are introducing the design and fundamentals of the semi-aperiodic phase mask. Subsequently, we will focus on the grating inscription and the characterization of the performance.
2. Phase mask design for a semi-aperiodic FBG
Our aim is to produce an FBG with multiple resonances. Herein, we want to utilize the phase mask technique to ensure a stable and reproducible inscription. The inscription approach is based on a phase mask with sections of different but constant periods. By this design, we can apply a single phase mask for a larger number of resonances. The phase mask design and the illumination of the fiber core is sketched in Fig. 2, which illustrates the working principle of our approach. In this figure, the laser beam illuminates the phase mask from the top, which produces the well-known interference pattern underneath the phase mask. To achieve a compact filter each grating section is not produced by a single phase mask period but by adjacent sections of two different periods. Here, the neighboring periods $\Lambda _{\mathrm {PM}}^{0}$ with its $+1$st diffraction order and $\Lambda _{\mathrm {PM}}^{1}$ with its $-1$st diffraction order interfere at a certain distance $d$ from the phase mask and produce the FBG period $\Lambda _{\mathrm {FBG}}^{1}$. The $+1$st diffraction order of period $\Lambda _{\mathrm {PM}}^{1}$ interferes with the $-1$st order of $\Lambda _{\mathrm {PM}}^{2}$ producing FBG period $\Lambda _{\mathrm {FBG}}^{2}$ and so on. Due to this mixed interference of adjacent phase mask sections we call them semi-aperiodic gratings. In order to produce the multi-notch filter with resonances located spatially very close to each other inside the core, we place the fiber at the position $d$ of the two-beam interference overlap behind the phase mask. The resulting FBG periods $\Lambda _{\mathrm {FBG}}^{i}$ produced by the phase mask sections $\Lambda _{\mathrm {PM}}^{i}$ can be calculated by
Fig. 2. Working principle of the semi-aperiodic phase mask design. The interference of neighboring phase mask sections produces the corresponding FBG sections. The overlap of period 0 and period 1 produces FBG 1 and so on.
In the following we describe some geometrical properties that determine our phase mask design. The maximum length of each phase mask section $L_{\mathrm {max}}^i$ is restricted by the diffraction angles $\vartheta _{i-1}$ and $\vartheta _i$ and the distance $d$ between the phase mask and the fiber. Longer sections would no longer create the desired pure overlap of two different sections $i-1$ and $i$. The interference pattern of the $\pm 1$st diffraction orders of one section itself would reach into the fiber core creating a modification with $\Lambda _{\mathrm {PM}}^i/2$ period. If the section is too short, this would result in the generation of an interference pattern influenced by the next but one section. Consequently, the maximum section length is determined by the equation
Fig. 3. The schematic illustrates the requirement of a gap in-between the phase mask sections. On the left-hand side it is shown by the green marked area that an unwanted interference occurs. By inserting a gap, this can be avoided, which is shown on the right-hand side. In addition, the lines, which are marked yellow, highlight the determination of the section lengths by their corresponding angles $\vartheta _{i-1}$ and $\vartheta _i$.
After the consideration of the physical dimensions of the semi-aperiodic phase mask, we like to discuss which periods to choose. One can see from Eq. (1) that we have two periods involved to define a single FBG period. Thus, the phase mask design consists of $n+1$ grating periods for $n$ targeted resonances. As the resonances are defined by the application, this allows to freely choose one period of the phase mask, e.g. the first one and then all upcoming periods are defined. However, this might not be the best strategy, because another effect also plays an important role: The limited coherence length of ultrashort laser pulses. For the interference behind a phase mask with one constant period, both diffraction orders travel the same distance until they interfere [26]. This is not the case anymore if the interference pattern results from gratings with different periods leading to distinct diffraction angles. The greater the difference between the periods, the greater the mismatch between the optical path lengths $s_i$, which can be described by the equation
3. Semi-aperiodic phase mask design parameters
After this general introduction of the working principle of the semi-aperiodic phase mask, we introduce the specific design parameters for realizing the saFBG used during the investigations presented here. For this first design the spectral region of the so-called H band, i.e. the atmospheric transmission window centered around $1.65$ µm, is addressed because here measurement and characterization equipment are well developed due to applications in telecommunication. The wavelengths composition used was chosen from Ref. [30] which addresses the wavelengths to filter out hydroxyl emission lines. Due to the nature of the two-beam interference behind the phase mask, we can only work in a specific distance between phase mask and fiber to have the optimum interference of two neighboring sections. Therefore, for our design we set the distance to $d=1$ mm. We chose the value of $1$ mm because this leads to acceptable optical path differences (see Eq. (8)) while not shortening the grating sections $L_0$ too much. After this, we defined the phase mask periods based on Eq. (2) and Eq. (10), assuming equally distributed grating strengths of around -30 dB transmission loss. The periods are listed in Table 1. For the chosen wavelengths we have one unavoidable large step inside (number 4) where the wavelength distance and, thus, the optical path difference to the neighboring resonances is larger than for the others. The order of the periods is sorted where each subsequent period gets smaller ($\Lambda _{\mathrm {PM}}^{i} > \Lambda _{\mathrm {PM}}^{i+1}$) as this leads to a minimal optical path difference. Alternating phase mask periods would result in issues with the coherence length as described before. Once the distance $d$ and the phase mask periods $\Lambda _{\mathrm {PM}}^{i}$ are defined, we can calculate the section length $L_0$ and the gaps $\Delta x_{\mathrm {PM}}^i$. According to Eq. (6) the grating section length is $L_0=2.142$ mm. The total phase mask length is $20.37$ mm including the gaps. The values of the phase mask section periods, the gaps, and the resulting interference patterns of the phase mask are listed in Table 1, too.
Table 1. Design parameters of the semi-aperiodic phase mask. Listed are the periods of the grating sections (all sections have a length of 2.142 mm), the gaps on the phase mask, and the resulting interference (IF) periods. The gaps follow the before-listed period. The resulting interference (IF) period $i$ is calculated based on the $(i-1)$th and $i$th grating section (see Eq. (1)). This also applies to the optical path difference (calculated by Eq. (8)). Compare with Fig. 2 and 4 for visualization.
As described in the previous section, we must consider the walk-off effect due to the different optical path lengths of each phase mask section [26]. However, while the walk-off restricts the choice of the periods, it also reduces constraints on the alignment accuracy. The approach of semi-aperiodic phase mask requires careful placement of the fiber at the right position behind the phase mask. Figure 4(a) shows the diffracted rays of the semi-aperiodic phase mask design calculated by the grating equation. The graph illustrates the overlapping fields of the individual grating sections including the gaps under the assumption of ray optics. To highlight the critical areas where one grating part changes to the next, Fig. 4(b) and (c) depict magnified areas of the graph. One can see that placing the fiber exactly at 1 mm distance results in optimum interference of the sections. Placing the fiber too far away is less critical than placing it too close, because being too close to the phase mask results in coverage with the self-interference area which creates unwanted resonances inside of the saFBG. These resonances would be clearly visible in the measured spectra because here no optical path mismatch occurs and, thus, the interference contrast is maximal. In contrast, placing it too far from the phase mask is less critical, since here an overlap from the next but one section ($\Lambda _{\mathrm {PM}}^{i}$ and $\Lambda _{\mathrm {PM}}^{i+2}$) occurs. In this case the interference contrast is very low due to the low coherence length of the ultrashort laser pulses and the large path differences (see Eq. (8)) and, thus, no permanent index modifications are induced. Based on these considerations as visualized in Fig. 4(b), the fiber should ideally be placed at the design distance, however in any case not closer than this with a deviation of $20$ µm. In conclusion, placing the fiber too far away is not as critical as placing it too close; however, it should also not exceed a certain value. Positioning the fiber not exactly at this specified distance results in a decreased length of the saFBG sections.
Fig. 4. The graph (a) shows the calculated diffracted rays according to the parameters given in Table 1 and two zoom-ins of the intersection areas of the phase mask in (b) and (c). Herein, the striped fields indicate by the color which periods contribute to the interference. White plus a color means self-interference.
Based on the presented design, we subsequently shortly estimate the resonance properties, we can expect from such a saFBG. Using the equation for the maximum reflectivity [29]
We applied the transfer matrix algorithm from Ref. [29] for simulating the reflected and transmitted spectra observed in the experiment. Herein, the Eqs. (11) and (12) are indirectly solved to estimate the properties of the inscribed saFBG. For instance, a lower refractive index change $\Delta n_{\mathrm {eff}}$ than assumed leads to resonances with a reduced reflectivity and bandwidth and vice versa. Deviations of the fiber to phase mask distance lead to decreased grating section lengths inside the fiber as described above. The section length $L_0$ inside the fiber is a function of the distance $L_0=L_0(d)$. In particular, it is sensitive to the deviation from the design distance between phase mask and fiber ($L_0=L_0(\Delta d)$), which we will utilize later to estimate the placement accuracy of the fiber behind the phase mask during our experiments. According to Eqs. (11) and (12) smaller $L_0$ will reduce the reflectivity and consequently the suppression while the bandwidth increases.
4. Experimental inscription setup and results
For the inscription of the saFBG, a Titanium-Sapphire laser (Spectra Physics, Spitfire ACE) delivering 100 fs pulses at 800 nm center wavelength. The maximum pulse energy is 5 mJ and the laser beam has a Gaussian shape with a diameter of 10 mm (determined at $1/e^2$). The pulse energy was reduced for the saFBG inscription by an external attenuator to 450 µJ in order to induce a homogeneous refractive index change [10]. The repetition rate of 1 kHz is reduced to 100 Hz to avoid a thermal influence during the inscription. The laser beam is focused by a cylindrical lens (focal length 25 mm, $\mathrm {NA_{eff}} \approx 0.2$) through the phase mask into the fiber core of a singlemode fiber (SMF) (standard telecom fiber, j-fiber, IG09/125). The length of the induced refractive index modification along the beam propagation direction amounts to roughly 10 to 15 µm. The phase mask was placed in a distance of 1 mm to the fiber core according to the design presented above. The phase mask was fabricated in-house by means of electron beam lithography. Herein, the phase mask periods can be addressed with a resolution of 0.1 nm. This translates into a resolution of 50 pm for the Bragg period, which was calculated by the error propagation of Eq. (1). For our experiments, this resolution is sufficient to address the specified wavelengths as this value is well below the bandwidths of the resonances. In addition, we have measured the diffraction efficiency of the phase mask to be $(40\pm 1)$% along all sections, to assure an equal efficiency across the mask. The fiber and phase mask are mounted on a translation stage (Aerotech GmbH) and can be moved precisely with respect to the laser beam to extend the modified region. The fiber and phase mask are moved together underneath the laser beam with a velocity of 0.5 mm/min across the fiber core perpendicular to the fiber axis over a distance of 30 µm. This scanning across the fiber core assures a homogeneous refractive index modification covering the whole core cross-section. Accordingly, coupling to cladding and radiation modes is avoided [25,31]. In addition, these scans perpendicular to the fiber axis are repeated along different fiber axis positions in 0.5 mm steps to extend the grating length and cover the whole phase mask (total length 20 mm). Furthermore, the focus position behind the phase mask is shifting depending on the phase mask’s period. Smaller periods lead to larger diffraction angles and thus to a focus position closer to the phase mask and vice versa. Therefore, while we are moving along the fiber axis, we compensate this focal shift by moving the cylindrical lens stepwise over a total distance of 80 µm.
This scanning enables for a homogeneous growth of the saFBG strength if the focal position is aligned accordingly. The spectral analysis of the saFBG inscribed is performed with a sweeping laser source (Micron Optics sm125) that allows to have a sampling distance of 5 pm with an accuracy of 1 pm. To reduce the noise, the spectral signal is averaged over 20 successive measurements.
The measurement of the resulting transmission spectrum is shown in Fig. 5 and the reflection spectrum in Fig. 6. The corresponding experimental results are listed in Table 2. In the following, we describe and discuss the properties of the inscribed saFBG. The transmission spectrum in Fig. 5 shows strong resonances perfectly matching the design wavelengths, a suppression ranging from $-32.1$ to $-13.5$ dB for the different resonances, and very low out-of-band losses of $-0.15$ dB. The deviation of the resonances from their corresponding design wavelengths is in the order of $0.1$ nm and only exceeds this value for resonance number 4 to $0.17$ nm. The larger wavelength deviation of resonance number 4 is due to the higher optical path difference and the therefore reduced interference contrast, which resulted in a weaker grating strength, too. As described by Eq. (2) and later in Sec. 3, we assumed equally strong resonances. As this resonance is much weaker than the others it has a lower resonance wavelength due to lower $\Delta n_{\mathrm {eff}}^{\mathrm {DC}}$ induced.
Fig. 5. Transmission of the saFBG. The red curve shows the measurement and the blue one the simulation both in good agreement. In addition, the measurement matches very well to the addressed wavelengths (depicted with dotted green lines). The numbers next to the resonances are used for referencing in the text and tables.
Fig. 6. The graph shows the measured reflection signal of the saFBG in red and the simulation in blue. The dotted green lines denote the positions of the addressed wavelengths. The numbers above the resonances are used for referencing.
Table 2. Data for the saFBG. The design wavelengths (wl.) are the initial values on which the phase mask design is based on. The resonance wavelengths (Meas. wl.) and the transmission values are measured at the channel center. The bandwidth is measured as FWHM. The values for the induced refractive index change $\Delta n$ are obtained by the simulation described in Sec. 3.
To obtain a detailed insight into the properties of the saFBG, we applied the transfer matrix algorithm, a numerical tool for calculating the reflection and transmission spectrum of a given grating structure [29]. For evaluating the grating structure inscribed with the phase mask, we compare the simulated and measured reflection and transmission spectra, respectively. The inscription laser always covered multiple phase mask sections and in combination with the scanning we can assume the inscription of rectangular modified grating sections. To determine the grating section lengths, we set up a simulation which takes the given semi-aperiodic phase mask design with the fiber placement deviation $\Delta d$ behind it and the induced refractive index change $\Delta n_{\mathrm {eff}}^{\mathrm {AC}}$ as variable parameters. The refractive index change $\Delta n_{\mathrm {eff}}^{\mathrm {AC}}$ is determined for each individual section of the saFBG. We used these parameters to fit the simulated spectra to the measured ones. The index changes as evaluated by the simulation are listed in Table 2. Based on this model, we can estimate the placement accuracy of the fiber with respect to the phase mask. The distance between fiber and phase mask is the fit parameter which we discuss in the following. It is important to highlight, that we can only estimate a deviation of the placement $\Delta d$ with respect to the assumed $d=1$ mm of the semi-aperiodic phase mask design, because the simulation result is symmetric in placing the fiber closer or further away. The fit estimates the fiber misplacement to $\Delta d = (60\pm 10)$ µm that leads to a shortening of each section of about 6%. This shortening is very small and has a negligible influence on the grating strength or the spectral bandwidth. Next, we answer the question whether the fiber is placed too close or further away. Considering the ray optics depicted in Fig. 4 and the discussion in Sec. 3, the fiber is most likely further away from the phase mask. Otherwise self-interference would occur resulting in intermediate peaks in the reflection spectrum, which is however not present in the measured spectrum. As described above, being further away of the phase mask leads to interference with sections one field apart. However, due to the low coherence length of the laser the interference contrast is too low to induce a refractive index modification.
The measured reflection spectrum of the saFBG in Fig. 6 shows the appearance of side lobes which is expected due to the rectangular shape of the refractive index modification of the saFBG. This is further confirmed by the simulation depicted in blue. According to the theoretical value of $\Delta \lambda _0 = 1.3$ nm calculated above with Eq. (12), the measured bandwidths of the resonances ranging from $0.77$ to $1.31$ nm are in good agreement when considering their respective refractive index modulation $\Delta n$ and its influence on the bandwidth (see Eq. (12)).
One may notice that the resonances have a variation in their transmission loss at the resonance wavelength which directly correlates to the induced refractive index change $\Delta n$ (see Eq. (11)) and which was not intended. One reason is the short coherence length of ultrashort laser pulses as described in Sec. 2 influencing the interference contrast and, thus, the resulting refractive index modulation. The optical path difference (also see Table 1) between two periods of our design is in the range of 5 µm to 9 µm as long as the periods are close to each other. But for the resonance number 4 the difference is 20 µm which is much larger and almost as large as the coherence length of our laser system (around 30 µm). Thus, resonance 4 is significantly weaker than the others. Another fact influencing the grating strength is the focus shift along the fiber axis due to the change in the phase mask period which results in variation of the diffraction angles leading to a difference in optical path lengths behind the phase mask. This shifts the focus roughly about 80 µm when scanning the laser beam from one end of the semi-aperiodic phase mask to the other. As described above, we adapted the focus position of the cylindrical lens inside the fiber as we moved along the fiber axis. However, if the fiber core is not covered perfectly along the fiber axis, it will lead to variations in the coupling coefficient as the modified region only partially covers the fiber core.
In principle it might be possible to apply the technique of the semi-aperiodic phase mask to inscribe fully aperiodic FBGs by drastically decreasing the section lengths and vary only the distance between the sections but not the period. A way to inscribe aperiodic FBG with a UV laser is theoretically discussed by Rahman et al. [32], where the model potentially is applicable to our phase mask design.
5. Conclusion
In this work, we presented the realization of semi-aperiodic fiber Bragg gratings (saFBG) by an innovative approach utilizing the phase mask technique. The phase mask consists of consecutive, constant sections with stepwise decreasing periods. The diffraction at these sections is overlapped in a certain distance to create regions with periodic index modulation inside the fiber core. Thereby, we inscribe an saFBG showing 8 non-equidistant resonances into an SMF matching the chosen wavelengths with a deviation of less than $0.17$ nm. The transmission at the resonances is reduced by 13.5 dB up to more than 30 dB while the overall broadband losses are very low ($-0.15$ dB). Yet, the achieved bandwidths (in the range of $0.77$ to $1.31$ nm) are larger than required for the application of hydroxyl emission line suppression. We are working on reducing the bandwidth of the notches for future phase mask designs by adapting the refractive index modification and realizing longer grating sections. In conclusion, the application of the semi-aperiodic phase mask allows for a fast, compact and reproducible inscription of saFBG with a large number of resonances. These results show in an outstanding way the potential of utilizing neighboring period sections on a phase mask to create more complex grating designs and realizing future high-count notch filters for applications like the filtering of hydroxyl emission lines in astronomy.
Funding
Bundesministerium für Bildung und Forschung (03Z1H534, 13N13654); Deutsche Forschungsgemeinschaft (GRK 2101).
Acknowledgments
The authors like to thank Martin M. Roth, Kalaga Madhav, and Ziyang Zhang for discussions within the framework of our project "MetaZIK astrooptics" (BMBF grant no. 03Z1H534 and 03Z22A511). T. A. Goebel acknowledges support from the IMPRS-PL within the international Ph.D. program.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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