The combination of fiber Bragg grating inscription with femtosecond laser sources and the usage of the Talbot interferometer setup not only gives access to the fabrication of Bragg gratings in new types of materials but also allows, at the same time, to keep the high flexibility of an interferometric setup in choosing the Bragg grating wavelength. Since the spatial and temporal coherence properties of the femtosecond laser source differ strongly from those of conventional laser sources, specific limits and tolerances in the interferometric setup have to be considered. Such limits are investigated on the basis of an analytical ray tracing model. The results are applied to tolerance measurements of fiber Bragg grating reflections recorded with a DUV sub-picosecond laser source at 262 nm. Additionally we demonstrate the wavelength versatility of the two-beam interferometer setup for femtosecond inscription over a 40 nm wavelength band. Inscription experiments in Al/Yb doped silica glasses are demonstrated as a prove for the access to non-photosensitive fibers.
©2008 Optical Society of America
The inscription of waveguides and fiber Bragg gratings with femtosecond laser sources is a very attractive method for refractive index modulation, since it avoids the need for a specific photosensivity of the waveguiding material requiring e.g. germanium dopants or additional hydrogen loading. It holds the promise to create, in a simple way, passive optical functionality such as Bragg reflection in many transparent optical materials. Therefore, fiber Bragg grating inscription in different glass materials with femtosecond laser pulses is a current research field. The most common technology used today is the phase mask technique for IR and UV femtosecond inscription. Typical IR femtosecond-written gratings use higher-order Bragg reflections and are generated by using multi-photon absorption. These gratings have been successfully demonstrated to show type I-fs-IR and temperature-stable type II-fs-IR gratings in silica fibers . Furthermore, gratings in sapphire fibers have been presented which can withstand temperatures above the silica glass transformation temperature . DUV femtosecond inscription allows nanostructuring in pure silica-glasses [3, 4] and in germanium-free rare-earth doped silica glasses which makes it a promising technology for fiber laser applications. The successful transfer of the conventional phase mask technique to DUV femtosecond inscription has been reported [4, 5], but the inscription of type II-fs-UV gratings is critical due to phase mask degradation [4, 6]. Type II-fs-UV grating formation requires high power intensities. For inscription, the fiber is usually placed close to the silica-based phase mask, and the combination of high intensity and high photon energy results in phase mask degradations. This phenomenon is related to non-bridging oxygen hole (NBOH) defect centers , which have a broad absorption at 4.8 eV (260 nm) and reveal a characteristic luminescence at 1.9 eV (650 nm). Therefore, we suggest the combination of a DUV femtosecond laser source and the Talbot interferometer as a very flexible recording concept [8, 9, 10]. The interferometer allows high wavelength versatility [10, 11, 12] and increases the space between the phase mask and the target fiber, which allows using a focusing lens without putting the phase mask at risk of degradation. The use of a femtosecond pulse light source in an interferometer requires specific consideration of the coherence properties. In the following we analyze the impact of the temporal coherence properties based on an analytical ray tracing model for such an interferometer setup. We will demonstrate that it is possible to employ the versatility in Bragg reflection wavelengths provided by an interferometric Talbot setup also in case of femtosecond pulse inscription.
2. Theoretical analysis of coherence properties
The fiber Bragg grating fabrication setup to be considered is a Talbot interferometer as shown in figures 1 and 3, comprising a phase mask as beam splitter and two deflecting mirrors. In order to achieve first-order Bragg wavelengths in the visible or near-infrared wavelength region, laser wavelengths in the UV range are required. The overlapping interference beams form a diamond-shaped overlap region in which the fibers have to be positioned. In order to achieve an interference pattern with good contrast in this overlap region, spatial and temporal coherence requirements have to be fulfilled. Depending on the coherence properties of the light source, the usable overlap area for obtaining interference fringes may therefore be reduced compared to the diamond-shaped area. We want to analyze these restrictions especially for the limited temporal coherence of femtosecond laser pulses. We analyzed the interferometer using a vector-based basic linear algebra method and applying the scheme shown in figure 1(a). Analytic calcula- tions were done with the help of Mathematica™ software. Analytic expressions for the path length differences under different interferometer conditions were derived.
We start for the analysis with two rays, departing from one point O at the phase mask at the angle α, with
where λlaser is the wavelength of the inscription laser and Λpm the phase mask period. Figure 1(a) shows the case in which the rays from the center of the phase mask reach the pivot points A and B. At the mirror surface, the rays are redirected to the angle of incidence on the fiber:
ϕ is the tilt angle of the mirrors. This angle defines (together with the recording wave-length) the period of the interference pattern and therefore also the period of the Bragg grating and its reflection wavelength according to
where n eff is the effective refractive index of the guided mode. We will now calculate the extension of the coherence area. This coherence area defines the possible displacements of a fiber within the diamond shaped overlap for grating inscription.
For the calculation of the influence of a fiber displacement and an off-axis position of the interference point in the fiber the setup is assumed to be symmetrical (ϕ 1=ϕ 2=ϕ).
2.1. Influence of fiber displacement
Figure 1(b) reveals that for different displacements Δz from the ideal position the interfering wave fronts originate from different positions O 1 and O 2 on the original wave in the phase mask position, spaced by a distance lx according to
This distance should not exceed the spatial coherence length of the laser lsc and therefore defines the possible maximum value of Δz. For typical values (tan α ≈ 0.25 and ϕ ≪ α), the maximum value Δz can be estimated as Δz ≈ 2lx.
2.2. Influence of the off-axis position
For the extension Δx of the interference area in x-direction, we have to consider the resulting path length differences between the redirected +1 and -1 ray according to figure 1(c):
We can identify a special case in equation 5 for non-tilted mirrors (ϕ=0) or λBragg=n eff Λpm. Here the path length difference lt is zero and independent of Δx and there is theoretically no additional restriction of the coherence area extension in x-direction for a femtosecond laser pulse. In this case, the two laser pulse discs emerging from the phase mask stay parallel to each other and to the fiber orientation after reflection at the mirrors and can therefore interfere over a long distance.
With variation of the angle ϕ, as required for different Bragg reflection wavelengths, the coherence area will be restricted, also in x-direction depending on the coherence length of the laser. The reason for it is that the laser pulses are tilted by 2ϕ, and only such wave fronts that depart near the optical axis arrive at the fiber position with sufficient simultaneity so as to interfere. Then the time delay is shorter than the pulse length or the temporal coherence length.
As indicated in figure 2 the physical meaning of equations 4 and 5 is that the coherence area does not necessarily fill the diamond-shaped overlap region of the interfering beams completely (figure 2). Following equation 4, laser systems with short spatial coherence length lsc have a limited interference pattern range Δz along the optical axis and require accurate fiber alignment in z-direction as it is stated for excimer laser sources in references [13, 14]. However, for short pulse lasers with a poor temporal coherence length ltc, according to equation 5, the whole diamond-shaped area is accessible in case of parallel mirrors (ϕ=0). Restrictions arise when the mirrors are tilted (ϕ≠0) in order to change the Bragg reflection wavelength; they are due to the limit in the achievable grating length 2Δx. This predicts a restriction of the wavelength versatility of the interferometer in combination with a femtosecond-laser, whereas with lasers with long temporal coherence lengths (e.g. frequency doubled Ar+-lasers) a wide range of Bragg wavelengths can be addressed [11, 15]. Section 4 shows that in our setup the limitation of the achievable grating length exceeds the length of the focus line beyond the telecom-C band.
2.3. Antisymmetric angular tolerances
Finally, we consider the case of antisymmetric mirror tilts ϕ 1=ϕ+Δϕ and ϕ2=ϕ-Δϕ for a fixed wavelength. For the change of the optical path length difference we obtain:
where the approximation sin(Δϕ) ≈ Δϕ has been used, and OM̄ is the distance between the phase mask and the mirrors along the z-axis. Equation 6 shows that there is a direct relation between path length difference and mirror tilt. Therefore, the contrast measurement of the interference structure or the measurement of the resulting fiber Bragg grating efficiency (grating strength) gives a direct possibility to characterize the maximum path length difference and thus allows the temporal coherence length to be measured without the use of a nonlinear crystal autocorrelator.
3. Experimental characterization
The sub-picosecond-laser system used for the fabrication of the FBG, as outlined in figure 3, employs the third harmonic of a Ti:sapphire femtosecond-laser system (MIRA 900 from Coherent). IR pulse duration is 130 fs and the spectral bandwidth 10 nm. Pulses go through an amplifier (Quantronix Titan) and pass a tripler from U-Oplaz Technologies. Following ref.  polarization of the DUV laser beam was perpendicular to the fiber axis. The DUV laser beam (262 nm, 350 fs, 1 kHz, 170 mW ave. power) is focused onto the fiber by a cylindrical lens with a focal length of f=335 mm, which is placed close to the beam splitter phase mask. This phase grating is optimized for 262 nm and has a grating period of 1065.3 nm. The intensity distribution of the diffracted beams was measured to be 57% for the first orders and 3% for the zero-order. The first diffracted orders are then used in the interferometer setup and are redirected by the mirrors placed on rotary stages. The interferometer itself has already been used successfully to achieve first-order Bragg-grating reflection wavelengths from 460 nm  to more than 2 µm for cw-radiation and for nanosecond pulses. The intention here is to study the performance of the interferometer in the case of femtosecond pulses. To separate the performance of the interferometer setup and the material response to the radiation, photosensitive [3, 14, 16] or hydrogen-loaded standard single-mode fibers [9, 11] are commonly used. Therefore a specifically developed photosensitive fiber with 18 mol-% germanium was chosen as target fiber, which is usually used for draw-tower grating inscription .
In order to characterize the coherence area experimentally, fiber Bragg gratings were recorded for different positions and for different angle orientations of the interferometer mirrors.
3.1. Measurement of the influence of the fiber position
Equation 4 indicates the dependence of the grating strength versus fiber position on the spatial coherence length of the laser. In order to measure the influence of the fiber position, several gratings were written in different fiber positions along the z-axis. The height of the beam was scanned at a well defined speed (0.06 mm/s) across the fiber for each grating to prevent intensity fluctuations due to insertion errors of the fiber inside the fiber holder. At first, all gratings were written with the same mirror position; consequently, all gratings have the same resulting reflection wavelength. The grating strength, represented by reflection, is shown in figure 4 for different z-positions of the fiber. The result shows that the femtosecond-laser system allows tolerances of about ±7 mm (20 dB limit) in z-direction. Taking a scan way of 14 mm we get, using equation 4, a spatial coherence length about 3.6 mm. This is slightly less than the beam diameter of around 5 mm. The additional ripples in the grating strength curves are due to a non-homogenous beam profile.
3.2. Optical path differences
While the grating inscription setup was shown to be tolerant with respect to the fiber position in z, it is highly sensitive to optical path difference variation OAO ′-OBO ′ by slight antisymmetric mirror tilts. As shown in figure 5, the optical path difference was then tuned by variation of the angular offset Δϕ. As a result, tolerances for strong gratings of 0.25 mrad were obtained. Due to equation 6 with OM̄=120 mm, the tilt angle corresponds to a pulse delay length of 4×120 mm×0.26×2.5×10-4=31 µm. If the time delay of the pulses between the two beams is lower than 105 fs, then good interference patterns are achieved, and this value determines the adjustment accuracy of the interferometer mirrors. The accuracy should be better than ±0.25 mrad.
The overall pulse length can be estimated from the grating strength result in figure 4 with a tolerance of about 0.75 mrad for the angular tilt of the mirrors. At this tilt angle, the pulse delay is equal to the pulse length and no interference occurs. From equation 6 we get an optical path difference of 95 µm. This corresponds to a pulse length of 315 fs.
For comparison with the mirror tilt measurement of the coherence length, the result for two-photon absorption (TPA) autocorrelation measurements following reference  in KCl are shown in figure 6. From these data an fwhm overlap time of 531 fs is derived. Assuming a sech2 profile such as is generated by the passive mode-locked titanium-sapphire femtosecond laser, the fwhm has to be divided by 1.54 to retrieve the pulse duration . The resulting pulse length is then 345 fs, which is comparable with the value obtained from the tilted mirror measurement.
4. Wavelength versatility of the interferometric setup with femtosecond pulses
The possibility to choose freely the wavelength with the Talbot interferometer is limited using ultrashort pulse sources due to the pulse duration. As long as the limit of the grating length 2Δx exceeds the spot size of the laser, there is no specific restriction for grating inscription without scanning. The corresponding wavelength range can be calculated by extracting the Bragg reflection wavelength from equation 4. Since we get good interference for a pulse delay of 105 fs (≈ 31 µm), a beam diameter of 5 mm allows us to expect a wavelength range for the presented setup from 1520 nm to 1595 nm, which covers the hole telecom C-band (1528 nm-1565 nm). In order to prove this flexibility in achievable Bragg reflection wavelengths, the reflection spectrum of an array of 7 different fiber Bragg gratings made by femtosecond inscription is shown in figure 7. The result shows that the achievable grating strength is constant over the full wavelength range.
5. Gratings in fibers without germanium
Some applications require the inscription of fiber Bragg gratings in fibers where the standard technologies to increase the photosensivity using Ge/B codoping is strongly limited. Fiber Bragg grating stabilized fiber lasers actually are made in combination with reflection mirrors in special photosensitive fibers with the same mode field diameters than the active fiber. These hybrid fiber laser solutions are vulnerable to splice and coupling losses which can be hazardous for high power applications with more than 100 W output power. Femtosecond laser inscription of fiber Bragg gratings in rare-earth doped fiber as presented by ref.  with IR femtosecond exposure allow monolithic and compact fiber designs.
To demonstrate the possibility to write gratings in non-photosensitive fibers, a non-hydrogenated germanium-free Al/Yb (2.5 mol-%/0.43 mol-%) doped fiber is used as a target for inscription. The fiber was made in-house and can be spliced directly to a single-mode fiber. The wavelength shift and reflection bandwidth increase, shown in Fig. 8(a), correspond to a standard grating inscription using an excimer laser and a photosensitive fiber. The resulting spectrum after 15 min inscription time can be found in Fig. 8(b). After the inscription the Bragg wavelength is recorded to make a wave-length shift around 1.8 nm. Assuming that the wavelength shift can be attributed to temperature increase with a wavelength shift of 11 pm/°C one can estimate a temperature increase inside the fiber around 160 °C during inscription. This indicates a strong interaction of the light with the target fiber.
In this paper we have investigated the coherence conditions and limits for fiber Bragg grating inscription with a two-beam interferometric setup and a DUV femtosecond laser. We have successfully demonstrated the interferometric inscription of such fiber Bragg gratings at DUV wavelengths and with femtosecond pulses and we have been able to derive the coherence length of such a DUV laser source from grating strength measurements. It was demonstrated that despite limiting factors of short coherence light sources, it is possible to use the flexibility of a Talbot interferometer setup for fiber Bragg grating inscription over a wavelength range of about 75 nm. Inscription experiments in non-photosensitive Al/Yb doped silica glasses are demonstrated.
The funding of this work by the Thuringian Ministry of Cultural Affairs is gratefully acknowledged.
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