A new UV-writing technique is proposed for fabricating custom fiber Bragg gratings (FBGs). A continuously moving fringe pattern is generated by use of two electro-optical UV modulators and synchronized with a moving fiber. This scheme potentially enables the fabrication of infinitely long FBGs with arbitrary profiles and chirp without any mechanical perturbation of the writing interferometer. Preliminary results of this technique are presented and discussed.
©2008 Optical Society of America
Since the first demonstration of fiber Bragg gratings (FBGs) nearly three decades ago , much effort has been focused on obtaining high quality gratings. Many of these techniques are based on the phase-mask [2–5] after the first demonstration of the holographic method for inscription . Ultra-long gratings were first written by stitching a large number of phase-mask written gratings sequentially . Traditional techniques combined with the use of a piezoelectric stage allow writing of FBG with custom apodization, but fabrication is still limited by the phase masks own period profile and length . However, the major developments that ensued tried to remove the dependence on the phase-mask for the generation of custom apodization and phase. In the past few years, a number of techniques have been proposed to fabricate arbitrary profile and long FBGs with the aim of not relying on phase mask characteristics (more than 10 cm) [9–13].
Some of these techniques rely on a sequential writing approach where a moving fiber is periodically exposed after a displacement of the equivalent of N periods in the fringe pattern . By controlling the writing parameters over the time of the writing, a customized grating with an arbitrary chirp, apodization and phase profile may be achieved. The laser pulse power stability, fiber speed stability and the accuracy of the grating period limit the grating quality. Another recent approach  is to carefully monitor the fiber position with the side-diffraction and stitch sub-gratings written with more conventional methods. This allows the introduction of phase shift between sub-gratings potentially creating good quality long gratings. The drawbacks of this technique are that it is still dependent on the phase mask characteristics and is limited by the degree of customization that may be achieved.
Recently, Liu et al. demonstrated an electro-optic shutter technique . Based on a translate-and-write configuration, this technique used an electro-optic shutter combined with a continuous wave UV laser to obtain greater writing accuracy.
These techniques have been motivated by many applications such as dispersion compensation for telecommunication links  or optical coherence tomography , DFB fiber lasers  narrow-band optical add-drop-multiplexers  and filters with desired amplitude and phase for pulse shaping . Also, recent advances in numerical modeling of FBG allow designs of complex profiles and precise calculation of the high reflectivity that one could expect from such long FBGs [19,20].
In this paper, we present a new writing technique that allows fabrication of custom FBGs. The technique could be considered a variation of the translate-and-write configuration. Instead of periodically sending a pulse to a moving fiber, two electro-optical phase modulators are introduced into the two arms of the interferometer to synchronize the movement of the fringe pattern with the fiber’s own velocity. A similar technique based on piezo-crystal mounted mirrors acting as phase modulators was demonstrated by Petermann et al. . This scheme allows continuous writing of the grating. This has the advantage of obtaining averaging of the power that a section of the grating receives without the use of a CW laser. UV light power can be kept relatively low, as the exposition is not periodic, also preventing any physical damage to the fiber. This can potentially overcome the need of position monitoring for subsequent sweeps, as the index change can be sufficient with a single passage.
The proposed technique has several other advantages over previous schemes. It has no moving parts, other than the movement of the fiber which is also common to most of the other published schemes. In particular, the mechanically driven system reported by Petermann et al.  requires the adjustment of several mirrors and is much more complex to realize. In their scheme, a He-Ne interferometer is used to trigger the saw-tooth signal and the mirrors of the writing interferometer are mounted on step-motor to change the period if they want a chirp without apodization, contrary to our technique which just needs a change in the voltage amplitude. In comparison to a moving phase-mask or path length alteration using a piezo transducer, the presented EO interferometer does not have any moving parts to tune the interferometer or to write apodized profiles. Mechanical techniques are limited by the frequency at which the phase change may be induced (~10’s Hz), which is significantly lower than the modulation frequency that can be achieved optically (kHz), allowing a faster inscription.
2. Experimental setup
A schematic drawing of the first experimental setup is shown in Fig. 1. The writing beam is a Spectra-Physics Q-switched Nd: YLF laser operating at 1064 nm. The frequency is quadrupled to obtain 266 nm UV radiation. The Q-switched frequency was set to 25 kHz and the UV average power was around 400mW. The spot size diameter is around 0.1 mm which gives a power density of 5kW/cm2.
An Agilent function generator was used to generate a drive signal to a Matsuhada ± high voltage amplifier, which is used to apply high voltage to the phase modulators. Beside the two phase modulators, a phase mask in a conventional interferometer is used to split the beam into two paths to create an interference pattern at the fiber .
BBO was used as the crystal for the phase modulators, as it is UV transparent and resistant to high peak power damage (>500 MW/cm2 @1064nm). The low capacitance ensures high-speed operation. Propagation was arranged to be along the z-axis of the crystal. The phase modulators are oriented at 180 degrees to each other so that the incident polarized light is oriented along the x-axis in one arm and -x-axis in the other arm of the interferometer. In this configuration, they act as a push-pull phase modulator pair. By applying a linear ramp voltage, the fringe pattern is moved at a fixed speed. The linearity of the phase change induced by the applied voltage on the phase modulators was experimentally verified with a HeNe Michelson interferometer . The Vπ, the voltage required to move the fringe pattern half a period, was measured experimentally to be 0.7kV. A continuously moving fringe pattern can be obtained by applying a ramp signal with this value as the amplitude on each crystal or twice this value on one modulator. The linearity of the ramp generator was found to be better than measurement error.
The alignment of the phase modulators needs some care, as the birefringence is large and slight misalignment causes two orthogonal polarizations to be present in the writing beams. However, the tolerance on the alignment may actually allow better gratings to be written. As is well known  the birefringence induced in the grating is dependent on the polarization of the interference pattern and can be as high as 8%. The lowest birefringence occurs when the polarization of the writing beams is along the propagation axis of the fiber. Nevertheless, even with this polarization, birefringence is always induced when gratings are written owing to the projection angle of the oncoming beams. The angle of projection is approximately 12° (for λ~1550nm) for the phase-mask used for the measurements, and thus this produces a horizontally polarized transverse intensity pattern of Ih=I0sin(12°), where I0 is the total intensity of the beams. As the writing process is highly nonlinear the induced birefringence due to the horizontally polarized transverse intensity is comparatively low . Similarly, if the EO modulators are not correctly adjusted the resulting polarization of the writing beams is off by around 12° from the plane of the incoming beams, the induced vertically polarized transverse refractive index change due to vertical component of intensity, Iv will be of the same order as the horizontal transverse refractive index change, thus cancelling the induced birefringence. It can therefore be suggested that our proposed scheme is superior to all other techniques, provided the polarization is slightly off axis.
The alignment procedure is thus relatively simple. The two beams pass through the EO crystals and are brought together at the fiber by the two folding mirrors as in a standard Talbot interferometer. The EO crystals are rotated around the propagation axis so that they are in the correct orientation for phase-modulation of the beams. This is done by minimizing the beam’s power and power fluctuation measured after passing through a reference polarizer. Once this is done, no other adjustments to the interferometer are required. Also note that compared to a tunable Talbot interferometer , in the EO interferometer the position of the overlapping beams remain fixed forever. In the Talbot interferometer, it is necessary to change the position of the fiber in the plane of the incoming beams when tuning the wavelength, whereas the tuning of the wavelength in the new interferometer requires no moving components. The alignment of the two mirrors becomes much simpler since the beam is not moving during the writing process.
Once the system is aligned, two mirrors are placed at the output from the modulators and the beams returned along the same path. This forms a Michelson interferometer and the beams are recombined at the phase-mask. This beam is directed towards a photodiode. A schematic of this interferometer is shown in Fig. 2(a).
When one of the modulators is switched on, the photodiode detects a homodyne signal, with a frequency of phase shift given by the signal frequency and the voltage applied to the modulator as:
where ϕmeas is the measured phase change, Vapplied is the applied voltage, and fapplied is the applied frequency of the signal. As the beams are displaced relative to each other, a fringe pattern can be seen whose period changes with the angle of separation and whose angle of fringe planes are a function of the displacement in either x or y-axes. When a white card is illuminated with the fringes, the UV interference patters is seen via fluorescence from the papers surface. Further, the relative position of the beams allows the direction of the fringe shift to be altered as well. This is displayed in the movie caption shown in Fig. 2(b).
Figure 2(b) thus shows for the first time how the fringes may be moved continuously by the application of a repetitive asymmetric ramp signal. The velocity of the fiber is synchronized with the fringes by controlling their speed.
Two different schemes were used to move the fiber. The first one shown in Fig. 1 used a high-precision Newport linear motor stage to synchronize the mounted fiber with the moving fringe pattern. This limits the maximum length of the grating to 10 cm. The fiber is mounted on a custom made holder. No position monitoring system was used and since the position accuracy that can be achieved with the translation stage is of the order of magnitude of the grating period, only one exposure was used.
In the second approach, with the aim of fabricating longer FBGs, a rotary Aerotech motor stage was used to pull the fiber placed on vacuum v-grooves mounts as shown on Fig. 3. Instead of using the special 250 microns v-grooves under a vacuum, air is injected to create an air bed under the fiber to minimize the friction that could create irregularities in the grating. A small weight was placed at the end of the fiber to keep it under low tension. It is also possible to fabricate FBGs by keeping a small vacuum that keeps the fiber under tension while pulling without having too much undesired friction that could apodize the grating. The obvious advantage of this method is the guarantee that the fiber is not going to move with respect to the writing beams during the exposition.
A JDSU swept wavelength system was used to measure the reflection of our gratings. The resolution of this system was 3 pm.
3. Arbitrary profile fiber Bragg gratings design
The writing parameters of a uniform fiber Bragg grating can be simply calculated so that the speed of the fiber matches the speed of the fringes as:
where M is the number of grating periods that are moved during a phase modulation period, f is the ramp signal frequency of the high-voltage and neff the effective index of the fiber. The effective index of the fiber has to be calculated precisely to be able to obtain the desired Bragg wavelength. An error in the effective index, as will be shown, is equivalent to a frequency shift and will lead to a shift in the measured Bragg wavelength. A more precise effective index approximation can then be calculated from the difference between the measured and expected Bragg wavelength.
As one of the main interests of this technique is the possibility to obtain arbitrary profile FBGs, the dependence of the grating period and of the apodization over the frequency and applied voltage were calculated using a matlab program. The unsaturated index change due to UV exposure is modeled as:
where f ’ is the applied frequency, f is the velocity-matching frequency calculated from Eq. (2), Λ is the grating period, Λ’=Λf ’/f is the Doppler shifted period and δx=(V/Vπ-1)Λ. Eq. (3) allows the determination of the characteristics of the different gratings which one could obtain with a set of writing parameters.
Figure 4 shows the Bragg wavelength shift as a function of the frequency of the ramp. It is interesting to note that the Bragg wavelength is not a function of the applied voltage. It is then possible to design a chirp FBG by dynamically changing the frequency for different positions in the grating. As Fig. 5(a) shows, this also adds a visibility reduction function, which limits the maximum chirp that can be obtained at a fixed voltage. The maximum chirp that can be achieved without changing the applied voltage amplitude can be deduced from Fig. 4 and 5(a). For a tolerance of 1% change in the visibility, a conservative estimate of the achieved chirp is approximately 230nm at a nominal central Bragg wavelength. By tuning the folding mirrors, a different Bragg wavelength may be chosen with a similar chirp limit. This scheme also trades refractive index change against chirp. However, according to Eq. (3), any unintended apodization may be compensated for by adjusting the frequency and applied voltage together.
Figure 5(b) shows the visibility as a function of the ratio e=V/Vπ. It is interesting to note that the Bragg wavelength has no dependence on the applied voltage and is only a function of the applied frequency and the speed of the fiber. It is preferable to keep the latter fixed to minimize positioning error.
To design an arbitrary profile grating, one can use these simple calculations to obtain the needed frequency and voltage for every segment of the grating.
4. Experimental results
This section presents the preliminary results obtained with a writing setup as shown on Fig. 1 and 3 with the aim of testing the capability of the technique. The first scheme, using a linear stage as shown on Fig. 1 was found to have some limitations. Besides the length of the FBG being limited to the length of the stage, it is also very sensitive to the alignment of the mount that must remain perfectly parallel to the linear stage itself.
Small errors in alignment will give unwanted chirp and apodization that can be observed after only a few centimeters. Another issue noted during the use of this method was the vibration of the stage that creates a reduction in the visibility function. This is supported by the fact that gratings were formed in a certain interval of speed of the linear stage, and only low reflection FBGs were fabricated using this approach in un-hydrogenated fibers. It is believed that the use of an air bearing linear stage with a laser interferometer feedback would significantly improve the capability of this scheme by providing a smoother displacement and an excellent positional accuracy which will permit multiple exposures.
Better results were obtained with the second scheme. The reflection spectrum of a uniform 14 mm FBG written at constant speed is shown in Fig. 6. The fiber used to write the FBG was not hydrogenated prior to the writing. Again, the alignment of the fiber is critical for achieving good quality FBGs. Typical ramp frequency was chosen around 500 Hz to account for the apparent greater fiber speed’s stability associated with this ramp frequency.
The fiber has to remain without deviation from the rotary stage to the mount and to the weight support to avoid an unwanted chirp caused by unstable fiber speed. Friction can also cause irregularities in the grating.
The fabrication of chirped FBGs was achieved by sweeping the frequency of the applied voltage. Figure 7 shows the reflection spectrum of a 5 cm chirped grating obtained by sweeping the ramp frequency over 1 Hz. It is the chirp value that would be expected from the Fig. 4 (~4nm/Hz). Although there is ripple in the spectrum, this demonstrates that the technique allows the fabrication of custom FBGs by changing only the applied voltage function and by leaving the interferometer unperturbed.
More detailed results of complex profiles and longer gratings will be published in a subsequent article.
The principle and preliminary results of a novel custom fiber Bragg gratings fabrication technique using a push-pull electro-optic modulation scheme have been demonstrated. Two electro-optical phase modulators under an asymmetric ramp signal are placed in each arm of an interferometer to create a moving fringe pattern, which can be synchronized with the fiber translation speed. The influence of the writing parameters on the grating structure was modeled to show the capability of writing custom FBGs without any need of mechanical perturbation of the writing interferometer. Preliminary results of uniform and chirped FBGs were shown. We believe that this technique is potentially excellent for the fabrication of continuous long gratings with arbitrary profiles.
The authors acknowledge the support from CIPI’s BP5 Project: ‘Biopsy’ and RK also acknowledges support from NSERC’s Canada Research Chairs Program.
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