1. Introduction

Since their initial demonstration in the mid-eighties, fibre Bragg gratings (FBG’s) have become ubiquitous in the fields of telecommunications and optical sensing. Their uses range from channel selection in dense wavelength division multiplexed systems and gain flattening filters for telecommunications1 to sensors for structural health monitoring2 and in-vivo biomedical diagnostics3. FBG’s are typically fabricated by exposing a photosensitive optical fibre to an interference pattern of ultra-violet radiation so that the sinusoidal interference pattern creates a sinusoidally varying refractive index profile along the axis of the fibre core. It is this variation in refractive index that forms the Bragg reflector. The interference pattern can be formed using many different arrangements such as internal writing, free-space interferometry or Sagnac interferometers4,5. However, the most common technique now employed is to use a transmission phase mask positioned close to the side of the fibre6 as is shown in Fig. 1. Typically, a ‘zero-order-suppressed’ phase mask is used so that the majority of the transmitted power goes into the m = ± 1 diffraction orders to form the required interference pattern in the region immediately adjacent to the mask. This set-up has proved popular due to its simplicity and stability and also the ability to form extended grating structures along the fibre by scanning the UV beam along the length of the fibre through the phase mask. A further advantage of this side-writing technique is that different FBG structures can be created by moving the phase mask relative to the fibre during inscription to shift or blur the sinusoidal index variation7. For example, discrete phase jumps can be introduced into the grating structure by moving the phase mask by a distance equivalent to the phase shift required as the UV beam passes the desired location. The grating strength can also be modulated by oscillating the mask back and forth as the beam traverses the fibre to create a grating with spatially and/or spectrally varying strength. For example, oscillating the mask by a distance exactly equal to the FBG pitch (half that of the phase mask period) will totally wash out the grating structure and so by varying the oscillation amplitude in a controlled manner allows full control over the grating strength as a function of axial position along the fibre. It is also possible to average out small scale irregularities in the phase mask structure by moving the phase mask in discrete steps by exact multiples of the phase mask pitch as the UV beam traverses the mask, hence resulting in reduced noise on the resultant FBG. In all of these instances, it is critical that the motion of the mask is precisely known and, more importantly, can be set to a pre-determined fraction or multiple of the phase mask period.

 

Fig. 1. Typical layout for side-writing of a fibre Bragg grating using a transmission phase mask. The outgoing UV beams are marked with their respective diffraction orders.

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Although it is theoretically possible to set the motion of the translation stage to exactly match the quoted period of the phase mask being used, this does not always prove accurate enough due to inaccuracies in the translation stage’s position sensor, errors in the phase mask metrology, or to the phase mask structure not being mounted exactly perpendicular to the stage’s motion. Typically, to set the amplitude of motion more accurately, a series of FBG structures are written while the phase mask is moved back and forth, or ‘dithered’, in a triangular wave fashion using a voltage waveform from a function generator to drive a piezo-electric translation stage. Changing the amplitude of the applied voltage waveform generates different oscillation amplitudes for each successive FBG so that a series of gratings is formed, each with a different reflectivity. By plotting the strength of the resultant FBG’s as a function of applied voltage, and then interpolating the curve to find the minimum, an accurate determination of the voltage required to exactly extinguish the grating can be made. The corresponding amplitude is then known to be exactly equal to half the phase mask period.

Although this process works well and, given time can result in an accurate calibration of the phase mask amplitude, it can require five or more gratings to be fabricated and tested which can be laborious and time consuming. Furthermore, in a high volume production environment it can result in wastage of several meters of high cost photosensitive fibre each time the calibration is carried out.

In this paper we present an alternative technique that does not require any gratings to be written, and can set the phase mask oscillation amplitude to an accuracy of ±1 nm in a single automated process. Furthermore, since the process uses the diffracted beams transmitted by the phase mask itself, the calibration inherently determines the amplitude as a fraction of the phase mask period rather than a fixed physical distance equal to the quoted design period of the mask.

2. Phase mask motion

Our technique uses the motion of the phase mask itself to form a time-varying Michelson interferometer or ‘Phase Mask Interferometer’ (PMI), from which the exact excitation voltage required for a given phase mask motion can be directly determined. To understand the calibration process it is necessary to first understand the effect of motion on the UV beam passing through the phase mask. Figure 1 shows a schematic of a typical side-writing set-up for inscribing FBG’s. The fibre is located close to, but not touching, the etched surface of the phase mask. In this region, the beams diffracted into the m = ± 1 diffraction orders interfere, creating the necessary variation in UV intensity to inscribe the FBG structure in the fibre. If the fibre is removed, the diffracted orders will be free to propagate away from the phase mask, and it is these transmitted beams that are used to form the PMI.

Figure 2 shows a close up of the phase mask surface and a snap shot of the phase fronts of the diffracted first order beam. The phase of the outgoing beams can be thought of as being anchored to specific features of the mask, such as the top right hand edges of the lamellar structure of the phase mask. If the mask is then moved incrementally to the right, these features also move and the phase of the +1 diffracted order is advanced with respect to its original position. Similarly, the -1 diffracted order is retarded. This is indicated in Fig. 2 by the dashed phase mask and phase fronts in the +1 diffracted order. Furthermore, if the higher orders are considered, the same phase mask motion results in an m^th order multiple phase shift.

 

Fig. 2. Schematic of the action of phase mask motion on the transmitted phase fronts through a diffraction grating. Note that as the phase mask is translated to the right, the phase fronts in the +1 diffracted order advance.

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If the transmitted ±1 order beams are then reflected back on themselves by positioning two mirrors so that the diffracted orders are reflected normal to the mirror surfaces, the beams will pass through the phase mask structure a second time and will pick up a further phase shift due to the motion of the phase mask that is additive to the initial phase shift. Since these retro-reflected beams are also diffracted by the phase mask the -/+1 orders will be coincident and counter-propagating along the axis of the incoming beam. Since these two retro-reflected, counter-propagating beams vary in relative phase as the phase mask is moved from side-to-side, measuring the time-varying intensity of the retro-reflected spot generated by the beams provides a direct method for calibrating the phase mask motion. In order to detect the amplitude of the retro-reflected spot a beam splitter cube was placed in the incident beam to direct the spot onto a large area detector. This is shown in Fig. 3.

 

Fig. 3. Set up of the PMI showing locations and fixturing of the retro-reflecting mirrors and beam splitter cube for detecting the intensity of the reflected interference spot

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Since the effect of phase mask motion is doubled as the beams pass through the phase mask twice, a movement of one quarter period of the mask results in a full cycle of the detected PMI amplitude. Similarly, if higher order beam pairs are used then the sensitivity of the PMI amplitude to the motion of the phase mask is increased by a factor equal to the order number used. The choice of which order to use is usually dependent on the quality of the phase mask since there may be insufficient diffraction efficiency into the higher orders and the m = ±1 orders may be the only practical option. For a good ‘zero order nulled’ mask there is often enough power in the higher orders to allow the m = ±2 or 3 orders which results in a doubling or trebling of the achievable sensitivity of the technique. However, all the results presented here were based on interference between ±1 order beams.

3. Operation of the PMI

Using this PMI set-up, the phase mask amplitude can be determined in a number of different ways, depending on the desired outcome. For example, if the dynamic response of the phase mask oscillation is required for apodisation of the FBG structure, then a saw-tooth motion with an amplitude exactly equal to the phase mask pitch will result in a perfect sine-wave that is continuous if the periodic repositioning of the phase mask is ignored. The amplitude of the phase mask motion can then be set to an exact multiple of the phase mask period by applying a sinusoidal curve fit to the measured data recorded during the saw-tooth ramp and then programmatically adjusting the amplitude of the phase mask motion until a good fit is obtained to the data. The detected amplitude from the m = ±1 orders of the PMI using a saw-tooth motion of exactly 1/4 of the phase mask period is shown in Fig. 4. The apparent noise seen at ~0.75 and 1.75 seconds corresponds to the fly-back period of the saw-tooth and is due to the rapid re-setting of the PMI and also to a period of ringing following the rapid motion. This will be covered in further detail below. This technique can be used to determine the dynamic voltage that needs to be applied to the piezo-electric dither stage to achieve full washing out of the FBG structure (the required voltage in this instance would be twice that used to achieve the best sinusoidal fit). It is also possible to calibrate a triangular oscillation of the phase mask using this approach however a further step is then necessary to adjust the phase mask offset so that the output of the PMI generates a continuous sinusoid when the correct amplitude is achieved.

 

Fig. 4. Detected intensity in the retro-reflected spot.

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Precise jumps in the phase mask position such as would be applied when inducing a phase shift or when introducing step-wise changes in the phase mask position to average out phase mask noise need a slightly different calibration technique because the steady state positioning of the piezo-electric stage can be slightly different than the dynamically varying values. In these instances the interference signal will be stable between jumps and, if set to an exact multiple or sub-multiple of the phase mask period, will have the same intensity before and after each jump. The calibration is then achieved by applying a linear curve fit to the data recorded between jumps and optimising the amplitude of the jumps to achieve the best linear fit to the data. In this instance, the sensitivity of the calibration can be enhanced by adjusting the offset of the phase mask motion so that the plateau regions between jumps occur at or near the point of inflection of the interferometer output. When the measured intensities are equal before and after each jump, the phase mask motion is an exact multiple or sub-multiple of the phase mask period. If fractional-wave phase shifts are required then the peak-to-peak voltage applied to the translation stage needs to be divided by the appropriate factor to achieve the necessary phase shift. The results from the calibration of a phase mask using this approach are shown in Fig. 5 a, b, & c. The plots show the PMI amplitude for applied square wave oscillations of the phase mask using square wave excitation of the piezo-electric dither stage of 267, 268, and 269 mV (The voltage calibration for the translation stage used was approximately 1 mV / nm so this corresponded to approximately 267 – 269 nm translation of the phase mask). It can be clearly seen that a voltage of 268 nm gave the best linear fit to the data within the stable regions of the measurement. Thus with the technique used in this configuration an accuracy of ~±1 nm in the dither amplitude can be achieved. As with the dynamic calibration described above, this process can be readily automated by programmatically varying the square wave voltage applied to the piezo-electric stage and applying a linear fit to the stable regions of the resultant data. The best voltage is determined by minimising the mean-square-error between the linear fit and the data.

 

Fig. 5. Detected intensities from the PMI during steady state calibration of discrete phase mask motion, showing (a) optimum oscillation amplitude using a square wave oscillation amplitude of 268 mV, (b) insufficient oscillation amplitude using a square wave oscillation amplitude of 267 mV, and (c) excessive oscillation amplitude using a square wave oscillation amplitude of 269 mV.

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4. Optimising phase mask motion

An additional benefit of this technique is that it provides a direct indication of the motion of the phase mask itself. It was found that this can be significantly different to the motion of the translation stage used to provide the motion, so that simply using the stage’s in-built position sensor and feed-forward routines, can give misleading results. For example, the translation stage used for this investigation (PI P-752 NanoAutomation stage) could be operated under closed-loop control via its capacitive position sensor and the motion could be optimised to reduce ‘ringing’ of the stage following a step change in position. Although this built-in control was highly efficient at controlling the motion of the stage itself, when the motion of the phase mask was measured directly it was clear that it was still possible for the mask to ‘ring’ after each jump. This is shown in Fig. 6 (a) & (b). An optimised square profile ramp was applied to the dither stage, Fig. 6(a); however the output of the PMI shown in Fig. 6(b), clearly indicates that the phase mask itself was not so well controlled. This is probably due to the combined mass of the phase mask and mount and also the inherent Abbé error created by the geometrical necessity of having the mask located some 3 cm away from the axis of the stage position sensor. Using the output from the PMI, this ringing was reduced by providing a profile to the control voltage instead of an instantaneous jump, as shown in Fig. 7 (a) & (b). Although the voltage profiling increased the time taken to execute the move, the overall duration of the motion could be made significantly shorter than the duration of the ringing that resulted from the instantaneous jump. The best result was obtained using a sinusoidal voltage profile on the piezo-electric stage motion.

 

Fig. 6. Response of the phase mask to a square wave motion of the piezo-electric translation stage optimised using the proprietary driver supplied with the stage. (a) stage motion measured by the on-board capacitive sensor, (b) motion of the phase mask measured using the PMI.

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Fig. 7. Response of the phase mask to a square wave motion of the piezo-electric translation stage optimised using the PMI output. (a) stage motion, (b) motion of the phase mask measured using the PMI.

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5. Physical layout

A significant advantage of this technique is that the hardware needed to form the interferometer can be readily mounted on a typical direct write FBG fabrication rig. In our case, the retro-reflecting mirrors were mounted on a bracket that was directly clamped in place using the pneumatic clamps used to hold the fibre close to the phase mask; and the detector used to record the intensity of the interferometer spot was placed onto the main translation stage of the FBG writing jig using a small kinematic mount. This mount also held the miniature beam splitter cube so that the trajectory of the incoming UV beam was not affected by the placement of the PMI detector. The arrangement of the fixtures is shown in Fig. 3. The detector and mirror assemblies could be readily mounted onto the FBG production rig and adjusted for use within a few minutes with a minimum of effort. A typical calibration routine at a single location takes no more than 1 minute to complete and can be realised under full computer control. Calibration of chirped masks can be achieved by repeating the single-point calibration at multiple points along the phase mask.

6. Conclusions

A technique has been presented for calibration and optimisation of the motion of phase masks for inscription of complex FBG structures using an interferometric side-writing technique. The technique is fully automatable and significantly reduces the time taken for calibration compared to the common technique of writing a series of gratings and mapping grating strength against phase mask oscillation amplitude. Accuracies of phase mask oscillation amplitude of ±1 nm have been achieved using this technique.