We demonstrate a novel method that can detect period fluctuations of periodic structures such as fiber Bragg gratings at an accuracy of approximately 0.5 ppm. These fluctuations can consist of chirp rates, phase shifts etc. The method can also be used to measure phase masks or work as a position control device with spatial resolution in the order of 10 nm. The technique is a modified side diffraction method with interference between two diffraction orders.
©2003 Optical Society of America
The side-diffraction technique was devised by Krug et al.  as a non-invasive method to measure the index modulation externally along the length of a fibre Bragg grating. A short wavelength laser (typically ~630 nm) is focused onto the core of the fibre at the angle where the first-order diffracted Bragg condition is met for the probing wavelength. The diffracted light is collected by a second lens and an optical detector. The diffracted intensity is directly proportional to the square of the index modulation. As the beam is scanned along the length of the grating the diffracted intensity gives the spatial refractive index modulation profile.
The diffraction angle is dependent on the wavelength, incident angle and the grating period. This was recently used by Baskin et al.  to measure slow variations in Bragg period (accuracy 4ppm), and in extension chirped grating group delay ripple.
In later work, Fonjallaz and Börjel  proposed an extension of the method to include measurement of the grating phase. This was achieved by detecting an interference pattern between the zeroth and first diffraction order. Petermann et al.  analyzed the limitations of that method in detail.
In this paper we introduce a novel utilization of side-diffraction: we compare the period of two nominally identical Bragg gratings. The principle is however not limited to fiber geometries, it applies to all transparent media with a periodic refractive index modulation. It is a very sensitive method which can detect differences in period between two periodic structures with approximately 0.5 ppm accuracy depending on length and period. This extreme accuracy is necessary when, for instance, chirp rates, phase shifts etc, are to be measured in fiber Bragg gratings, or when two optical phasemasks are compared for differences in period or for stitching errors.
To demonstrate the principle, we applied it as a validation of the complex grating structure in a fiber based mode inverting grating coupler . The mode inverting grating coupler is a wavelength division multiplexing (WDM) add-drop device which was proposed theoretically in a planar waveguide geometry by Perrone et al.  and realized experimentally by Åslund et al.  in fiber. It consists of a directional coupler with two Bragg gratings written out of phase to each other in each of the two cores of the coupler. It is imperative for the functionality of that device that the two gratings have identical period to within 4 ppm. In the side-diffraction experiments we focused a HeNe beam on the coupler region containing the two Bragg gratings written into each of the two D-fibers and formed an interference pattern with the two first diffraction orders from both gratings; see Fig. 1 (the figure is discussed in detail in the next paragraph).
The probe beam is then translated along the length of the grating, and any change in alignment of the currently illuminated gratings (typically 10–15 periods per D-fiber) would show up as a change in the fringe pattern. Consequently, the method can also be used as a fringe alignment device. It can detect fringe translations of approximately 10 nm of one of the fringe patterns in relation to the other.
The principle of the method is illustrated in Fig. 1(b). The incoming probe beam (HeNe λ=632.8 nm) is focused onto the two cores containing a grating each. The light is reflected by each of the individual gratings and the two emerging diffraction orders, one from each of the fibers, form an interference pattern on a screen in the far-field. The solid line represents the extent of the probe beam, the short dashed line the diffracted light from the top D-fiber and the long dashed line the diffracted light from the bottom D-fiber.
The D-fibers were identical and of a highly photosensitive boron co-doped germanosilicate GF1 type with a 10 micron diameter core. The refractive indices were estimated to be n core=1.45202, n clad=1.44527. The fiber was hydrogen loaded (170 atm, 80°C, 72 hrs) before it was mounted with the flat side out onto a glass slide. The natural curvature of the D-fibers away from the flat side ensured a better than 1° uniformity of the orientation of the flat side once the D-fiber was attached to the slide. It is necessary with vertical alignment for uninterrupted core-core contact when brought together.
The gratings were subsequently direct written with a phasemask using an excimer laser (ArF-λUV=193nm, ΛPM=1061.5nm, Lg=10mm,E ≃ 18 kJ/cm2). The D-fiber ends were spliced to standard telecom fibers and the broad band amplified spontaneous emission from an erbium doped fiber amplifier (EDFA) was used in transmission with an optical spectrum analyzer (OSA) to verify that the gratings had approximately the same Bragg wavelength, bandwidth and reflection strength (ΛBragg ≃ 1538 nm, Δn mod ≃ 5 × 10-4). The coupler setup required arbitrary relative positioning of the gratings. So one slide was mounted on an xyzθϕ sub-micron stage whilst the other was kept fixed. Index matching liquid was used to mediate optical coupling.
The probe beam was mounted on a translation stage with a range that allowed the whole length of the grating to be scanned. The probe beam was focused onto the two D-fibers, through the slides, at an incident angle of approximately 45°; and the far-field of the diffracted light was subsequently monitored on a screen at a distance of about 150 mm.
The 3 to 15 µm separation between the cores created the two-source condition for the necessary transverse interference pattern. Consequently, the properties of the interference pattern depended on the proximity of the two cores. A reproduction of various cross-sections of the coupler and their associated interference pattern is depicted in Figs. 2 (a), (b) and (c). The probe beam comes in from the top of the picture. Fig. 2(a) represents the two D-fibers when they are in-line and close, Fig. 2(b) when they are transversely shifted and close and Fig. 2(c) when they are in-line but slightly separated. We can see when we compare Figs. 2 (a) and (b) that the fringe pattern rotates as the fibers are separated transversally. This occurs because the fringe pattern is always perpendicular to the plane determined by the two point sources and their direction of propagation. Consequently, the same rotation of the fringe pattern would occur if the fibers were rotated together along their longitudinal axis whilst keeping the probe beam fixed. The fringe pattern would be aligned parallel to the fibers after 90° rotation of the fibers, as the probe beam would then arrive at the fibers simultaneously side on.
Comparing Figs. 2(a) and (c) we can see that as the fibers are separated, the period of the fringe pattern decreases. This occurs as the distance between the point sources increases. The period can thus be used as an indication of separation between the cores,
Here d stands for the core-core separation, D the distance to the screen and a the distance between two fringe maxima. The equation is a derivation from the common formula used for fringe period in a two-slit diffraction experiment . For the interference pattern in Fig. 2(a) the following data were estimated: D=0.1 m, λ=633 nm and a=4 mm. This gives a core (center) separation of 11 µm, or 5 µm at the closest point.
The fringe pattern cycled within the illuminated spot as one fiber was translated longitudinally with respect to the other, because the phase front from each grating translates with the grating structure itself. The phase fronts emerge in the manner described by Huygens principle of superpositioned spherical waves, where each of the illuminated refractive index modulations acts as a point source.
A shift of 560 nm (a grating period) restored the original interference pattern. If the beam was translated along the fibers and the gratings had identical period the fringe pattern remained static within the illuminated spot. Consequently, the fringe pattern also remained static when both fibers were moved together and the beam was static. If, however, the gratings had different physical period, the fringe pattern cycled within the illuminated spot under the same phase condition it cycled when one of the fibers was translated. So, it acted as a translation detector.
The method is limited by the grating period, grating length and the capacity to detect changes in the fringe pattern. We estimated that we could discern changes of approximately 1/50th, ≈10 nm, of a fringe period, and the expression for the resolution (Res) is therefore,
So for a grating length of L g =20 mm with a period of Λgrat=530 nm, the setup is capable of detecting period fluctuations in the order of 0.5 parts per million. The accuracy goes up with increased grating length, reduced grating period or an improved fringe movement detection system. A possible version of the latter could include a CCD detector array with lock-in detection systems and dedicated analysis software.
During our measurements of the device under test we did not notice any shifts of the fringe pattern. This suggests that the periods of the two gratings were identical to better than one part in a million, calculated as above. Further, the fringe period did not change more than 5% either, and as the fringe period is directly proportional to the distance between the fiber cores, it suggests that any curvature of the D-fibers induced less than 5% difference in separation between the cores. Any change in separation would, however, not be difficult to automatically compensate for.
Though the method was developed with gratings in D-fiber in mind, the method also applies to standard fiber gratings and slab structures. However, in those cases, there is a greater separation between the cores. This requires in turn, a greater distance to the screen, or detector head, for comparable resolution. The other, preferred, alternative would be to set up a diffraction interferometer as is illustrated in Fig. 3(a). In that interferometer the probe beam is split in two by a beam-splitter, and each beam is made to diffract on a separate fiber grating. The two diffracted orders are then aligned and correctly brought together by mirror M1 and beam-splitter M2. This diffraction interferometer works equally well with optical phasemasks instead of fiber Bragg gratings.
In a dedicated translation detection setup the design of the side-diffraction rig would need to be more robust and easy to align. One plausible design would be to use two transparent slabs with broad area gratings as is sketched in Fig. 3(b). In such a device there is no critical need to align the probe beam. The resolution would be directly proportional to the grating period and the capacity to detect changes in the fringe pattern. The period of the two gratings would not be required to be identical as the inequality could be measured by translating the slabs together in a calibration sweep. In a more elaborate setup the zeroth order could be included to the interference pattern. This would give phase information of the individual gratings as well, which could, for instance, be advantageous if the grating contained stitching errors. Naturally, the technique applies to any reflective periodic structure, so the period of two phasemasks could for instance be compared. It is most convenient, though, if the slabs are transparent as the diffraction can be used without taking surface reflections in consideration.
In conclusion, we introduce a novel method that can detect period differences between two Bragg gratings with accuracy in the order of 0.5 ppm. It is a modification of the side diffraction technique. It is also well suited to measure longitudinal changes in period in Bragg gratings such as chirp, stitching errors and phase-shifts. Further, the technique is also suitable for period comparisons in slab structures such as phasemasks.
The method can also be used as a position control device with resolution proportionalto the grating period, which in this case gave resolution of the order of 10 nm.
This work was supported by the Australian Research Council, Australian photonics cooperative research centre and by Ericsson Australia Pty Ltd. The authors also thank Tom Ryan for fabricating the D-fiber.
References and links
2. L. Baskin, M. Sumetsky, P Westbrook, P. Reyes, and B. Eggleton,“Side-diffraction technique for highly accurate characterization of fiber Bragg grating index modulation,” Conference Proceedings: Optical Fiber Conference, OSA, 1, Wed. pp383, (OFC2003).
3. P.-Y. Fonjallaz and P. örjel, “Interferometric side diffraction technique for the charcterisation of fibre gratings,” Conference Proceedings: Bragg gratings, photosensitivity and poling in glass waveguides, OSA Technical digest, pp 230 FF3-1, Optical Soc. of America, Washington DC, (1999).
4. I. Petermann, S. Helmfrid, and A. T. Friberg, “Limitations of the interferometric side diffraction technique for fibre Bragg grating characterization,” Optics Commun. 201, 301–308, Jan. 15, (2002). [CrossRef]
5. G. Perrone, M. Laurenzano, and I. Montrosset, “Design and Feasibility Analysis of an Innovative Integrated Grating-Assisted Add-Drop Multiplexer,” IEEE J. Lightwave Technol.19, Dec., (2001). [CrossRef]
6. M. Åslund, L. Poladian, J. Canning, and C.M. de Sterke, “Mode inverting grating coupler: experimental results,” Submitted to Appl. Opt. LPEO, Jan. (2003).
7. M. Alonso and E. Finn, “Fundamental university physics, Fields and waves,” Addison-Wesley Publishing Company, second edition, pp. 511, (1983).