A Bragg grating fabrication method based on a phase-controlled interferometric approach with both coarse control and fine tuning of Bragg wavelength in the range of 1200-2200 nm is demonstrated by fabricating multiple Bragg reflectors in a single fiber device. With the fine tuning method, we achieved ~113 nm of FWHM bandwidth centered at ~1545 nm and ~174 nm of FWHM bandwidth centered at ~2005 nm, which were limited only by the size of the overlap of the interfering beams and by the Bragg wavelength. We used the wide range of the coarse wavelength control and the precision of the fine wavelength setting to determine the fiber Sellmeier coefficients with a mean squared error <3.5 × 10−9.
© 2014 Optical Society of America
There are a growing number of applications of large periodic structures for light manipulation which require complex designs with a broad range of design parameters. One of the most versatile methods of fabrication of complex periodic structures is based on phase-controlled interferometry . Since its publication in 1999, the approach has seen a variety of implementations by a diverse range of research and industry teams [2–4], and important advantages over both conventional  and more advanced  phase mask fabrication techniques have been demonstrated.
This technique is distinct from the direct write methods for making complex gratings in optical fibers demonstrated by various groups during the 90s. The ‘stitching’ concept [7,8] pioneered at the Royal Institute of Technology evolved into the powerful beam intensity modulation methods [9,10] demonstrated by the groups at Southampton and 3M. Intensity modulation of the UV writing beam allows stitching of single fringes to fabricate long fiber Bragg gratings with arbitrarily complex reflectivity profiles but also results in an inefficient use of the UV light because the beam is effectively ‘blocked’ for half of the fringe period. Moreover, the fiber is translated with constant speed relative to the UV fringes resulting in reduced fringe visibility of the induced refractive index change. Those drawbacks were addressed by using pure phase control of the interfering beams and moving the UV fringes along with the fiber .
A fundamental problem with using phase masks as compared to two-beam interferometry  is the presence of zero and high diffraction orders which reduce the contrast and uniformity of the interference pattern created in the overlap of the fundamental diffraction orders and, therefore, reduce the efficiency and fidelity of the grating photo inscription in a photosensitive medium. Another problem is a fixed  or limited  wavelength range for Bragg gratings that can be fabricated using a single phase mask, thus imposing a requirement for a stock of phase masks to cover the wavelength range of interest. This is especially a problem when fabricating gratings in large core diameter fibers since the overlap of the interfering beams has to be large enough for the efficient exposure of the fiber core to the interference pattern, while the wavelength range, using method , is inversely proportional to the width of the overlap and is reduced for large core diameter fibers.
Large core diameter fibers represent a conventional solution for power scaling of fiber lasers, and the laser operational wavelengths range widely, depending upon application. Mid-infrared Ho- and Tm-doped fiber lasers are attractive for laser surgery  as superficial ablation of tissue is very efficient at 2 um. Ho-doped fiber lasers are an enabling technology for applications involving light propagation in the atmospheric transparency window at 2.1 um . The wavelength range of Tm-doped fiber lasers around 2 um overlaps with atmospheric CO2 absorption lines which can be used in remote sensing applications. It has been shown  Tm-doped fiber lasers can be used to resonantly pump Ho-doped fibers with high efficiencies suitable for potential power scaling at 2.1 um. Near-infrared Er-doped fiber lasers operating around 1.57 um are often used for pumping Tm-doped fiber lasers  which have been shown to operate at wavelengths as short as 1.66 um  and can be used as pumps to achieve lasing at 4.5 um in Dy:InF glass fibers .
A motivation for the work presented in this paper was to develop a fabrication technique capable of photo inscription of Bragg gratings in small and large core diameter optical fibers, with Bragg wavelengths covering the near- to mid-infrared (IR) wavelength range . The capability to fabricate wavelength matched Bragg gratings into the photosensitive core of the optical fiber to form a laser resonator enables realization of all-fiber monolithic laser architectures which require no optical alignment.
In this paper, we expand upon the version of the phase-controlled interferometric method introduced in  and demonstrate the ability to fabricate multiple Bragg gratings at wavelengths in the range of 1200-2200 nm into a single fiber device, with the coarse wavelength control over 1000 nm being accompanied by fine wavelength tuning within ~113 nm of the FWHM bandwidth centered at ~1545 nm and within ~174 nm of the FWHM bandwidth centered at ~2005 nm. Accurate measurements of the fiber dispersion in the near- to mid-IR wavelength range are enabled by the precision of the wavelength control.
2. Fabrication method
There is no fundamental limit on the grating length when the phase-controlled approach  is applied to fiber Bragg grating fabrication - an optical fiber is continuously translated at a rate of through an overlap of coherent beams at UV wavelength tightly focused at an angle onto the photosensitive core of an optical fiber, and sequential portions of the fiber core are exposed to an intensity pattern of the UV irradiation resulting from the beam interference (Fig. 1).
In the version of the phase-controlled method presented here, the period of the interference pattern is changed by moving the beams across the lens as shown in Fig. 1 using mechanical or non-mechanical means . Such an approach requires no additional optical realignment as compared to the lens assisted imaging  since the beam overlap is located in the focal plane of the lens and, therefore, maintains its position on the fiber core as long as the incoming beams remain parallel.
In order to photo imprint the UV intensity pattern with period into the fiber core moving at velocity without the resulting fiber Bragg grating being erased by sequential exposures, the fringes of the interference pattern have to move along with the fiber through the beam overlap which can be achieved by frequency shifting the interfering beams:
Acousto-optic modulators (AOM) made of UV transparent fused silica typically operate at frequencies of hundreds of MHz and, compared to bulk electro-optic modulators (EOM), do not have issues associated with applying kV control voltages . In addition, frequency shifting is achieved naturally in AOM, making them more versatile for the phase-controlled grating writing technique.
For instance, the grating period can be detuned from the period of the interference pattern , when the frequency shift is detuned by from the value given in Eq. (1):Fig. 2.
Equation (8) can be simplified for small wavelength detuning, when the dispersion of the effective refractive index can be neglected, i.e.:
With tight focusing, the apodization effect is negligible in most practical situations, e.g. a 20 nm wide chirped grating with central wavelength at 2000 nm would have to be corrected for only 0.03 dB reduction in the refractive index modulation (~0.06 dB reduction in reflectivity) at the ends of the grating spectrum when the interfering beams are focused to a 6 um wide overlap. The FWHM of the wavelength detuning range estimated from Eq. (9):Fig. 2). If so desired, the refractive index modulation can be sacrificed beyond 3 dB (as was done in ) to achieve ultra-wide detuning from the optimal Bragg wavelength .
The wavelength tuning method shown in Fig. 1 is free from the apodization limitations on the refractive index modulation resulting from the frequency detuning, however, the shortest achievable Bragg wavelength depends on the lens :Fig. 1 as coarse wavelength control of the 'center' wavelength of the envelope described by Eq. (8). In this context, we refer to the frequency detuning method as fine wavelength tuning. With coarse tuning, the period of the interference pattern is changed, not the actual Bragg period of the fabricated grating. The Bragg period of the grating is described by Eq. (3) regardless of the tuning method and the accuracy of the fabrication method is not limited by the fiber velocity error which can be compensated for by using the phase control of the interfering beams as has been shown in .
Apodization of the refractive index modulation required when fabricating gratings with complex designs (6) is usually achieved by using dithering waveforms to rapidly alter the phase of the interference pattern whereby a controlled wash-out effect is achieved. Using a square dithering waveform with period :Eq. (8).
We used a cw frequency-doubled Ar-ion laser producing 150 mW of output at 244 nm, with the total loss in the optical path of the grating fabrication system being ~6 dB. The UV laser beam was split, and separate AOMs were used to frequency shift each of the resulting beams by individual amounts determined from Eq. (1). Each AOM was driven by an Agilent RF signal generator, with a phase modulation waveform from a function generator being applied to one of the RF carriers. The phase modulation waveform downloaded to the function generator was calculated from a desired period profile in accordance with Eqs. (3), (4) and (6). A separate function generator was used to apply a dithering waveform (12) calculated from a desired apodization profile (13). The signal and function generators were synchronized using ultra-stable timebase to achieve coherence of the RF signals. The fiber was mounted on an Aerotech air-bearing translation stage with a laser interferometer feedback to ensure stable motion. We used commercially available infinity-corrected microscope objectives with the focal lengths in the range 10-20 mm to overlap/focus the interfering beams on the fiber.
Using the coarse wavelength control method shown in Fig. 1, we fabricated multiple 4 mm long gratings, each at a different 50 nm spaced wavelength, in a single piece of GF3 fiber from Nufern which was translated at 4 mm/min. The gratings were written in two runs, with a characterization run in between. In the first run, we fabricated ~50 nm spaced gratings between 1550 nm and 2200 nm. Our initial assumptions for the effective refractive index of the fiber and its dispersion led to wavelength errors in the first run, which varied from ~2 nm to ~6 nm. After characterizing this set of fabricated gratings, we made corrections to the fiber effective refractive index in the wavelength range covered in the experiment and determined Sellmeier coefficients for the GF3 fiber (Table 1) using the methodology described in [21,22].
The obtained fit is referred to as Sellmeier fit since we used the Sellmeier equationEq. (7), we reduced the wavelength error of the gratings fabricated in the second run, in the range of 1200 nm to 1500 nm, to about 0.1 nm. This residual error can be attributed to the measurement error and to variations in the fiber velocity and fiber tension when the gratings were being written. The values of the effective refractive index of the Nufern GF3 fiber derived from the measured grating wavelengths are shown in Fig. 3 along with the Sellmeier fit, the mean squared error (MSE) due to the aforementioned factors being <3.5 × 10−9. This corresponds to the standard deviation of 6 × 10−5 in the measured effective refractive index values.
The transmission spectra of the fabricated multiple gratings combined in Fig. 4 were measured using a supercontinuum light source and an optical spectrum analyzer (OSA) with 0.05 nm wavelength resolution. Each spectrum represents a 10 nm span around the corresponding grating Bragg wavelength, with the measurements in the rest of the 1200-2200 nm wavelength range not being performed. Spectral features additional to the grating transmission spectra around 1400 nm and 1900 nm are associated with water vapor absorption in the air gaps of the measurement setup. The fine details of the grating transmission spectra are not resolvable in the graph with the enormous 1000 nm wavelength range, and are shown for two gratings (at 1500 nm and 2045 nm, representative of the two experimental runs) in the insets. The bandwidth of the 1500 nm grating is narrower than the bandwidth of the 2045 nm grating because the former grating contains more of shorter grating periods in the same 4 mm length and, therefore, has higher spectral selectivity.
In an experiment to demonstrate the fine wavelength tuning, we locked the coarse wavelength control to ~1550 nm and fabricated multiple gratings in combs of five, each 4 mm long grating at a different 5 nm spaced wavelength, in a single piece of the GF3 fiber. In another experiment, the coarse wavelength control was locked to ~2000 nm. For fine wavelength tuning, we used phase modulation as described by Eq. (2) to detune the frequency shift individually for each grating from the optimal value given by Eq. (1). We used Sellmeier coefficients obtained for the GF3 fiber in the previous experiment to calculate the required frequency shifts, and the Bragg wavelength error remained within 0.1 nm.
The transmission spectrum of one of the combs is shown in Fig. 5 centered at ~1545 nm, with this optimal Bragg wavelength for a corresponding pattern period being set by the coarse wavelength control. The inset in Fig. 5 shows the details of the comb design used as the phase modulation waveform.
Multi-wavelength combs can also be fabricated using complex sinc-sampling apodization profiles . In order to demonstrate the apodization capability of the phase-controlled approach, we used a similar but more efficient sampling design  shown in the inset of Fig. 6 to fabricate a 5 mm long five-channel grating aligned with the 100 GHz ITU grid and centered at 193.3 THz [Fig. 6]. In the case of five channels, the efficient sampling design requires only 65% of the refractive index modulation as compared to the sinc-sampling.
The values of the refractive index modulation calculated from the measured reflections of the gratings fabricated in the experiments described above are plotted versus their Bragg wavelengths in Fig. 7(a), and the wavelength errors are shown in Fig. 7(b). The background silica loss sets the practical limit to ~2200 nm at the longer wavelengths. The actual of the lens used in the experiment was slightly larger than the specification of which allowed the shortest achievable wavelength that was measured to be shorter than the 1250 nm calculated in Section 2. The refractive index modulation at this wavelength was reduced due to the beams being clipped at the lens edge. The variation in the measured refractive index modulation can be attributed to both measurement errors and the variation in both material and waveguide properties of the fiber over the 1000 nm band.
The results obtained for the control bandwidth of the fine tuning method showed a good fit [see Fig. 7(a)] with Eq. (9), a simplified version of Eq. (8). The fit parameters are ~113 nm and ~174 nm for the FWHM of the induced refractive index modulation, ~6.4 um and ~7.1 um for the beam overlap width, ~1545 nm and ~2005 nm for the optimal wavelength when the coarse wavelength was set at 1550 nm and 2000 nm correspondingly. The mismatch between the intended (1550 nm and 2000 nm) and the actual (~1545 nm and ~2005 nm) optimal wavelengths can be attributed to the calibration error in angle which sets the period of the interference pattern to and no prior knowledge of the value and dispersion of the effective refractive index of the fiber. This mismatch does not affect the Bragg period of the grating described by Eq. (3), its only effect is in the unintentional grating apodization associated with the frequency detuning from the actual optimal wavelengths as discussed in Section 2. The measured center wavelengths of the fine tuning envelopes were used to re-calibrate the coarse tuning means. The difference in the beam overlap widths and the refractive index modulations can be attributed to differences in UV laser parameters between the measurements of the fine tuning effects at the different optimal wavelengths (there was a significant time lag between the fine wavelength detuning experiments). Grating transmission levels calculated from the Gaussian fit at ~1545 nm are plotted as a dashed line in Fig. 5 showing a good match with the measured transmission spectrum of the grating comb.
In order to measure the beam overlap, we photographed the UV-induced luminescence in the Ge-doped core of a large core diameter fiber shown in Fig. 8 when the grating writing system was coarse tuned to 2100 nm. The microscope was focused onto the plane of the UV beam overlap, which explains the lack of sharpness at the fiber boundaries and distortions in the image of the fiber core. The UV beams were attenuated to the levels where the intensity of the UV-induced luminescence was comparable with the background illumination of the fiber so that the fiber and the beam overlap dimensions can be visually compared in Fig. 8.
Images in Fig. 9 show the luminescence traces in the Ge-doped core of the large diameter fiber induced by either left or right or both UV beams when the grating writing system was coarse tuned close to the extremes of the wavelength range at 1300 nm and 2100 nm. It is evident from the photographs that the angles between the beams are different at these wavelength settings, however, the beam overlap is largely maintained within the fiber core. The UV beams are incident onto the fiber core from the bottom of the figure and are propagating up.
We have proposed a version of the phase-controlled interferometric method for fabricating Bragg gratings in optical fibers and waveguides. Complex fiber Bragg grating designs can be implemented by changing the frequency and/or phase of the interfering beams. The benefits of the proposed approach are in simple and precise wavelength setting without sacrificing refractive index modulation in a very wide range of wavelengths limited only by the NA of the lens used in the interferometer.
We have demonstrated both coarse and fine methods of tuning the grating Bragg wavelength by fabricating multiple Bragg reflectors in the range of 1200-2200 nm in a single fiber device. The FWHM bandwidth of the fine Bragg wavelength tuning method was measured to be ~113 nm at ~1545 nm and ~174 nm at ~2005 nm, limited by the Bragg wavelength and by the size of the interfering beam overlap region. We used the wide range of the coarse control and the precision of the fine tuning of the Bragg wavelength to measure the wavelength dependence of the effective refractive index of the optical fiber and to calculate its Sellmeier coefficients.
We acknowledge useful discussions with our DSTO colleagues John Haub, Alexander Hemming, Michael Oermann and Nikita Simakov, contributions to the mechanical design of the grating fabrication system made by Phil Davies, and comments on the manuscript made by Jae Daniel and Simon Rees.
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