Fiber Bragg gratings intended for DWDM applications must be apodized. An apodized phase mask, which is a mechanically straightforward means of obtaining pure ac apodization in high-volume, repeatable production, has the apodization function built into the phase mask.
Owing to its fiber compatibility and low insertion loss, the fiber Bragg grating (FBG) has come to play a central role in dense wavelength-division multiplexing (DWDM). Fiber Bragg grating technology is found at the heart of several major multiplexing and demultiplexing architectures. The grating in an FBG consists of a sinusoidal modulation of the refractive index in the core of the fiber, the modulation being in the direction of the fiber axis (see Fig. 1). An FBG acts as a selective in-fiber wavelength filter that reflects only the light that has a wavelength that is twice that of the grating period, and allows all other wavelengths to pass. This principle is expressed mathematically in the basic equation governing FBGs,
λ = 2nΛ(FBG)
where λ is the free-space wavelength of the reflected light (called the Bragg wavelength), n is the index of refraction of the fundamental mode of the fiber, and Λ(FBG) is the period or pitch of the in-fiber grating. The period of FBGs for DWDM is typically in the neighborhood of 535 nm. FBGs vary in length between several millimeters and several centimeters, depending on the application.
For FBGs to perform properly on a dense grid, the reflection peaks must be as wide as possible, but at the same time the overlap with neighboring channels must be minimal (see Fig. 2). The flat, highly reflective section of the peak is required to be at least 30 GHz wide. At the same time, to minimize overlap, the peak must be narrower than, say, 80 GHz at -25 dB. As a result, FBG engineers must achieve spectral responses with maximally steep slopes and with the highest possible precision on the central wavelength and bandwidth.
Fiber Bragg gratings are recorded in the fiber core using the interference of two coherent ultraviolet (UV) beams at around 244 nm. Since the refractive index of the germanium-doped silica core increases through exposure to UV radiation, the fringes in the interference pattern leave a permanent sinusoidal modulation in the index. In this way, a fiber Bragg grating is recorded in the fiber core. The angle between the recording beams controls the period of the fringes, which translates directly into the period of the FBG.
There are many ways to generate the two required interfering beams. One category of methods—called holographic—involves splitting a single laser beam into two, and then redirecting the resulting beams onto the fiber at an appropriate angle with the aid of mirrors. For such a setup, the mirrors must be vibrationally stable, of high flatness, and their angular position must be controllable to within extraordinary small increments on the order of 0.001°. This method of fabrication permits good flexibility with regard to the FBG period, although it suffers the disadvantage of posing a serious mechanical challenge.
An alternate method of FBG fabrication involves an enabling piece of optical hardware known as a phase mask. A phase mask is a wafer of fused silica several millimeters thick with a binary grating on one of its surfaces. This device serves as a high-precision beamsplitter. In this method of FBG fabrication, the fiber is placed alongside the phase mask (see Fig. 3). A UV beam is split by the mask into diffractive orders. The interference of the +1 and -1 orders results in a fringe pattern, and this pattern is recorded in the fiber core to make the FBG. If the grooves of the binary grating on the phase mask are sufficiently close to being perfectly rectangular, and if they have the proper depth and duty cycle, then, in the theoretical limit, the zeroth order can be completely suppressed, and the diffraction efficiency for each of the +1 and -1 orders is ~ 40%. The remainder of the energy from the UV beam is transmitted in the higher diffraction orders.
The period of the resulting FBG is exactly one half of the period of the binary grating on the phase mask. Thus, manufacturers who opt for the phase-mask approach require a separate mask for each FBG period they want to produce, and must accumulate a large inventory of masks. For high-volume production, it has been established that this is a small price to pay for the mechanical simplicity and repeatability afforded by phase masks.
Consider the simplest possible type of FBG: one with a constant grating period, and in which the grating starts and stops abruptly in the fiber core. Such an FBG is said to have a rectangular profile. The reflection spectrum of a rectangular profile FBG contains a series of sidelobes surrounding the central peak (see Fig. 4). To add insult to injury, the envelope of the sidelobes has a relatively slow drop-off. The sidelobes and their slow drop-off can also be seen in mathematical studies of the transmission and reflection of electromagnetic waves in the grating. The anomalous broadening effects are due to extra harmonic content arising from the abruptness of the rectangular profile. Consequently, an FBG with a rectangular profile cannot successfully perform the function of a multiplex-demultimplex filter on the ITU grid, where the spectral response of an FBG must have steep slopes such as those appearing in Fig. 2. How then does one achieve such FBGs?
The answer is that less abrupt profiles must be used. If the grating in an FBG starts and stops smoothly as a function of position, then, with the offending abruptness eliminated, the harmonic content due to the profile is minimal. This leads to the removal of the sidelobes, and also to a steeper slope. Such an FBG is called "apodized," and the amplitude of the ac index modulation is governed by an apodization profile. Apodization profiles typically espouse a Gaussian shape or some qualitatively similar function.
As shown in Fig. 4, the theoretical reflection spectra for FBGs with and without apodization are quite different. The unapodized FBG is roughly 8 mm long, and the full-width-half-maximum of the apodized device is also roughly 8 mm. For both gratings, the flat, highly reflective section of the peak is 30 GHz (0.24 nm) wide or more, as required. The apodized FBG satisfies the requirement of a steep drop-off for channel overlap avoidance, since it is no more than 80 GHz (0.64 nm) wide at -25 dB; this grating can serve effectively on the 50-GHz ITU grid. However, the unapodized grating comes nowhere near meeting this requirement.
Fiber Bragg gratings intended for DWDM applications must be apodized. How can apodization be achieved inexpensively, conveniently, and with high repeatability?
One way is to shade the ends of the FBG during recording, so they receive less UV exposure than the middle. This technique is called amplitude apodization or amplitude shading. There are many ways of implementing this concept, the simplest method is to exploit the natural Gaussian profile of the UV laser beam itself. This general approach to apodization has a severe drawback, however. In the recording of an FBG, not only does the refractive index acquire an ac modulation, but it also acquires, at each point along the grating, a dc contribution that happens to be equal to one-half the peak-to-peak ac modulation. This dc contribution arises because the spatial average of the index is unavoidably increased by the UV radiation. The dc index of the fiber starts out with some value n at the beginning of the grating, evolves slowly up to some maximum value n +Δn as one moves to middle of the grating, and then drops back to the fiber's original value of n as one approaches the end of the grating (see Fig. 5, top).
What is the effect of this variation in n? According to the basic equation governing FBGs (see p. 75), changes in the refractive index of the fiber (Deltan) have the effect of shifting the wavelength by an amount 2 DeltanL. Since the period of FBGs for DWDM is around 535 nm, and since the index change is typically on the order of 0.001, variations in the Bragg wavelength are seen to be roughly 0.5 nm. That is, the FBG reflects light in a band that is actually so wide as to exceed the 0.4-nm spacing between the 50-GHz ITU grid channels. Obviously, an FBG with these properties cannot serve on the grid.
The harmful effect of single exposure-amplitude shading can be overcome by performing a second exposure with a single UV beam instead of two interfering beams. This second exposure alters only the spatial average of the index. Thus, the dc component of the modulation is adjusted appropriately while leaving the ac component untouched. The result is an FBG with "pure ac apodization," (see Fig. 5, bottom). The method of double exposure, while capable of realizing pure ac apodization, is fraught with technical difficulties. First, it is time-consuming; second, the corrective exposure is difficult to calibrate; and third, the two exposures need to be very precisely aligned with respect to one another.
One solution to the challenges associated with apodization involves moving the fiber rapidly back and forth with respect to the interference pattern, during recording. This method, called the dither method, can be implemented holographically or with a phase mask. The technique involves scanning the interfering beams along the fiber at a steady speed, applying a strong dose of "dither" when the ends of the FBG are being recorded, and turning the dither off completely to obtain maximum fringe visibility when the center of the FBG is exposed. The dither method achieves pure ac apodization because the spatial average of the index is increased by the same amount at all points along the grating. The band-widening effect occurring in single-exposure amplitude apodization is thereby avoided. Dithering, although capable of yielding excellent results in the best case, is obviously mechanically problematic. The dither has to be carefully worked out for each FBG period and bandwidth, and repeatability is difficult to achieve.
A solution for the apodization of FBGs is the apodized phase mask, which is a convenient, mechanically straightforward means of obtaining pure ac apodization in high volume, repeatable production. An apodized phase mask has varying diffraction efficiency, with the apodization function being built into the phase mask. Apodized phase masks are manufactured by varying the duty cycle and/or the groove depth of the binary grating. The +1/-1 diffraction efficiency reaches a maximum at the center of the mask and the zeroth order is at a maximum at the ends of the mask (see Fig. 6). The spatially averaged (or dc) modulation of the index in the core is constant because the total UV fluence to which the fiber core is exposed does not vary as one moves along the fiber during recording. Thus, pure ac apodization is achieved.
The apodized phase mask results in an FBG with excellent DWDM properties, and allows high performance FBGs to be produced in great volume without a mechanically complicated apodization process.
Ivan Maksymyk is senior product manager, optical components, at StockerYale Canada Inc., 275 Kesmark, Dollard-des-Ormeaux, Quebec, H9B 3J1, Canada. He can be contacted at firstname.lastname@example.org.