Measuring chromatic dispersion of fiber gratings
The lack of a standard procedure complicates the measurements, but with proper attention to detail, they can still be made accurately.
Chad Clark, Mark Farries, Kumar Visvanatha, and Alex Tager
Dense wavelength-division multiplexing (DWDM) has firmly established itself as a cost-effective technology for increasing optical-fiber capacity to meet the rapidly increasing bandwidth requirements of data traffic. Currently, 16- and 32-wavelength systems are being deployed in networks, with 80- and higher-channel systems on the near horizon. Since only a small fraction of wavelengths need to be dropped at intermediate nodes in these large multiwavelength networks, the optical add/drop multiplexer (OADM) has emerged as a key network component.
At higher bit rates (2.5 and 10 Gbits/sec), the optical signal at the output of the OADM may require compensation for link dispersion before detection by the receiver. The two basic technologies for incorporation within the OADM are thin-film interference filters and fiber Bragg grating (FBG) filters. Of these two, the fiber grating OADM has the advantage of allowing dispersion compensation to be built into the design, thus providing both lower insertion loss and a lower-cost solution. In other applications, fiber gratings are also used for their dispersive properties, such as that of dispersion slope compensation in transoceanic links. Therefore, an accurate method of measuring dispersion in fiber gratings is crucial to ensuring system performance.
The specification for the controlled dispersion requirement for fiber gratings used in high-speed systems can be defined by two parameters: the mean dispersion that the filter is to generate across its passband and the limit to the deviation from this mean dispersion across the same passband. We call these two parameters "target nominal dispersion" and "dispersion ripple," respectively.
The combination of these two requirements produces a dispersion template that the device must meet to be considered suitable (see Fig. 1). Devices that provide a nominal dispersion differing from the target nominal dispersion effectively reduce their allowance for the magnitude of dispersion ripple. If the dispersion ripple in two devices is equal, but one device suffers from having its nominal dispersion further away from the target nominal value, the probability that the device will not meet the overall dispersion specification is increased.
The values of D0, D۫, D۬, l0, l۫, and l۬ are dependent upon the system requirements. In the dispersion template, a smaller band, l-1 to l+1, is normally defined as having a smaller tolerance in dispersion than is required at the edges of the filter passband, l۫ to l۬. The stricter tolerance at the center of the passband is required because that is where the majority of signal power will be present.
More detailed analysis of system requirements can lead to dispersion templates with more-complex boundary shapes. For most applications, an ideal filter has zero nominal dispersion, with Di=0ps/nm. That is true for many types of filters--such as thin-film interference devices, waveguide grating routers, and bulk diffraction gratings--at the center of the passband of each filter. The relative time-delay response of these types of filters and fiber gratings has been studied extensively elsewhere, with categories of optical filters defined according to the nature of their phase response in both transmission and reflection.1
Fiber gratings have an apparent disadvantage: For uniform gratings, a significant amount of dispersion exists at the edges of the passband, and for chirped gratings, there is nominal non-zero dispersion across the entire passband. However, controlling the dispersion in fiber gratings can be very powerful and can be used effectively to provide dispersion compensation at the same time that the fiber grating is filtering the signal.
In the absence of any established standard for the measurement of chromatic dispersion in optical filters, the industry has turned to the procedure outlined in TIA/EIA-455-175A for optical fibers. In this procedure, the test consists of measuring group delay through a long stretch of fiber (>1 km) at several discrete wavelengths, separated by up to 20 nm. The data points are then curve fitted to a three- or five-term Sellmeir (depending on the class of fiber), generating an accurate view of dispersion as a function of wavelength.
The procedure has been changed slightly to determine chromatic dispersion response through narrowband optical filters. In this case, a tunable laser is swept across the wavelength band of interest to generate a complete set of group delay-versus-wavelength data, but with no specific function shape assumed. As in the optical-fiber standard, the laser source is modulated at a known frequency, fmod, and the output light travels through the device under test.
After transmission/reflection from the optical device, the optical signal is converted to an electrical signal through a photoreceiver. For each wavelength step, the frequency response of the device under test is compared to a reference electrical signal, thus generating a data file of relative phase shift versus wavelength. This procedure is referred to within the industry as the Differential Phase Shift Method.
The relative phase measurement can be made using a network analyzer or a stripped-down dedicated test set consisting of a signal generator to provide reference and drive a modulator, and a vector voltmeter to be used for phase determination. A simple schematic representation of the optical and electrical signal paths is shown in Fig. 2.
The phase-delay data are directly converted to a relative time delay, t, through the relation:
The sensitivity of the measurement is apparently improved by modulation at higher rates and the use of a high-resolution phase discriminator in determining f. With the phase resolution of the vector voltmeter at 0.1, time-delay resolutions of 1.1 and 0.14 psec are obtained for fmod = 250 MHz and 2 GHz, respectively. Accordingly, sampling at high fmod would seem to be a natural way to increase accuracy in the measurement.
However, the side bands inherent in amplitude modulation produce a unique effect similar to averaging over a small band, one with the width of 2 ¥ fmod. As a result, by increasing the modulation frequency, the optical filter is effectively sampled at wavelength points further apart, and any fine structure in t(l) that may occur between the wavelength points is smoothed out. In fact, the modulation frequency uniquely determines the wavelength window over which the group delay is "sampled." For example, fmod = 250-MHz, 1-GHz, and 2-GHz probe windows having widths of 4, 16, and 32 pm (picometers), respectively. The result is that higher modulation frequencies not only reduce the noise resulting from phase-resolution error but also suppress the real group delay ripple of the device (see Fig. 3).
Several companies have reported that fmod in the 250- to 350-MHz range provides the most accurate results for long fiber-grating dispersion compensators.2 This finding, however, may not apply to shorter fiber gratings.
Due to the sampling nature of the measurement, the result can also be completely insensitive to ripple with a spectral period that coincides with integer multiples of the modulation frequency. Taking two measurements at two different modulation frequencies is virtually the only way to ensure that all real ripple is uncovered.
In addition to the fundamental choice of proper fmod during the measurement, other sources of error must be addressed to ensure reliable data. Most of these precautions are common to other optical measurements requiring high accuracy, such as controlling the polarization of light along the optical path to avoid rapid power fluctuations at the receiver. (The power measurements can then be used to construct the optical filter transmission spectrum, against which the group delay can be directly mapped). It is also necessary to ensure that there are no elements in the optical path with a wavelength-dependent time delay, apart from the device under test.
Further, accurate determination of wavelength is obviously of prime importance. For this purpose, a wavemeter is recommended to guard against errors due to mode hopping in the source laser. If direct modulation of the laser is used, the chirp of the laser must be small enough to provide a stable fmod. The consideration does not arise if external modulation is used.
Finally, unwant ed discrete reflections in the optical path can be very troublesome. For example, these wavelength-independent reflective sources can interact with a fiber grating (the device under test) and form Fabry-Perot cavities. This situation produces multiple path lengths for the light to travel along and thus leads to increased noise in t(l), which in the case of small reflections can be mistaken for real group delay ripple. The problem is avoided by using a backreflection meter to verify a high return loss in the optical path before use; the source is often a connector that has been corrupted with debris.
Noise can be determined by measuring a device with a theoretically flat group delay response, such as the center of a dielectric filter in transmission, and by noting the magnitude of the repeated spikes in the measured group delay response. To minimize noise in the data, the tunable laser sweep rate should be slow enough to permit statistically relevant averaging of f at each wavelength step. Repeatability of the system can be evaluated by measuring the same device several times and subtracting one result from another.
Dispersion, being the slope of the group delay versus wavelength, is readily available from the data converted according to the equation noted earlier. But the incremental slope cannot simply be taken between data points, because--even when using a relatively large step size of 10 pm--group-delay noise of ۫ psec results in dispersion noise of 𫏌 psec/nm. Therefore, some sort of averaging technique is required.
There are several ways the dispersion can be represented from the group delay data obtained. A classical method is to fit the data to a simple function and then differentiate this smooth function. For uniform fiber gratings, a fit to a second-order (parabola) or third-order polynomial may be suitable. Linearly chirped gratings can be fit to a linear function. But in both cases, the form fitting ignores the real ripple that exists. Dispersion derived in this manner therefore does not usually allow any firm conclusions on a device`s suitability for high-speed filtering. Nevertheless, this fitting does at least give a good first approximation of the magnitude of dispersion across the filter`s passband.
Another approach is to apply a linear least-squares fit over a moving wavelength window. This technique provides a balance between saving the real ripple that impacts system performance and removing measurement noise. Window size is a critical parameter and can produce vastly different results (see Fig. 4). For linearly chirped gratings, increasing the window size decreases the magnitude of dispersion ripple. For uniform gratings, increasing the window size steepens the V-type response.
A window size that has real physical meaning should therefore be preferred to any arbitrary choice. A good first approximation would be to average over a wavelength range similar to that of the transmission system`s laser spectral width. The exact width will be dependent upon the type of laser and modulation scheme employed, but window sizes in the 50- to 150-pm range are common. The period of the ripple has also been shown to impact system performance, so this has to be taken into account when choosing a data-smoothing technique.
Correlating the peak excursions of the measured dispersion to increased power penalty in the system is the first step. Defining the acceptable magnitudes of the peak excursions is the final goal.
Fiber Bragg grating add/drop multiplexers with integrated dispersion compensation are well-suited for high-capacity optical networks because of their improved performance and potential lower cost. Fiber gratings also offer distinct performance and cost benefits in dispersion slope compensation. To prove a fiber grating`s suitability for such applications, an accurate measurement of dispersion is necessary to guarantee system performance.
Given the potentially large variation in results for the same device due to data-analysis procedures or small changes in measurement method, a standard is clearly required for measurements of this kind. Data-acquisition techniques should be consistent throughout the industry, and data smoothing should be done in a manner that retains the real nonlinearities of filter response. With an industry-wide standard, the dispersion specifications of different vendors will be directly comparable, and customers will be able to select the proper products for their requirements with full confidence. u
1. G. Lenz, B.J. Eggleton, C.K. Madsen, C.R. Giles, and G. Nykolak, "Optimal Dispersion of Optical Filters for WDM Systems." IEEE Photonics Technology Letters, Vol.10, No. 4, pp. 567-569 (April 1998).
2. Y. Li, D. Way, N. Robinson, S. Liu, "Impact of Dispersion Compensation Gratings on OC-192 Systems." Conference on Optical Amplifiers and their Applications, Monterey, CA (May 1998). Paper TuB5.
Chad Clark is product line manager, fiber-grating devices; Mark Farries is director, advanced components; Kumar Visvanatha is vice president, optical components and modules; and Alex Tager is a research scientist at JDS Fitel (Nepean, ON, Canada).