Fiber Bragg gratings are well positioned to respond to the growing need for more
stringent control of dispersion compensation. Thermal tuning has proven to be
an effective technique for achieving this goal.
Pulse broadening due to chromatic dispersion Broadening occurs in transport fiber and recompression using a chirped fiber Bragg grating.
Tunable chromatic dispersion compensators are known to be critical components of 40 Gb/s systems. They are already required at 10 Gb/s, and there was an extensive deployment over the past 10 years of fixed dispersion compensation modules, mainly based on dispersion compensating fiber and, more recently, fiber Bragg gratings.
At 40 Gb/s and higher, the control of the residual dispersion is even more stringent, and a dynamic per-channel dispersion trimming is required. Different technologies have been proposed for accomplishing this function, including fiber Bragg gratings, etalon filters, Mach-Zehnder interferometers and virtually imaged phased arrays. Among these technologies, fiber Bragg gratings are particularly well adapted because they allow a high clear channel bandwidth and a large tuning range. Furthermore, this technology is already recognized and adopted for dispersion compensation, and is being deployed for fixed in-line compensation.
Chirped fiber Bragg gratings for dispersion compensation
Chromatic dispersion refers to the temporal spreading of a short light pulse as it propagates along an optical fiber. This effect is due to the dispersion property of the fiber—that is, the fact that its index of refraction, and thus the light velocity, varies as a function of wavelength. Short pulses are not monochromatic but rather have a certain spectral bandwidth. The shorter the pulse, the wider its spectrum and, thus, the stronger the temporal broadening due to chromatic dispersion.
In its basic form, a fiber Bragg grating is a piece of fiber containing a modulation of its core refractive index over a certain length. This feature is obtained by exposing the fiber to ultraviolet light, which creates a permanent increase in the refractive index. This increase can be spatially modulated when the UV light that illuminates the fiber is itself modulated, as occurs at the intersection of two interfering beams.
It is fortunate that this photosensitivity to UV light is related to germanium within the fiber: It is located only within the core—that is, where the photosensitivity is desired. The main optical property of a fiber Bragg grating is to reflect light of the proper wavelength. The light is reflected when its wavelength is close to the Bragg wavelength λB given by:
λB = 2neff p , (1)
Compensation takes place in many locations in a transmission link.
Complex phase masks are used for mass-producing complex fiber Bragg gratings such as multi-channel dispersion compensators.
Measured reflectivity and group delay spectra of a multi-channel fiber Bragg grating for tunable dispersion compensation.
where neff is the effective index of the fiber and p is the period of the grating. If the period varies along the fiber axis, then the different parts of the grating reflect light of different spectra. In particular, a chirped fiber Bragg grating—that is, one having a period that varies linearly with position—is of particular interest for dispersion compensation. It can be made such that it reflects the light of long wavelength at the front and the light of short wavelength at the back. The longer delay experienced by the light reflected at the back can be adjusted to compensate for the effect of the chromatic dispersion and then recompress broadened pulses, where a three-port optical circulator is used to collect the reflected signal. This scheme was first proposed in 1987 (Opt. Lett. 12, 847-9) and is increasingly being integrated into today’s telecommunications networks.
Multi-channel Bragg gratings
Dispersion compensation is required at many locations in a telecom network. Compensation of a fixed predetermined level is typically performed periodically along the transmission line. Such a fixed compensation is required for data rates of 10 Gb/s or higher. Many signals of different optical carriers travel along the same optical fiber in a wavelength division multiplexing (WDM) system. All these signals benefit from the dispersion compensation provided by the same multi-channel compensator.
While early fiber Bragg gratings were narrowband, wideband multi-channel Bragg gratings are now common. In particular, complex phase masks allow for very efficient manufacturing of such state-of-the-art gratings. A phase mask acts as a master that can be easily replicated within many pieces of fiber. Complex gratings can be fabricated using a complicated UV exposure scheme, but the complex phase mask approach enables manufacturing that is as easy as that required for simple filters.
Multi-channel fiber Bragg gratings can be fabricated using the complex phase mask technique, which yields nice, flat-top channel passbands and linear group delay spectrums. The optical performances of today’s state-of-the art multi-channel fiber Bragg gratings meet the requirements of system manufacturers and allow their use at 10 Gb/s as in-line dispersion compensators for transmission distances up to 2,000 km. This kind of grating also meets the requirements of manufacturers for tunable compensation at 40 Gb/s at the receiver end.
A negative thermal gradient (high temperature at the front, low temperature at the back) causes a decrease of the dispersion magnitude of a negative dispersion grating (left) and an increase of the dispersion for a positive dispersion grating (right).
Tunable dispersion compensation with fiber Bragg gratings
At 40 Gb/s and higher, the effect of chromatic dispersion is larger, since the optical spectrum is wider and the temporal separation between bits is smaller. The proper dispersion compensation then becomes more stringent and a per-channel tunable compensation is required. In addition to trimming the residual dispersion on a per-channel basis, the tunable dispersion compensator compensates for fluctuations of chromatic dispersion within the transport fiber such as those caused by temperature changes.
Although the tunable compensation is performed per-channel at the receiver end, a colorless device is needed—that is, a compensator that can be used at any WDM port. This ensures that the inventory management is kept at its simplest level.
The amount of dispersion that a chirped fiber Bragg grating provides is directly related to its length L and bandwidth ΔλBW. The group delay difference between a reflection at the front and back of the fiber Bragg grating is simply given by the propagation time:
Δtg = 2ngL/c , (2)
where ng is the fiber group index and c is the light velocity in vacuum. Note that the length L in the equation corresponds to the active length of the grating. The active length is shorter than the physical length, which also contains some apodization edges required for obtaining proper spectral properties. The dispersion, typically expressed in units of ps/nm, corresponds to the variation of group delay as a function of the wavelength:
D = Δtg/ΔλBW . (3)
The channel bandwidth changes as the dispersion is tuned. The maximum dispersion is limited by channel narrowing while the minimum dispersion is restricted by channel crosstalk.
The fiber Bragg grating bandwidth ΔλBW is the difference between Bragg wavelengths at the back and front. As expressed by equation (1), these Bragg wavelengths depend on the local values of the grating period and effective index, both of which vary by changing the temperature. When the temperature rises, both the refractive index and the grating period increase. Accordingly, when one end of the grating is heated and the other is cooled, the Bragg wavelengths at the back and front change in opposite direction, thus providing a change in the dispersion. This is depicted in the top left part of the figure on the right, where the dispersion, given by the slope of the group delay spectrum, is shown.
The direct relationship between position and group delay is also illustrated in the figure. Such a scheme allows tuning the dispersion around a certain nominal value. However, a zero dispersion cannot be obtained because it would require a temperature gradient of infinite amplitude.
A dual-grating configuration can be used to achieve a dispersion tuning range around zero, which is typically required in 40 G/s tunable dispersion compensation applications. In that case, two gratings of opposite chirps are placed in the same thermal platform that imposes the temperature gradient. A four-port circulator is then used to collect the light that is sequentially reflected by the two gratings. In the nominal isothermal condition, the overall dispersion of the device is zero. However, when a temperature gradient is applied, the dispersion of one grating increases in magnitude while the dispersion of the other decreases.
The graph was done for a single channel but also applies for a multi-channel fiber Bragg grating, which can be simply seen as the superposition of several non-interacting gratings. However, to some degree, the multi-channel character changes the tuning range that can be accomplished. The channel bandwidth changes as the dispersion is tuned, and interference between adjacent channel must be avoided. When the magnitude of
the dispersion is maximum for one grating, it is minimum for the other.
Accordingly, the dispersion tuning range of the device is given by:
Tuning Range = ±(|Dmax|–|Dmin|), (4)
where Dmin and Dmax are the minimum and maximum values of the dispersion of the individual fiber Bragg gratings. Channel narrowing limits the highest dispersion Dmax while channel interference restricts the minimum dispersion Dmin. This assumes that the achievable thermal gradient is not the limiting factor—which is typically a valid statement. For each individual fiber Bragg grating, the product of dispersion and channel bandwidth is constant over the tuning range. This product corresponds to the difference in the group delay of the light reflected by the front and back ends of the grating. This behavior provides a relationship between the minimum and maximum dispersion of each grating. Assuming that the gratings are designed to have a reflectivity spectrum of supergaussian shape of order m, this relationship is expressed as:
Dmin = Dmax• Δλbw/Δλsp •(Rbw/Rsp)-½m, (5)
where Δλbw is the minimum bandwidth occurring at the maximum dispersion, Δλsp is the channel spacing, Rbw is the reflectivity in dB at the edges of the minimum bandwidth (typically –0.5 or –1 dB) and Rsp is the reflectivity at the channels crossing point (lower than about –5 dB). Since the order m is typically around 4 to 7, the factor
f = (Rbw/Rsp)-½m (6)
varies only weakly on the different parameters (about 1.1 to 1.6).
A fiber-Bragg-grating-based dispersion compensator (left) as well as one incorporated in a module that contains the control electronics (center and right).
Not surprisingly, the combination of equations (4) and (5) indicates that the largest tuning range is obtained when the fiber Bragg gratings are designed to provide the greatest dispersions. The dispersions are in turn limited by the achievable fiber Bragg grating length, which is typically on the order of 10 cm. Longer gratings could also be possible, although a larger temperature gradient would be required and could become the limiting factor. Combining equations (2) and (3), the maximum dispersion is expressed as a function of the fiber Bragg grating active length as:
Dmax = = 2ngL/cΔλbw . (7)
The minimum bandwidth Δλbw is equal to the operation bandwidth, plus some guard band to take into account possible central wavelength shifts between the two gratings. The grating active length L varies from 50 to 85 percent of the full length, depending on the design parameters, especially the channel bandwidth. The combination of equations (4) to (7) provides the relationship between the tuning range, the operation bandwidth and the channel spacing:
Tuning Range = ± 2ngL/cΔλbw (1– f • Δλbw/Δλsp) . (8)
Maximum tuning range as a function of the channel spacing and channel bandwidth. A few configurations of interest are also shown.
The figure on the right shows the achievable tuning range as a function of the operation bandwidth for 100 and 200 GHz channel spacing, assuming a 10 GHz channel guard band, a 58 percent fiber Bragg grating active length and a factor f = 1.2. The curves stop when the achievable thermal gradient becomes the limiting factor. Although some assumptions are taken into account, the graph provides a comprehensive and fairly accurate prediction of achievable tuning ranges for many device configurations. The figure also shows a few configurations of interest for different modulation formats (OOK, DPSK and duo-binary).
The format dictates the signal bandwidth and thus the required passband for the tunable dispersion compensator. One sees that the channel spacing should be limited to 100 or even 200 GHz, although the WDM channels could be at 50 GHz spacing. This means that the solution could be not 100 percent colorless: two- or four-part numbers could be required for covering all channels of interest.
Making tunable dispersion compensation a reality
The temperature profile is conveniently achieved by using two thermo-electric coolers (TECs), allowing for a compact package. A heater also minimizes the impact of external temperature fluctuations. The TEC controllers and appropriate control electronics are designed to achieve a stand-alone tunable dispersion compensator module. These advances make the fiber-Bragg-grating-based tunable dispersion compensator the preferred solution of system manufacturers. Both the tunable dispersion compensator alone and the module with electronic control are included in many currently deployed systems.
Typical measurements over few channels of the reflectivity and group delay spectra of a dispersion compensator based on a pair of multi-channel fiber Bragg gratings. The measurements are shown for zero, minimum and maximum dispersion.
A typical optical performance over the tuning range is shown in the figure on the right, where experimental reflectivity and group delay spectra are demonstrated over a few channels and for a few dispersion settings.
Fiber Bragg grating technology is well adapted for tunable dispersion compensation requiring a simple temperature gradient as the tuning mechanism. In addition to this chirp tuning, the control of the average temperature or fiber stretching could be used to shift the spectral response. This would allow one to obtain a 100 percent colorless device, even if the multi-channel character of the gratings is at a spacing higher than desired: as long as the wavelength could be tuned over one channel spacing, any wavelength could be tuned on.
Future increases in the data rate will push further the need for more stringent management of chromatic dispersion. Again, fiber Bragg gratings are well positioned to respond to this requirement. For example, a grating-based tunable dispersion compensator has already been demonstrated in a 85.4 Gb/s telecom system. While the deployment of 40 Gb/s network has just begun, service providers have already expressed the need to go further. In this context, for developing solutions enabling 100 Gb-Ethernet transmission, system designers will be able to count on the availability of tunable dispersion compensators based on fiber Bragg gratings.
[ Yves Painchaud, Carl Paquet and Martin Guy are with TeraXion, in Québec, Canada. ]
References and Resources
>> F. Ouellette. “Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,” Opt. Lett. 12(10), 847-9 (1987).
>> Y. Painchaud et al. “Multi-channel fiber Bragg gratings for dispersion and slope compensation,” Proceedings of OFC 02, 581-2 (2002).
>> J. Rothenberg et al. “High-channel-count fiber Bragg gratings fabricated by phase-only sampling,” Proceedings of OFC 02, 575-7 (2002).
>> K. Schuh et al. “85.4 Gbit/s ETDM transmission over 401 km SSMF applying UFEC,” Proceedings of ECOC 05, postdeadline paper Th4.1.4 (2005).
>> Y. Painchaud et al. “Low-penalty cascade of low-ripple FBG-based dispersion compensators,” Proceedings of ECOC 06, postdeadline paper Th4.2.7 (2006).
>> D. Cooperson et al. “OFC/NFOEC highlights industry gains, challenges and uncertainties,” Ovum RHK report, April 10, 2007.
>> Y. Painchaud et al. “Recent progress on FBG-based tunable dispersion compensators for 40 Gb/s applications,” Proceedings of OFC 07, paper OThP3 (2007).
>> D. van den Borne et al. “Cost-effective 10.7-Gbit/s long-haul transmission using fiber Bragg gratings for in-line dispersion compensation,” Proceedings of OFC 07, paper OThS5 (2007).