Abstract A bandpass optical filter, based on fiber Bragg gratings, is presented in which the bandwidth of a Gaussian spectrum can be continuously adjusted, whilst maintaining near zero group delay slope over the filter bandwidth. The device is also wavelength tunable and the spectral profile is selectable by appropriate grating design. This novel device is employed in a 2R-regenerator, enabling data rate reconfiguration and wavelength conversion, with negligible phase distortion. It will find application wherever a dispersionless reconfigurable bandpass optical filter is required.
©2005 Optical Society of America
Optical components which are fully reconfigurable are of significant interest for pulse shaping, fiber lasers and particularly for communications since they allow dynamic changes to be made on the network . This is an important capability enabling data rate variation on links and even system upgrades, without the need to swap out optical components. There is also the need to dynamically fine tune networks as parameters change due to the influence of environmental factors and aging.
Previous work on reconfigurable components has focused on tunable dispersion compensators, primarily for the exacting requirements of 40 Gb/s communication systems and beyond, as well as for add/drop multiplexers  and gain equalization . Several examples of devices with tunable dispersion have been based on fiber Bragg gratings (FBGs) using various techniques [4–7], including the application of a temperature gradient which chirps the grating via the thermo-optic coefficient [8,9]. In such applications, the linearity of the temperature gradient is of prime importance and, while this may be achieved in a number of ways, thin film heaters have proved superior for commercial application in terms of power consumption, response time and gradient linearity in a compact package [10,11].
One particular optical component of interest for reconfigurable systems is a bandpass optical filter. Such a device may find application in wavelength conversion, and optical regeneration  as well as in phase to amplitude modulation converters [13,14], intra-cavity fiber laser filters [15,16] and for enhancing direct, adjustable current modulation of DFB diode lasers . In these applications, the filter should have an adjustable bandwidth, in order to convert or maintain pulse formats, without introducing dispersion as the bandwidth is changed. In addition, it should be wavelength tunable and it may also be advantageous to arbitrarily choose the spectral response of the filter.
An early concept for a dispersion flattened filter was proposed by Ibsen et al. . In reflection, a uniform grating has a parabolic group delay response. In the design by Ibsen et al, additional lobes, with specific amplitude and phase, were added to the grating apodization profile, which contributed to the reflected light in such a way as to flatten the in-band group delay. This represented a leap forward for dispersionless WDM filters, yet the bandwidth was unchangeable, fixed by the grating design permanently written in the core of the fiber. In wave division multiplexing a dispersionless solution is provided by Array Waveguides [19,20].
In this paper an optical, dispersionless, adjustable bandwidth bandpass filter (ABF) is presented. This filter is wavelength tunable from ITU channel to ITU channel and may be designed with an arbitrary spectral profile. In the device presented here, we also exploit a linear temperature gradient to induce chirp in an FBG. The dispersion resulting from the chirp is nulled by appropriate configuration of two identically chirped gratings with respect to the temperature gradient, whilst tunability is enabled through appropriate simultaneous tensioning of both FBGs. First of all, the design principles applied are described, followed by measurements of the bandwidth and dispersion for various temperature gradients. We then demonstrate how non-ideal properties of the device manifest in the transmitted pulses, with regard to pulse distortion and the appearance of temporal sidelobes. Simulations are performed to compare the output of an ideal filter with the device using the measured CW characteristics to demonstrate the suitability of the device for pulse manipulation. In addition, the dispersion slope and shape are varied until the pulse is distorted, providing tolerances on grating and device design. Finally, an optical 2R-regenerator is demonstrated which employs the adjustable bandwidth, dispersionless filter.
2. Concept and Set-up
The principle of the ABF device is shown in Fig. 1. The fundamental components include a means of generating a linear temperature gradient, two identically chirped FBGs and a four port circulator. There are two key aspects to the correct functioning of this device; a) the generation of a linear temperature gradient and b) the grating design to allow the bandwidth to be varied whilst maintaining both the initial spectral profile and zero dispersion.
The set up consists of two FBGs, used in reflection, with chirps identical in magnitude but opposite in sign. One grating (FBG 1) contains the required spectrum, which may be arbitrarily chosen, whereas the other grating (FBG 2) is flat-topped and designed to cover the entire spectral range of the first grating. The purpose of FBG 2 is to exactly compensate for the dispersion of FBG 1, without changing the spectral characteristics imparted by FBG 1.
In order to adjust the bandwidth of FBG 1, a temperature gradient is applied. This has the effect of changing the chirp in the grating via the thermo-optic coefficient. If the gradient is applied in the same sense as the grating chirp, i.e. hot end to long wavelength end of the grating, increasing the temperature gradient increases the chirp, thus broadening the reflection spectrum. If the gradient is applied contra-sense to the grating chirp, then the chirp is reduced and the bandwidth decreases. To exactly null the effect of the chirp on FBG 1, FBG 2 is physically aligned in the same sense to the temperature gradient as FBG 1. In this way, the chirp in FBG 2 changes in an identical way to FBG 1. However, since the light enters FBG 2 from the opposite end to FBG 1, the dispersion experienced by the light at each grating remains exactly equal, but opposite in sign, for all temperature gradients.
One less desirable, but unavoidable, effect of applying the temperature gradient is that the strength of the reflection decreases with applied gradient. Therefore, it is important that FBG 1 is designed in the weak grating regime, such that the spectral profile does not change as the strength decreases . The grating FBG 1 presented here has an index modulation of Δnmax=9×10-5, or a reflectivity less than 50%, which is sufficient to ensure that changes in spectral profile are negligible as the bandwidth is increased.
In the case presented here, a grating with a Gaussian spectrum is written so that pulses with a Gaussian temporal profile are generated. In the weak grating limit, this spectrum requires a Gaussian apodization along the length of the grating. In addition, the grating chirp must also satisfy the following requirements. The chirp along the grating should be such that the grating both covers as much of the temperature gradient as possible and, at the same time, yields the required bandwidth.
Note that in designing FBG 1, FBG 2 must also be considered since it must precisely match the chirp of FBG 1, whilst also completely reflecting the spectrum of FBG 1. In this case, the Gaussian grating (FBG 1) is chosen to be 36 mm in total length (with some smoothing to zero near the edge) with 1st order dispersion of D2=340 ps/nm (which translates to 35 mm/nm since light travels 0.104 mm in 1 ps in the fibre). The FWHM is 14 mm, giving rise to a spectral FWHM of 330 pm. The complementary FBG 2 is apodized using a super Gaussian of order 8 over a total length 50 mm, with dispersion D2=-340 ps/nm. The flat-topped reflection spectrum covers 1.15 nm with reflectivity greater than 90% for Δnmax=2×10-4.
The temperature gradient is generated by conducting heat along a bar between a heat source at constant temperature Thot and heat sink at temperature Tcold. In the ideal case, where the heat conduction is lossless and the connecting rod is perfectly uniform, the temperature curve will be exactly linear with distance along the rod, as given by the equation governing lossless heat flow (Q) in a bar is ; where λ is the conductivity, A is the cross sectional area and T(x) the temperature profile along the bar.
The device is constructed in Aluminum, closely approximating the ideal conditions described, and is shown in Fig. 2. Note that in operation the connecting rod and top of the hot source would be wrapped in mineral wool insulation. A heating power of 30 W can raise the block to an equilibrium temperature of Thot=260°C. The heat sink also made of Aluminum is cooled by a thermoelectric cooler 30 mm×30 mm capable of sinking a 30 W load. A small fan cools the fins attached to the hot side of the thermoelectric cooler, maintaining the temperature Tcold of the heat sink at near ambient. The FBGs are located in a groove in the connecting rod, which is made from two sections clamped together.
In Fig. 3, the spectral profiles of two typical gratings are shown. The spectrum a) belongs to FBG 1 and can be fitted with a Gaussian curve, yielding a FWHM of 387 pm. The spectrum b) is that of FBG 2, and is fitted well by a super-Gaussian of order 8 and FWHM=1.35 nm.
These two gratings are annealed to ensure long term stability when exposed to the temperature extremes of the gradient (T>260°C). The two gratings are then combined in series, via the 4-port circulator to form the adjustable bandwidth filter (ABF).
In Fig. 4, four different temperature gradients are applied and the effect on the bandwidth of the device is demonstrated. The spectra are shown for each of four temperature differences (ΔT=Thot-Tcold) a) ΔT=0°C, b) 33°C, c) 129°C and d) 232°C. As ΔT is increased, the bandwidth correspondingly increases, from 330 pm to 860 pm, whilst the reflectivity decreases. Note that, the Gaussian spectral profile is maintained for all bandwidths, as demonstrated by the Gaussian fit to each of the spectra. In Fig. 5, the plot shows that the bandwidth varies linearly with the temperature difference, with a bandwidth expansion coefficient of 2.27 pm/°C.
Including the loss of the 4-port circulator of -2dB, yields a total loss of -6 dB in the cold state and -10 dB when the maximum gradient is applied. Note that these losses are unavoidable since the grating must be weak (R<50%) to maintain the spectral profile as the bandwidth is increased. That is, for strong gratings, the apodization profile needed for a particular spectrum changes with the strength of the grating (κac) . If greater distortion of the profile may be tolerated as the bandwidth changes, then the gratings may be made stronger and the total loss may approach that of the circulator or -2dB.
Whilst maintaining a Gaussian profile for each bandwidth is important, it is also crucial that the phase of the pulse is not significantly distorted by the GDR of the combined gratings. In Fig. 6, the transmission spectra of the ABF, the individual group delay curves for each grating as well as the group delay of the ABF are shown for each of the two temperature difference extremes ΔT=0°C (left) and ΔT=232°C (right). The Gaussian grating, FBG 1, possesses a negative dispersion and the flat top grating, FBG 2, possesses a positive dispersion, which extends beyond the bandwidth of the Gaussian grating. As can be seen from the figure, whilst the group delay slope is large for each grating D2=±340 ps/nm when ΔT=0°C and D2=±130 ps/nm when ΔT=232°C, the net effect of both gratings nulls to zero as in the lower portion of Fig. 6. There is a residual error in the combined group delay due to the ripple on each grating. Note, that in the wings of the Gaussian profile the measured group delay becomes increasingly noisy due to a drop in the signal power available for the group delay measurement.
The question remains as to whether this level of residual group delay ripple (GDR) will cause significant distortion of the pulses as they pass through the device. Indeed, it has been shown that GDR which has a period on the order of the spectral width of the pulse is the most deleterious . In order to probe this question, we simulate the effect of the measured spectra and group delay ripple on a pulse as it passes through the ABF.
5. Pulse shaping simulations
In order to determine the effect of non-ideal aspects of the adjustable bandwidth filter on real pulses, a test application is chosen in which a very short pulse Δτ=0.1 ps (and therefore a spectrum much wider than the adjustable bandpass filter) is input into the device. The effect on the pulse of the measured grating amplitude spectrum and group delay is simulated and the pulse which emerges from the device is plotted for various cases.
In Fig. 7, the effect of the transmission spectrum and GDR of the ABF on the pulse, as shown in Fig. 6, is simulated for each of the two transmission bandwidths FWHM=330 pm or Δτ=10.4 ps, equivalent to 30 Gb/s (left) and FWHM=860 pm or Δτ=4.2 ps, equivalent to 80Gb/s (right). Outside of the region in which GDR is measurable, the group delay is set to zero but has negligible influence, as there is little intensity in that part of the spectrum. In the plots a) and d) the pulse is shown for the case when there is no GDR and the filter spectrum is a pure Gaussian, with the same FWHM as the real filter. This is the ideal case. In the next two plots b) and e), the measured GDR is added to the simulation whilst the amplitude of the spectrum is maintained as a pure Gaussian. Note the appearance of small temporal sidelobes on either side of the pulses. In the final plots c) and f), the measured transmission spectrum is added to the simulation whilst maintaining the measured GDR. In each case, the pulses are changed only slightly compared to the case where the GDR alone (i.e. with perfectly Gaussian transmission spectrum) was added to the simulation. This shows that the main contributor to the pulse distortion comes from the residual GDR in this case.
Clearly, there is always some mismatch in the combined response of the two gratings. In order to set limits on the amount of mismatch that may be tolerated, small amounts of quadratic dispersion (D2) and cubic dispersion (D3) are added and their effect on the pulses is simulated. In this simulation all other parameters are assumed to be ideal.
In Fig. 8, the transmitted pulse is shown for the case when D2 is added. Quadratic dispersion, i.e., a non-zero slope, linear group delay spectrum, has the effect of broadening pulses but does not alter the shape of Gaussian pulses. The case shown is for a Gaussian grating FWHM=860 pm or 4.2 ps pulse duration which corresponds to a temperature difference between source and sink of ΔT=232°C. In plot a), there is no D2 and represents the case when the group delay slope of each grating perfectly nulls. In plot b), a dispersion of D2=5 ps/nm has been added. The effect is to broaden the pulse to Δτ=5.9 ps or by 44% whilst maintaining a Gaussian profile. In plot c), the dispersion is increased to D2=10 ps/nm. This results in a significantly broader pulse of Δτ=9.6 ps, or an increase of 131%. The temporal shape remains Gaussian.
Ideally, for a pulse duration of Δτ=4.2 ps, if the pulse should not be broadened by more than 10%, the net dispersion should remain below ±3ps/nm, which is achieved in this experimental demonstration.
Small amounts of cubic dispersion D3 (i.e., parabolic curvature of the ABF group delay spectrum) may also be present. Indeed, close examination of Fig. 6 for ΔT=232°C shows that a slight group delay curvature is present, with D3=-15.2 ps/nm2, obtained from a second order polynomial fit. However, it is possible that this curvature of the group delay is an artifact due to falling intensity for the phase measurement at the edge of the spectrum. In any event, the effect of a quadratic curvature on the pulses is shown in Fig. 9. The particular case of D3=-15.2 ps/nm2, as for the real experiment, is shown in b). Note the similarity of the temporal sidelobe structure compared to the simulation in Fig. 7e) using the actual, measured GDR data. This indicates that the simulated temporal sidelobes are predominantly due to a curvature error in the dispersion.
In order to determine the minimum acceptable curvature allowed, the D3 components was doubled as shown in plot a), halved as in plot c) and halved again as in plot d). In plot d) the temporal sidelobes are below 1% of the peak intensity. Ideally, to keep the temporal sidelobes below 1%, the curvature should be such that |D3|<4ps/nm2. This value may be difficult to achieve, though generally some sidelobes may be tolerated in a communications system.
6. Application in a 2R-Regenerator
In order to demonstrate the efficacy of the device in a real application, the ABF replaces the fixed bandwidth, bandpass filter in an optical regenerator [23–26] While it is not the focus of this paper to describe in detail the operation of a regenerator, briefly, an ideal optical regenerator has a step like transfer function which suppresses low intensity noise whilst pegging intensities above a certain threshold to a fixed value. This is achieved by using a process with a nonlinear response, such as self phase modulation, and then filtering a portion of the spectrum to generate the pulse sequence.
In Fig. 10, the transfer functions are shown which were recorded at the output of an optical regenerator using the dispersionless, adjustable bandwidth filter described in this paper. Note that the bandwidths of 420 pm (Δτ=8.3 ps) and 860 pm (Δτ=4.2 ps) correspond 40 Gb/s and 80 Gb/s systems, respectively The dots are the experimental results and the solid curves are from the theory. The small insets show the autocorrelation traces of the output pulses.
In plot a) the bandwidth is set such that the output pulse duration is matched to the input pulse duration. In plot b), the input pulse duration has changed and the bandwidth of the ABF has been changed accordingly. Two different transfer functions in b) are obtained by tuning the filter by differing amounts with respect to the input wavelength.
An optical, adjustable bandwidth bandpass filter has been demonstrated which remains dispersionless, when changes in bandwidth or wavelength are made. The spectrum of the filter may be arbitrarily chosen but, in this case, a Gaussian profile was used leading to a Gaussian temporal response. Zero phase response was maintained by reflection from matched, identically chirped but contra-sign gratings, whilst the bandwidth was varied by applying a linear temperature gradient. Wavelength tuning was also possible by simultaneously tensioning both FBGs. Simulations showed that the device was able to filter and convert the duration of a pulse, whilst only introducing minimal temporal sidelobes. The sidelobes were found to result from a slight mismatch in the curvature of the dispersion slope of the two FBGs, and boundaries were set as to what linear and quadratic dispersion could be tolerated. As a demonstration of the filter’s efficacy, it was applied to the task of optical regeneration to generate transfer functions for two different pulse durations. This filter should find application in reconfigurable systems or wherever adjustable bandpass solutions are required which introduce no or negligible dispersion.
This work was produced with the assistance of the Australian Research Council under the ARC Centres of Excellence program. CUDOS (the Centre for Ultrahigh bandwidth Devices for Optical Systems) is an ARC Centre of Excellence.
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