1. Introduction

Fibre Bragg gratings (FBGs) consist of a periodic modulation of the refractive index along the core of the fibre. This periodicity creates a photonic bandgap and results in strong reflectivity near the Bragg wavelength. The narrow bandwidth and large dispersion of FBGs makes them ideal for linear dispersion compensator and for add/drop filters in WDM systems. In the nonlinear regime Bragg gratings are bistable devices¹ and could thus form the basis of an all-optical switch. Earlier we demonstrated and reported three types of nonlinear switching in Bragg gratings: a simple self-induced nonlinear switch², an all-optical AND gate³, and a pump induced switch⁴ (the optical pushbroom). In this paper we aim to present a unified account of these experiments focusing on the capacity of Bragg gratings for switching applications. This approach clearly shows the flexibility and potential of Bragg gratings as high-speed all-optical devices. To understand the operation of these switches it is necessary to recall the basic nonlinear properties of Bragg gratings.

In the CW regime it is well known that Bragg gratings are bistable with one state having zero reflectivity while in the other the transmission is vanishing small¹, although the input powers are the same in each case. The difference in output is due to the field structure inside the grating. In the low transmission state the electric field decays exponentially along the grating, i.e similar to the linear field profile. In the high transmission state the field has a resonant profile which is symmetric about the centre allowing perfect transmission. This resonant structure is called a gap soliton⁵ as the frequency of the light lies within the grating’s photonic bandgap and it can be described using a nonlinear Schrödinger equation⁶. Although the original gap solitons were stationary it was soon shown that they could propagate through a grating with any speed between zero and the speed of light⁷. This is due to the fact that in a photonic crystal the group velocity of light falls rapidly to zero at the bandedge and hence the gap soliton can have any velocity by choosing the centre frequency correctly⁸. We utilise gap solitons in the first two of the switches examined here while in the optical pushbroom⁹ switching is caused by the actions of a strong pump pulse on a weak probe beam. The experimental setup to do this is described in the following section. We then present the results of the various switches followed by a discussion.

2. Experimental Setup

Our experimental setup is shown in Fig. 1. Using the polarisation beam splitter we were able to couple one or two independent pulses into the FBG, however in all cases at least one of the pulses was a high power pump pulse. The pump pulses, derived from a directly modulated tunable DFB laser, were amplified to high power (> 20 kW) in an erbium doped fibre amplifier cascade based on large mode area erbium doped fiber¹⁰ and had a repetition frequency of 4kHz. The pump pulse shape was asymmetric due to gain saturation effects within the amplifier chain and exhibited a 30ps rise time and a 3ns half-width (see Fig. 2b). For the gap soliton generation only a single pulse was used, however for the AND gate this pulse was split into two orthogonally polarised components and recombined at the PBS with approximately zero time delay between the arms. Lastly in the optical pushbroom experiments the second source was a a low-power (1mW), narrow-linewidth (< 10 MHz) probe that could be temperature tuned right across the grating’s bandgap. The spectral half-width of the pump pulses at the grating input was measured to be 1.2 GHz.

In our experiments the two sources were orthogonally polarised within the FBG. The axes of polarisation of the light was oriented along the grating’s birefringence axes to ensure there was no polarisation coupling in the grating. Both the reflected and transmitted probe signals could be measured in our experimental system using a fiberized detection system based on a tunable, narrow-band (< 1nm) optical filter with >80 dB differential loss between pump and probe (sufficient to extinguish the high intensity pump signal), a low noise pre-amplifier, a fast optical detector and sampling scope. The temporal resolution of our probe beam measurements was ≈50ps.

 

Fig. 1. Schematic of the experimental setup. PBS: Polarisation beam splitter.

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The FBG was centered at 1535.93 nm and was 8 cm long with an apodised profile resulting in the suppression of the side-lobes. The grating had a peak reflectivity of 98% and a measured width of 32 pm as shown in Fig. 2(a) (solid line). In Fig. 2(a) the horizontal scale gives the difference in nanometres from the centre wavelength. The dashed line in Fig. 2(a) is a analytic fit of the reflection spectrum indicating that the grating is slightly chirped on the short wavelength side. The grating was mounted in a section of capillary tube and angle polished at both ends so as to eliminate reflections from the fibre end faces and was appropriately coated to strip cladding modes.

 

Fig. 2a. Reflection Spectrum of the Bragg Grating used in the experiments. The solid line is the measured spectrum and the dashed line is the theoretical model. (b) Input pulse profile. setup.

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3. Results

3.1 Gap Soliton Formation

We first examined the self-switching of a single optical pulse which was tuned to lie just inside the bandgap on the high frequency side. We measured the transmitted energy as a function of the input power and the result is shown in Fig. 3(a). In Fig. 3(b) we show the output pulse shapes as a function of increasing power. The front peaks which is present in all the traces are due to the chirp on the rising edge of the input pulse (caused by directly modulating the laser diode). As this peak is unaffected by the grating it can be used to directly measure the input pulse energy allowing accurate measurements of the transmitted pulse energy.

 

Fig. 3a. Self-Switching of a Bragg grating. Note that the transmission increases from 2% in the linear regime to over 40% at high peak powers. Fig. (b) shows the output pulse shape for a range of increasing peak powers.

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The source wavelength was set close to the short wavelength side of the center of the bandgap (-7 ± 2 pm wavelength offset, see Fig. 2a) and the grating pulse transmission and reflection characteristics recorded as a function of increasing peak power. The transmission results are summarised in Figure 3a. It can be seen that as the power increases the transmitted energy increases from ∼ 3% to 40%. Furthermore there is a sharp threshold for the onset of nonlinear behaviour near 2.5kW. To understand these results it is easiest to look at the output pulse shapes which are shown in Fig. 3b. At low powers (Fig. 3b, bottom trace) the pulse is seen to be almost completely reflected from the grating other than our chirped rising edge marker. However as the pulse peak power is increased strong pulse reshaping becomes apparent. The traces in Figure 3b show various stages in the growth of the nonlinearly transmitted pulses. Initially one gap soliton is formed (around 3kW peak power), however as the intensity is increased more solitons are generated. Each subsequent pulse then narrows to ∼ 100ps and moves forward allowing additional pulses to form at the rear of the bunch. We observed the generation of up to 5 gap solitons in our experiments (Fig. 3b, top trace) at a launched peak power of 8kW, corresponding to a peak intensity of ≈ 27 GW/cm². Note that the absence of Raman scattering or other nonlinear spectral distortion was confirmed by direct spectral measurements. These results are in good agreement with our numerical simulation of the system. The corresponding effects of the pulse formation are readily observed in the reflected domain where progressively larger amounts of energy are seen to be switched from the increasingly delayed reflected pulse. As evidenced by the small linear pulse transmission these pulses were formed at wavelengths well within the high reflectivity region of the FBG. Hence the majority of the optical power transmission was through the bandgap of the FBG and as such the pulses must have formed true in-band gap solitons. This was further confirmed by numerical simulations (using the experimental parameters) of pulse propagation within the bandgap of both apodised and unapodised FBGs (of the same index modulation depth and reflectivity) which were seen to give little change in the qualitative behaviour of the transmitted pulses.

3.2 An all-optical logic gate

Amongst the proposed applications for gap solitons is their use in all-optical logic gates. A specific proposal for an all-optical AND gate was put forward by S. Lee and S.T. Ho¹¹. The bits in this system are two orthogonally polarised pulses whose frequency lies within the bandgap of the FBG. The AND gate works as the intensity threshold for coupled gap soliton formation is significantly lower than that required for the formation of a gap soliton in an isolated arm. There is thus a range of intensities whereby a coupled gap soliton will form but a single incident pulse will be reflected. We note that CW operation of such a system has been described by Samir, et al.¹². The behaviour of the switch was examined as a function of the power in a single arm and the results are shown in Fig. 4(a). Note that as in Fig. 3(a) there is a sharp threshold of operation at around 2.5 kW. In Fig. 4(b) the output pulse shapes for both the 1 (solid line) and 0 (dashed line) can be seen. As expected the 1 state corresponds to the formation of a coupled gap soliton which contains most of the energy in the pulses. In this case over 17 dB of contrast was observed.

 

Fig. 4a. Power dependence of the AND gate; note the sharp threshold near 2.5 kW. Fig. (b) shows the separate (dashed line) and combined (solid line) output trace for an input peak power of 3 kW.

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3.3 The Optical Pushbroom

The preceding experiments both relied on soliton formation within the grating which heavily distorted the pulse shape. Also such a switch is unsuitable for WDM applications since the high intensity pump can only be tuned to a single wavelength. An alternative approach to observing nonlinear behaviour in Bragg grating is to use the cross-phase modulation (XPM) of a strong pump to alter the refractive index seen by a weak probe thus changing the detuning of the probe from the center of the photonic band gap. Although the power requirements are similar to those for self-switching, the advantage of XPM arises as the frequencies of the pump and probe can be widely disimilar. This allows the pump frequency to be chosen so as to maximize the power available. The probe frequency is then determined by other considerations thus ensuring optimal switching.

The all-optical switching of a fibre Bragg Grating (FBG) was first seen by LaRochelle et al. in 1990¹³ using a self-written grating centered at 514 nm. In their experiment the probe beam was centered on the grating, while the pump beam had a wavelength of 1064 nm. They observed an increase in transmission from 50% to 54% in the presence of the pump.

The optical pushbroom utilizes the linear properties of a Bragg grating by situating a CW probe close to the bandgap where the group velocity is close to zero. When the pump is incident upon the grating, light at the back of the probe “sees” the pump first and via XPM its frequency is lowered. Thus at any instant there is a frequency chirp across the probe and this chirp combined with the GVD compresses the probe. Furthermore as the frequency of the probe changes it speeds up allowing the back of the probe to sit on the leading edge of the pump where it experiences the maximum XPM for the greatest possible length of time⁹. This process continues throughout the length of the grating with more and more of the probe’s energy being swept up onto the leading edge of the pump.

In transmission one would then expect to see a narrow peak containing a significant fraction of the energy stored in the grating followed by long dip while the CW field distribution in the grating is restored. These features can be clearly seen in Fig. 5a which shows the results of a numerical simulation of the optical pushbroom for system parameters matched to those of our experiment as detailed below. The solid line gives the probe’s intensity as a function of time while the dashed line indicates the pump’s profile – on a different vertical scale. The probe’s input intensity was normalized to unity and the transmitted intensity prior to the pump gives the linear transmission for this frequency. The inset shows an expanded view of the spike in transmission which has a FWHM of approximately 50ps.

 

Fig. 5a. Numerical Simulation of the optical pushbroom. The solid line is the probe intensity while the dashed line shows the pump intensity of a different vertical scale. The insert shows an expanded view of the front peak. Fig. (b) shows the actual experimental results highlighting the agreement with the numerical model.

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Fig. 5b shows an experimental trace of the optical pushbroom with the lines styles the same as the numerical model. The solid line shows the transmitted probe power while the dashed line shows the pump profile (on a different vertical scale). The probe’s wavelength is close to the long wavelength side of the bandgap where the linear transmission is close to 100%. The peak power of the pump within the FBG is set to 25 kW. The transmitted probe is clearly seen to have developed a sharp (≈ 70 ps FWHM) spike in intensity, co-located in time with the peak of the pump pulse. The transmission then drops well below unity for a considerable length of time – note that even 10ns after the arrival of the pump pulse the transmission has still not fully recovered. The parameters used in the numerical model in Fig. 5b match the actual experimental parameters, and as can be seen excellent agreement between the experimental and the numerical results is obtained.

We examined the dependence of the pushbroom on both the pump power and probe wavelength. As the probe was tuned closer to the bandgap the quality of the optical pushbroom decreased. This is as expected as at these frequencies the amount of energy stored in the grating is less. Also the quality of the trace decreases with pump power as expected. It should also be noted that on the short wavelength side of the bandgap similar effects can be seen in reflection¹⁴. This is due to the nonuniformity of the grating and can not be observed with a uniform grating.

4. Conclusions

In this paper we have present our results on three different types of nonlinear all-optical switches which of all relied on the properties of a single Bragg grating. The first switch utilised gap soliton formation resulting in self-induced transparency. The second switch was an all-optical ’AND’ gate using two orthogonally polarised input pulses and had a contrast ratio of 17 dB. The last switch showed that it was possible to alter the transmission of a weak probe by a high intensity pump and is particularly suited to WDM applications.

These results highlight the unique flexibility of Bragg gratings as potential media for nonlinear switches. It should be noted that other nonlinear effects such as optical limiting and the nonlinear generation optical delays have also been predicted to occur in Bragg gratings. However there is still a long way to go before practical devices can be constructed. As is clear from our results the power requirements are severe restricting nonlinear devices to the laboratory at present. There are however a number of ways to reduce this with the most promising being the latest generation of novel glasses such as the chalocogenides which have a Kerr nonlinearity 100 times that of silica. As it has been demonstrated that Bragg gratings can be written in such fibres it should be possible to reduce the power needed in the near future.