The development in 1995 of the two dimensional deconvolution algorithm described in the next section made blind-FROG possible [25], and with that a new category of frequency resolved complete pulse characterisation methods was born. This algorithm removes the need for a known functional relationship between the pulse and the gate making up the spectrogram. The techniques described in the previous section could thus also be used with two different pulses, instead of replicas of the same pulse. Dorrer and Kang then demonstrated in 2002 that it is also possible to implement the gating with a modulator [19], instead of relying on nonlinear optics. This method is particularly interesting for telecommunication rate pulses, as it can be implemented using devices previously designed for optical telecommunications. The scheme is shown in Figure 2.5.
The stream of pulses under test is fed into the optical modulator, which has a modulation function represented byG(t). The sampling modulator is synchronised to the pulse stream, as it is driven by the same RF signal generator. As will be seen later, it can also be made self-referenced. An RF phase shifter in one of the paths is used to temporally shift (τ) the modulation relative to the pulses. The spectrum of the remodulated, or actually coarsely sampled signal E(t)G(t−τ) is then measured with an optical spectrum analyser (OSA), for a series of incremental
EAM OSA Input Pulse E(t) EAM window G(t) τ τ Sampled Pulse E(t)G(t−τ)
Figure 2.5: The linear spectrogram technique originally proposed by Dorrer and Kang.
delays τ that spans the full pulse period:
S(τ, ω) = Z E(t)G(t−τ) exp(iωt)dt 2 . (2.17)
It is interesting to note that as well as retrieving the complete pulse information, the phase retrieval algorithm simultaneously characterises the sampling function of the modulator used in the experiment. A particularly suitable modulator is the electro-absorption modulator, and is described in more detail in the following chapter. Its main advantages are that very fast switching speeds are achievable, and they can be made very much polarisation insensitive.
We first implemented this technique in our lab using an optical delay stage instead of the RF phase shifter. Initially, this delay stage was tuned manually whilst sav- ing each spectrum on a floppy disk, but it soon became clear that this was not an ideal arrangement. Due to the long time it took for one measurement – about 1 hour – the measured spectrogram was distorted due to changing lengths in the optical and electrical paths in the setup caused by fluctuating temperatures in the lab.
Two enhancements I developed drastically improved the quality of the spectro- grams, and with that the retrieval process. Figure 2.6 shows the schematic of the setup that we now regularly use in the lab to characterise pulses. First of all, by using a fast photo-detector followed by an electrical amplifier, the setup is made self-referenced. Part of the pulse under test is split off with an optical fibre coupler, and converted into an electrical signal that is used to drive the sampling modulator. The combination of a fast photo-detector (32 GHz bandwidth) and
a broadband amplifier also allows us to create shorter electrical pulses than the sinusoidal signals available from an RF signal generator. This makes it possible to create shorter sampling windows in the modulator.
EAM OSA
PD
Input Pulse
delayτ
Figure 2.6: The scheme of the self referenced linear spectrogram technique.
Secondly, I automated the whole spectrogram acquisition setup. A computer con- trollable delay stage and the optical spectrum analyser have been programmed in the programming language Delphi, heavily building on the general purpose inter- face bus (GP-IB) commands of both devices. A snapshot of the program interface is shown in Figure 2.7. This automated setup is now able to acquire a complete spectrogram in just under a minute, depending on the exact settings of the OSA (i.e. the number of points, the spectral resolution, averaging settings, etc.) The data transfer speed of the GP-IB and the wavelength scanning speed are the lim- iting factors in this acquisition setup.
As can be seen in Figure 2.6, an optical amplifier follows the delay stage. The saturated output power of the optical amplifier can be fixed and this is exploited to equalise the power after the delay stage, which has a delay dependent insertion loss. In theory, the position of the delay stage can be chosen arbitrarily between either within the path of the optical signal that is then modulated by the EAM, or within the path where the optical signal is converted to an electrical signal. How- ever, the fact that the delay stage has a delay dependent insertion loss forces us to choose the second option, in order to eliminate any distortion of the experimental spectrogram.
Further on in this thesis, various adaptations are made to this setup, to accom- modate for either higher bit rates, or more complex waveforms. The updated experimental setups will be explained where appropriate, but until further notice, the ‘standard’ setup for linear spectrogram acquisition is the one shown in Figure
Figure 2.7: Front end user interface of the spectrogram acquisition program, after the measurement of a gain switched pulse.
Note that an implementation allowing real-time retrieval of the pulse and gate fields has recently been demonstrated [26,27]. A fast scanning Fabry-P´erot etalon followed by a photodiode replaces the optical spectrum analyser, and the phase shifter is voltage controlled. Appropriate synchronisation between these two de- vices allows for a very fast acquisition of a complete spectrogram. To speed up the convergence of the reconstruction algorithm, the retrieved gating function of a particular spectrogram is fed into the retrieval of the following spectrogram as an initial guess. All this leads to an impressive refresh rate of 10 Hz.