High-Speed Pulse Sequences through Semiconductor Optical Nonlinear Amplification and Buried Fiber Propagation

— Microwave pulse bursts were obtained through optical domain intensity modulated microwave carriers, sliced by cascaded modulator technique, followed by non-linear semiconductor optical amplifier (SOA) pre-chirp. After 3 to 18 km of buried fiber propagation and photo detection, the microwave signals presented increased extinction ratio, up to 36 GHz, with pulse modulation windows from 166 to 1000 picoseconds, achieving rise times near to 10 ps. including experimentally amplified 19 ns width individual pulses. This work introduces SOA amplification of fast microwave pulse bursts aiming applications of photonic techniques for arbitrary waveform generation (AWG) of microwave and millimetric signals [15]- [19]. They are obtained through optical domain amplitude modulated microwave carriers, sliced by a pulse-gated modulator technique [16]. The high power of the fast pulse bursts produces SOA gain saturation and chirping. So, proper SOA adjusted parameters produced nonlinear amplification of those short pulse’s sequences (up to 10 ps rise times), imbedded in an adjustable window (from 333 ps to 1 ns). The SOA amplified chirped pulses were transmitted in optical fibers (from 3 up to 18 km) followed by photodetection. The tuned SOA and fiber parameters, followed by interaction of the pre-chirped pulses and fiber dispersion modulated optical (3 dBm) model XN-OEC-1550, ultra-nonlinear, CIP (UK), cavity length of 2 mm, optical output saturation power ( Psat ) of 15 dBm, maximum gain around dB (small at 220 mA to static optical gain around dB, operation under saturation bandpass filter is inserted after the the chirped have its SOA was followed by an optical isolator (OI), an OPC, and a cascaded second modulator (MZM2), zero chirp, with 3 dB bandwidth equal to 40 GHz. A 30 ps rise time pulse generator (PG) MZM2 to a level of 2.5 V (close to Vπ) converting the MZM2 as a gated switch ( on-off operation). With a proper synchronization of MG and PG, the gated modulator embedded the MG chirped sinusoidal signal in a variable length square window. A 50% duty cycle was with a window length of 333 ps up to 1 ns.


I. INTRODUCTION
The light amplification using semiconductors diodes was proposed by Basov et al. [1], using the electromagnetic energy generated by the recombination of electrical carriers in a p-n junction. For infrared wavelengths, gallium arsenide (Ga-As) was used for amplification [2]. However, useful Semiconductor Optical Amplifiers (SOAs) were achieved with multiple quantum-well (MQW) active regions and one-pass traveling wave SOAs were obtained using anti-reflections facets with small mirror reflectivity around 10 -4 [3], [4]. Theoretical analysis of MQW-SOAs have been performed including gain compression in polarization insensitive devices [5], including injected current dynamics effects [6], [7]. In particular, when very short pulses are amplified, non-linear SOA effects of self-phase modulation (SPM) cause pulse spectral broadening and distortion [8]- [10]. Also, SPM introduces a pulse chirp (time-dependent instantaneous optical carrier frequency deviation) related to the SOA carrier lifetime, SOA saturation and gain [11]- [14]. The SOA chirping has been recently analyzed [15] including experimentally amplified 19 ns width individual pulses. This work introduces SOA amplification of fast microwave pulse bursts aiming applications of photonic techniques for arbitrary waveform generation (AWG) of microwave and millimetric signals [15]- [19]. They are obtained through optical domain amplitude modulated microwave carriers, sliced by a pulse-gated modulator technique [16]. The high power of the fast pulse bursts produces SOA gain saturation and chirping. So, proper SOA adjusted parameters produced nonlinear amplification of those short pulse's sequences (up to 10 ps rise times), imbedded in an adjustable window (from 333 ps to 1 ns). The SOA amplified chirped pulses were transmitted in optical fibers (from 3 up to 18 km) followed by photodetection. The tuned SOA and fiber parameters, followed by interaction of the pre-chirped pulses and fiber dispersion High-Speed Pulse Sequences through Semiconductor Optical Nonlinear Amplification and Buried Fiber Propagation Ernesto M. M. Barrientos 1,2 , Evandro Conforti 2 enhanced the received signal format, extinction ratio, or rise-time. By adjusting the fiber length, the optical input pulse power and width, plus the SOA bias current, an improvement on the output pulse shape may be achieved as shown in the following sections. Section II presents a succinct theoretical background of the optical fast pulse SOA amplification, highlighting the optical chirp increment behavior (during the pulse rise and fall) and its interaction with the fiber dispersion. Section III shows the experimental setup description including the employed devices parameters. Section IV presents the experimental results with a discussion of how the output pulse shape improvement can be obtained. The conclusions are on Section V.

II. THEORETICAL BACKGROUND
The SOA amplification of fast pulses reaching the gain saturation produces nonlinear SPM effect.
The time changing signal being amplified causes a dynamic carrier depletion, changing the SOA gain and the active region dielectric constant along the propagation axis (z). Those complex effects were simplified by Agrawal and Olsson. For the case of unchirped Gaussian input pulse [8]: where  is the pulse chirp,  is the optical phase, and  is the time moving with a reference frame.
After same simplifying assumptions, the chirp increment, after SOA pulse amplification is given by [8]: where out is the SOA output signal chirp, in is the SOA input signal chirp,  is the carrier induced index-change, h is the SOA gain.
The derivative of the chirp increment, Cd is given by: At the pulse beginning (zero amplitude), the SOA gain is at the its maximum value, h= G0 , where G0 is the small signal SOA gain. Assuming instantaneous response of the SOA gain h , as soon as the pulse rises, the SOA gain decreases due to saturation. The chirp increment of (2) attains a negative (red-shift) value, since the gain time derivative is negative (  h /  . As the pulse continues to rise, the gain decreases even more (due to the increased saturation effect). When the maximum pulse intensity is reached, the SOA gain attains its minimum value (the gain second derivative  2 h /  2 >0), the first derivative is zero (  h /  and no chirp is produced. During the pulse fall, the SOA gain begins to increase ( h /  since the pulse signal is dropping, and the SOA saturation is decreasing. So, the chirp reaches a positive value. However, in practice the SOA behavior is intricate. The SOA gain does not have an instantaneous response. The solution of (2) for a pulse rise time much faster than the SOA carrier lifetime, predicts a sharper pulse trailing edge, and a slower decay in the remaining pulse [8]. Also, the output pulse spectrum has a red shift value whose peak decreases several GHz. At the pulse beginning (SOA bias of 70 mA), an experimental chirp value of -30 GHz was obtained for a 19 ps amplified pulse width [15]. Later, the chirp increment reached a value around  -12 GHz at the maximum pulse amplitude peak. And at the minimum amplitude (where the pulse ends) the chirp was around  +6 GHz. The SOA overall red shift was -12 GHz [15]. Also, the chirp nonlinearity is more intense when the pulse intensity and the SOA bias increase [15]. Likewise, the chirp increment and its time variation Cg depend on the SOA manufacture parameters, the SOA saturation level and bias current, the relation of the pulse width and the SOA carrier lifetime, plus the pulse shape and pre-chirp.
However, since the chirp increment (frequency variation) changes during the pulse rise and fall, the pulse shape can be improved after fiber propagation, since the fiber dispersion also changes with the light instantaneous carrier frequency. A standard 10 km fiber at 1550 nm has a dispersion of 170 ps/nm, or 2.1 ps/GHz of the instantaneous carrier frequency. A typical output SOA pulse has a negative chirp  at pulse rising and a positive chirp at pulse decaying. During the hole pulse duration, the total chirp variation can be 36 GHz [15] or more, and this frequency change is converted in a signal time variation (compression or enlargement) due to the fiber dispersion. Therefore, a 20 GHz chirp (frequency variation) during the pulse rising might reach up to 42 ps of pulse format variation in a 10 km fiber. By adjusting the fiber length, the optical input pulse power and width, plus the SOA bias current, an improvement on the output pulse shape may be achieved as shown in the following sections.
The numerical analysis is out of the scope of this work.

III. EXPERIMENTAL SETUP
The generation of the embedded optical pulse train employed a cascaded single-drive Mach-Zehnder modulators (MZM) [16]. As shown in Fig. 1 Fig. 2. Also, the dotted line signal is the chirped pulse just after the SOA. The continuous line of Fig.   2 shows the same signal after the fiber propagation of 3 km. Note the typical distortion due to SPM [8] of the dotted line chirped signal. After 3 km of fiber propagation, a discrete improvement on the signal format can be observed.
The same signals of Fig. 2 are shown in Fig. 3, but the fiber length is now 9 km. A better signal format now appears (continuous line) with an improvement on the extinction ratio and on the signal format. In addition, a good suppression of the microwave oscillation was obtained outside the 250 ps gate, but small microwave energy is still presented. The uncomplete suppression is due to insufficient extinction of MZM2. Also, the three pulses did not reach the zero level and the insufficient extinction ratio might be related to both MZM1 and MZM2 limited bandwidth.  The results for the same signals of Fig. 2 are shown in Fig. 4 for an overall fiber length of 18 km.
Note the higher extinction ratio of the propagated signal (continuous line). However, the received signal has distortions during the rising time of the internal pulses, shown by the letters A and B in Fig. 4. This behavior might be due to an over correction of the pulse format, since the longer fiber has greater dispersion and additional attenuation given by the 18 connectors at the fiber endings.
Similarly, several results (not shown) present a similar behavior, denoting the existence of an interaction of the pulse (with embedded chirp due to the SOA non-linear behavior) and the fiber length, since the dispersion at 1550 nm in a standard fiber is around 17 ps/nm.km. Indeed, the SOA chirp can reach over 100 GHz for short pulses [8]. However, the SOA chirp behavior is a complex feature and the analysis is out of the scope here. In general, the chirp intensity and its time format depend on the SOA itself, the bias current, the optical input pulse intensity, width, and format. In this case, the improvement of the extinction ratio can be noted. However, the microwaves outside the embedding window were not suppressed entirely. This behavior might be related to the MZM2 gated switch insufficient action to suppress the higher 20 GHz modulated carrier signal inside it.
The results for a 12 GHz microwave signal inside an embedded window of 166 ps are shown in Fig.6 for 9 km of fiber propagation. The dotted line presents pulse distortions, shown by letters C and D.
Also, the letters A and B represents the 10% and 90% signal levels of the continuous line after propagation. Those levels A and B were used to calculate the signal rise time as shown in Fig. 6. Also note the half cycle calculation in Fig. 6.
Several measurements have been made with the microwave signals going from 12 GHz up to 36 GHz, including the embedded windows from 166 ps up to 500 ps, for fiber lengths of 3.0 km, 9.0 km, and 18 km.   V. CONCLUSION A technique for the generation of fast chirped optical pulsed waveforms, including the format and extinction ratio measurements after the fiber propagation has been described. The chirped pulses have been produced by amplification and proper parameter adjustments of a nonlinear SOA with 2 mm length cavity. The experimental setup successfully regenerated gate embedded window microwave signals,