Phase retrieving from phase-sensitive second-harmonic patterns

An experimental verification of the new freezing phase scheme starts with grouping of the SLM pixels into two classes: the first group, which is composed of three consecutive pixels, plays the role of phase modulation. The other group, which contains the rest pixels, is used as the reference. We vary the phase of the modulation group from 0 to 2π to maximize the SH intensity. The procedure repeats by regrouping the SLM pixels until the phase retardations of all pixels are adjusted.

Figure 3.8 shows the measured SHG intensity of the optical pulse reflected from a gold-coated mirror. The spectrum of the mode-locked laser pulse is also plotted to label the related spectral positions of the SLM pixels. The experimental results confirm that the SHG modulation is proportional to the amplitude of the chosen

spectral components as predicted by Eq. (6). The SH modulation pattern shifts, reflecting the spectral phase of the optical field. Once the chosen pixels lie outside the spectral range of the coherent pulse, the SH intensity modulation is no longer observable. These findings reveal the spectral phase profile of a coherent pulse to be deducible from the measured SH patterns by adjusting SLM retardation with a pulse shaping apparatus.

Fig. 3.8: Dependence of the measured SHG intensity of an optical pulse reflected from a gold-coated mirror on the phase retardance of three consecutive pixels of SLM.

B.2 Complete-field characterization of semiconductor saturable absorber mirrors with an adaptive control pulse shaper

InAs quantum dots (QDs) have important applications for ultrafast optical shaping at 1.3 µm. Under conditions of strong excitation, the absorption is saturated because possible initial states of the pump transition are depleted while the final states are partially occupied. Within 50–300 fs of excitation, the carriers in each band

thermalize, and this leads to a partial recovery of the absorption. The faster time constant is more effective in shaping subpicosecond pulses [20].

Saturable Bragg reflector (SBR) structure consists of a highly reflective Bragg mirror and quantum well or quantum dots embedded in it. By proper choice of the position of the saturable semiconductor layer it is possible to change the effective field that bleaches its optical absorption and therefore the saturation fluence of the device. This type of device is cheaper, more robust, and has quite a low insertion loss.

The main limitation of SBR is most probably the strong wavelength dependence of the group delay introduced by the structure, which might be a problem for generating very short (<40 fs) pulses or for having large tuning range with fixed pulse parameters [21]. It is therefore important to characterize the complete-field profile of femtosecond optical pulse reflected from a variety of SBR structures in order to reveal the underlying pulse distortion processes. We employ our newly developed adaptive control apparatus on three types of SBR samples.

The first SBR device comprises of two Ga0.47In0.53As quantum wells which are embedded in an Al0.48In0.52As quarter wave layer on a distributed Bragg reflector (DBR) stack (hereafter is abbreviated as d-QW). The DBR stack is formed with 25 pairs GaAs/AlAs designed to yield a Bragg wavelength at λB=1.23 µm. The other is self-assembled InAs quantum-dots layer embedded in a quarter-wave-thick (QD-λ/4) or half-wave-thick (QD-λ/2) GaAs layer on a DBR stack. The DBR of the two devices is identical and contains 21-periods stack of 97 nm/112 nm GaAs/Al0.92Ga0.08As. The DBR was designed to yield high reflection at 1.3 µm. The schematic device structures with the corresponding field distribution at a wavelength of 1.25 µm are depicted in figure 3.9.

Fig. 3.9: Calculated field distribution (with blue-red color coding) is presented with the device structure of saturable absorber Bragg reflectors with InAs-QD or d-QW embedded in a (a) λ/4-thick layer or (b) λ/2-thick layer.

^{1.20 1.22} Wavelength (µm)^{1.24 1.26 1.28 1.30} 2.1

4.2 6.3

Spectral Phase (Rad.)

( C )

Fig. 3.10: (a) Measured and (b) retrieved SHG-FROG patterns of femtosecond optical field at 1.25 µm reflected from the QD-λ/2 SBR and (c) the retrieved spectral phase profiles from d-QW (solid curve), QD-λ/4 (long dashed) and QD-λ/2 (short dashed line) SHG-FROG traces.

We first employ SHG frequency-resolved optical gating (SHG-FROG) technique [21] to characterize the complete-field profiles of the femtosecond pulses reflected from the three SBR devices. The result for the QD-λ/2 structures is shown in Fig. 3.10.

The experimental SHG-FROG trace was retrieved with an error of 0.0025. The

retrieved spectral phase profiles for the three SBR devices are presented in Fig. 3.10 (c) and are found to overlap with each other near the central region but significant difference can be observed at the tails of the spectra of QD-λ/4 and QD-λ/2. As shown in Fig. 3.9 the field strength experienced by the InAs QDs in QD-λ/2 is smaller and therefore we expect to observe weaker pulse shaping effect and therefore larger phase distortion in QD-λ/2.

After performing the pulse analysis with standard SHG-FROG, we then proceed to diagnose the complete-field characteristics with our freezing phase adaptive phase compensation apparatus. The results are summarized in Fig. 3.11. We first use the modulation depth of SH signal (see Fig. 3.8) to determine the spectral profile. Fig.

3.11(a) presents a direct comparison of the deduced spectral profile of optical pulse reflected from the d-QW sample from freezing-phase algorithm (FA) and that measured with Fourier-transformed infrared spectroscopy (FTIR). An excellent agreement was found, indicating that our adaptive phase compensation scheme not only be able to yield the spectral phase profile but also the amplitude of a coherent optical pulse. We then present the measured spectral phase profiles with FA for the three SBR devices in Fig. 3.11(b). The global features of the measured spectral phase profiles are similar to that obtained with SHG-FROG technique. The most deviations occur at the regions with small spectral amplitude where retrieving with FROG algorithm is usually less reliable. The slight shift of the QD-λ/2 spectral phase profile (short dashed curve) from d-QW (solid curve) and QD-λ/4 (long dashed) also occurs in the spectra measured with FTIR. Note that the device structure of QD-λ/2 is very similar to QD-λ/4except a twice thicker QDs embedded layer employed in QD-λ/2.

The clearly distinguishable differences in the spectral phase profiles ensure that our new complete-field characterization scheme is sensitive and accurate to reveal influence on femtosecond optical pulse with subtle change in SBR structures.

Furthermore, unlike SHG-FROG with pulse characteristics to be retrieved with sophisticated mathematical procedure, our method belongs to a direct measurement approach.

Fig. 3.11: (a) Spectral profiles of optical pulses reflected from d-QW (open circles) measured with freezing-phase algorithm (FA) and from d-QW (solid curve), QD-λ/4 (long dashed), QD-λ/2 (short dashed) with Fourier-transformed infrared spectroscopy (FTIR) (b) Spectral phase profiles from Au-mirror (thin solid curve), d-QW (thick solid curve), InAs QD-λ/4 (long dashed), and InAs QD-λ/2 (short dashed) deduced with phase freezing scheme; (c) group delay time of the three SBR devices over the entire pulse spectral range.

As explained in the previous paragraph, the main limitation of SBR in ultrashort laser application is the strong wavelength dependence of the group delay introduced by device structure. With the measured spectral phase profiles we can further deduce the group delay caused by the SBR devices. To properly remove influences from laser optics, the phase profile of an optical pulse reflected from a gold mirror placed at the same position of the SBR devices were also measured. The group delay times of the SBR devices were deduced by first taking a difference between the spectral phase profiles of SBR and Au mirror. We then differentiated the phase difference profiles with angular frequency to yield the group delay times. The results are presented in Fig.

3.11 (c), show that the d-QW SBR exhibits much weaker wavelength-dependent group delay within the entire spectral range of the optical pulse. Indeed this device had been designed for passively mode locking femtosecond laser at 1.25 µm and was confirmed experimentally to be able to generate femtosecond laser pulse with pulse duration less than 60 fs. As expected, among the three SBR structures the QD-λ/2 shows largest variation in group delay within the spectral range, especially for the spectral components with wavelength longer than 1.27 µm. The larger variation in group-delay by QD-λ/2 can originate from weaker field strength being experienced by the InAs QDs and therefore weaker pulse shaping effect is yielded.

The position of the saturable absorber layer inside the structure is an important design parameter. Usually it prefers to place the saturable absorber layer at a high field location, such that the effective saturation fluence of the device is reduced.

However, Keller, et al. had recently pointed out that this may cause a pronounced absorption dip at the resonance wavelength, and the extra loss would push the lasing wavelength away from the negative GVD regime [21]. Therefore, those researchers suggested the absorber layer to be positioned close to the field minimum.