1. Introduction

Quantum-well waveguides designed for intersubband transitions (ISBTs) [1–7] with a carrier relaxation occurring on picosecond or sub-picosecond time scales have drawn much interest lately as compact devices capable of performing high-speed all-optical signal processing. Ultrafast optical switching in the 1550 nm wavelength region has been achieved by exploiting the saturable absorption effect in ISBT quantum-well waveguides. Although a switching time shorter than a picosecond can be achieved, it requires a large saturation energy (a 3-dB saturation energy of ~10 pJ or more) and has a large un-saturable loss (10 dB or more), which makes it difficult to use in optical systems operating at tens of gigahertz. Recently, a more efficient way of achieving optical modulation has been demonstrated, which is based on cross-phase modulation (XPM) using ISBTs in InGaAs/AlAs/AlAsSb coupled quantum wells [8,9]. It has been observed that within the intersubband absorption band, the optical phase of TE-polarized light can be efficiently modulated by excitation with TM-polarized short pulses. The origin of the cross-phase modulation of a TE-polarized wave by a TM-polarized pump pulse in InGaAs/AlAsSb ISBT device have been recently investigated based on two models, i.e. plasma dispersion model [9] and interband dispersion model [10]. In the plasma dispersion model, the induced phase modulation is attributed to a change in the total refractive index due to a change in plasma dispersion that is caused by the redistribution of electrons among subbands having different effective masses [9]. However, according to the interband dispersion model, the refractive index change causing the phase retardation is attributed primarily to the interband transition enhanced by intersubband transition [10]. When the ISBT device is excited using a TM-polarized intersubband-resonant light, the intersubband excitation causes partial depletion of carrier at the first subband, resulting in an enhanced interband transition around the Fermi edge [11,12]. This dispersion in the interband absorption results in a change in refractive index that is seen to be strongly dependent on the probe wavelength [10].

Compared to cross-absorption modulation in ISBT quantum-well waveguides, XPM is advantageous for signal processing because of its higher modulation efficiency requiring sub 10-picojoules of energy for picosecond pump pulses to achieve a phase change of 1 rad at 1550 nm. Besides, as the TE-polarized probe light remains unabsorbed in the ISBT waveguide, phase modulation can be achieved with essentially no loss, ensuring signal processing with better signal to noise ratio. The ultrafast carrier relaxation in ISBT devices also allows operation that is free from pattern effects, a problem commonly observed in semiconductor optical amplifier-based signal processors. Recently, by using the XPM effect in an InGaAs/AlAsSb quantum-well waveguide, efficient bit-error-free wavelength conversion of picosecond pulses at 10 Gb/s [8] and de-multiplexing from 160 Gb/s to 10 Gb/s [13] have been demonstrated with both the pump and signal lying within the 1.55 µm telecommunication band.

Previously, in all experimental studies on the intersubband relaxation dynamics in quantum wells [1,2] and their application to signal processing [8,9], the quantum wells were excited with pulses having picosecond to femtosecond durations. So far, there has been no report on the study of the cross-phase modulation effect in ISBT quantum-well devices excited with a slowly intensity-varying pump wave. If a pump wave exists over a period that is much larger than the carrier relaxation time, then excitation and relaxation of the carrier can take place concurrently, which allows us to study the quasi-steady-state dynamics of the device.

In this paper, we describe our study on the ultrafast dynamics in an InGaAs/AlAsSb coupled double quantum well (C-DQW) waveguide, which was excited with sinusoidal intensity-modulated (76 GHz) radiation at 1550 nm. A highly sensitive technique allowed measurement of phase retardations as small as 0.002 rad (corresponding to a peak pump power of ~10 mW). XPM of the probe with wavelength in the range of 1330–1620 nm was achieved with an efficiency of 0.653–0.142 rad/W. Based on the efficiency we derived a transfer function for the modulator that is useful in calculating the modulated output signal for long excitation pulses with arbitrary waveforms.

2. Experiment

In our experiment, we used a newly designed ISBT waveguide device having an active layer made of InGaAs/AlAsSb coupled double quantum wells (C-DQWs) with an InAlAs coupling barrier; the growth structure is shown in Fig. 1. The detailed fabrication process of the device can be found in Ref. [14]. The mesa-structured waveguide was 200-µm long and 0.8-µm wide allowing single-mode propagation, and had tapered structures on both ends that allowed efficient coupling to single mode optical fibers. Coupling of light into the device was achieved using polarization-maintaining fibers with a fiber-to-fiber coupling loss of about 8.0 dB (measured using TE-polarized probe light at 1550 nm). The loss in the waveguide arising from roughness of the mesa wall for TE-polarized light was measured to be about 4 dB, while the fiber-to-waveguide coupling loss per facet was about 2 dB. Coupling losses for the TE and TM waves were estimated to be the same.

 

Fig. 1. The InGaAs/AlAsSb intersubband coupled double quantum well waveguide device. a) Growth structure. b) Waveguide mesa structure.

Download Full Size | PDF

 

Fig. 2. Experimental setup used for characterization of XPM effect in ISBT quantum well device.

Download Full Size | PDF

An experiment to characterize the XPM effect in the ISBT switch was performed using the setup shown in Fig. 2. Sinusoidal intensity-modulated laser radiation at a repetition rate of 76 GHz was used as a pump. This pump was generated by modulating light from a 1552 nm cw laser source with a Mach-Zehnder (MZ) modulator, which was operated at the null point and excited with RF modulation at 38 GHz. By adjusting RF power to the modulator, we could achieve a sinusoidal intensity-modulated pump wave with ~100% modulation depth at a repetition-rate twice the RF frequency. The pump wave was split into two, amplified, and then launched into the ISBT device through a polarization beam combiner from one/both directions with TM polarization. The contribution to phase modulation for the bidirectional pumps could be added by adjusting the relative timing of the sinusoidal pumps using an optical delay line. Such bidirectional pumping allowed launching twice as much power as the damage threshold at the end facets. As a probe signal, we used TE-polarized continuous wave light with wavelength tunable within the range 1330–1620 nm. The waveguide device was maintained at a nominal temperature of 25 °C by a thermoelectric temperature controller.

The phase retardation of the probe output was characterized using an optical spectrum analyzer. If a sinusoidal intensity-modulated wave (with 100% modulation depth) were used as a pump, any cross-phase modulation in the probe light would generate optical sidebands on both sides of the carrier frequency. If we define an efficiency of XPM in relation to the instantaneous pump power launched into the PM fiber as η, then the peak phase retardation Δ can be expressed as Δ=η.P _peak, where P _peakrepresents the peak pump intensity of the sinusoidal pump. The phase retardation Δ can be determined from the ratio of intensities of the carrier and the first order sidebands, i.e. [J ₀(Δ)/J ₁(Δ)]². Here, J _o and J ₁ are the zero- and first-order Bessel functions, respectively.

3. Results

Figure 3 shows the optical spectra of the phase-modulated output with different probe wavelengths, measured for an average pump power of 70 mW (peak power of 140 mW). In each case, we can see modulation sidebands at ±76 GHz away from the carrier. From the intensities of the sideband and carrier, phase retardation Δ and the XPM efficiency η were determined.

 

Fig. 3. Optical spectra (normalized) of the output probe signal that was cross-phase modulated by a backward-propagating 76-GHz sinusoidal intensity-modulated pump wave at 1552 nm. The average pump power was 70 mW (peak 140 mW). The frequency spacing between the carrier and sidebands is 76 GHz. η is the cross-phase modulation efficiency.

Download Full Size | PDF

Also to investigate if there is any the dependency of XPM efficiency with pump power, we measured the phase retardation at different pump intensities. Figure 4 plots the phase retardation for a probe wavelength of 1504 nm measured at different pump powers. The abscissa represents the combined power for forward and backward pumping. A linear relationship with a XPM efficiency, η of 0.228 rad/W is obtained. Since the coupling loss per facet is ~2 dB, the efficiency in terms of power launched in to the ISBT waveguide will be 1.6 times higher than this value. The XPM efficiencies corresponding to other probe wavelengths in the range of 1330–1620 nm are also shown in Fig. 3. Phase modulation occurred with efficiencies of 0.653–0.142 rad/W for the sinusoidal excitation. For probe at 1330 nm, about a three-fold enhancement in efficiency compared to that for probe at 1540 nm was observed.

 

Fig. 4. Phase retardation of a 1504 nm probe wave plotted as a function of peak pump power. Blue circles: forward pump only. Green circle: with forward (140 mW) and backward (86 mW) pump powers.

Download Full Size | PDF

Using the technique based on sinusoidal excitation, we were capable of measuring phase retardation with a higher sensitivity and better accuracy and than attained from the interferometric method of phase measurements based on picosecond pulse excitation [8]. The sensitivity associated with the current method depends on the probe intensity and the noise floor of the optical spectrum analyzer. In our measurement, we could easily observe modulation sidebands more than 65 dB below the carrier level, thus allowing us to measure Δ as small as 0.002 rad.

4. Transfer function of ISBT modulator

Based on the linearity of phase retardation with the pump as shown in Fig. 4, we can derive a transfer function [15] of the ISBT quantum well device which will be useful in designing and numerically studying the performance of different optical systems such as modelocked lasers [16], optical millimeter-wave source [17] and all-optical synchronization [18], where IBST devices may play key role. If pump exhibits an amplitude variation of E _pump(t), the transfer function of the all-optical modulator can be expressed as, M̂=exp(-jηP_pump). Here, P_pump(t)=E_pump(t).E*_pump(t) represents the intensity variation of the pump wave. Therefore, for an incoming probe with amplitude E_probe, the amplitude of the modulated output can be expressed by E_probe.M̂, and the optical spectrum will be the finite Fourier transform [19] of E_probe.M̂.

To demonstrate this, we created a 10 GHz periodic train of dual pulses each 2.9 ps-width and separated by 9.5 ps, as shown in the inset of Fig. 5, and launched as a TM pump in the direction opposite to a continuous wave TE probe at 1547.5 nm. The average launched pump power was 43 mW. Figure 5 shows the optical spectrum of the modulated probe (center corresponds to 1547.5 nm), along with that obtained (blue dots) from the finite Fourier transform of exp[-jη.P _Pump(t)], where P(t)=P_o.exp[-t ²/τ²]+Po.exp[-(t-T _d)²/τ²] and τ=1.75 ps (FWHM of 2.9 ps), T_d=9.5 ps (measured using an autocorrelator), T_o=100 ps, and η=0.218rad/W (experimentally measured at ~1550 nm), P_o=0.74 W (peak intensity estimated from average power). An excellent agreement between the experiment and the simulation can be easily seen.

 

Fig. 5. Normalized spectrum (gray line) of the output probe that was modulated with a periodic train of dual picosecond pulses, as depicted in the inset. The blue points correspond to that calculated using the parameters τ=2.9 ps, T_d=9.5 ps, T_o=100 ps and η=0.218 rad/W and P_o=0.74 W.

Download Full Size | PDF

We have thus verified that the phase retardation efficiency (η) measured using sinusoidal pump (having a period of 13 ps, which can be considered as a quasi-steady state case), could be used for the case of picosecond pulse excitation. So, we can infer that when the temporal changes in the pump pulses are longer than the carrier relaxation time, the phase retardation efficiency can be conveniently applied to estimate the modulated output spectrum.

Besides high-speed optical signal processing [8,11], a wide range of other functions can be realized by cross-phase modulation in InGaAs/AlAsSb ISBT quantum well waveguide devices by pumping with sinusoidal or pulsed excitation. These include mode-locking for short pulse generation [16], optical millimeter-wave generation [17], pulse synchronization [18], pulse characterization, etc.

4. Summary

In conclusion, we have studied the cross-phase modulation effect in an ISBT InGaAs/AlAsSb quantum well waveguide device by excitation with a sinusoidal intensity modulated pump at a 76-GHz-repetition-rate. XPM of the probe with wavelength in the range of 1330–1620 nm was achieved with an efficiency of 0.653–0.142 rad/W. Based on the efficiency we derived a transfer function for the modulator that is useful in calculating the output of the device for pumps and probes with arbitrary waveforms. This device, capable of ultrafast all-optical modulation over such a wide band, should be useful for a rich variety of applications, such as high-speed all-optical modulation, mode-locking, ultrafast signal processing, and multicasting within the E to L band of optical communication, as well as in microwave photonics for optical millimeter wave generation.