10 Gbit/s free space data transmission at 9 $\mu$m wavelength with unipolar quantum optoelectronics

The realization of high-frequency unipolar quantum optoelectronic devices enables the demonstration of high bitrate free space data transmission in the second atmospheric window. Data-bits are written onto the laser emission using a large bandwidth amplitude modulator that operates by shifting the absorption of an optical transition in and out of the laser frequency.

the mid-infrared for several applications such as digital communications and high-resolution spectroscopy.

Introduction
Unipolar quantum optoelectronics (UQOs) comprises an ensemble of semiconductor devices operating at room temperature in the mid-infrared (  4 -16 μm) with bandwidths of tens of GHz. The devices exploit the presence of quantum-confined two-dimensional electronic states formed in the conduction band of technological mature semiconductors. They are thus unipolar as electrons are the only charge carriers present. UQOs enables the realisation of optoelectronic systems that combine in phase different devices to produce complex functions and operations. [1] In the mid-infrared this is highly sought after, not only for technological applications, but also to address fundamental physics questions. For example, highly sensitive and ultrafast optoelectronic systems are required for free-space communications, [2][3][4][5] light detection and ranging (LIDAR), [6] high resolution spectroscopy, [7] and in observational astronomy. [8,9] On the fundamental side, the coherent assembly of UQOs devices can enable unique experimental arrangements to be devised for quantum measurements, for example to study non-classical state emission from quantum cascade lasers. In this sense UQOs will greatly extend optoelectronic applications and quantum optics into the mid-infrared/THz region.
In this work, we present the realisation of an UQO system for data transmission in the 8 to 14 µm atmospheric window comprising a continuous wave (cw) quantum cascade (QC) laser, an external modulator, and a QC detector (Figure 1). In contrast to previous studies based on directly modulating a QC laser current, [2,[10][11][12] data-bits are written onto the laser emission in our system using a high frequency external modulator that operates by shifting the absorption of an optical transition in and out of the laser frequency. This device is designed to avoid charge displacement or electron depletion, [13] and therefore it is characterized by an intrinsically large bandwidth and very low electrical power consumption in comparison with direct current modulation of the laser. [10,14,15] This modulation scheme is a step forward to increase the bitrate for free-space communication with enhanced privacy in the midinfrared. [16] Using the set-up illustrated in Figure 1, we have demonstrated a data rate transmission of 10 Gigabits per second on a single channel, with bit error rate of the order of 10 -3 , compatible with common protocols for data transmission. To our knowledge this is the fastest data transmission ever reported in this wavelength range paving the way for commercial communication systems outside the saturated near-infrared telecom bands. In the future, the photonic integration of these devices will further increase their performance and make it possible to extend the realm of quantum technologies deeper in the infrared and THz frequency ranges [17] .

System description and high frequency devices
Our system is sketched in Figure 1d. Light from a commercial distributed -feedback (DFB) QC laser (Figure 1a) impinges on the modulator (Figure 1b) that writes the information, which is subsequently read by the detector (Figure 1c). The beam propagation across the modulator is shown in Figure 1f: the light coupling into the modulator is through a 60° wedge to increase the coupling length and to facilitate the laser beam alignment. In order to operate at high frequency, the detector and the modulator have been processed into mesa structures that are electrically connected to a 50 Ω coplanar waveguide through an air-bridge for a lowinductance top contact. [14,18] This is shown in the scanning electron microscope (SEM) image in the inset to Figure 1d. The device is then fixed on a custom-made holder and wire bonded onto an adapted PCB coplanar waveguide, as illustrated in Figure 1e. All devices are realised in III-V semiconductor heterostructures. Right arrows indicate the electronic path in the structure, while the blue arrows indicate 9µm photons. (d) Sketch of our experiment comprising QC laser, Stark modulator and QC detector, all of them operating at room temperature and at the same wavelength, 9µm (138 meV). The laser is a commercial cw distributed feedback QC laser (Thorlabs QD9000HHL-B). The modulator and the detector have been specially designed, fabricated and mounted to operate at high frequency. The inset shows a SEM image of the modulator connected via an air-bridge to the coplanar waveguide. (e) RF packaging of the Stark modulator. (f) Sketch of the light coupling geometry of the Stark modulator. This geometry complies with polarization selection rules.
The detector is a GaAs/AlGaAs quantum cascade detector, based on a diagonal transition. [19] The geometry for light coupling into the detector is a 45° polished facet, to comply with the polarization selection rules of optical transitions. [20] When photons are absorbed they excite electrons from state 1 to state 2, as sketched in the band diagram of Figure 1c. After photoexcitation, electrons relax very rapidly by cascading towards the ground state of the following heterostructure period. This unipolar detector operates in the photovoltaic regime and yet has a very wideband frequency response. [21] This is due to fast energy relaxation of the electrons and the asymmetry of the cascade region that acts as a pseudo electric field driving the electrons in one direction only, giving rise to a photocurrent. The electron relaxation time from one period to the adjacent one is estimated to be shorter than 10 ps and therefore the intrinsic bandwidth is of the order of 100 GHz. [14,18,22] However, the parasitic capacitance induced by the mesa structure limits the frequency range. The frequency response, shown in Figure 2a, is almost flat up to the device cut-off, at 5 GHz for a 50x50 µm² QC detector. Two different methods have been used to measure this response: a rectification technique (violet line) that relies on the non-linear current-voltage (I-V) characteristic, [18] and a direct optical measurement (green line) obtained by shining a midinfrared frequency comb (Menlo System FC1500-ULN) onto the detector. The beating between the optical teeth appears as beatnotes separated by 100 MHz. Figure 2b shows the detector photocurrent spectrum centred at an energy very close to that of the laser emission (green dashed line), while panel (c) presents the photocurrent as a function of the incident cw laser power. The photocurrent is linear with the injected optical power up to 50mW with a responsivity of 4.5 mA·W -1 . Above 50 mW a mild decrease of the responsivity can be observed, associated with a thermal heating of the detector. This saturation is not a problem in our experiment as the highest optical power on the detector is less than 20 mW. In order to exploit fully the large frequency bandwidth of our detector for data transmission, we have realized an extremely fast external modulator, based on a linear Stark effect, [23,24] which avoids the implementation of gates for charge depletion, and hence reduces intrinsic parasitic capacitances. The modulator is an asymmetric quantum well [25] made in the GaInAs/AlInAs materials system, n-doped at 1.5 x 10 18 cm -3 in the wider well (inset to Figure   3a and Methods). This Stark shift originates from the fact that the probability density of electrons in state 1 is essentially localised in the large quantum well, whilst that in state 2 is in the thin well. Under an applied bias , the energy shift of the transition E12 equals the drop in potential between the barycentres of the two distributions (which is approximately equal to the distance between the centres of the quantum wells) (see inset to Figure 3a): with ∆ = and the total thickness of the structure.
A shift of 30 meV can be seen in Figure 3a between the low energy absorption peaks of the two spectra measured at +4 V (blue line) and -4 V (black line). Therefore, the absorption at The absorption spectrum associated with the 1 → 2 transition can be written as a Gaussian function with voltage dependent peak energy, E12(V), and constant linewidth γ =17 meV: ) . [23] The transmittance of the structure is  The modulation depth has also been estimated by applying a square signal on the modulator and then measuring the optical power on the QC detector. Using the photocurrent measured when a -9 V bias is applied on the modulator as a reference, we retrieved the transmittance as plotted in Figure 3d (black dots), in very good agreement with our numerical estimations.
From these data, the modulation depth, ∆ = − , with ( ) the highest (lowest) transmitted optical power, is measured to be 47%. Our numerical estimations accurately reproduce these data.
Notably, the modulator shows an excellent linearity in transferring a microwave input to an amplitude signal on the optical carrier, an essential feature for the transmission of analog signals. This has been characterized by analysing the distortion of the optical signal as a function of the amplitude of a sinusoidal input on the modulator = cos( ) (see Supporting Information). When the modulator is biased close to the inflexion point of the transmittance as a function of voltage ( ) in Figure 3d, the distortion appears as third order sidebands, which allows us to quantify the non-linearity of the modulator. The sideband-tocarrier intensity ratio is over 20dB at 9 V and therefore we can conclude that the modulator operates in its linear regime and does not lead to a significant distortion for a wide range of injected RF power. Furthermore, the QC detector does not introduce distortion as it is operated in its linear regime. The optical frequency response of the full system for free-space data transmission, which has a cutoff at 2 GHz, is shown in Figure 4. The modulator, driven with a power sine wave, writes a signal onto the infrared beam emitted by the QC laser, which is then collected on the detector, and finally is analysed using a 16 GHz-cutoff oscilloscope (Teledyne Lecroy SDA Zi-B 16 GHz). In the following we illustrate how using these UQO devices we were able to transmit 10 Gbit ·s -1 with a bit error rate (BER) below 4 x 10 -3 in free space configuration.

Data transmission
For the data transmission experiments, the modulator was connected to a pulse pattern generator that outputs 127 bit-long pseudo-random bit sequences (PRBS 2 7 -1) using a simple on-off keying (OOK) scheme. The latter consists only of 'zeros' and 'ones', so that we have one bit per symbol. The bitrate ranges from 1 Gbit ·s -1 to 12 Gbit ·s -1 , limited by the pulse pattern generator. The modulated input signal from a random bit sequence at 7 Gbit ·s -1 and the output of the QC detector on the oscilloscope are shown in Figure 5a. The transmission characteristics are analysed using eye diagrams and BER. Figure 5c to Figure 5f display eye diagrams taken at 7 Gbit ·s -1 and 11 Gbit ·s -1 . Figure 5c and Figure 5d are the PRBS references on the oscilloscope, while Figure 5e and Figure 5f are the corresponding optical eye diagrams of the modulated signal received on the QC detector. Eyes at 7 Gbit ·s -1 are well-opened, i.e. the ones and zeros are well-resolved, which is typical of a high-quality transmission, while at 11 Gbit ·s -1 a degradation can be seen from the BER (Figure 5b). Figure 5b is obtained by acquiring 100 µs temporal traces for different bitrates and analysing them with an algorithm that we developed ourselves (See Methods).

The BER presented on
Below 9 Gbit ·s -1 the signal is error-free. Given that a BER ≤ 4 x 10 -3 can be corrected using error correction codes without excessive overhead, [2,26] we achieved an error-free transmission up to 10 Gbit ·s -1 which is far beyond the state-of-the-art at this wavelength in free-space using either external [27] or direct [2] modulation, without any post processing nor equalization.

Conclusion
In conclusion, we have realised a data transmission system with an external amplitude modulator that operates in the mid-infrared ( = 9 µm) and outperforms previous results obtained through external or direct modulation of laser current. This has been enabled by ultrafast UQO devices conceived with a multi scale approach from nanometric quantum design to dedicated RF packaging. We have achieved a data-bit rate of 10 Gbit·s -1 using an ON/OFF protocol that can be substantially improved further in the present devices, by multichannel modulation formats, for example through use of discrete multitone (DMT) modulation, and digital processing techniques [28,29] , routinely implemented with specific integrated circuits. Moreover, the foreseeable bandwidth of these devices is in the 50 to 100 GHz range and therefore Terabit·s -1 data rates should be within reach of this technology, thus positioning the UQO as a possible solution for 6G communications in unregulated frequency bands. Although our results have focused on data transmission, there is a broader scope of applications that arise from more complex UQO systems, involving different devices and different functions such as heterodyne/homodyne detection for instance.

Methods
Sample description. The modulator device is made of Data transfer measurements. The same arrangement as the one employed for the optical bandwidth was used, replacing the synthesizer with a pseudo-random bit sequence pulse pattern generator (Anritsu MP1763B). We used a 127-bit sequence which is well suited for our system, which presents a lower cutoff at 100 MHz. The quality of the transmission was first analyzed using the oscilloscope data analysis software to obtain the bit error rate, and then a 100 µs temporal trace was acquired and analyzed using a home-made algorithm to compute another estimation of the bit error rate.
Bit error rate algorithm. Measurements were performed with a home-made Matlab programme. Given the timetraces from the oscilloscope, this programme resamples the data at a constant sample-per-bit ratio and performs a time-correlation calculation on the input and received signals to calculate the delay between them and realign them accordingly. The sequences of bits associated with each signal were determined and finally compared to each other to get the bit error rate after selecting the most appropriate amplitude threshold.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.

Simulation of the electronic states of the Stark modulator and of the quantum cascade detector
The electronic states of the heterostructures are numerically calculated by using a three-band Kane model in the envelope function approximation, following reference. 1

Linearity of the Stark modulator
The operation of the Stark modulator was characterized by studying the detected power as a function of the electrical power on the modulator (Figure S3). In this expansion, is the sideband-to-carrier intensity ratio. The third order allows quantifying the non-linearity of the modulator through the calculation of the input third-order intercept point (IIP3), which was found to be equal to 18 dBm, corresponding to an applied bias of 44 V on our 80 x 80 µm² modulator. Even at large biases covering a large part of the absorption range, this third harmonic lies 20 dB below the fundamental. The input 1 dB compression point (P1dB), where the output signal is 1dB below its linear regime value, is 5.75 dBm (9.5 V). From these observations we can conclude that operating the modulator up to 9 V keeps the device in its linear regime and does not lead to a significant distortion in the modulated signal. Figure S3. Detected power as a function of the electrical power at the modulation frequency (green) and at 3 (orange). Figure S4 presents the power dissipated by the modulator as a function of the applied bias, as extracted for each device from the Current-Voltage characteristics measured with Keithley 2450.

Electrical power dissipated by the modulator
For our data transmission experiment, we used a 7 Vpp square signal centered around 1.1 V DC. At this voltage the modulator dissipated approximately 1 pJ/bit. This energy per bit is comparable to state-of-the-art modulation even in the telecom wavelengths. 3

Rectification measurements on the Stark modulator
Rectification measurements were realized on the Stark modulators using a 40 GHz RF probe.
This measurement allows extracting the intrinsic bandwidth of the devices without the parasitic capacitance of the PCB mount. Figure S5 shows the normalized rectified current for four different sizes of the mesa. The four devices exhibit a flat response up to their cutoff and behave like first-order devices (-20 dB/decade) above this point. Note that there is no resonance due to relaxation oscillations near the frequency cutoff, as expected for a unipolar device.
From these measurements we extracted the cutoff frequencies of the four devices, that are plotted in the inset to Figure S5 (symbols) as a function of the inverse of the device surface.
The blue line shows the calculated cutoff frequency only considering the size of the devices, while the orange line includes a parasitic capacitance of 61 fF.