Tunable electro-optic frequency-comb generation around 8 µm wavelength

. Electro-optic frequency-comb is an interesting method for comb generation as it offers the possibility to electrically tune the generated frequency-comb by simply tuning the electrical signal applied on the modulator. Integrated modulators operating in a wide spectral range in the mid-IR have been demonstrated recently, relying on free carrier plasma dispersion effect in a Schottky diode embedded in a Ge-rich graded SiGe waveguide. Such integrated mid-infrared modulators have been used to generate electro-optic frequency-combs with more than 200 lines around the 8 µm wavelength optical carrier.


Introduction
Many molecules have specific absorption lines in the midinfrared (mid-IR) spectral range, driving the development of high performances sensors for the detection of chemical substances.In this context frequency comb sources are of a high interest, especially in dual comb spectroscopy (DCS) experiments.Frequency combs can be generated in different ways, including electro-optic frequency-comb (EOFC), which offers the versatility of a tunable repetition rate within the modulator electrooptical bandwidth.Integrated modulators based on a Schottky diode and free carrier plasma dispersion effect, operating in the 5.5 to 9 µm wavelength range, up to 1 GHz has been reported previously [1].Based on this previous work, we report now EOFC generation using different kinds of RF signal applied on the modulator.Interestingly, combs with more than 200 lines have been obtained around 8 µm wavelength.

Electro-optic modulator
The electro-optic modulator (EOM) is schematically described in Figure 1.It consists of highly N+ doped silicon substrate, on which is grown a non-intentionally doped graded SiGe alloy [2], with an increasing Germanium concentration along the graded layer.Interestingly the refractive index of SiGe increases with Ge concentration, which allows light confinement on top of the SiGe layer as shown in Figure 1.The residual doping in the graded layer is estimated to be n-type, with doping concentration on the order of 10 15 cm −3 .300nm thick gold electrodes are deposited on top of the graded layer to form a Schottky contact as shown in Figure 1, allowing to deplete carriers when a reverse bias voltage is applied between the bottom electrode and the top contact.This generates both a transmission variation due to free carrier absorption (FCA) and a phase variation due to effective index variation via free carrier plasma dispersion (FCPD).A 2.2 mm-long waveguide modulator is used to exploit the FCA to generate EOFC.

Characterisation and experimental results
In order to characterise the EOFC generated using such modulators, light coming from a continuous wave (CW) QCL emitting around 8 µm wavelength is coupled to the device and collected using a pair of aspheric ZnSe lenses.The collected light is then sent to a fast mid-IR mercurycadmium-telluride (MCT) detector, whose preamplifier presents a cut-off frequency at 700 MHz.The electrical output of the photodetector is then sent to an electrical spectrum analyser.It should be noted that this is not a direct measurement of the EOFC generated, as this measurement allows us to observe the sum of the beating between the central optical carrier line and the generated side-lines, and the beating between the different side lines together.Furthermore, it should be noted that lines in the right and left part of the spectrum around the optical carrier cannot be distinguished from this measurement.However, this method still allows to estimate the number of lines generated around the carrier, and so the extension of the generated EOFC.Combs have been generated using different kinds of RF modulating signal, as using only sinusoidal modulating signals strongly constrains the shape of the generated EOFC [3]. Figure 3   One can see from Figure 3 that only 2 different beating lines are observed using a sinusoidal modulating signal, while 12 successive ones are observed using a 40% duty cycle (DC) square signal of the same frequency.Increasing the number of harmonics in the RF modulating signal undoubtedly increases the number of generated lines in the EOFC, as they are strongly linked together.In order to increase the number of lines generated, other RF modulating signals have been explored.Sinc shaped signals appear as a natural solution for flat EOFC generation, since the spectrum of these signals is flat.The periodic signal  of which the temporal expression is given by Equation 1, with a 1 MHz repetition rate and 5 Vpp amplitude is thus used as a modulating signal.

𝑆(𝜑, 𝑛
Where  is the instantaneous phase and  the order of the signal, which directly gives the number of lines in the spectrum of this signal.The electrical spectrum of the beating detected at the photodiode is given in Figure 4, for an order  = 101.50 lines separated by the signal repetition rate (1MHz) are obtained.The oscillations in amplitude are attributed to distortions introduced by the travelling wave electrodes and the drop of amplitude beyond a few MHz is attributed to the inability of the AWG used to generate the RF signal.Finally in a last measurement, an electrical pulse generator has been used, with a 10 MHz fundamental frequency and 739 ps full width at half maximum (FWHM) pulses.This electrical pulse generator allows to obtain sharp pulses at a large repetition rate, giving us spectrally rich RF signals that appear to be very useful in this case.The electrical spectrum at the output of the photodiode using these pulses as an RF modulating signal is given in Figure 5.One can still observe the oscillations in the output spectrum, but beating between generated lines is observed until 1.2 GHz spacing, using 10 MHz repetition rate which means that more than 120 lines are generated on both sides of the optical carrier, corresponding to a total of more than 240 lines.This work demonstrates a frequency and shape-agile EOFC generation in the mid-IR using the full 1 GHz bandwidth of a modulator with repetition rates as low as 10 MHz.Furthermore, thanks to the wide spectral range of the EO modulator in the 5-9µm wavelength range, this result can be easily translated in this wavelength range, simply by tuning the input laser wavelength.These results pave the way towards absorption spectroscopy in the mid-IR based on integrated electro-optical frequency combs.
This work was supported by ANR Project (ANR-19-CE24-0002-01).The fabrication was performed within the C2N technology platforms and partly supported by the RENATECH network and the General Council of Essonne.

Figure 1 .
Figure 1.Left.Schematic cross-section view of the EOM used.A 6 µm thick, non-intentionally doped graded SiGe layer is epitaxially grown on a highly N + doped silicon substrate.Right.TE optical mode profile in the waveguide at 8 µm wavelength.
first reports the acquired spectrum of the photodiode signal using both a 5Vpp 10 MHz sinusoidal signal and a 4.4 Vpp square signal with 40 % duty cycle and 10 MHz repetition rate.

Figure 2 .
Figure 2. Measured beating at the output of the photodiode for 10 MHz sinusoidal and square modulating signals.One can observe some parasitic lines, coming from the setup.

Figure 3 .
Figure 3. Electrical spectrum of the beating measured at the output of the fast mid-IR MCT detector, when using the 1 MHz electrical signal given by Equation 1 to modulate and an 8 µm wavelength CW input light.

Figure 4 .
Figure 4. Output electrical spectrum of the beating at the output of the photodiode using tunable electrical pulses generator set at 10 MHz reference frequency and 739 ps FWHM pulses.