1. Introduction

Numerous frequency comb applications are based on two modelocked lasers with slightly different pulse repetition rates. One specific application is dual-comb spectroscopy [1–5]. Using heterodyne detection with two frequency combs offers excellent accuracy and very high sampling rates because no mechanical scanning technique is required. Another application benefiting from two modelocked lasers is asynchronous optical sampling (ASOPS) [6] which allows for pump-probe measurements without mechanical delay scanners. However, two separate modelocked lasers is complex, bulky, expensive and needs special stabilization efforts. Therefore, these applications would greatly benefit from a simple, compact and cost-efficient way of generating two modelocked pulse trains. Here we present a very simple solution which becomes even more attractive and more compact with optically pumped semiconductor disk lasers (SDLs).

Optically pumped SDLs is a family of vertical emitting semiconductor lasers with the first device demonstration referred to as the vertical external-cavity surface emitting laser (VECSEL) [7]. They have become very attractive because of their large spectral range of operation ranging from the visible to the infrared [8–10] and with intracavity frequency conversion covering high power operation from the visible to the UV [11, 12]. Modelocking was achieved with a semiconductor saturable absorber mirror (SESAM) [13, 14] the first time in 2000 [15, 16]. Since then SESAM-modelocked VECSELs generated pulses as short as 107 fs [17] and peak power levels of up to 4.35 kW [18]. The first detection of the modelocked frequency comb offset, i.e. the carrier-envelope offset (CEO) frequency [19], from an amplified and pulse-compressed SESAM-modelocked VECSEL [20] has demonstrated the potential for low-noise frequency comb generation using optically pumped SDLs. As VECSEL and SESAM in most cases rely on the same semiconductor material system and fabrication techniques, the vertical integration of the saturable absorber into the gain structure of a VECSEL was the next level of integration to reduce complexity of ultrafast SDLs. Hence in 2007 the first modelocked integrated external-cavity surface emitting laser (MIXSEL) has been demonstrated [21]. In contrast to a MIXSEL a SESAM-modelocked VECSEL has two separate semiconductor elements in the modelocked laser resonator, i.e. the VECSEL chip and the SESAM. With a MIXSEL a simple straight cavity is formed comprising the gain chip and an output coupler. The total cavity length determined by the MIXSEL chip (which adds less than 10 µm to the cavity length) and the air space before the output coupler then sets the pulse repetition rate. This technology allows for stable and self-starting fundamental modelocking. An average output power of up to 6.4 W [22] and also femtosecond operation [23] has been demonstrated with a MIXSEL. Using the same MIXSEL chip and changing the cavity length we recently could adjust the pulse repetition rate between 5 and 100 GHz [24]. In addition, MIXSELs have demonstrated very low noise performance similar to diode-pumped solid-state lasers [25].

In this paper we demonstrate for the first time a dual comb MIXSEL. With the MIXSEL device we substantially reduce complexity for dual comb generation because of the straight linear cavity made possible by the additional integration of the gain and absorber layers inside the same semiconductor chip. We then applied a method that has already been used in continuous wave (cw) operation to generate dual frequency emission from an optically pumped VECSEL [26, 27]. We insert a birefringent crystal into the cavity to separate the modelocked cavity beam into two spatially separated beams with perpendicular polarization on the MIXSEL chip. This results in the first SDL emitting simultaneously two different gigahertz modelocked pulse trains from a single gain chip using the same cavity components. The microwave frequency comb-lines are the beat signal between the optical frequencies of the two modelocked laser beams observed with a photo detector and a microwave spectrum analyzer (MSA) even without any active cavity length stabilization. In addition with a second birefringent crystal placed inside the cavity to compensate the different path length introduced with the first crystal we can obtain two pulse trains with the same pulse repetition frequencies. This gives direct access to the relative CEO frequency between the two pulse trains without using an f-to-2f interferometer [19]. In addition, we show that both pulse repetition frequencies can be stabilized.

Recently, dual frequency comb spectroscopy was presented using only one Kerr-lens modelocked Yb:YAG thin disk oscillator, by creating a second beam with a slightly lower repetition frequency using an acousto-optic programmable dispersive filter (AOPDF) [28]. The two beams were directed through a gas cell to measure absorption features of acetylene. The dual-comb MIXSEL approach presented in this manuscript could be potentially used for similar gas spectroscopy, with the benefit of providing both lasers directly from a compact laser cavity. The absorption of one or several optical lines of the lasers in the gas cell can be directly detected in a decrease in amplitude of the corresponding beat-lines of the microwave frequency comb (Fig. 1). Another advantage of our systems is the fact that both output beams are collinear, fully overlapping and can be separated by a simple polarizing beam splitter. This typically simplifies potential applications such as pump-probe experiments for example. With the difference in pulse repetition frequency Δf_rep of the two beams a total measurement time window T = 1/f_rep can be scanned with a step increment size Δf_rep/f_rep² without using any mechanical delay line (Fig. 2).

 

Fig. 1 Potential gas sensing application using a dual comb MIXSEL: The two modelocked beams are separated with a polarizing beam splitter and one of the beams is guided through a gas cell. Both beams are then superimposed on a photo detector (PD) and measured with a microwave spectrum analyzer (MSA).

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Fig. 2 Potential pump-probe measurement without a mechanical delay line using a dual comb MIXSEL: device under test (DUT) in reflection (shown here) or transmission simply using a PD. The difference in pulse repetition frequency allows for a time dependent measurement.

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2. Experimental setup

The MIXSEL chip used for this experiment was grown with a VEECO GEN III (Veeco instruments Inc.) molecular beam epitaxy machine. It consists of an anti-reflection section, followed by the active gain region, which contains 7 InGaAs quantum wells (Fig. 3). Between the gain region and the InAs quantum dot absorber layer we inserted a distributed Bragg reflector (DBR) for the pump light to prevent any bleaching of the saturable absorber layer by the pump light. The absorber is followed by a DBR for the laser wavelength. The detailed parameters of the saturable absorber, for example the modulation depth and the saturation fluence, can be found in Ref [29]. The structure is grown in a single epitaxial growth run in reverse order and is then flip-chip bonded to a 600-µm thick diamond heat spreader [30]. The GaAs substrate is removed subsequently by chemical wet etching. For more details on the MIXSEL design we refer to Ref [22].

 

Fig. 3 Structure of the MIXSEL chip: an anti-reflection (AR) section is followed by the gain region containing 7 InGaAs quantum wells. The InAs quantum dot saturable absorber is placed between the distributed Bragg reflector (DBR) for the laser light and the pump light. The chip is flip-chip bonded to a diamond heat spreader.

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Since the saturable absorber and the gain region are integrated into a single chip, the MIXSEL can be modelocked in a simple straight cavity, with only the MIXSEL chip and a curved output coupler (OC) as the two end mirrors. We then inserted a calcium carbonate (CaCO₃) birefringent crystal into the cavity to spatially separate the one cavity beam into two collinear but spatially separated beams with perpendicular polarizations on the MIXSEL chip (Fig. 4). We use CaCO₃ due to its relative high refractive index contrast of 0.165 at 960 nm and its low group delay dispersion (GDD) of 52 fs²/mm and 33 fs²/mm along the extraordinary and the ordinary axes, respectively [31]. The length of the crystal is 2 mm, which leads to a spatial separation of the cross-polarized beams of 210 µm. The beam diameter of the individual beams on the MIXSEL chip is estimated to be 220 µm. In addition, an anti-reflection coated 20-µm thick fused silica etalon is placed between the crystal and the OC for wavelength tuning. We chose a small angle of incidence to reduce polarization-dependent effects.

 

Fig. 4 a) A design image of the laser housing with the optically pumped dual comb MIXSEL. The linear straight cavity is formed by the MIXSEL chip end mirror and the output coupler (OC). An intracavity birefringent crystal is used to generate the two combs. One of the two pumping configuration is shown here with the orange path of the pump light. An aluminum housing surrounds the cavity and all optical elements are mounted directly on the base plate to minimize mechanical vibrations. b) Schematic of the setup, showing the paths of the two modelocked beams, p-polarized in red and s-polarized in blue. Again the pump beam is shown in orange. PBS: polarizing beam splitter, BS: beam splitter, PD: photo detector, OSA: optical spectrum analyzer, MSA: microwave spectrum analyzer, λ/2: half-wave plate

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Both cavity spots on the MIXSEL are pumped at 808 nm with the same multi-mode (M² ≈36) fiber-coupled laser-diode array. We used two different pump configurations that worked equally well. In one configuration the collimated pump beam is split by a 50:50 beam splitter and both beams are separately focused onto the two cavity spots on the chip (Fig. 4). In another configuration the pump beam shape is adapted with cylindrical lenses to have an elliptical beam shape covering both cavity spots. The first configuration offers more flexibility on the position and size of the pump spots. It also improves the efficiency due to a better overlap of the pumped region with the high-field optical gain region. On the other hand the second configuration is more compact and requires less optical elements.

The cavity and pump optics are placed inside a closed aluminum housing to prevent disturbing airflow. All optical elements are mounted directly on the base plate to minimize mechanical vibrations (Fig. 4(a)).

The two orthogonally polarized pulse trains are coupled out collinearly with an OC of 0.5% transmission and a radius of curvature of 100 mm and are then separated by a polarizing beam splitter (PBS) (Fig. 4(b)). To allow for optical interference of the two pulse trains, the polarization of one of the beams is turned by 90° with a half-wave plate and then both beams are collinearly combined by a non-polarizing beam splitter (BS). By superposition in the optical domain and detecting the combined beams on a photo detector all possible beat notes can be measured in the microwave frequency domain. Furthermore the optical spectrum, the microwave spectrum and the autocorrelation of each individual pulse train are recorded.

3. Experimental results

At a total pump power of 10 W, divided equally for pumping the separate laser beams, both cross-polarized pulse trains show stable and self-starting fundamental modelocking (i.e. only one pulse per cavity roundtrip). The temperature of the MIXSEL chip is stabilized with a Peltier element to 15° C. The modelocking results are shown in Fig. 5 and Table 1. With 1.890 GHz, the pulse repetition frequency of the p-polarized beam is 5 MHz lower than the s-polarized beam due to the slightly longer optical path length in the birefringent crystal. The cavity length was chosen for a pulse repetition frequencies around 2 GHz. However, higher repetition rates up to 10 GHz are feasible with the same MIXSEL structure [29]. The separation of the individual beams on the MIXSEL is 210 µm. The individual Gaussian beam diameters of approximately 220 µm gives only a small overlap of the two laser beams in the tail of their Gaussian beam profiles. Figure 5(a) and Fig. 5(b) show the optical spectra of the s-polarized and the p-polarized beam, respectively. The center wavelengths around 966 nm exhibit a small difference, but the two spectra show a sufficiently strong overlap. The 2nd harmonic intensity autocorrelations of the two beams are displayed in Fig. 5(c) and Fig. 5(d) with pulse durations of 13.5 ps and 19.1 ps, respectively. The different pulse durations of the two beams originate from the spatial separation on the MIXSEL chip, because the semiconductor growth of the MIXSEL chip is not perfectly homogeneous. In addition, the pulses are chirped because the GDD for the MIXSEL chip was not optimized [22]. Previously we have shown that better GDD compensation can generate much shorter and close to transform-limited pulses [23].

 

Fig. 5 Modelocking results of the dual comb MIXSEL: a) Optical spectrum of the s-polarized pulse train; b) Optical spectrum of the p-polarized pulse train; c) 2nd harmonic intensity autocorrelation of the s-polarized beam; d) 2nd harmonic intensity autocorrelation of the p-polarized beam

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Table 1. Modelocking parameters of the two pulse trains

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The electric field E_k of both pulse trains in time with k = 1,2 can be written as

the pulse envelope

(2)$$A_k(t)=\text{sech}\left(\frac{t}{{\tau }_k}\right).$$

The Fourier transformation of [Eq. (1)] gives the expression for the pulse trains in the frequency domain

(3)$${\tilde{E}}_k(f)={\tilde{A}}_k(f-f_{\text{center},k}){\displaystyle \sum _n\delta \left(f-n{f}_{\text{rep},k}-f_{\text{CEO},k}\right)}+c.c.,$$

where the pulse envelopes are normalized accordingly. The center frequency f_center,k is given for both beams by the carrier-envelope-offset frequency f_CEO,k plus a multiple m_k of the pulse repetition frequency f_rep,k

(4)$$f_{\text{center,}k}=f_{\text{CEO,}k}+m_k{f}_{\text{rep,}k}.$$

The difference Δf_rep between the pulse repetition frequencies of the two beams arises from the difference in the optical path length in the birefringent crystal, leading to

(5)$$f_{\text{rep,2}}=f_{\text{rep,1}}+\Delta f_{\text{rep}}.$$

The photo detector (PD) measures then a photo current I_PD, which is

(6)$$I_{\text{PD}}={\left|E_1(t)+E_2(t)\right|}^2.$$

The microwave spectrum analyzer (MSA) then measures the frequency-resolved power of this PD signal, which is proportional to I_PD². Thus the Fourier transformation (FT) determines the measured microwave spectrum S_freq:

(7)$$S_{\text{freq}}=FT\left({\left|E_1(t)+E_2(t)\right|}^4\right).$$

With [Eq. (1)-(7)] we simulated the expected microwave spectrum using as an input the measured pulse durations, center wavelengths, and pulse repetition rates of the two pulse trains. The simulated microwave spectrum (Figs. 6(f)-6(j)) shows excellent agreement with the measurements (Figs. 6(a)-6(e)). All features of the microwave spectrum are clearly visible for all measured higher harmonics (Fig. 6(a)). The drop of the harmonic signal above 5 GHz is due to the limited amplifier bandwidth after the PD before the MSA.

 

Fig. 6 a) Microwave spectrum analyzer (MSA) signal from DC to 10 GHz showing the pulse repetition frequencies and their higher harmonics as well as the beat-combs. The drop of the harmonic signal above 5 GHz is due to the limited bandwidth of the amplifier used to amplify the signal after the photo detector (PD) before the MSA. b) Zoom-in from DC to 1.9 GHz with a resolution bandwidth (RBW) of 3 kHz. c) Zoom-in around the first comb with a span of 150 MHz and a RBW of 1 kHz. d) Zoom-in around the pulse repetition frequencies with a span of 28 MHz and a RBW of 3 kHz. e) Zoom-in around DC with a span of 20 MHz and a RBW of 10 kHz. f -j) Simulated microwave spectrum in the corresponding frequency spans; In g) “mod” means modulo.

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Between DC and the pulse repetition frequencies, two comb structures (comb₁ and comb₂) are visible (Fig. 6(b)). The center frequency of the first comb f_comb1,center is given by:

(8)$$\begin{array}{l}{f}_{\text{comb1,center}}\\ =\left(f_{\text{center,2}}-f_{\text{center,1}}\right)\mathrm{mod}{f}_{\text{rep,1}}\\ =\left(\left(f_{\text{CEO,2}}+m_2{f}_{\text{rep,2}}\right)-\left(f_{\text{CEO,1}}+m_1{f}_{\text{rep,1}}\right)\right)\mathrm{mod}{f}_{\text{rep,1}}\\ =\left(\Delta f_{\text{CEO}}+\left(m_2-m_1\right)f_{\text{rep,1}}+m_2\Delta f_{\text{rep}}\right)\mathrm{mod}{f}_{\text{rep,1}}\\ =\left(\Delta f_{\text{CEO}}+m_2\Delta f_{\text{rep}}\right)\mathrm{mod}{f}_{\text{rep,1}}\end{array}$$

where “mod” is the modulus-function. The spacing of the comb lines is set by Δf_rep (Fig. 6(c)), set by the length of the birefringent crystal. Since both lasers are not stabilized in repetition frequency in this measurement, slight drifts are causing deviations from the exact difference in repetition frequency. These microwave combs, comb₁ (green in Fig. 6(b) and Fig. 6(c)) and comb₂, result from interference between the optical frequencies of the two modelocked laser beams and represent a direct link between the optical frequencies and the electronically accessible microwave frequencies. They are only visible if the two optical spectra overlap and if both beams are detected in the same polarization. On the other hand, the pulse repetition frequencies f_{rep p-pol} and f_{rep s-pol} (Fig. 6(d)) and the difference in pulse repetition frequencies Δf_rep or multiple of Δf_rep (Fig. 6(e)) are independent of the polarization and can be measured in cross-polarized detection as well as in the same polarization. In the simulation (Fig. 6(f)) two additional combs are visible, which result from the beat between the two combs comb₁ and comb₂. They are not visible in the measurement (Fig. 6(b)) because they are below the noise level. The amplitudes of the frequencies in the simulation (Figs. 6(a)-6(e)) differ from the amplitudes of the frequencies in the measurement (Figs. 6(f)-6(j)) because the simulation is on a linear scale and the measurement is on a logarithmic scale.

The position of the first comb (Fig. 6(g)) depends directly on the difference between the CEO frequencies Δf_CEO of the two beams. This becomes more obvious when both beams have exactly the same pulse repetition frequency. For an experimental demonstration we add a second identical birefringent calcite crystal between the first crystal and the MIXSEL chip with the same thickness but with the optical axis rotated by 90° with respect to the first crystal. The thickness of each of the crystals are chosen in this configuration to be 150 µm in order to have approximately the same separation of ≈210 µm of the two cavity spots as in the previous configuration. This leads to two modelocked cross-polarized beams with identical pulse repetition frequencies. In this case, Δf_rep = 0 in [Eq. (8)] and the interference between the optical frequencies of the two beams results in two strong relative CEO frequencies Δf_CEO1 and Δf_CEO2 (Fig. 7(a)). A zoom-in around Δf_CEO1 with a frequency span of 8 MHz and a reduced resolution bandwidth (RBW) of 3 kHz is shown in Fig. 7(b). Again, the simulations agree very well with the measurements (Figs. 7(c) and 7(d)). The additional peaks in the simulation (Fig. 7(c)) result from a beat between Δf_CEO1 and Δf_CEO2. They are below the noise level in the measurement (Fig. 7(a)).

 

Fig. 7 a) Measured microwave spectrum showing both relative CEO frequencies Δf_CEO1 and Δf_CEO2 and the pulse repetition frequency f_rep. b) Zoom-in around Δf_CEO1 with a frequency span of 8 MHz and a reduced RBW of 3 kHz. c) Simulated microwave spectrum showing both relative CEO frequencies Δf_CEO1 and Δf_CEO2 and the repetition frequency f_rep and the beat between the two relative CEO frequencies. d) Simulated Δf_CEO1 in an 8 MHz span.

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We were able to simultaneously stabilize the different pulse repetition frequency in both output beams of the dual comb MIXSEL and measured the resulting phase noise with a signal source analyzer. In stabilized operation a noise reduction of up to 100 dB/Hz for frequencies below 100 Hz compared to free-running operation is achieved (Fig. 8). Further details on the feedback mechanism and stabilization dynamics will be discussed in the near future and is beyond the scope of this paper.

 

Fig. 8 Phase noise of both beams in free-running and stabilized operation, measured with a signal source analyzer.

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4. Conclusion and outlook

We have presented a novel straightforward technique of generating two fundamentally modelocked pulse trains within the same laser cavity. We utilized the key advantage of the MIXSEL, having the saturable absorber integrated into the gain chip, to enable a compact design with a linear straight cavity. We simultaneously stabilized the different pulse repetition rates of the two output beams of the dual comb MIXSEL. The beat signal of the optical interference of the two pulse trains detected with a photo detector (PD) and a microwave spectrum analyzer (MSA) provides a strikingly simple setup to down-convert terahertz optical frequencies into the electronically accessible microwave regime. This experiment offers for the first time access to the relative CEO frequencies of an SDL. We will further study the dynamics of the CEO frequencies and possible stabilization mechanisms. Our first proof-of-principle concept experiments were performed with a MIXSEL structure that only supports rather long picosecond pulses. However recently femtosecond operation of a MIXSEL has been demonstrated [23]. In the near future the experiments will be performed with a MIXSEL structure that generates shorter pulses with a much larger optical bandwidth and therefore also a larger microwave beat comb. This will make the dual-comb MIXSEL a very compact and inexpensive source for applications in frequency metrology, optical sensing or pump-probe experiments for example.

Acknowledgments

The authors acknowledge support of the technology and clean room facility FIRST of ETH Zurich for advanced micro- and nanotechnology. This work was financed by the Swiss Confederation Program Nano-Tera.ch, which was scientifically evaluated by the Swiss National Science Foundation (SNSF).

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