Ultrabroadband air-dielectric double-chirped mirrors for laser frequency combs

Design of pump-DUT dimension and measurement procedure

As shown in Fig. 2a in the main text, broadband illumination from section II is coupled on-chip to the short DUT (section I). Since both facets of section I are partially reflective, the probe light will travel many round trips inside the DUT cavity. For simplicity, only one round-trip copy is shown in the illustration. These reflected copies of broadband illumination (pulses) all carry different group delays proportional to the number of round trips traveled inside the DUT cavity. They will then interfere when the moving mirror of FTIR arrives at specific echo locations, causing distorted interference peaks (see Supplementary Information A.4.). Dispersion can be calculated from the collected interferogram.

The measurement is conducted using the following procedure:

Pulse-bias the pump laser to generate broadband illumination with a continuous spectrum.

Conduct FTIR measurements and calculate the transmission spectra of light through the DUT (Device Under Test) at a CW bias.

Process the transmission spectra to calculate GVD. The uneven Fabry-Pérot (FP) mode spacing yields a frequency-dependent mode index, which reflects the dispersion of the biased DUT cavity.

It is imperative that (1) the DUT section is not lasing; (2) the coupling between the DUT and the source laser is not too strong to cause considerable feedback to the pump laser. In terms of device design, these requirements set an upper limit on DUT cavity length and a lower bound on DUT-laser gap size. In practice, a DUT cavity size from 200 to 400 μm is used, and the gap sizes are kept between 10 and 20 μm. Since the DUT has to be biased at the exact operating condition of the actual CW devices, electroplated Au is required for pump-DUT device fabrication, even though the pump laser does not need to be CW-biased.

Dispersion calculation from DUT FP resonances

Dispersion calculation begins with the measured interferograms. We apply a Hanning window and pad the data 1000 times (add zero arrays 500 times the size of the original data, on both left and right sides) before we apply a Fourier Transform to obtain the transmission spectrum of DUT devices. The scan length of the interferogram for DUT transmission measurement is 8 mm, corresponding to a spectral resolution of 0.625 cm−1. This length is chosen so that no observable interference peaks can be observed beyond the scan length. Padding does not increase the spectral resolution of such a transmission measurement but rather improves the peak-finding accuracy. For consistency, we have verified that other peak-finding methods, such as the polynomial fit of transmission peaks, yielded identical results as the zero-padding method. Given this confirmation, finding the FFT of zero-padded interferograms was much faster to perform and, therefore, was used throughout this work.

We then implement a custom peak-finding algorithm to obtain the discrete series of Fabry-Pérot resonances, denoted as $f\left[n\right]$, where n is the mode number. Based on the cavity resonance condition, adjacent FP modes have a round-trip phase difference of 2π. We can then create the phase array defined as $\phi \left[n\right]=2\pi n$. Strictly speaking, there is an unknown phase constant ${\phi }_{0}$ that is missing in the expression. However, the linear part of the phase-frequency relation will not affect the dispersion calculation result because it will be removed after the derivatives. For this reason, we set ${\phi }_{0}$ to be 0. The nonlinear $\phi \left[n\right]-f\left[{\rm{n}}\right]$ relation yields the dispersion information. Finally, we arrive at the GVD of the DUT waveguide under operating conditions. In Fig. 2f, we plot the residual phase, which is $\phi \left[n\right]$ with the linear components removed. The curvature of the remaining parabolic curve of $\phi \left[n\right]-f\left[{\rm{n}}\right]$ is proportional to GVD.

For device design, laser cavity Group Delay Dispersion (GDD) is calculated by multiplying the measured GVD by the cavity length. We adopt the physics convention for the calculation of the spectral phase and all other related physical quantities, including group delay (${GDD}\equiv \frac{{\partial }^{2}\phi }{\partial {\omega }^{2}}$) and group velocity dispersion (${GVD}\equiv \frac{1}{{\rm{L}}}\frac{{\partial }^{2}\phi }{\partial {\omega }^{2}}$).

Numerical simulation of DUT-pump measurement result

In order to quantitatively understand the effect of Dispersion on DUT transmission spectra and the source of noise in dispersion calculation, we set up a numerical model to simulate the interferograms and spectra for given cavity gain and dispersion values. In this model, we use a pulse source with a Gaussian-shaped power spectral density (PSD). The center frequency is 1000 cm−1, the standard deviation is 15 cm−1.

The frequency range of the simulation is 800 to 1200 cm−1, with 0.2 cm−1 spacing between each frequency point. The electric field is calculated by the summation of guided waves (mode propagation constant β). During propagation, each frequency component will experience the same gain and loss (simplified in this model), but their accumulated phase is frequency-dependent and given by the DUT GVD. Up to 8 facet reflections are considered, or until intra-cavity power is below 0.1% of the input power.

In the simulation, a constant GVD value is used for the DUT section, which corresponds to a parabolic accumulated phase shape. Gain in the DUT section is introduced as an imaginary mode index. The facet power reflectivity is 0.29, calculated from the waveguide mode index of 3.3. The interferogram is calculated using the sum of the E field from two arms of the FTIR (the auto-correlation); one is fixed, and the other is the one with moving mirrors producing the time-delayed/advanced copy of the E field. For the case without DUT, only the coherent lasing E field from the source is considered, along with its time-delayed (advanced) copy from the FTIR moving arm. The simulated interferogram and its FFT without the DUT are shown on the right side of Fig. 2b. When the DUT is introduced to this simulation, multiple copies of the source light will enter the FTIR at different time delays from traveling different numbers of round trips inside the DUT cavity.

In the simplest case, when only one round trip is considered, the added phase of these four fields can be expressed as follows:

$$\begin{array}{ll}{\phi }_{1} & =\,{\phi }_{0}+{\phi }_{{\rm{f}}}\\ {\phi }_{2} & =\,{\phi }_{0}+{\phi }_{{\rm{m}}}\left(x\right)\\ {\phi }_{3} & =\,{\phi }_{0}+{\phi }_{{\rm{f}}}+{\phi }_{{\rm{rt}}}\\ {\phi }_{4} & =\,{\phi }_{0}+{\phi }_{{\rm{m}}}\left(x\right)+{\phi }_{{\rm{rt}}}\end{array}$$

where ${\phi }_{{\rm{f}}}$ denotes the phase accumulated before reflected by the FTIR fixed mirror, ${\phi }_{{\rm{m}}}\left(x\right)$ denotes the phase accumulated before reflection by the moving mirror and is a function of mirror position. ${\phi }_{{\rm{rt}}}$ represents the phase delay from one DUT cavity round trip and is a function of the GVD parameter. All phase parameters are functions of time and frequency.

As expected, with dispersion introduced, the FP mode spacing is not constant. This effect manifests itself in the interferograms as distorted side interference peaks (“echoes”), with increased span in space but decreased peak intensity. This behavior is well captured by this simple yet powerful numerical model; see Supplementary Information A.4. As shown in Fig. 2b without a DUT, we get a single interference peak at the center of the interferogram and a Gaussian spectral profile by taking the Fourier Transform of the interferogram. This is to be expected as the Fourier transform of a Gaussian is also a Gaussian. When DUT is introduced, FP peaks show up as a result of multiple reflections in the DUT. As a result of dispersion, distorted side echoes also show up in the interferogram, as discussed in more detail in A.4.

Device fabrication

There are several key challenges imposed by the dimension and aspect ratio of chirped Bragg reflectors. First, precise dispersion compensation demands critical dimension variation (CDR) of photonic device features much beyond the resolution of photolithography tools. Electron-beam lithography (EBL) provides sub-100 nm resolution and is implemented to fulfill such requirements. Furthermore, undercut from chemical wet etch50 distorts the mask feature and produces a curved sidewall. We adopt chlorine-based dry etch chemistry41 and optimize the etch condition for sidewall verticality, smoothness, and minimum micro-loading effect (aspect-ratio-dependent etch rate).

Second, conventional EBL-compatible etch mask (metal) cannot guarantee deep etch (≥15 μm) in narrow unmasked regions (air layer in Bragg reflectors), and the removal of damaged etch mask after the dry etch process is quite difficult. We developed a novel hybrid Nickel/Silicon Dioxide (Ni/SiO2) etch mask (Supplementary Information A.3) for the patterning of laser cavities as well as DCM compensators (also pump-DUT dispersion characterization devices). The fabrication flow chart, including the electroplating process of the thick layer of Au, is illustrated in Figure S1 in Supplementary Information.

The gain medium wafer was epitaxially grown with cladding and active region at Thorlabs; the photonic layer stack consisted of lattice-matched InP/InAlAs/InGaAs. The QC gain medium contains two QC cores with similar designs stacked together. One core has a gain peak roughly at 9.8 μm (30.6 THz), and the other has a gain peak roughly at 9.2 μm (32.6 THz). The ratio of the number of stages of the two cores is 7:5 in order to achieve a gain profile as flat as possible.

Fabrication of the comb device then starts with the deposition of 1.5-2 μm of SiO2 through plasmon-enhanced chemical vapor deposition (PECVD, step (1) in Fig. S1). Negative EBL resist (polymethyl methacrylate, PMMA) is then coated and patterned with optimized dose and proximity effect correction (steps (2) and (3)). 200 nm of Ni hard mask is deposited with an electron-beam evaporation tool and liftoff by stripping the PMMA mask (steps (4) and (5)). We then conduct photolithography on positive photoresist to form the patterns with lower resolution requirements, for instance, the non-device side of the double channel region (see Supplementary Information A.3). The SiO2 layer is then dry etched with CHF3/CF4 chemistry (step (6)). The positive photoresist is removed afterward. This concludes the preparation of a hybrid Ni/SiO2 hard mask for high-aspect-ratio III-V gain material etch.

A dry etch of the cladding and active regions is then conducted in a SAMCO ICP-RIE tool using Cl2/BCl3/SiCl4/Ar gases at 250 °C (step (7)). The pressure, gas ratio, ICP, and RF power are optimized for vertical sidewall and deep etch into narrow air gaps of DCM (with several microns of extra etch into the substrate to reduce mode coupling to the substrate). The damaged hard mask (Ni and SiO2) is then removed with a 30 min immersion in buffered oxide etch (BOE, step (8)). Without the SiO2 underlayer, the damaged Ni mask after the dry etching will be difficult to remove. We use atomic layer deposition (ALD) to grow Al2O3 as an insulation layer on the sidewall (step (9)), with an estimated optical loss of 2661 cm−1 at 10-µm wavelength51). Contact windows are opened with thick positive photoresist and 2.5 minutes of BOE etch (step (10)).

Afterwards, a Ti/Au (300/2500 Å) seed layer for electroplating is deposited via electron beam evaporation. 10 μm of electroplated Au is then deposited using Transene TSG-250 solution (step (11)). Plating patterns are defined by thick (>20 μm) positive resist. We then selectively etch Au and Ti to electrically isolate devices on the same chip and to avoid accidental shorting after each device is cleaved (not shown in Fig. S1). Conformal ALD Al2O3 covering the DCM reflectors are also removed with BOE and photoresist mask (see Supplementary Information A.5). The lasing threshold will significantly increase without this step because the Al2O3 coating the chirped grating mirrors will cause a high optical loss. Notably, since BOE has a substantial undercut, the Al2O3 covering the first several periods of the grating is chosen not to be removed to avoid device shorting. If we choose to remove Al2O3 for all grating layers, BOE might affect the Al2O3 insulation on the sidewall of the main laser cavity, creating an electrical short, thus preventing lasing. We then lap and cleave each die and bond either epi-up or epi-down for pulsed or CW operation. For epi-up mounting, we use indium solder on copper mounts. For epi-down mounting, we use AuSn eutectic solder on AlN submounts.

Design: double chirped mirror (DCM) Bragg compensator

We describe the generation of Bragg mirror slice thicknesses based on the ten design parameters. We will also explain the choice of parameter range based on physical intuition and coupled mode theory analysis21. A total of ten design parameters are involved in creating a double-chirped DCM (as shown in Fig. S2 in Supplementary Information) with enough degree of freedom to act as a robust dispersion compensator. These include:

semi-duty-start: ${\eta }_{1}$, starting value of the semiconductor duty cycle.

semi-duty-end: ${\eta }_{2}$, ending value of the semiconductor duty cycle.

air-T-min: ${T}_{{\rm{air}}1}$, lower bound of the air gap size, mainly due to fabrication constraints.

air-T-max: ${T}_{{\rm{air}}2}$, upper bound of the air gap size.

dc-m-num: ${m}_{{\rm{c}}}$, total number of grating periods where the duty cycle is chirped.

total-m-num: ${m}_{{\rm{tot}}}$, total number of grating periods, has to be larger or equal to dc-m-num.

alpha-duty: ${\alpha }_{{\rm{d}}}$, power law coefficient for duty cycle chirping.

alpha-T: ${\alpha }_{T}$, power law coefficient for grating Bragg wavelength chirping.

lambda-begin: ${\lambda }_{1}$, starting point of grating Bragg wavelength chirping.

10.

lambda-end: ${\lambda }_{2}$, finishing point of grating Bragg wavelength chirping.

For each period of the Bragg mirror, the grating period (Bragg wavelength) is determined by:

$$\lambda \left[n\right]=\left[\frac{{\left(\frac{n}{{m}_{{\rm{tot}}}}\right)}^{{\alpha }_{T}}-{\left(\frac{1}{{m}_{{\rm{tot}}}}\right)}^{{\alpha }_{T}}}{1-{\left(\frac{1}{{m}_{{\rm{tot}}}}\right)}^{{\alpha }_{T}}}\right]\left({\lambda }_{2}-{\lambda }_{1}\right)+{\lambda }_{1}$$

where n is the grating (numbering) index, it takes an integer value from 1 to ${m}_{{tot}}$. The semiconductor slab duty cycle is denoted as $\eta \left[n\right]$ and can be calculated using the following relations:

$$\eta \left[n\right]=\left[\frac{{\left(\frac{n}{{m}_{{\rm{c}}}}\right)}^{{\alpha }_{d}}-{\left(\frac{1}{{m}_{{\rm{c}}}}\right)}^{{\alpha }_{d}}}{1-{\left(\frac{1}{{m}_{{\rm{tot}}}}\right)}^{{\alpha }_{d}}}\right]\left({\eta }_{2}-{\eta }_{1}\right)+{\eta }_{1}$$

Here, n only takes integer values from 1 to ${m}_{{\rm{c}}}$. For $n > {m}_{{\rm{c}}}$, $\eta \left[n\right]=0.5$. We enforce this condition in order to form quarter-wavelength Bragg mirrors at the end. Once the Bragg wavelength and duty cycle are determined for each period, the air and semiconductor can be calculated using the following equations:

$$\begin{array}{ll}{T}_{{\rm{air}}}\left[n\right] & =\,\lambda \left[n\right]\left(1-\eta \left[n\right]\right)/2\\ {T}_{{\rm{semi}}}\left[n\right] & =\,\lambda \left[n\right]\eta \left[n\right]/{n}_{h}/2\end{array}$$

where ${n}_{h}$ represents the mode index of the waveguide and is obtained from 2D FEM mode simulation. Notice the extra $1/2$ in the calculation. Finally, we check if the series of ${T}_{{\rm{air}}}\left[n\right]$ lie within the range defined by $\left[{T}_{{\rm{air}}1},{T}_{{\rm{air}}2}\right]$, if not, we normalize ${T}_{{\rm{air}}}\left[n\right]$. Due to fabrication constraints, we set a lower bound for air slab thickness. The etch rate will significantly decrease, and it will also produce a slanted etched facet if the air gap is too narrow. We set the upper bound to minimize mode loss into free space and the substrate.

Given the enormous parameter space, we adopt a hybrid optimization approach. The optimization flow is concisely outlined in Fig. S3 in Supplementary Information. We first use a 1D Transfer-Matrix-Method (TMM) method (details see Supplementary Information A.2) to conduct a coarse search in a larger parameter space and a fine search in a more localized parameter space pinpointed by the coarse search. Two to ten million designs were evaluated in each individual step. The objective function is defined as the difference between group delay dispersion (GDD) provided by the compensator and the required GDD (for a 4 mm laser cavity) to achieve close-to-zero dispersion, as shown in

$${\rm{obj}}\left(\text{design}{\rm{i}}\right)=\mathop{\sum }\limits_{j=2}^{{j}_{\max }}{\left[\frac{\phi \left[j+1\right]-2\phi \left[j\right]+\phi \left[j-1\right]}{\varDelta {\omega }^{2}}-\text{target GDD}\right]}^{2}$$

where ${\rm{i}}$ is the design index, $j$ is the index for frequency sampling points, $\phi \left(j\right)$ is the unwrapped accumulated phase for each frequency point, and $\varDelta \omega$ is the angular frequency spacing between sampling points. The best seed designs serve as starting points for local optimization using 2D Finite-Element-Method (FEM) simulation in the curved Bragg grating geometry (see Fig. 3a). The 2D FEM simulations are approximately two orders of magnitude slower than the 1D TMM. For both 1D TMM and 2D FEM simulation, S-parameter is first calculated. The phase of ${S}_{11}$ is extracted, unwrapped, and differentiated to calculate group delay dispersion, while its amplitude gives the DBR reflectivity (see Fig. 3b–d).

For curved DCM combs, the design parameters are: ${\eta }_{1}=45 \%$, ${\eta }_{2}=55 \%$, ${T}_{{\rm{air}}1}=2\,\mu m$, ${T}_{{\rm{air}}2}=4\,\mu m$, 16 chirped periods, 37 total periods, ${\alpha }_{d}=0.01$, ${\alpha }_{T}=0.01$, ${\lambda }_{1}=36\,\mu m$, ${\lambda }_{2}=30\,\mu m$. For the negative GVD measured from DUT characterization (Fig. 2f), the effective cavity length for the higher frequency component should be larger to provide the proper sign of group delay after DCM reflection. This matches well with this design parameter, where ${\lambda }_{1} > {\lambda }_{2}$, which means a longer wavelength has a shorter effective cavity length. As a matter of fact, all designs in parameter space match this condition based on a physical understanding of this structure. At the end of this DCM design, $\lambda \left[n\right]=30\,\mu m$, and the air slab thickness is 3 times the quarter-wavelength (of 10 μm). This means the DCM design is approximately a doubly-chirped design of a third-order Bragg mirror, which is designed to ease the requirement for lateral resolution in fabrication. DCM curvature follows the phase front of 10-μm-wide waveguide mode emitting into free space. Phase fronts are obtained through a dense 2D FEM simulation.

Laser comb measurement

All laser devices reported in this paper (combs and reference lasers) are epi-up mounted on a copper mount and placed on top of a TEC (thermoelectric cooler). A thermistor is attached to the copper mount for temperature monitoring and control. Room-temperature CW measurements are conducted at a heat sink temperature of 5 degrees Celsius. The laser signal was coupled into an FTIR system with a ZnSe lens. A liquid nitrogen-cooled mercury cadmium telluride (MCT) detector (IR Associates FTIR-16-0.50) was used to collect light at the output of the FTIR. The detector signals, together with the HeNe interference signals, are both inputted to the computer through a data acquisition system (DAQ). The electrical beatnote is gathered through a bias-T directly from the laser electrical bias channel. The signal is then amplified with two RF amplifiers, providing roughly 40 dB of gain. The RF signal is measured by an HP8592B spectrum analyzer.

Dispersion measurement

For pump-DUT dispersion measurement, we bias the pump laser using a pulsed voltage driver from Avtech. The driving voltage is selected to produce the broadest and continuous lasing bandwidth. DUT is CW-biased at various voltage levels. The interferogram is collected using an FTIR and MCT in the same way as discussed above for laser comb measurement. A boxcar averager (SR250, Stanford Research Systems) is used for coherent detection of the pulsed signal. For the dispersion measurement result shown in Fig. 2c–e, the pump laser is pulse-biased at 12 V, with a repetition rate of 5 kHz and a pulse width of 200 ns. Its spectrum is shown in Fig. S4 in Supplementary Information, which is continuous over a broad gain bandwidth from 29.5 to 33.8 THz spanning 143.4 cm−1. FP modes of the DUT are located with a peak-finding algorithm.

Ultrabroadband air-dielectric double-chirped mirrors for laser frequency combs

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