2.1.

Concept of Micro-Resonator OFC for Frequency Division

An immediate choice for achieving a reduction in size is to replace the traditional mode-locked-laser-based OFC with a micro-resonator-based OFC.^9–13 Indeed, other groups are developing octave-spanning micro-resonator-based OFCs^14,15 including as part of at least one effort to develop an entire on-chip optical atomic clock.¹⁴ Hence, in the remainder of this paper, we will not focus on the development of the micro-resonator-based OFC.

2.2.

Concept for Achieving Short-Term Stability

The ULE cavities that provide optical clocks with exceedingly low phase noise are typically 10 s of cms long¹⁶ and typically require high-SWaP-C external housing to provide environmental isolation. Here, we propose to replace the ULE-cavity-stabilized laser with a photonic-integrated short-path delay-line interferometer that stabilizes the OFC without the need for an intermediate laser.^17–19 Although optical-fiber-based delay-line interferometers are a well-established tool to stabilize single-frequency lasers,¹⁷ they are not commonly used on PICs. By bringing this technique to the PIC platform, we face a major challenge to overcome the waveguide propagation loss, which is orders of magnitude higher than the propagation loss of optical fiber. Buried waveguides on the common 220-nm silicon-on-insulator platform typically achieve propagation losses of approximately 2 dB/cm at wavelengths near 1550 nm.²⁰ By moving to more complicated waveguide geometries, silicon waveguides have been reported with losses below 3 dB/m.^21–23 Additionally, some approaches toward ultra-low-loss ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides have been reported demonstrating less than 1 dB/m loss.^24,25 Nevertheless, regardless of the technology, the propagation loss of an integrated photonic delay line is significantly higher than the $\sim 0.17\mathrm{dB}/\mathrm{km}$ propagation loss of commercial optical fiber.

Our expectation of increased propagation loss of the integrated photonic delay line had a significant impact on the design of our interferometer. First, we limited the interferometer delay to less than 10 m, which significantly decreased the sensitivity of the interferometer. Second, even with a relatively short delay, we expect a high power imbalance between the delayed and non-delayed components of the light at the output of the interferometer, which may result in an increased contribution from laser relative intensity noise. Consequently, our development strategy was to first construct a fiber-optic prototype to demonstrate that a short-path interferometer has sufficient sensitivity to enable the generation of a low-phase-noise microwave. Future work will extend this prototype to an integrated photonic chip that stabilizes a micro-resonator-based OFC. Toward that end, we also designed and fabricated an integrated-photonic tunable coupler in order to mitigate the expected power imbalance. The results of these experiments are presented in Sec. 3.

2.3.

Concept of Environment-Insensitive Device for Long-Term Stability

Any oscillator is susceptible to long-term frequency drift. One of the most pervasive sources of this drift arises from the oscillator’s sensitivity to environmental fluctuations, including acoustic, vibrational, and temperature perturbations. The atomic reference in the laboratory-scale clock serves to mitigate this drift, because the atomic transition is relatively insensitive to the environment. Cold atoms are a particularly high-performing reference since they are extremely well isolated from the environment. Nevertheless, atomic sources inherently increase the SWaP‑C of a clock.

Rather than pursuing an on-chip atomic reference, we propose an approach to obtain long-term frequency stability. We are developing an environmentally insensitive hollow-core micro-resonator that is clad with an ENZ metamaterial.²⁶ Although we do not expect the frequency accuracy or frequency stability at very long timescales (e.g., $>{10}^3\mathrm{s}$) of the ENZ reference to be competitive with cold atom references, we expect its frequency stability to compete with miniaturized atomic clocks such as the CSAC. Moreover, when we consider the possibility to incorporate the fabrication of the ENZ resonator into a CMOS process, we expect that the overall SWaP-C will be greatly reduced, resulting in a cheap, compact, and easily manufacturable frequency reference.

Our concept is to use the ENZ metamaterial as waveguide cladding to form an air or vacuum core resonator.²⁶ Figure 1 shows a schematic illustration of the air-ring, ENZ-metamaterial-cladding resonator device. The idea is to make an intrinsic environment-insensitive cavity/resonator device.

Fig. 1

Air-core-ring and ENZ-metamaterial cladding resonator: (a) 3D illustration and (b) cross-section view.

For a typical ring resonator, the resonant optical frequency is $f_{\mathrm{op}}=m\times f_0$, where $m$ is the number of modes and $f_0$ is the fundamental frequency. The fundamental wavelength ${\lambda }_0=C/f_0$, which is the round-trip optical path. Also, ${\lambda }_0=n\times d$, where $n$ is the effective refractive index of the ring path and $d$ is the physical dimension of the resonator. Both temperature and vibration may change the physical dimension of the resonator. In general, the environmentally induced frequency change is given by Eq. (1):

In a typical micro-resonator containing ${\mathrm{SiO}}_2$, ${\mathrm{Si}}_3{\mathrm{N}}_4$, Si, etc., the change in refractive index, $\mathrm{\Delta }n$, can be significant due to temperature changes and vibration-induced strains. In case of a material with thermal expansion ${\alpha }_{\mathrm{th}}$, Eq. (1) can be written as Eq. (2):

In contrast, in a vacuum/air resonator embedded in ENZ metamaterial (e.g., in ENZ cladding layer), as provided by the embodiments herein, $\mathrm{\Delta }n$ is negligible. The $\mathrm{\Delta }d$ can be less significant due to the geometry of the material where vacuum is enclosed by the ENZ cladding layer. In addition, with the ENZ condition, optical phase changes very slowly in the ENZ media, thus environmentally induced small geometry variations have less effect on optical phase variation, and therefore generates less phase noise.

3.1.

Proof of Concept Demonstration Using Fiber Delay-Line Interferometer

The theory of operation of the delay-line-interferometer-stabilized OFC is as follows. The OFC illuminates a fast photodiode to generate a microwave with a frequency, $f_m$, that is an integer multiple, $m$, of the OFC’s repetition rate, $f_r$, such that $f_m=m{f}_r$. Meanwhile, the optical power at the output of the interferometer, $dP(t)$, is proportional to fluctuations of the OFC’s carrier frequency, $d{f}_c(t)$, according to $dP(t)\sim {\tau }_{g}d{f}_c(t)$, where ${\tau }_g$ is the group delay imposed by the interferometer delay. Notably, the carrier frequency of the OFC is nearly an integer multiple, $N$, of the repetition rate; it is given by $f_c=N{f}_r+f_{\text{CEO}}$, where $f_{\text{CEO}}$ is the carrier-envelope offset frequency of the OFC. If $f_{\text{CEO}}$ is stabilized so that its noise contribution is negligible, then the output power of the interferometer is proportional to the noise of the repetition rate, $d{f}_r(t)$, according to $dP(t)\sim N{\tau }_{g}d{f}_r(t)$. This signal is filtered and fed back to the OFC in order to stabilize the repetition rate. The key point is that the interferometer’s sensitivity to the repetition rate noise is proportional both to the length of the interferometer delay and to the integer $N$, which corresponds approximately to the ratio of the carrier frequency to the OFC’s repetition rate and is typically on the order of ${10}^5$ or ${10}^6$.

One consequence of the higher propagation loss on an integrated chip is that the path imbalance in the interferometer will be limited to the scale of meters or less. This limitation is also related to the limited area available on a PIC. By contrast, the delay lines used to stabilize single-frequency lasers are typically kilometers long since the additional length increases the interferometer sensitivity.¹⁷ Hence, the integrated-photonic interferometer will necessarily have orders of magnitude lower sensitivity than the typical fiber-optic interferometer. Nevertheless, we expect that the fact that the interferometer is sensitive to frequency noise at the carrier frequency—and therefore proportional to the large integer $N$—will afford us some leeway in the sensitivity. To prove our concept for a short-path interferometer, we constructed a fiber-optic prototype interferometer with a 40-ns delay line, corresponding to 8 m of optical fiber. We stabilized a commercially available OFC with this interferometer and generated a 10‑GHz microwave signal with phase noise of $-130\mathrm{dBc}/\mathrm{Hz}$ at 1-kHz offset frequency.¹⁸

The architecture of the system used to generate the 10‑GHz signal is shown in Fig. 2. The OFC was a commercially available fiber-based comb from Menlo Systems with a center wavelength of approximately 1550 nm and a $f_{\text{rep}}$ of 250 MHz. A commercially available $f\text{-}2f$ interferometer (Menlo Systems) measured the $f_{\text{CEO}}$ of the comb. The output of the OFC was split into two parts.

Fig. 2

System architecture used to stabilize the OFC. The $f_{\text{CEO}}$ is stabilized using an AOFS1 and the $f_{\text{rep}}$ is stabilized by a Michelson interferometer. A 10-GHz microwave signal is generated by a photodiode.

The first portion of the OFC output was used to generate the 10‑GHz signal. The light from the OFC entered a fast PIN photodetector (Optilab PD-20), where it generated a microwave frequency comb, with frequency components at the $f_{\text{rep}}$ of 250 MHz and its integer harmonics. We used a microwave bandpass filter (BPF) with a center frequency of 10 GHz to isolate the 40th harmonic and amplified it with a low-phase-noise RF amplifier. Since the frequency of the microwave output was directly related to the OFC repetition rate, its phase noise was also directly proportional to the phase noise of the OFC repetition rate.

The second portion of the OFC output was used to stabilize the OFC’s repetition rate, thereby reducing the phase noise of the 10‑GHz microwave. The light from the OFC passed through an acousto-optic frequency shifter (AOFS1), which imparted a frequency shift on the OFC according to the frequency of the signal at its voltage input. This signal was the $f_{\text{CEO}}$ of the OFC and was provided by the output of the $f\text{-}2f$ interferometer. The polarity of the frequency shift imparted by AOFS1 was chosen such that it canceled the $f_{\text{CEO}}$. The $f_{\text{CEO}}$-free comb light entered a 0.8‑nm optical BPF and then a fiber-optic Michelson interferometer with a path imbalance of 40 ns. We used single-mode fibers and non-polarization-maintaining components. The Faraday rotating mirrors mitigated the impact of polarization fluctuations. The output of the Michelson interferometer illuminated a set of balanced photodiodes, which converted the fluctuations of the $f_{\text{rep}}$ into a photocurrent. We used balanced photodiodes to reduce the current associated with the laser intensity noise. The photocurrent from the balanced photodiodes passed through a loop filter and fed back to an electro-optic modulator within the OFC cavity in order to stabilize the $f_{\text{rep}}$.

The phase noise of the 10‑GHz microwave generated by the OFC is shown in Fig. 3. When the OFC was free-running (i.e., when the self-stabilization circuit is turned off), the microwave had a phase noise of approximately $-93\mathrm{dBc}/\mathrm{Hz}$ at a 1‑kHz offset frequency. When the OFC was stabilized, the microwave had a phase noise of approximately $-130\mathrm{dBc}/\mathrm{Hz}$ at a 1‑kHz offset frequency. Hence, the self-stabilization circuit reduced the phase noise of the microwave by over 35 dB in this offset frequency range. In the stabilized case, the noise at offset frequencies below 1 kHz is consistent with environmental fluctuations in the laboratory, such as temperature variations, vibrations, and acoustics. Hence, we believe that with improved packaging, the noise in this offset-frequency range will decrease.

Fig. 3

Single sideband (SSB) phase noise of the 10-GHz microwave generated by the OFC when free-running (top, blue curve) and when stabilized (bottom, red curve).

These results demonstrate that a 40‑ns fiber-optic interferometer has sufficient sensitivity to stabilize an OFC such that we could generate a microwave signal with ultra-low phase noise. We expect the interferometer on the integrated platform to introduce additional loss, so further work may be required to achieve similar performance with a PIC. On the other hand, due to its smaller size, an integrated circuit can be more easily isolated from environmental fluctuations than the fiber-optic prototype, which suggests that the noise at some offset frequencies may decrease. In any case, these results are a significant and encouraging step toward the realization of an on-chip stabilization circuit.

3.2.

Development of Integrated-Photonic Tunable Couplers

Another consequence of the high propagation losses in a photonic integrated waveguide is that the loss imparted by a centimeters- or meters-long delay line imparts a large power imbalance between the interferometer paths. Such an imbalance may lead to exaggerated noise contributions from laser intensity noise. So, we designed, fabricated, and tested a 1-by-2 splitter with a tunable splitting ratio to balance the optical power of the short delay with a meter-long delay at the output combining point of the asymmetric interferometer.

The tunable 1-by-2 splitter was fabricated using a commercial integrated-photonics foundry (AIM-Photonics). We also designed and had fabricated a delay-line waveguide, an asymmetric Mach–Zehnder interferometer, and balanced photodetectors using the same process. Optical images of these components are depicted in Fig. 4.

Fig. 4

Layout of the integrated lock circuit.

The splitting ratio of the 1-by-2 power splitter is adjusted using a doped silicon heater that runs parallel to the evanescent coupling region. The silicon heater is partially etched to prevent mode coupling from the evanescent coupling region into the heater itself, which would otherwise cause excess loss. The thermal tuning performance is depicted in Fig. 5. This adjustable power split allows the unequal loss in the two interferometer paths to be offset so that the output power is roughly equal. The relative splitting ratio can be adjusted by up to $-35\mathrm{dB}$.

Fig. 5

Output power into one arm of the 1-by-2 power splitter, adjusted using a doped silicon heater. This adjustment of input power into the two asymmetric MZI arms can balance the net loss in each arm so that the output power in each path is roughly equal.

4.1.

Thick ENZ-ITO Meta-Film Development

We fabricated a variety $\sim 2\text{-}\mu \mathrm{m}$-thick ENZ ITO films via pulsed DC sputtering onto a ${\mathrm{SiO}}_2$ layer placed on top of a Si substrate and subsequently thermally annealed them. We performed a systematic study of these metafilms and discovered a non-uniform variation of the ENZ property.²⁹

The experimental results of these ENZ properties are shown in Fig. 6. Since no equipment exists that can directly measure an unknown variable (vertically) permittivity, $\epsilon$, of a multi-layer material system, we developed a comprehensive method to obtain the permittivity as a function of vertical location in the film. The method involves taking variable angle spectroscopic ellipsometry and fitting the measured data with an appropriate physical model, which also sliced the thick ITO film region into 30 thin layers.

Fig. 6

(a) ITO metafilms’ ${\epsilon }_1$ as function of wavelength for four different annealing temperatures; (b) ${\epsilon }_1$ profiles as function of distance from substrate in the $2\text{-}\mu \mathrm{m}$-thick ITO film for different annealing conditions; (c) both ${\epsilon }_1$ and ${\epsilon }_2$ deep profiles for 250°C annealing.

The different zero-crossing frequencies are shown in Fig. 6(a), for 10 min annealing with temperatures ranging from 250°C to 400°C. Figure 6(b) shows that for all annealing temperatures, the ITO layer permittivity was not constant with respect to the depth. At lower annealing temperatures, the samples’ permittivity depth profile showed a relatively small amount of non-uniformity, which is qualitatively consistent with the behavior reported for thin ITO films as shown in Fig. 6(c). However, at higher annealing temperatures, a sharp transition region appeared midway through the depth of the ITO film. Above this transition region—i.e., near the top of the ITO film—the real part of the permittivity was positive, whereas below the transition region—i.e., near the bottom of the ITO film—the real part of the permittivity was negative.

To understand this variation behavior, we conducted several microanalysis experiments on three of our ITO samples: as-deposited, annealed at 250°C, and annealed at 350°C.²⁹ Specifically, we examined the crystallinity and texture using x-ray diffraction (XRD), the crystallite morphology using cross-sectional transmission electron microscopy (TEM), and the chemical composition using energy dispersive x-ray spectroscopy (EDS). The XRD revealed that the as-deposited sample was predominantly amorphous, whereas the annealed samples were polycrystalline with no dominant crystal orientation. The TEM picture as shown in Fig. 7(a) revealed that the crystal grains in the high-temperature-annealed sample changed size and shape partway through the film’s thickness, whereas the crystal grains in the low-temperature-annealed samples showed no such change. The EDS result as shown in Fig. 7(b) further showed that in the high-temperature-annealed sample, the oxygen concentration increased sharply partway through the film, whereas the low-temperature-annealed sample showed no such change. These results indicate that the crystal grain morphology and oxygen vacancy density may contribute significantly to the permittivity of the ITO film.

Fig. 7

(a) Dark field TEM image and (b) EDS plot of the ITO metafilm annealed at 350°C.

We are developing a new fabrication technique to improve the uniformity of the ENZ ITO thick films. The goal is to make both ${\epsilon }_1$ and ${\epsilon }_2$ closer to zero through the thickness of the film because higher ${\epsilon }_2$ will increase the absorption loss for our future device. For this, we deposit the ITO film with high-power impulse magnetron sputtering (HiPIMS), a relatively recent innovation in sputter deposition tools that allows for more control over film growth. Below is the real part and imaginary permittivity behavior of 80-min annealed sample at 650°C. The results are shown in Fig. 8. The permittivity depth profile is still not uniform. The real part of the permittivity crosses 0 at 1557 nm, and the imaginary part of the permittivity remains at 0.39. However, ${\epsilon }_2$ is closer to zero through the layer thickness compared with our previous ENZ ITO samples.

Fig. 8

The plots of real (black) and imaginary (red) parts of permittivity of ITO metafilms, made by HiPIMS growth and 80 min of 650°C thermal-annealing: (a) as a function of wavelength and (b) as a function of distance from the substrate.

We are also studying different annealing techniques such as annealing under oxygen gas to control formation of oxygen vacancies in ITO. The detailed results will be discussed in future publications.

4.2.

Design and Modeling of Air-Core, ENZ-ITO Cladding Ring Resonator

Light-guiding properties of the air-core, ENZ-ITO-cladding ring resonator were numerically modeled using a finite-element-method (FEM) eigenmode solver. The ENZ-ITO resonator consists of a bus waveguide and an optical ring cavity. The bus waveguide and ring cavity guide light in air through a hollow channel embedded in the ENZ-ITO film. The light-guiding mechanism in the hollow waveguide is based on total external reflection (TER) at the air-ITO interface.

In our TER-based waveguide analysis, the fabricated ITO was modeled as a superlattice with 30 sublayers due to the non-uniform distribution of its dielectric constant. The thickness of the individual layer was set to be 60 nm. According to the ellipsometry analysis, the fabricated ITO sample exhibits ENZ properties near the bottom of the film. The region where the absolute value of the real part, ${\epsilon }_1$, of the dielectric constant of the ITO is less than 1 was defined as a low-epsilon region. In the air-core waveguide design, this low-epsilon region was used as a cladding layer directly interfacing the air core. Figures 9(a) and 9(b) present the dielectric constant distribution of the air-core ENZ-ITO waveguides. Both real and imaginary parts of the dielectric constant vary gradually along the deposition direction. In this design, a ridge-shape air-core, enclosed by the ITO film, provides the lateral mode confinement.

Fig. 9

(a) The real ${\epsilon }_1$ and (b) the imaginary ${\epsilon }_2$ parts of the dielectric constant distribution across the air-core ENZ waveguide.

Figure 10 shows the calculated electric field distribution of the fundamental transverse magnetic mode using a commercial FEM solver, COMSOL Multiphysics^TM. The electric field in the air-core waveguide is described by $\mathbf{E}(x,y,z)=\mathbf{E}(x,y)·e^{-j\beta z}$, where $\beta$ is the propagation constant of the guide mode. As shown in the figure, the electric field is tightly confined in the ridge waveguide. Due to the large refractive index contrast between the core (air) and the cladding (ITO), the evanescent tail of the guided mode rapidly decays in the low epsilon region in the ITO film. The simulation parameters used in the mode analysis are $t_1=t_2=2\mu \mathrm{m}$, and $w_1=w_2=4\mu \mathrm{m}$. The calculated effective refractive index of the fundamental mode is $\beta /k_0$ is $0.96641-j$ $8.3207\times {10}^{-4}$, where $k_0(=2\pi /{\lambda }_0)$ is the wave vector and ${\lambda }_0$ is the free-space wavelength. The estimated propagation loss is 29.3 dB/mm.

Fig. 10

Calculated electric field profile of the guided mode in the air channel waveguide at ${\lambda }_0=1.55\mu \mathrm{m}$.

4.3.

Developing Fabrication Technique for the Air-Core, ENZ-ITO Cladding Ring Resonator

We have designed several fabrication methods for the air-core, ENZ-ITO-cladding ring resonator. The goal is to use an air cavity as the waveguide core in a ring resonator configuration that is then covered with 1- to $2\text{-}\mu \mathrm{m}$-thick ENZ ITO material as cladding for the waveguide as shown in Fig. 1. The fabrication process of such device structure involves multiple processing steps. The first processing step is depositing ITO on a ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate. The second step is depositing a sacrificial material layer such as Si or Ge, and lithographically forming a disk or ring for the resonator. The third step is depositing additional ITO to cover the disk/ring and then annealing it to achieve the desired ENZ property. The final step is etching small windows on top of the disk to expose the sacrificial layer and then remove it using ${\mathrm{XeF}}_2$ vapor.

Due to the nature of ENZ materials, there is some absorption that may increase the propagation loss and reduce the $Q$-factor of the resonator device. Therefore, a major challenge is to reduce the propagation loss for our air-core/ENZ ITO cladding ring-resonator. For that we take two approaches in the fabrication: first, from our experimental data as shown in Figs. 6 and 8, the ENZ ITO layers have lower ${\epsilon }_1$ and ${\epsilon }_2$ near the substrate and high ${\epsilon }_2$ at the top surface, which increases absorption near the surface. Therefore, we developed a fabrication method for a mushroom-shaped sacrificial Si/Ge structure, on which we conformally deposit ITO to cover the “mushroom,” Figure 11 shows the SEM picture of the mushroom-shaped Si disk and pictures after the ITO is deposited on the sacrificial Si disk. After the annealing process, the ENZ ITO near the interface with the sacrificial Si/Ge mushroom has lowest ${\epsilon }_2$. Therefore, once the sacrificial Si/Ge is removed by the vapor etching process, the air-core ring-resonator will be surrounded by low loss ENZ ITO material. Second, using the lithographic process, we created the air-ring resonator with a notched ridge waveguide cross-section shown as Figs. 9 and 10 to reduce interaction between the optical mode and ITO cladding and reduce the amount of light leaking into the ITO.

Fig. 11

(a) An SEM picture of the mushroom-shaped Si disk; (b) and (c) ITO covered Si disk.

We are in the process of fabrication and testing such air-ring, ENZ-ITO device structures; further fabrication details and testing results will be reported in future publications.