1. Introduction

The quality factors (Q) of cavities and microresonators have reached astounding levels in many regions of the spectrum from the ultraviolet to the infrared, with Q reaching values of hundreds of thousands or even higher. Ready examples are aluminum nitride (AlN) microring resonators with quality factors near 10⁵ at 390 nm in the ultraviolet (UV) [1], paraffin or silicone oil droplets with quality factors of near 10⁷ at 640 nm in the visible [2], silicon microtoroids with quality factors above 10⁸ near 1.55 µm in the near-infrared [3], and fluoride microdisks with quality factors near 10⁸ at 4.4 µm in the mid-wave infrared [4]. Further, the above works represent only a fraction of many other outstanding devices that illustrate high Q in many regions of the spectrum [1–23].

In the thermal infrared and beyond, however, much lower quality factors of cavities and resonators have been demonstrated. Germanium racetrack was recently reported with a quality factor of ∼3200 at the wavelength of 8 µm, which is on the edge of the long-wave infrared [24]. Beyond 9 µm, microresonators are barely reaching 50 in most reported work [25–29]. Much of the difficulty in reaching high Q at long wavelengths lies with the high absorptions of even the most transparent materials. One of the most technologically important infrared regions lies between wavelengths of 8–12 µm, near the peak energy density of room temperature thermal emission. We will note that the wavelength ranges between 8–12 µm or 8–14 µm are often called the long-wave infrared (LWIR) in engineering parlance, although the definition of what constitutes mid-wave and long-wave infrared varies considerably in different fields such as astronomy, and we merely use this definition for consistency with our measurement cameras and detectors. In this region of the spectrum, chemically stable

materials such as germanium and zinc selenide are often used as optical elements, but their absorptions are only low enough to support single-pass optical propagation or a few passes at most especially for wavelengths over 9 µm. High Q resonators require extreme transparency so that the effective optical propagation length within the cavity or resonator is compatible with long coherence lengths.

Figure 1 shows a plot of absorption versus wavelength for a number of common infrared materials. In this plot a dotted line is shown that corresponds to the maximum absorption that would allow a Q on the order of 10⁵, which is a level that is unremarkable at shorter wavelengths but far above currently achievable values in the LWIR. Unfortunately, there are very few materials that meet the appropriate absorption criteria. There are several types of ionic salts, such as potassium bromide (KBr), that have very low absorption in the thermal infrared; however, these materials dissolve in water and are chemically unstable in many fabrication processes and non-laboratory end-user environments.

 

Fig. 1. Absorption coefficients versus wavelength for many common infrared materials [30–33]. The grey dashed line indicates an absorption coefficient, $\alpha = 0.01\textrm{cm}^{ - 1}$. Using $\textrm{F} = \frac{{{\pi}\sqrt {1 - \textrm{A}}}}{\textrm{A}}$, this corresponds to a cavity finesse of about $\textrm{F} = 628,000$, which is achievable in other wavelength ranges but has never been approached in the room temperature thermal infrared. Black dash line is the expected absorption coefficient of Ge between ∼2 and 10 µm based on the properties of typical semiconductors due to free carrier absorption [34].

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The other possible choice is diamond. Diamond has a series of strong multiphonon absorption peaks extending from roughly 3 to 6 µm in the infrared, but beyond these wavelengths in its pure state, it has no other major solid-state vibrational states that can interact with thermal infrared light. Therefore, in theory the Q of a diamond microresonator would be limited by impurity absorption, or more likely, scattering due to fabrication imperfections. The fabrication technology for diamond is still in its early stages, but significant progress is being made [35–41] to increase the types of fabrication processes in which diamond can be used and, perhaps most critically for microresonators, to reduce the surface roughness caused by etching and patterning. With these advances, whispering-gallery mode resonators of diamond have been demonstrated with high optical quality factors at short wavelengths [35,36,41–45].

In this paper, diamond microdisks were fabricated from single crystal substrates and oxygen-based ICP RIE at high angles. LWIR light from a tunable quantum cascade laser emitting from λ ∼ 9.0 µm to 9.7 µm was introduced into the microresonator whispering gallery modes via free-space coupling, and out-coupling was performed with an As₂Se₃ chalcogenide fiber that guided the light to a cryogenically cooled HgCdTe detector. Although previous articles have reported tapering of As₂S₃ chalcogenide fibers to evanescently couple light into the whispering gallery mode microresonators [4,46], our As₂Se₃ fiber is much softer than As₂S₃, which results in more challenges and difficulties in tapering it. Therefore a free-space coupling technique similar to that of [2] using the As₂Se₃ fiber was utilized to characterize the optical properties of the diamond microdisks in our experiment. The microresonator and the rest of the laboratory environment were at room temperature. The measured quality factors for two specific wavelengths on two separate samples were found to be 3648 and 3130 at 9.601 µm and 9.541 µm, respectively. However, many resonances were measured with comparable performance. A Fourier analysis of the resonances as a whole showed that the free spectral ranges of the microdisks were slightly greater than 40 GHz which matches our theoretical predictions based on the microresonator diameter and the whispering gallery mode overlap with the diamond.

2. Fabrication of single-crystal diamond microdisks

Figure 2 shows the fabrication process flow. Microdisks were patterned from chemical vapor deposition (CVD) single-crystal diamond plates ($3 \,\textrm{mm} \times 3 \,\textrm{mm} \times 250 \,\mu \textrm{m}$, Element Six). Before processing, the single-crystal diamond plates were cleaned in a set of boiling acids and bases for few minutes. Specifically a sequence of RCA1, RCA2, and piranha solutions were used. The substrates were rinsed in deionized water for few minutes between etch step. After cleaning, silicon nitride was deposited in a high density plasma chemical vapor deposition (HDPCVD) process and used as a hard mask. After standard photolithography, ICP RIE was used to pattern the silicon nitride and etch the diamond. The etch rate of the diamond was approximately 150 nm/min with conditions of 30 sccm oxygen flow, 100 W RF power, 700 W ICP power, and a 5 mtorr background pressure. Next, an additional layer of silicon nitride was deposited over both the microresonator disk and the substrate. Another ICP RIE step removed the substrate portion of the nitride, but leaving nitride on the disk. Since ICP RIE is a high aspect-ratio process, we designed the etching to leave substantial material on the resonator disk sidewalls. This step is shown from Fig. 2(e) to Fig. 2(f). The sidewall silicon nitride surrounding formed a protective layer that prevented it from attack during subsequent processing.

 

Fig. 2. Fabrication process flow. (a) Silicon nitride was deposited on a diamond substrate. Photoresist was subsequently applied. (b) The photoresist was patterned using standard lithography. (c) The silicon nitride was etched by ICP RIE. (d) The diamond substrate was etched by ICP RIE. (e) Silicon nitride was deposited again. (f) The silicon nitride on the top surface was etched by ICP RIE, which left residual silicon nitride on the sidewall. (g) The diamond was etched again by ICP RIE to create the desired microresonator height. (h) The diamond substrate was mounted vertically and etched at a high angle by ICP RIE to create an undercut. (i) The rest of the silicon nitride was removed by a buffered oxide etch. Acronyms used in the diagram: PR: photoresist, SiN_x: silicon nitride, SCD: single-crystal diamond, ICP RIE: inductively coupled plasma reactive ion etching, HDPCVD: high density plasma chemical vapor deposition, and BOE: buffered oxide etch

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After this, another ICP RIE process etched the diamond to produce the desired height of the microdisks. This height was chosen both for ease of processing and to ensure that whispering gallery mode coupling to the substrate would be minimal. The diamond substrates were then mounted vertically and an angled ICP RIE etch undercut the microdisks to create the propagation ring of the resonator. Finally, the rest of protective silicon nitride was removed using a buffered oxide etch (BOE).

Figures 3(a) and 3(b) are the images taken by scanning electron microscope (SEM) when sample was tilted at 75 degrees. The undercut can be observed at the edge of diamond microdisk in Fig. 3(a). Figure 3(b) is a close-up of a region in Fig. 3(a), zoomed and rotated to the appropriate direction. Since the scale bar in this figure is 1 µm, the surface roughness of sidewall was in the sub-micron regime, which makes the roughness less than one tenth of the wavelength of the propagating whispering gallery mode; however, this roughness is likely the limiting factor for the Q of the current devices. The oxygen ICP RIE angle etch also produced a non-uniform undercut depth in the diamond, which could also contribute to cavity losses.

 

Fig. 3. SEM images of diamond microdisk and Dimensions of microresonator (cross-sectional view). SEM images of the cross-sectional views of diamond microdisk were taken with a tilt angle of 75 degrees. Scale bars in (a) and (b) are 100 µm and 1 µm, respectively. Note that the 1 µm sidewall is the disk ring waveguide, and it is a smooth surface that protrudes from the rough sidewall by about 5 µm. (c) displays the dimension of the microdisk. The diameters of the diamond microresonators were 1 mm with a height of 11 µm. The thickness of the protruding disk waveguide was 1 µm, and the depth of undercut was approximately 5 µm.

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The dimensions of the diamond microdisks are shown in Fig. 3(c). The diameters are approximately 1 mm, the heights are approximately 11 µm, the thicknesses of the protruding disk edges (waveguiding regions) are approximately 1 µm, and the depths of the undercut of the protruding edges are around 5 µm.

3. Optical measurement and discussion

The schematic diagram of the optical measurement experiment is given in Fig. 4. A quantum cascade laser (QCL) (Mircat, Daylight Solutions, Inc) emitted a collimated long-wave infrared beam, which was scanned across the wavelengths from 9.0 µm to 9.7 µm with a 0.1 cm⁻¹/s scan rate. The laser linewidth is less than 0.1 cm⁻¹. The laser beam propagated through a chopper and focused by a BD-2 chalcogenide lens (focal length of 4 mm from Thorlab, Inc.). By adjusting the location of diamond microdisk via a three-axis precision stage, the focal point was positioned at the rim of the microdisk and therefore light at the proper resonant frequencies could be coupled into the microdisk. The uncoupled light was then collected by a single-mode As₂Se₃ chalcogenide fiber (IRF-Se-12, IRflex). Finally, an HgCdTe photodetector (Electro-Optical Systems, Inc.) with a lock-in amplifier was used to record the signal at the output end of the fiber.

 

Fig. 4. Optical measurement setup. An experimental setup consisting of a tunable quantum cascade laser (QCL) (λ∼9–10 µm) coupled to a single-crystal diamond microdisk was used. The uncoupled light was collected by a single-mode As₂Se₃ chalcogenide fiber, and was detected by an HgCdTe photodetector with a lock-in amplifier to record the signal.

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In this experiment, two single-crystal CVD diamond microdisks were made. Before delving into the details of the data, we should note that Figs. 5(a) and 6(a) represent the Fourier transforms of “control” measurements where no microdisk was present, and we were simply sending light through free space to the chalcogenide fiber. The philosophy behind the control measurements was to ensure that we were not generating spurious resonances within the basic optical apparatus of Fig. 4, for example via an unintentional cavity formed from parasitic reflections. The spectrum we measured for first microdisk is given in Fig. 5. In the first microresonator, whose data is shown in Figs. 5(b) and 5(c), some silver-coated silica microparticles (diameter ∼ 2.5 µm) were spread on the surface of the microresonator as suggested in Ref. [16] in order to enhance the Rayleigh scattering and further boost the free-space coupling efficiency. [Note that the second microresonator whose data is shown in later in Figs. 6(b) and 6(c) was not treated in this manner.] Since the wavelength range over which the LWIR laser was tuned covered many free spectral ranges of the microresonators, we were able to use a novel Fourier analysis of the spectrum versus laser frequency scan rate. These transforms are shown in Figs. 5(a) and 5(c), for the control and microresonator measurements respectively. With the microresonator, a prominent peak around 0.065 Hz is observed in Fig. 5(c), which implies an obvious resonance pattern. This peak is completely missing in the control group of Fig. 5(a). We note that there can be inherent DC and/or low frequency peaks in the Fourier transform spectra of a microresonator [47], which do not present any obvious frequency pattern at all. In our measurement, the scan rate was fixed at 0.1 cm⁻¹/s. 0.065 Hz corresponds to 15.38 seconds or 1.538 cm⁻¹. The resonance condition of a whispering-gallery-mode microresonator satisfies the relationship, $\textrm{m}{{\lambda}_\textrm{m}} = {\textrm{n}_{\textrm{eff}}}\,2\pi \textrm{R}$ where m is the mode number, ${{\lambda}_\textrm{m}}$ is mode wavelength, ${\textrm{n}_{\textrm{eff}}}$ is the effective refractive index, and R is the radius of the microresonator. As the wavelengths were scanned around 9.5 µm (with refractive index, n = 2.4 for diamond in the range), the calculated free spectral range is approximately 40 GHz or 1.33 cm⁻¹, with perfect overlap between the whispering gallery mode and the diamond waveguide. However, we note that perfect overlap of the mode with the diamond is highly non-physical. There will always be evanescent fields that extend into the air around the microresonator guiding ring, just as with any core cladding waveguide. This gives an effective index for the mode below that of 2.4. The measured value of the free spectral range matches this expected effective mode index. One of the resonant modes in Fig. 5(b) is circled by black dashed line and a zoom-in of this mode is shown in the inset and the shape of the mode was fit to a quality factor simulation. For this mode, the Q is around 3648 at 9.601 µm. We note that many modes had comparable values and that this mode was not unique in its properties.

 

Fig. 5. Control and optical measurements before and after the insertion of the diamond microresonator 1. Part (a) represents the Fourier transform of the optical measurement taken by the experimental setup (shown in Fig. 4), however, without the presence of the first microresonator (control groups). This plot shows that there was no spurious parasitic cavity in the optical setup that might interfere in the microresonator analysis. Part (b) represents the intensity (in terms of signal voltage) versus wavelength plot for the first microresonator, when included in the experimental setup. In part (b), the inset shows the expanded views of the experimental data circled by the black dashed line. The blue lines in the inset show the curve fitting of the experimental data. The quality factors for the first is found ∼3648 at 9.601 µm. Part (c) is the Fourier transform of the data presented in part (b). Obvious peak is found near ∼45 GHz in part (c), which is expanded in their corresponding inset with curve fitting (blue line). Please note that the bottom x-axis (black) of the Fourier transform plots (Parts (a) and (c)) denote the free spectral range when the scan rate of tunable laser is at 0.1 cm⁻¹/s. In addition, the top x-axis (red) of the Fourier transform plots denote the sampling rate of the lock-in amplifier.

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Fig. 6. Optical measurements for the control group and the experimental of the second diamond microdisk. Part (a) represents the Fourier transform of the optical measurement taken by the experimental setup but the second microresonator is missing (control groups). Once again, this plot shows that there was no spurious parasitic cavity in the optical setup that might interfere in the microresonator analysis. Part (b) shows the intensity versus wavelength plot when the second microresonator was included in the experimental setup. In part (b), the inset shows the expanded views of the experimental data circled by the black dashed line. The blue lines in the inset show the curve fitting of the experimental data. The quality factors for the second microdisk is found ∼3130 at 9.541 µm. Part (c) is the Fourier transform of the data presented in part (b). Obvious peak is found near ∼45 GHz in part (c), which is expanded in their corresponding inset with curve fitting (blue line). Please note that the bottom x-axis (black) of the Fourier transform plots [Parts (a) and (c)] denote the free spectral range when the scan rate of tunable laser is at 0.1 cm⁻¹/s. In addition, the top x-axis (red) of the Fourier transform plots denote the sampling rate of the lock-in amplifier.

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The optical measurement of a second control and a second microresonator are shown in Fig. 6. The dimensions of the second microdisk are very similar to the first, varying only by small microfabrication variations. As mentioned previously, there were no microparticles dispersed on the surface of this resonator. Similar measurements and analyses were performed. A Fourier transform of the control experimental spectrum is plotted in Fig. 6(a), showing no obvious peaks except for low frequency noise far outside the microresonator range. The Fourier transform of the microdisk spectrum in Fig. 6(c) shows a prominent peak at 0.065 Hz (inset) which closely matches the modal effective index free spectral range as in our calculation for disk 1. As before, one resonant mode is shown with a circular dashed line in Fig. 6(b). This mode is then zoomed in an inset and curve fitted for determining the Q. The Q value for this mode is found around 3130 at 9.541 µm, which is comparable to the first one. As mentioned earlier, many other modes of this resonator have similar properties.

It is noted that the transmission spectra of the microdisks [shown in Figs. 5(b) and 6(b)] are non-uniform, with magnitudes lower for shorter wavelengths but higher for longer wavelengths. This is due to the fact that the QCL was scanned at a constant current instead of constant power in our measurements. Therefore, the baseline power level of the transmission spectrum simply resembles the shape of the output power of QCL at a fixed current.

Comparing the spectra of the first and second microdisks, we can conclude that the microparticles on the surface of the first microdisk did not have a major impact on coupling the light into or out of our particular microresonator structure. If there were a strong interaction between the laser beam and the microparticles, we might have observed the mode splitting because of the mismatch of light travel in the clockwise and counterclockwise directions at the microdisk [8]. The poor coupling performance of the microparticles can be explained by two reasons. The first is a relatively low Purcell factor. The Purcell factor is proportional to the Q/V ratio, where V is the volume of mode resonance and largely depends on the dielectric function of the microresonator material [48,49]. Compared to the Q and dielectric function of the microresonator reported in [16], the Purcell factor of our microresonator structure is at least three orders of magnitude lower (again note the absence of any mode splitting). Second, the microparticles are unlikely to be well-positioned on the vertical sidewall of our microresonator, resulting in nearly negligible coupling to the cavity mode.

4. Conclusion

The quality factors of the analyzed diamond microresonators far exceed the existing state of the art for deeper LWIR cavities with wavelength beyond 9 µm. We have demonstrated the first whispering-gallery mode single-crystal diamond microdisks for the long-wave infrared. In the experiment, millimeter-size diamond disks were made by oxygen plasma ICP RIE with angled etching to create a protruding ring waveguide. The diamond microdisks have quality factors higher than 3000, exceeding prior deeper LWIR cavity Q by more than an order of magnitude. Fourier analysis further confirmed that the measured results match the theoretically calculated free spectral range.