Raised-microdisk resonators, in which the microdisk is supported above the substrate by a pedestal at its center, are useful for their high-quality factors and their ability to confine light in relatively low-index materials such as $\mathrm{Si}{\mathrm{O}}_2$, erbium-doped glass, or Si nanocrystal (Si-nc) films. These attractive features led to the application of raised microdisks and microtoroids for lasing [1, 2], enhanced spontaneous emission [3, 4], and sensing [5, 6]. They are also useful as a platform for investigations of material properties [7, 8]. Owing to the raised nature of these cavities, standard waveguide coupling techniques cannot be used to characterize these devices, leading to the development of two alternative characterization techniques. In the first technique, a tapered fiber is positioned in close proximity to the microdisk, creating a situation analogous to that of a conventional waveguide coupled resonator. This technique was used to demonstrate lasing [1] and sensing [6] in raised microdisks. Unfortunately, this technique is time consuming, as it requires manually aligning the fiber to each microdisk. In addition, tapered fibers are not commercially available, and a fiber pulling process must be developed. The alternative is a free-space collection technique in which microdisk luminescence is collected in the far field. This technique was used to study whispering-gallery modes (WGMs) in raised Si-nc microdisks [3, 4, 7, 9], leading to observations of Purcell enhanced spontaneous emission and free carrier absorption. This far-field technique is experimentally simpler and more efficient than the fiber technique; however, to our knowledge, its limitations have not been investigated. In this work we present a detailed comparison of the two techniques, identify the limitations of the far-field collection technique, and discuss the regimes of operation in which each technique is appropriate.

To compare the tapered fiber and far-field collection techniques, we selected raised Si-nc microdisk resonators as a test structure. Si-nc microdisks support WGMs in their photoluminescence (PL) spectra and have been studied in the past using both far-field [3, 4, 9] and tapered fiber techniques [8]. Our Si-nc microdisk fabrication process began by depositing a $200\text{-}\mathrm{nm}$-thick Si-nc film on a Si substrate. Owing to the low refractive index of the Si-nc film $(n\sim 1.7)$, this thickness ensured that only a single axial mode was supported. The Si-nc film consisted of alternating layers of a-Si and $\mathrm{Si}{\mathrm{O}}_2$ deposited by plasma-enhanced chemical vapor deposition and annealed at $1100°\mathrm{C}$ in a nitrogen environment to precipitate nanocrystal formations in the a-Si layer [10]. We then used photolithography to pattern disks with diameters ranging from $6\text{to}20\mu \mathrm{m}$. We transferred the disk patterns into the Si-nc film using an inductively coupled plasma (ICP) etching process in a ${\mathrm{C}}_4{\mathrm{F}}_8$, $\mathrm{S}{\mathrm{F}}_6$, and Ar environment. A subsequent ICP etch, preformed in an $\mathrm{S}{\mathrm{F}}_6$ environment, undercut the microdisk such that the distance from the edge of the disk to the Si pedestal was $1.7\mu \mathrm{m}$. A scanning electron microscope (SEM) image of the fabricated device is shown in Fig. 1a .

We performed microdisk characterization using two experimental setups: a far-field collection setup [Fig. 1b] and a tapered fiber collection setup [Figs. 1c, 1d]. In the far-field setup, two lenses were used to capture the emission. We aligned the lenses to focus emission from the edge of the disk onto the entrance slit of our spectrometer because microdisk WGMs radiate primarily in the plane of the disk [3]. The lens closest to the disk had an NA of 1, resulting in a collection angle of 23.6°. In the fiber setup, we positioned the microdisk sufficiently close to a tapered fiber to allow for evanescent coupling of WGMs. The end of the fiber was then connected to our spectrometer. In both cases the microdisks were excited from above with a $532\mathrm{nm}$ laser. Using these setups, we measured PL spectra for Si-nc microdisks with diameters ranging from $6\mu \mathrm{m}\text{to}20\mu \mathrm{m}$.

The collected PL spectra for identical disks varied dramatically depending on the collection setup. In Figs. 2a, 2b, 2c , we present the PL spectra collected from an $8\mu \mathrm{m}$ diameter Si-nc microdisk using the far-field technique and the tapered fiber technique. We made two measurements using the tapered fiber, one in which the fiber was positioned at the edge of the disk [Fig. 2a] and the other in which the fiber was positioned on top of the disk [Fig. 2b]. When the fiber was positioned at the edge of the disk, we collected the first radial WGMs across the entire Si-nc emission spectrum. In this case, the quality factor of each mode was limited by the resolution of our spectrometer to $\sim 2\times {10}^3$. When the fiber was positioned above the disk, we still collected the first radial modes, which aligned with the modes in Fig. 2a; however, at shorter wavelengths, we also collected second order radial modes. The higher-order radial modes did not couple efficiently when the fiber was at the edge of the disk owing to their spatial confinement further inside the disk. The quality factor of the first radial mode is reduced in Fig. 2b owing to loading effects, as we collected this measurement with the fiber in contact with the disk. This loading effect highlights one of the disadvantages of the fiber collection technique. If we wanted to measure the intrinsic Q of the cavity, we could collect a series of PL spectra as the fiber was moved away from the disk. By moving the fiber away from the disk, we would reduce the coupling loss, and eventually the Q would cease to change with fiber position, indicating that we were measuring the intrinsic cavity Q. Of course, one advantage of the far-field technique is that there is no risk of loading effects and the WGMs measured always reflect the intrinsic Q of the cavity.

The PL spectrum collected from the microdisk using the far-field collection technique is shown in Fig. 2c. The PL spectrum in this case is significantly different from either spectra collected using the tapered fiber. At long wavelengths, we collected the first-order radial modes, and at short wavelengths, we collected the second-order radial modes. Interestingly, the first radial modes were no longer collected at shorter wavelengths. To understand this phenomenon, we note that the far-field collection technique relies on collecting a signal that escaped the microdisk through radiative bending loss and was therefore emitted tangentially to the edge of the disk. If energy in a WGM is absorbed because of losses in the disk material, the far-field collection technique fails to measure it. If energy is lost because of surface roughness induced scattering, it may be collected, but the collection efficiency is reduced because of the lack of directionality. This interpretation implies that the radiative bending loss in the $8\mu \mathrm{m}$ diameter disk studied in Fig. 2 decreased sufficiently at shorter wavelengths that the first radial modes could no longer be collected using the far-field technique. This behavior could also be interpreted based on the relative collection efficiency of the different azimuthal modes, as determined by the positioning of the collection optics. However, translation of the collection optics did not significantly affect the relative intensity of the WGMs in the PL spectrum. Also, owing to the large collection angle, we do not expect a significant difference in collection efficiency between WGMs.

The contrast between the two collection techniques was even more dramatic when we considered larger disks in which the radiative bending loss was further reduced. In Figs. 2d, 2e, we show the PL spectra for a $20\mu \mathrm{m}$ diameter disk collected using the far-field technique and the tapered fiber technique. The far-field technique failed to detect any modal structure in this device, whereas PL collected using the tapered fiber setup revealed the expected WGM spectra. This difference highlights the low radiative bending loss regime in which the tapered fiber collection setup is required to accurately study WGMs in raised microdisks. We also note from Figs. 2d, 2e that the far-field technique collects a significant background signal corresponding to PL that does not contribute to WGMs, while the tapered fiber setup collects virtually zero background signal.

To confirm our conclusion that changes in the radiative bending loss are responsible for the device behavior observed using the far-field collection technique, we calculated the fraction of energy in a WGM lost to radiative bending loss for the devices considered in this work. We defined this fraction as the radiative loss divided by the total loss, where the total loss is a sum of the radiative losses and all remaining loss mechanisms, including band-to-band absorption, Mie scattering, and surface roughness [3]. The radiative loss was calculated based on a ray optics model that used the total internal reflection (TIR) condition to compute the energy transmitted at each reflectance of a WGM at the edge of the disk. Based on this ray optics model, the radiative loss limited Q is given as [3]

This fraction decreases rapidly as diameter increases, explaining the inability of the far-field technique to collect modes for large microdisks. We also observe that at a diameter of $\sim 8\mu \mathrm{m}$, corresponding to the microdisk investigated in Figs. 2a, 2b, 2c, the fraction decreases significantly at shorter wavelengths. This explains the trend observed in the PL spectra collected using the far-field technique, as shown in Fig. 2c. Based on this analysis, the far-field technique is appropriate when studying microdisks in the light colored area of Fig. 3, when radiative bending loss is a significant component of the total loss in the disk. When radiative bending loss is weak, in the dark region of Fig. 3, the tapered fiber technique will provide more accurate characterization.

In summary, we presented a detailed comparison of two characterization techniques that have been employed to study raised-microdisk resonators: one is based on the collection of WGMs in the far field; and the other is based on coupling WGM emission to a tapered fiber. Both techniques were applied to study active WGMs in the PL spectra of raised Si-nc microdisks. We observed significant differences in the collected spectra using the two techniques. By analyzing the fraction of energy in a WGM escaping the microdisk due to radiative losses as a function of diameter and wavelength, we were able to interpret our experimental observations. Based on this analysis, we conclude that the far-field collection technique is applicable only when the radiative bending losses are greater than or comparable to the internal loss mechanisms in a microdisk.

This work was sponsored by the Si-based Laser Initiative of the Multidisciplinary University Research Initiative (MURI) under the Air Force Aerospace Research OSR grant FA9550-06-1-0470 and supervised by Gernot Pomrenke.

 

Fig. 1 (a) SEM of a fabricated Si-nc microdisk. (b) Far-field collection technique uses lenses to focus microdisk emission to spectrometer. (c) Micrograph and (d) schematic of tapered fiber collection technique.

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Fig. 2 PL spectra collected from an $8\mu \mathrm{m}$ diameter Si-nc microdisk using a fiber aligned to the edge of the disk (a), a fiber positioned on top of the disk (b), and the far field technique (c). PL collected from a $20\mu \mathrm{m}$ diameter disk using a fiber aligned to the edge of the disk (d) and the far-field technique (e).

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Fig. 3 Fraction of energy in a WGM that is lost radiatively for a $200\text{-}\mathrm{nm}$-thick Si-nc microdisk. When this fraction is large, the far-field collection may be used; as it approaches zero, the tapered fiber technique is preferable.

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