Before starting the transduction project described in the thesis, I had worked on the design and fabrication of optical photonic crystal cavities in YVO4 and YSO substrates using focused ion beam (FIB) milling. This work started as an undergrad- uate internship in the Faraon group. At that time, the group had only tried to make cavities using FIB with YSO (led by a previous postdoc, Dr. Tian Zhong, and some work also by Evan Miyazono), and my work involved extending those efforts into YVO4. Generally speaking, making FIB cavities in YVO was relatively successful, and we were quickly able to get higher quality factors in YVO4 compared to YSO for cavities at the same wavelength. This was largely thought to be due to the higher refractive index of YVO4compared to YSO.
The photonic crystal cavities consist of a triangular waveguide cross-section where the photonic crystal pattern is achieved by milling thin slots across the beam. We could control the photonic bandgap by the waveguide width, the slot depth, the slot width and the lattice constant between adjacent slots. The defect mode in the center of the cavity was introduced by perturbing the mirror lattice constant. The lattice constant was by far the most reliable parameter from the fabrication process since it was introduced in the milling pattern file and did not depend on any user input. The simulated electric field distribution of a TM cavity mode is shown in Figure A.1.
This design would result in simulated intrinsic quality factors nearing one million, so the fabricated device quality factors were not limited by this, but more by our ability to perfectly reproduce the design using the FIB. The simulated cavity mode volumes were around 1 cubic wavelength.
Using this fabrication technique, I fabricated devices using FIB for different projects including optical quantum memories [175, 176], single rare-earth ions [108, 177, 178] and microwave-to-optical transduction [57], and others [179] during my time as a PhD student. This included devices for Er3+:YSO (𝜆∼1536 nm), Nd3+:YVO4 (𝜆 ∼ 880 nm), and Yb3+:YVO4 (𝜆 ∼ 984 nm). SEM images of a fabricated nanobeam cavity are shown in Figure A.2.
Figure A.1: Simulated electric field of the nanobeam cavity. a) Top view of the cavity field. b) Side view of the cavity field.
The general recipe for fabricating these resonators is provided in reference [75], but I will provide some additional insight here. On a given chip, normally 9 devices would be fabricated at a time before the devices were tested. It would take ∼3-4 hours to mill three triangular waveguides at a time. The time was on the longer side for the longer wavelength cavities (i.e. for coupling to erbium) since they required longer waveguides (25 𝜇m compared to 15𝜇m for shorter wavelengths).
Typically each milling step was kept below 10 minutes to ensure that the sample would not drift to much during the step. There were a minimum of 6 milling steps for each beam. This includes milling on both sides of the waveguide and first starting at a high beam current (∼1 nA) to remove material quickly and then finishing at a low beam current (∼30 pA) to precisely shape the waveguide. The additional time was to align each beam current as we switched between them and for moving between devices. To create all 9 devices, this process would be repeated two additional times.
It was important to make sure the waveguide was milled to the correct width (typically within 10 nm of the design target). One convenient aspect of the FIB is that there is a SEM in the same tool so it was relatively easy to measure the waveguide width and make the required corrections to make it more narrow.
Figure A.2: SEM images of optical resonators from FIB milling. a) full nanobeam cavity. b-d) close up images of the photonic crystal patterns of the cavity.
Another important aspect of milling the triangular waveguides was the angle. We targeted to create an equilateral triangle cross-section. Naively, one would set the focused ion beam at that angle and mill the structure. However, the focused ion beam has a Gaussian beam shape, so the tails of the beam can also mill material and can change the angle by∼5° (i.e. interior angles at the top of the triangle was
∼65° if not corrected). The FIB angle was adjusted accordingly to minimize the deviation of nanobeam angle. It is also worth noting that this angle is sensitive to the alignment and focus of the FIB, so it is important to optimize this consistently every time.
The photonic crystal pattern and the 45°end couplers would then all be patterned in a single 3-4 hour session. So typically it would take a total of at least 12 hours to fabricate 9 devices. The milling of the slots would be recalibrated for every device as the shape of the slots highly depends on how well the FIB is focused, which was aligned by the user. For alignment, typically one waveguide was sacrificed for test milling the slots to make sure the dimensions were as perfect as possible. Again, we took advantage of the SEM to optimize this step.
Another issue during the milling of the photonic crystal slots was the drifting of the FIB relative to the sample. Typically, we would let the sample stage settle for some time until we did not notice any more movement. Also, in order to prevent any drift from charging effects, the SEM was left on at the correct current to null the additional positive charge from the FIB.
The 45°end couplers would be milled as the last FIB step, which was our method for coupling light into and out of the photonic crystal cavities. The devices were then placed in chrome etchant for one minute to remove the 50 nm chrome hard mask used during the milling process.
In terms of the highest quality factors, we measured Q’s up to∼25,000 and∼50,000 at wavelengths of∼900 nm and∼1050 nm, respectively, in YVO4. We also measured Q’s up to 70,000 at a wavelength of∼1500 nm in YSO.
A p p e n d i x B
TRANSDUCER DESIGN AND SIMULATION
For𝑍1-𝑌2transduction, we used a TE mode resonator (parameters are in Table B.1).
The designs for TE and TM mode cavities on sapphire are shown in Table B.2 and Table B.3.
Table B.1: Optical cavity geometry parameters—YVO TE mode
Parameter Value
Waveguide Height 225 nm Waveguide Width 600 nm Waveguide Length 100𝜇m
𝑎0 312.5 nm
𝑟∥,0 50 nm
𝑟⊥,0 50 nm
𝑎𝑡 275 nm
𝑟∥,𝑡 20 nm
𝑟⊥,𝑡 20 nm
Mirror Periods 0, 25 Taper Periods 15
Table B.2: Optical cavity geometry parameters—sapphire TE mode Parameter Value
Waveguide Height 225 nm Waveguide Width 600 nm Waveguide Length 100𝜇m
𝑎0 325 nm
𝑟∥,0 60 nm
𝑟⊥,0 70 nm
𝑎𝑡 280 nm
𝑟∥,𝑡 20 nm
𝑟⊥,𝑡 20 nm
Mirror Periods 0, 25 Taper Periods 15
Table B.3: Optical cavity geometry parameters—sapphire TM mode Parameter Value
Waveguide Height 300 nm Waveguide Width 600 nm Waveguide Length 100𝜇m
𝑎0 370 nm
𝑟∥,0 125 nm 𝑟⊥,0 115 nm
𝑎𝑡 310 nm
𝑟∥,𝑡 20 nm
𝑟⊥,𝑡 20 nm
Mirror Periods 4, 25 Taper Periods 15
A p p e n d i x C