nanophotonic waveguides on rare-earth doped crystals

This fiber taper coupling method holds promise for integration into silicon nanophotonic resonators on crystals doped with rare earth ions and enables highly efficient quantum memories and solid-state quantum light-matter interfaces. As we will see in the next section, rare earth ions (REIs) in solids have been shown to be a very promising potential platform for the implementation of both QLMI and quantum memories.

Figure 1.1: Schematic of a quantum network connecting two nodes (represented by atom traps) with an optical fiber carrying a photon with the quantum informa-tion

Rare-earth ions for quantum information applications

Repeated applications of entanglement exchange between pairs of entangled particles allow the two endpoints to eventually share an entangled Bell pair, even though the distance between them is too great for any single photon to have traveled all the way between them. As part of this scheme, a necessary component is a quantum memory that can store quantum states that we can read on demand, since the entanglement exchange process is probabilistic and thus the photon from each Bell pair will have to are held in memory for some time while waiting for its counterpart to prepare before they can be measured at the Bell base for scramble exchange.

Nanophotonic coupling interfaces

As such, it is beneficial for us to investigate more efficient methods of coupling laser light from optical fibers to the silicon nanophotonic waveguides that we will deposit on top of the REI-doped crystal. The silicon waveguide will taper along the region of overlap with the tapered fiber to adiabatically change the effective mode index from that of the fiber to that of the silicon to achieve maximum transmittance and minimal reflection or scattering.

Figure 1.2: Photonic crystal triangular nanobeam resonator fabricated in Nd:YSO using focused ion beam milling

Overview of thesis

We also study photonic crystals and how they create a band gap and reflect light so that we can measure the coupling efficiency at the fiber-waveguide interface. The results of the fabrication process and coupling measurements are then presented and discussed in Chapter 5.

THEORETICAL BACKGROUND

Electromagnetic wave theory Wave equationWave equation

For a given choice of z-wavenumber k, we can solve for the eigenvalue ω as part of the eigenvalue equation. Burek et al [35] also present an alternative rewriting of this adiabatic condition in terms of the effective mode index.

Figure 2.1: Schematic of a tapered fiber with relevant lengths labeled. Image from [39].

Photonic crystals

First, this is consistent with the direct reflection calculation earlier, where we saw that there is perfect reflection when each layer has a thickness equal to λ/4. Looking at the length of the waveguide (ie the axis of light propagation from left to right), this appears to be a remarkably similar system to the multilayer film considered earlier.

Figure 2.2: Schematic of a quarter wave stack, which is the simplest 1D photonic crystal

Acid fiber etching

First, it helps to wash off any residual HF on the fiber and results in cleaner taper [36]. Additionally, for a given choice of organic solvent, this method still has the potential for a wide variety of possible fiber taper geometries by translating the fiber up or down during the etching process.

Figure 2.6: Sample fiber illustrating the possibility of creating fibers with multiple

TAPER GEOMETRY DESIGN

Photonic crystal simulations

Another important parameter of the photonic crystal mirror is the bandwidth, which measures the range of wavelengths of the incoming light that it can effectively reflect. Light was then sent into the waveguide in the fundamental TM state and the power transmitted to the other end of the waveguide was calculated. More systematically, we then varied the width of the support beams and plotted the simulated transmittances as shown in Fig.

At the same time, we also need to determine the positions of the support beams relative to the photonic crystal holes that will be formed on the waveguide. As such, for our final design, we chose to place silicon support beams width 300 nm placed 5 µm in front of the photonic crystal holes to balance the contribution to structural stability and the negative impact on reflectance.

Final taper geometry design

3.20, and so the supports would not provide much stability to the breakwater as it is too close to the anchor point. Therefore, to calculate a more accurate estimate of the total reflectance of this structure, it would be ideal to simulate the entire structure as shown in Fig. However, we were unable to do this in this project as there are structures with very different length scales in this geometry, making meshing and numerical convergence difficult and time consuming.

Nevertheless, we expect the effect of this interference to be minimal since the tip of the fiber is placed several microns away from the support beams, which corresponds to several wavelengths of distance since λ0=1536 nm. This chapter describes in detail the procedures for the three main parts of the experimental setup – etching the fiber to form a taper, etching the silicon wafer to make a tapered waveguide and a photonic crystal mirror, and aligning the fiber with the waveguide to the coupling efficiency of the interface.

Optical fiber etching Setup constructionSetup construction

The fibers were placed with a 5 cm overhang above the holder and the coating was removed from the last 1.5 cm of the fibers to expose the cladding. In addition, the relatively fast HF etch rates tend to lead to surface roughness on the fiber surface, which can cause scattering and loss of strength. In the first etching step, the fibers are gradually lowered until the tip of the fiber reaches the thio-xylene-HF boundary.

The fiber is lowered to position x−5.5 mm, which is 2 mm lower than the etch height during the first HF etch. We terminate the buffered RF etching when the length of the fiber cone is approximately 300 µm or shorter.

Figure 4.2: Fiber holder used to clamp the fibers during acid etching.

Waveguide fabrication

Since we will be using negative photoresist, the areas of the resist exposed to the e-beam will cross-link and become resistant to dissolution in the developer. The width of the boundary between the yellow and green rectangles is determined by the BHF etch rate in the last step of the fabrication process, as shown in Figure 4.7, as the SiO2 layer under the top silicon layer would be etched, resulting in possible undercutting of the top Si layer.

Finally, the oxide layer is etched in 25-minute buffered HF, leaving undercut portions of the top silicon layer hanging above an air gap. Three arrays of waveguides are etched onto this wafer, each consisting of 64 individual copies of the waveguide.

Figure 4.6: AutoCAD design for a typical tapered waveguide with various colors indicating various features of the structure.

Fiber-waveguide coupling

In order to properly align the fiber with the waveguide, the waveguide is observed with a confocal microscope (Figure 4.11b) with an LCPLN50XIR objective lens, which has a 50x magnification and provides a field of view of about 80 µm. At the same time, a side view of the fiber is monitored with a USB camera to align the fiber vertically and verify that it is indeed touching the waveguide chip (Figure 4.11d). The fiber is then moved in the x (transverse) direction using a piezoelectric stage while being observed under a confocal microscope until it appears aligned with z.

Finally, the fiber is moved in the (axial) direction and any changes in the power meter reading are observed. a) Fiber carrier placed on top of the rotary stage and the piezoelectric translation stage. The untapered end of the fiber is spliced with an optical connector and connected to the EDFA.

Figure 4.10: Schematic of optical coupling experiment. The silicon waveguide is tapered in the dimension going into the page and has a constant thickness, and thus appears as a rectangle here.

Fiber geometry characterization Fiber taper geometryFiber taper geometry

The entire cone is approximately 200 µm long, and we measure an initial half-cone angle of 12.5◦ for this initial portion of the fiber. In our simulations, the design taper length of 25.8 µm was assumed to be measured starting from the point where the fiber had a radius of 1 µm. Finally, we observe the diameter of the fiber at the tip, which we measure to be approximately 51 nm.

The dashed white line indicates the boundary between portions of the fiber that were exposed to HF only and portions that were exposed to buffered HF after HF. This can be a problem as these properties can lead to scattering of the light guided by the fiber and greatly reduce the coupling efficiency if they are of the order of one wavelength.

Figure 5.1: Optical microscope view of tapered fiber at different etch times, showing how the end of the etch was determined by observing whether the long and thin taper portion at the fiber tip was present.

Waveguide geometry characterization

A cross-sectional measurement of the top silicon layer gives a thickness of 259 nm, which is close to the expected thickness of 300 nm. We see that there is very low reflection with most of the light passing through because the hole size no longer creates a band gap at the light frequency. If we rerun our simulation in Figure 5.6, we see that this smaller hole size gives us a greatly reduced reflection performance, with most of the light passing straight through, because we no longer have a band gap at the light frequency.

These low-energy electrons then interact with the resist, causing exposure and cross-linking of the resist molecules in areas that may be far away from the original beam location. Other options include lowering the dose of the waveguide taper region or by changing the distance of the boundary from the waveguide so that they are physically further apart.

Figure 5.6: Reflection simulation of photonic crystal with actual fabricated hole sizes of 264 nm by 100 nm

Coupling efficiency measurements Fiber observationsFiber observations

Finally, to measure the fiber-to-wave coupling efficiency, we place a tapered fiber next to a tapered waveguide and make fine adjustments to the angle of the fiber until it touches the surface of the waveguide. Therefore, we take care of these two observations to verify that the fiber is in contact with the silicon surface. We believe we are observing scattering at these waveguide points because they are all vertical surfaces that can scatter any IR light coming from the fiber.

Therefore, this measured peak in reflectance was likely the result of the fiber passing over the optimal coupling location. The first is our poor alignment of the fiber with the waveguide, which results in incomplete transmission of power in the waveguide.

Figure 5.8: Optical (left) and IR (right) images of tapered fiber with EDFA light sent through it

CONCLUSION

Future Directions

Other possible variables to optimize for include hole size bias as well as how far from the boundary the holes are located, as we suspect that most of the proximity effect arises from the doses to the boundary. There are also several opportunities to improve our second point of difficulty, which is the difficulty of properly aligning the fiber with the waveguide to achieve optimal coupling. Part of the reason is probably due to the fact that the waveguide taper is extremely narrow in the region where most of the light is coupled from the fiber into the waveguide, and thus any transverse displacement of the fiber will cause the fiber to miss the waveguide entirely and instead couple the light into the air.

To circumvent this, it may be possible to consider reducing the waveguide taper rate or increasing the waveguide minimum width. One possible method could be to try to automate the fiber alignment procedure, since our piezoelectric controller has inputs that can be used to automatically adjust the output voltage, thereby precisely controlling the fiber position.

BIBLIOGRAPHY

Parameter control, characterization and optimization in the fabrication of optical fiber near-field probes”.