Optical Material Characterization Using Microdisk Cavities

With my vision I'm totally relying on the interference in the fiber transmission because I have trouble seeing the taper. After I was free from the clean room, I began to gain dominance over equipment in the test lab, giving me far too much contact with the New Focus laser repair department.

Quasi-normal Modes

Microdisks also support modes with higher vertical order (more than oneFzantinode along ˆz) which can be found using Eq. 1.6) using neff for the appropriate order sheet mode; however, the devices in this work only support the fundamental sheet modes. Comparison of approximate effective-index solutions with FEM results in Fig. 1.3 for two disk microdisk devices indicates the effectiveness of Eq. 1.6) to rapidly explore wide areas in parameter space.

Figure 1.1: (a) Perspective sketch of a microdisk and the e ±imϕ field dependence for a second-order mode (m = 35, p = 2)

Coupled-Mode Theory

In addition, the integral in the numerator of Eq. 1.10) makes |κcb| proportional to the ±2m Fourier spatial component of the roughness: R. The phase of the backscatter parameter (ϕo) determines the azimuthal orientation of the standing waves with respect to the roughness with the highest frequency as the mode (low frequency AC mode) standing more in low (high) index regions.

Figure 1.3: Comparison of the eigenvalues (k o ) found using effective-index and finite-element models for (a) TE modes in a Er 2 O 3 disk and (b) TM modes in a Si disk plotted against free-space wavelength [λ o = 2π/ ℜ (k o )]

Cavity Parameters

Since the phase velocity (vp) tangential to the disk edge can vary with radius (r), it can be found by its usual definition. While Veff generally scales with cavity size, this behavior can be misleading for slotted structures [18].

Taper Pulling and Molding

Conical drawing with fibers placed at the edge of the flame to create a small hot zone. 2.2(a,c); adjustments on a pair of goniometers ensure that the straight course of the cone is parallel to the surface of the specimen.

Figure 2.1: Process for producing dimpled fiber-taper probes. (a) Taper pulling with the fiber placed at the edge of the flame to produce a small hot zone

Microphotonic Testing with a Dimple-Taper Waveguide

Second, the loss is measured as a function of probe height (ˆz-direction) over the 11.6 µm wide GaAs meso. Since only the lowest part of the well affects the sample, this method can only determine the profile of the cone within ~1.25 µm of the surface. At voltages that give acceptable noise levels, the recess depth is still adequate for testing densely spaced planar devices.

A large phase mismatch exists between the cone and the microcavity due to the additional dielectric beneath the guided modes of the Si-core. Much of the surface roughness at the top of the waveguides is probably due to SiNx gradually exfoliating from Si.

Figure 2.3: Non-resonant insertion loss (a) as a function of axial position (ˆ x) as a narrow cantilever is moved along the taper length and (b) as a function of transverse position (ˆ z) as the dimple is raised above a mesa

Conclusions

In addition, the longer etch allows HF to penetrate defects in the silicon/oxide layers and partially undercut the BOX layer; it is uncertain whether these defects are process-induced or intrinsic to the Si layer in the original SOI wafer. The first demonstrations of vacuum Rabi splitting in this system, a result of coupling a single QD to localized optical modes of a surrounding microresonator, have been greatly aided by previous improvements to the design and fabrication of semiconductor microcavities. At the shorter wavelengths involved in these Rabi splitting experiments (740–1200 nm), the optical quality factors (Q) of the host AlGaAs microcavities were limited to Q≈2×104 – corresponding to a loss rate comparable to the coherent QD cavity switching rate.

A further reduction in optical loss would increase the relative coherence of the QD cavity system and enable greater coupling efficiency with the cavity mode. After estimating and removing the contribution of surface scattering to the losses in the cavities, we find that the residual absorption, consisting of losses in the bulk and on the surfaces, depends significantly on both wavelength and material composition.

Estimation of Scattering and Absorption Rates

The Urbach tail makes a small contribution in the 980-nm band (≤15 percent) and is otherwise negligible [132]. This leaves deep electron (hole) traps as the main source contributing to absorption of bulk material in the observed resonances. The calculated surface overlap ratio is Γ′TM/Γ′TE≈2.65 for p= 1 states in the 1460-nm band, where all surfaces of the wafer (top, bottom and etched edge) are treated equally.

For these modes, the measured absorption ratio is γa,TM/γa,TE in the AlGaAs (GaAs) microdisks, indicating the presence of significant surface state absorption in the AlGaAs resonators. Attempts to incorporate Er3+ into the Si material system, with erbium emission in the 1550 nm telecommunications band, have had limited success.

Figure 3.3: (a) Sample surface roughness measurement on a AlGaAs microdisk showing the disk edge extracted from a high-resolution SEM image and a fit to a circle

A few extra C2 ions are added to illustrate the symmetry of the crystal, even though they are not in the unit cell. Rare earth ions, however, are in the intermediate coupling regime, where the Coulomb and spin-orbit terms are approximately equal. In crystals, the inhomogeneous electric field of neighboring ions (i.e. the crystal field) splits the (2S+1)LJ terms of the free ion by breaking their degeneracy into MJ, but the field does not appreciably shift the levels of the free ions . ion case.

In the bixbyite crystal, ions at the C2 sites experience a crystal field without inversion symmetry [Fig. Thorough reviews of the optical processes in crystals containing rare-earth ions are available in Ref.

Figure 4.1: (a) The bixbyite unit cell for R 2 O 3 with the ionic radii approximately correct for Er 2 O 3

Optical Properties

Long-range spectroscopic data must also be corrected for second-order diffraction of the spectrometer, that is, the lattice equation for a given diffraction angle (θd) is simultaneously satisfied for wavelengths (λj) in two different orders (mj): a(sinθd−sinθi) =m1λ1 =m2λ2 where a is the lattice pitch and θi is the incident angle. Other pathways can also contribute to the upconversion process, but this pathway is consistent with pump dependence and involves the least energy mismatch between excitations: the phonon bath must supply or absorb the excess so that energy is conserved. The appearance of the Nth pulse serves as a marker for sampling the (N−1)th decay curve with a fixed delay - i.e. the pulse period separates the (N−1)th peak from its tail just before the Nth pulse.

As the mode moves through the optical transition, the resonances anticross (i.e., vacuum-Rabi splitting) and produce symmetric hybrid modes (i.e., cavity-polaritons) that appear in both cavity transmission and PL. Considering Rabi splitting in the context of linear absorption [213], we expect polaritons to form at 8 K around transitions originating from the lowest sublevel (Z1) of 4I15/2, and we observe excitation splitting from Z1 to all seven Stark sublevels . (Y1−7) of 4I13/2 at C2 lattice sites—the inhomogeneous distributions for the Y3 and Y4 subplanes overlap around 1516 nm. 4.14(b)], while the bare cavity modes tune as a quadratic polynomial of the pump power—the nonlinearity originates from Er3+ cooperative upconversion.

However, neighboring resonances between higher sublevels have significant dipole moments and may also contribute to polariton behavior—e.g., the Y2↔Z2 (C2) and Y3↔Z3 (C3i) transitions near 1537 and 1549 nm, respectively [ 178].

Figure 4.4: Microdisk transmission spectrum for quasi-TE modes of a cavity with R ≈ 20 µm; the fundamental radial-order WGMs are highlighted (gray).

Conclusions

Exploratory pulse measurements using a Tm3+ doped fiber amplifier at 1480 nm also indicate that some of the upper levels may be longer (about 100 µs). In summary, upconversion processes near transparency are fast enough to produce significant populations in all levels up to and including 4S3/2, and the 4I13/2 level is unlikely to be the first level to reach transparency when pumped at ~1480 nm. Finally, the spectral response of rare earth oxides can be tailored for specific applications.

As in III-V systems, high-quality epitaxy will become critical in controlling material structure and optical properties as we move toward CMOS-compatible rare-earth laser diodes and photodetectors.

Mach-Zehnder Interferometer

The most accurate method is to count only fringes starting at the beginning of the scan and to ignore the wavelength data from the laser. In the current implementation, the MZI reference signal is loaded into an (N×1) matrix and analyzed as a function of the matrix index. These positions in the matrix are separated in wavelength by half the fringe spacing, and they provide a piecewise function for interpolating the indices of the original vector at calibrated wavelengths.

The dependence of the fringe spacing on wavelength is included by quadratically scalingδfsat each "zero" crossing. The inset contains a 10-nm section of the calibration signal showing measured data points (∗) and the interpolated “zero” crossings (◦). b) Difference between the calibrated and raw wavelengths for a long Vidia laser scan.

Figure A.1: (a) Raw TE- and TM-polarized transmission spectra for a Si-SiO 2 microdisk after calibrating the wavelength

Pulse Optimization for EOSPACE Modulators

The output does not need to be stabilized to the same extent as the input, but movement of the output fiber should not cause the modulator input to shift. Before collecting data, it is wise to examine the optical signal produced by the modulator and a particular voltage source. 1The FPC may not be necessary when using polarization-maintaining (PM) fiber, but this procedure assumes that the polarization of a standard single-mode fiber must be matched to the PM input fiber of the modulator. . depending on the pulse width and amplitude.

In addition, the optical transmission between the pulses is increased by 1.2 dB compared to the transmission without the RF signal. Otherwise the laser is partially attenuated by the polarization filters and not by the LiNbO3 MZI in the modulator.

Effective Index for the HE 11 Mode

It is useful to include a few splitters in the optical path so that the pulses can be easily monitored without constantly breaking the fiber optic connections. The high extinction modulator (>40 dB) uses polarizing filters at the input and output and an additional port for fine tuning the DC bias, and the above procedure can be used to generate pulses with an extinction ratio> with one adjustment 62 dB. Once the bias and polarization have been optimized for maximum transmission, the input polarization should not be changed at any time.

Coherent Coupling to a Uniform Density of Dipoles

Painter, “Photoluminescence measurements of semiconductor microdisk resonators containing quantum dots using optical fiber tapered waveguides,” Phys. Vahala, “Ideality in a fiber-coupled microresonator system for application in cavity quantum electrodynamics,” Phys. Yamamoto, “Anti-photon stacking by a single quantum-dot-microcavity system in the strong coupling regime,” Phys.

Moos, “Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals,” Phys. The influence of structural disorder and light coupling on the excitonic response of semiconductor microcavities,” Phys.