To this end, the propagation of light in photonic crystals and the creation of cavities by creating defects in the photonic crystal lattice are discussed. The dashed line corresponds to Q∞ when there is no substrate near the plate.
Spontaneous Emission
Practical implementations and related issues are also outlined. coupling between an atom and a large number of states must be considered and, as mentioned earlier, the interaction energy for each mode depends on the orientation of the atomic dipole with the field polarization. It should be noted that the Weisskopf-Wigner theory predicts an irreversible exponential decay of the excited state of an atom and is valid in the presence of a continuum of electromagnetic modes.
Atom in a Cavity
Weak Coupling
Similarly, rearrangement of the κ terms in Γc shows that inhibition is observed by increasing the cavity Q and detuningδ. Furthermore, under the simplifying assumptions of Γ0 = 0, δ= 0, and atom placement at the field antinode, the enhancement in the spontaneous emission rate due to the cavity is found to be proportional to Q/V, where V is the cavity mode. volume.
Strong Coupling
The solid line indicates the spectrum of the coupled system and the dotted lines indicate (Lorentzian) spectra of individual eigenstates for the case of a single photon in the cavity. Thus, a single photon in the cavity can dramatically change the transmission through the cavity. ω/V), again pointing to highQ/.
Atom-Optics to Semiconductor Cavity QED
Quantum Dot Dynamics
The second is the observation of a third peak [16] between the two peaks predicted by the Jaynes-Cummings model in the strong coupling regime (see right panel of Figure 1.2). Rich theoretical and experimental work in the field of semiconductor cavity QED is rapidly underway.
Thesis Organization
Practical Considerations
As already mentioned, the bandgap range depends on the dielectric contrast in the structure. Such structures have periodic permeability in one or two in-plane dimensions and uniform (in-plate) permeability in the remaining dimension.
Computational Electrodynamics
The spectral location of the photon band is a function of the slab thickness (see Figure 2.3). In practice, frequency domain simulations are performed for the defect-free case to reveal the spectral extent and location of the photon gap.
Photonic Crystal Cavities
Fabry-Perot Etalon Model
The purpose of the taper is to reduce the mode mismatch by gradually increasing the (imaginary) wave vector κ (see equation 2.16) in the mirror section. In the mirror-waveguide-mirror geometry discussed above, a taper is now introduced into the twelve-hole mirror section by linearly decreasing (in steps of 2%) the radius of the six holes in the mirror section closest to the waveguide section (as well as a corresponding step contraction of the same amount), that is, the first hole of the mirror section has a radius equal to 88% of the final holes. 9A technical point to note: the flux (through the plane) is first calculated without the mirror and subtracted from the flux in the presence of the mirror.
As previously noted, the slight decrease in effective cavity length appears in a blue-shift of the cavity wavelength. As seen in Figure 2.12 and in all tunings considered, the Q exceeded the Qs of the waveguide of holes. In addition, some holes in the immediate vicinity of the holes are modified to increase the cavity Q.
This can be seen by the distribution of the QD ensemble in the photoluminescence (PL) spectrum, evident in Figure 3.3, which is obtained by upper-band optical excitation of the QD layer.
Device Fabrication
- Wafer Preparation
- Resist Application
- Lithography
- Resist Development
- Dry Etching
- Wet Etching
- Resist Removal
- Subtleties
In the event that this does not work, evaporating a thin (≈10 nm) layer of gold on top of the e-beam resist layer usually helps the laser to register a height. In the worst case, this leads to the merging of relatively close features (see Figure 3.7). Therefore, the optimization of the CAIBE conditions for a symmetrical, vertical etching with beads offers an efficient technique for improving the etched hole sidewalls (see Figure 3.10).
In the first step, the sample is immersed (and mixed) in a series of solutions for a few minutes. During HF wet etching, the Al hydroxides formed from the AlGaAs layer float in the solution and deposit on top of the resist. In the first step of resist removal, the wafer is shaken in various chemical solutions and the residues that have accumulated on top are removed together with the resist layer.
The photonic band gap of the device is manifested in the suppression of the QD PL ensemble.
Q-Degrading Mechanisms
- Irregular Air Holes and Contour FDTD
- Remnant PMMA and Debris
- Non-vertical Sidewalls
- Effect of a Bottom Substrate
- GaAs-AlGaAs Interface and Crystal-axis Dependent Surface Roughness
As a result, the far-field radiation pattern of the cavity mode changes, which changes the total transmitted power [ 62 , 63 ]. The dashed line corresponds to Q∞ when there is no substrate near the plate. In Figure 4.9, the Q of the L3 cavity mode is calculated by varying the size of the air gap, t.
In one such experiment [ 16 , 65 ], several QD layers were stacked on top of each other up to the top surface of the photonic crystal plate. Temperature - The QD transition frequency can be varied by changing the temperature of the He cryostat [12, 13], or by local laser heating [67]. When the cavity is heated (by increasing the cryostat temperature), the condensate leaves the surface, thereby allowing reversible tuning of the cavity.
In this case, the improvement of the QD brightness is even more evident, as indicated in the right panel of Figure 5.1, and seen quantitatively in the plot of output power.
Photon Statistics and Correlations
It is a well-known property of the Poisson distribution that the standard deviation (square root of the variance), ∆n is equal to the square root of the mean, ∆n=√. Such a histogram is quantified by means of the second-order correlation function g(2)(τ), which is classically expressed in terms of light intensity I(t). In the quantum picture, the intensity is proportional to the photon number3,n(t), and this leads to [5].
The pulse repetition period was chosen to be larger than the radiative lifetime of the QD. For concreteness, it is proposed to fabricate the device in a GaAs wafer that has a gain medium (either QDs or quantum wells (QWs)) embedded in the center of the GaAs wafer. Four alignment marks are defined during e-beam lithography, along with the illumination of a 20 µm × 20 µm square in the left half of the outer rectangle.
The cavity region is placed in the middle of the 0.150 µm gap between the two gold squares so that the cavity region does not have gold directly above it.
Material System Optimization
The QD emission wavelength is highly size-dependent, and by increasing the size of the QD, its emission can be shifted to a longer wavelength. One has been the use of InAs/InP structures [49], which have a mismatch of ≈3%, while another technique [86] relies on covering the QD layer in a strain-relaxing GaxIn1−xAs layer. Further, this entire structure is sandwiched between higher bandgap [88] Ga0.32Al0.15In0.53As layers.
This composite structure is grown on an Al0.48In0.52As layer that is lattice-matched to an InP substrate. Alternatively, a hydrogen iodide (HI) etching chemistry can be used, as the corresponding iodides of In have lower sublimation temperatures. Because the plate layers contain Ga, Al, In, and As, it is critical to control the relative rate of etching byproduct formation for all these elements to obtain smooth and vertical sidewalls.
Preliminary fabrication experiments have shown this to be a major challenge [89], as can be seen from the non-ideal sidewalls of the fabricated microdisk in Figure 6.3(b).
InAs Quantum Dots in Si Cavities
The following recipe is for etching photonic crystal holes in GaAs using patterned electron beam resist (PMMA/ZEP) as the etching mask. When the Ar gas flow is turned on, the chamber pressure should be 2 × 10 − 4 torr, and this corresponds to an Ar flow rate of 3–4 sccm (standard cubic centimeters per minute). It is advisable to run the recipe for 2 minutes without sample in the source conditioning chamber.
After etching, the gas lines must be completely pumped out, and to prevent corrosion of the chamber diffusion pump, it is necessary to flow Ar when Cl2 is flushed. When opening the chamber for filament replacement, it is important to properly disassemble and clean the ion gun. In particular, dust particles between the closely spaced accelerator grids must be carefully removed using an N2blow gun for repeatable etching.
ICP-RIE Resist Stripping
A few operational notes on the use of the self-resolving frequency-domain software (MPB) and the finite-difference time-domain software (MEEP) are presented below. When simulating 3D structures that have incomplete confinement, i.e. there are radiation modes, it will happen that guided modes lying close to the light line have errors. For example, if the PML layer is applied in the +x direction, (x, y, z) must be independent within the PML.
Source Location: To successfully find a mode, a source should not be placed at highly symmetrical points, but should be located near an expected field anti-node. If a certain symmetry is enabled for the simulation, the source must be placed in the negative half-space. From the distance between the modes one can calculate the source Q required to excite only a certain mode in a narrowband simulation.
The detector does not need to be confined to the same location as the source location, but should be placed near the field antinode.
Lithography Mask Generation
Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature, vol. Yao, "Theory of quantum lysis emission from a strongly coupled single quantum dot photonic-crystal cavity system." Optics Express, vol Yokohama, "Extremely large group velocity dispersion of line defect waveguides in photonic crystal slabs," Physical Review Letters, vol.
Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Physical Review B, vol. Hugonin, “Enhancement of modal reflectivity by tuning geometry in microcavities of photonic crystals,” Optics Express, vol. Noda, “Theoretical investigation of a two-dimensional photonic crystal sheet with truncated conical air holes,” Applied Physics Letters, vol.
Noda, “Experimental demonstration of a full photonic band gap in two-dimensional photonic crystal plates,” Applied Physics Letters, vol.
