The limitations on Q stem from a number of possible factors, including intrinsic material ab- sorption, etch-induced surface roughness and surface-state absorption, and other fabrication irregu- larities that prevent ideal replication of a given design. These issues aside, the fundamental design of these cavities had left room for improvement, and as such, the focus of this chapter primarily lies here. Our main objective is to consider simple design rules that can be used to significantly reduce the vertical losses from these structures, while maintaining or even improving upon the in-plane losses. In section 2.2, we describe a simple picture which illustrates that the vertical radiation loss of a mode is characterized by the presence of momentum components within the light cone of the cladding of the host slab waveguide (WG). We then consider (section 2.3) the use of symmetry to eliminate in-plane momentum components (k ⊥ ) at k ⊥ = 0 (DC), thereby reducing the vertical loss in the structure. Drawing heavily from chapter 1, we summarize the different defect modes available in hexagonal and square lattice PCs, and proceed to choose target symmetries for modes in these lattices based upon the constraints they impose on the dominant field components of the modes. In section 2.4, we propose simple defect geometries that support such modes and present the re- sults of three-dimensional (3D) finite-difference time-domain (FDTD) calculations of their relevant properties. In section 2.5, we consider further improvements in the designs based on a Fourier space tailoring of the defect geometries that reduces coupling of the mode’s dominant Fourier components to components that radiate. The results of FDTD simulations of these improved designs in a square lattice are presented, and show that a modal Q-factor approaching 10 5 can be achieved by a careful consideration of the mode and defect geometry in Fourier space. Similar considerations are given in sections 2.6 and 2.7, where we consider the design of high-Q defect modes within standard and compressed hexagonal lattice photonic crystals. Comparable results in terms of Q ( ∼ 10 5 ) and V eff
The z-scan measurement was carried out by moving the microcavity along the propagation direction o f the input beam. The microcavity is translated from z = - 150 |im to z = 150 |im w ith the beam being kept centred in the aperture o f the microcavity. The input signal for all measurements is placed as close to normal incidence on the m icrocavity as the measurement setup allows. The optimum focus position which is the position which maximizes the TPA response is set as being z = 0 |jm. This optimum focus position does not correspond to the z = 0 |jm position as outlined in the theory as experimentally this position can not be found (as all that is found experimentally is the position which maximises the level o f the TPA generated photocurrent and not the position with the smallest spotsize centred in the spacer region o f the cavity). The optical power on the microcavity was kept constant at 10 m W for the z-scan measurements. As z increases the microcavity is being moved away from the lens. A t each z position the spectral dependence o f the microcavity with TPA dominant is measured. This spectral response is asymmetric w ith the TPA response showing stronger wavelength dependence for wavelengths which are greater than resonance, see Fig. 5.2. The maximum photocurrent fo r each focus position is recorded, see Fig. 5.3. It is seen that the dependence o f the peak TPA response on focus position is asymmetric about z = 0 )jm. For positions with z > 0 fxm less TPA is generated than for equivalent distances o f z < 0 |im.
Abstract: For applications in sensing and cavity-based quantum computing and metrology, open- access Fabry-Perot cavities – with an air or vacuum gap between a pair of high reflectance mirrors – offer important advantages compared to other types of microcavities. For example, they are inherently tunable using MEMS-based actuation strategies, and they enable atomic emitters or target analytes to be located at high field regions of the optical mode. Integration of curved-mirror Fabry-Perot cavities on chips containing electronic, optoelectronic, and optomechanical elements is a topic of emerging importance. Micro-fabrication techniques can be used to create mirrors with small radius-of-curvature, which is a prerequisite for cavities to support stable, small-volume modes. We review recent progress towards chip-based implementation of such cavities, and highlight their potential to address applications in sensing and cavity quantum electrodynamics.
Since the first observation of exciton-polaritons in a strongly coupled microcavity, 1 planar microcavities have become a standard tool for studying their fundamental proper- ties. The bosonic nature of polaritons allows for observation of Bose-Einstein condensation in a non-equilibrium system up to room temperature, 2–6 and their non-linear properties give rise to a range of interesting physical properties, includ- ing bistability 7 and bright and dark solitons. 8–11 When polari- tons undergo condensation within a microcavity, coherent light is emitted and the cavity acts as a polariton laser. Since polariton lasing does not require population inversion, it can have a lower threshold than conventional lasers. 12
riers may relax and form bright exciton-like polaritons at large wavevector, which in turn relax down the polariton dispersion via spontaneous or stimulated scattering un- til they reach the ground state and join the condensate. Both the changes in population dynamics and the pres- ence of free carriers will result in changes of the relative transmission, but they will do so on the short timescale required for carriers to form polaritons, reach the ground state and leave the cavity. Both are typically on the order of tens of ps . Even considering a possible slow-down of relaxation at small carrier densities, an upper limit for this timescale is given by the bright exciton lifetime. For high-quality quantum wells, it may be as short as tens of ps, but even for low-quality structures, it will usually not exceed the bulk value of about 1 ns . Therefore, bright carriers fail to explain the long timescale seen in the ex- periment. This suggests that optically dark excitations play a significant role for long times after non-resonant excitation.
Introduction With the advent of highly controlled semiconductor epitaxies, both elec- tronic and photonic wavefunctions and their interactions can be specifically manipu- lated. This has been the basis of the immense success of vertical cavity surface-emitting semiconductor lasers (VCSELs), which couple quantum well emission with high effi- ciency into a single cavity photon mode. However, because of the large carrier density under operating conditions, the system shows weak coupling of light and matter and the dispersion relations of the electron±hole pairs and the cavity photons remain free- particle like (quadratic). It is thus reasonable to treat carriers and photons as indepen- dent objects. The availability in recent years of heterostructures in which resonant photon and exciton modes can become strongly coupled changes this description pro- foundly, leading to the clear observation of mixed photon±exciton modes (polaritons). These exciton polaritons possess rather different emission and absorption properties to the bare quantum wells [1, 2], however, there is still strong discussion as to whether new physics operates in the low density linear regime since most experiments can be straightforwardly explained using a non-dispersive oscillator model [3 to 5]. At high occupation densities, it is possible to saturate the exciton oscillator strength, in which case the strong coupling regime is destroyed and the system can once again be simply
persion and are completely off the branches of the unperturbed lower polariton dispersion. They are not exactly at the resonant Rayleigh scattering energy either, as sug- gested in recent experiments. 7,18 Polariton branches, corre- sponding to different scattering channels cross and anti- Hermitian coupling, leads to their attraction and the flattening of the dispersion in that region 共 as for the mea- sured dispersion around k ⫽ 0, Fig. 3 兲 . The emission is ex- pected to be particularly intense at these crossing points be- tween branches. The branch, corresponding to the pump- pump scattering channel, completely overlaps with the perturbed polariton dispersion in the entire region between 0° and 35° 关 Fig. 5 共 a 兲兴 and is responsible for the strong para- metric luminescence observed in the absence of a probe beam. 10 On the other hand, its crossing with the branch cor- responding to the pump-signal scattering channel, is respon- sible for the bright emission spot at the pump back-scattering angle of ⫺ 16.5° degrees, seen in Fig. 2. This is the origin of the enhanced coherent backscatter observed universally in semiconductormicrocavities. In addition, the crossing point between the pump-signal and signal-signal branches is also exactly at the pump back-scattering angle of ⫺ 16.5°, and results in the buildup of efficient low-energy off-branch emission at that angle.
A schematic diagram of a typical structure is shown in Fig. 1(a). The structure consists of a GaAs cavity ( is the wavelength of light in the medium) surrounded by 20 (below) and 17 (above) layers of Al Ga As–AlAs high reflectivity Bragg mirrors. The quantization of light in the vertical direction with free propagation within the plane leads to the approximately quadratic photon dispersion shown in Fig. 1(b). Two sets of three In Ga As quantum wells are embedded within the GaAs cavity and provide 2-D excitonic states, which are also confined in the vertical direction. Pro- vided the broadenings of both the exciton and photon states are small compared to their characteristic interaction energy [see Fig. 1(b), the vacuum Rabi splitting is 6 meV for the sample investigated], the strong coupling limit  is achieved where new quasi-particles arise, termed cavity (exciton)–polaritons. As a result of the coupling, pronounced anticrossing of the exciton and cavity mode dispersions is observed, leading to the formation of new polariton branches with dispersion relations possessed by neither photons nor excitons alone [Fig. 1(b)]. Most notably, the lower polariton branch exhibits a dispersion which is photon-like at small wave vector and exciton-like at large wave vector, with a point of inflection in the dispersion between these two extremes, as shown in Fig. 1(b). It is this dispersion which leads to much of the new physics reported in the present paper. It gives rise to new energy and wave vector conserving scattering processes, it has a minimum at finite energy as opposed to the dispersion of polaritons in three dimensions, and its shape is controllable by changing the detuning , the energy separation between the uncoupled exciton and photon modes.
We present next the basic findings of Ref.  that relate the frequency shift and loss of amplitude to undetected Rayleigh scattering. The analysis is valid for a single four-level atom–two ground states and two excited states–with constant coupling strength to a weak coherent drive. If we neglect spontaneous emissions, it serves as closed four-level model. In practice it is an approximation to a 4-level submanifold that shuttles backward and forward in response to spontaneous emission within the larger angular momentum manifold of our experimental system [see Fig. 1(a)] as we track the coherence through many scattering events. It neglects differences in detunings and Clebsh Gordon coefficients, but works rather well because we consider time scales that are short compared with the long-time optical pumping limit. Using quantum trajectories [23, 26], we follow the evolution of a ground-state coherence, | g = (|g − + |g + )/
sity and temperature depend logarithmically on this length scale. Due to the peculiarity introduced by the 2D character of semiconductormicrocavities, the grid uniform in energy considered in Ref. 18 is not well suited for the study of the transition towards BEC. Instead, a uniform grid in k space, related with the inverse of the quantization length, L c ⫺ 1 , has to be considered. Unfortunately, the number of levels that one has to consider for the description of the polariton dy- namics is dramatically increased, and a numerical calculation that includes all the possible polariton-polariton scattering processes is not possible. Thus some simplification has to be done, which still allows to describe satisfactorily the polar- iton dynamics, and to predict the possibility of Bose-Einstein condensation.
small region in the center of the Gaussian WP is expected to excite a single soliton whose size is determined by the polariton-polariton interactions and the cavity parameters . At higher WP powers, the area across the injected polariton wave packet where solitons may be excited becomes larger than the soliton size, so multiple bound solitons are triggered. This is similar to atomic condensates, which break up into soliton trains when the condensate size is larger than the condensate healing length . Figures 2(a) – 2(e) show spatiotemporal profiles of solitons for different WP powers. The number of created solitons increases with the WP power. At first, at a WP power of 0.3 mW, only one soliton is excited [Fig. 2(a)], whereas at 0.5 mW two parallel soliton traces are observed [Fig. 2(b)]. Notably, as the WP power increases, the spacing between solitons gradually increases, and more soliton traces appear at higher WP power [Figs. 2(d) and 2(e)]. Profiles in time of the five-peak and three-peak structures are shown in Figs. 2(g) and 2(h) with the FWHM of a single peak ranging from 4 to 7 ps (corresponding to ≈ 8–14 μ m along the x axis). All solitons travel at the same speed, indicating the formation of stable soliton patterns. Figure 2(f) shows FIG. 1 (color online). (a) Schematic diagram of the experiment.
In conclusions, vertical cavitysemiconductoroptical amplifiers VCSOAs based GaInNAs/GaAs quantum wells QWs have been designed using MATLAB® program. Device analyses are based on the theory of the Fabry-Perot semiconductoroptical amplifier (SOA). VCSOAs are usually made by sandwiching a thin layer of high optical gain between two epitaxial growths of distributed Bragg mirrors (DBRs). Once the correct composition of material is selected for operating at 1.3 µm emission wavelength, the design is moved to the Bragg mirrors with different Al composition and into dilute nitride QWs in an active region. In VCSOAs, mirror with high reflectivity are necessary to reduce the resonant cavity losses and to achieve stimulated emission process. In VCSOAs, the decreased top mirror reflectivity allows for the higher pump power to achieve a higher saturation output power without losing gain.
pany very strong, superlinear near exponential increases in k s 0 intensity, characteristic of a process with gain, stimulated by transitions to a final state with macroscopic occupancy. Such final state stimulation can occur for any bosonic quasi-particle; the transition rate is proportional to Ž 1 q N final . , where the 1 describes spontaneous processes, and N final describes stimulation of the transition by occupa- tion of the final state. By contrast to fermionic particles, N final for bosons can be greater than one and gives rise, e.g. to stimulated emission in lasers where stimulation occurs when the occupancy of a photon mode of the cavity exceeds unity. 1 Such stimulation behaviour is characteris- tic of any bosonic particle. Since excitons are bosons Ž although their constituent electrons and holes are fermions . and photons are bosons, polaritons are expected also to exhibit bosonic behaviour such as final state stimulation. The small polariton density of states arising from the small polariton mass, of order 10 4 times smaller than for exci-
Figure 3 gives an overview of the technological process to realize the chip by wet-etching both the substrate and the superstrate in the same way with mirror-inverted channel patterns. First both have to be thoroughly cleaned and prepared for photoresist wetting. Then both are spin-coated with the photoresist; different resist options are possible   . Then the latter is exposed to ultraviolet light in the pattern of the channel lay-out, de- veloped, and hardbaked. The opening in the photoresist layer allows for wet-chemical etching of the substrate and superstrate by buffered hydrofluoric acid. The wet-etching causes half-round cross-sections (giving half-cy- lindrical channels). After photoresist descum in an oxygen plasma the fluid inlet holes have to be drilled or sand-blasted. Then sub- and superstrate are aligned and bonded by pressure and heat treatment with severe alignment tolerances of less than 1 µm . At the bottom of Figure 3 a microscope image of a channel cross- section after bonding of sub- and superstrate is shown; as intended no optical interface between both chip halves can be observed. (Note that in this case the chip has only been transversely sawed to make the microscope image of Figure 3 possible.)
Optical measurements. The optical measurements are performed in a liquid helium flow cryostat with a base temperature of ,10 K. The PL is excited using a continuous wave (CW) or pulsed laser tuned to 850 nm, focused to a ,1 m m diameter using a 503 microscope objective (NA50.42). For the time-resolved measurements, presented in Figures 2 and 3 a Ti:Sapphire laser with a pulsewidth of ,100 fs is used to excite the PL. The emission from a single QD is filtered using a single grating spectrometer and detected with a charge coupled device (CCD) camera or avalanche photo-diode (APD), which has a time-resolution of ,350 ps. In the case of the g (2)
In order to shed light on the origin on the central peak in the RRP, a two-level model for the exciton-cavity coupling is employed to calculate the energies of the uncoupled cavity and exciton modes. 2 These are calculated at each bias, to- gether with the vacuum Rabi splitting ( D VRS ), from the mea- sured energies and relative intensities of the dips in reflec- tivity. The results are shown in Figs. 4~a!– ~b!. The energy of the uncoupled cavity mode @open squares, Fig. 4~a!# is found to be independent of field, as expected. The energy of the uncoupled exciton @filled squares, Fig. 4~a!# decreases with increasing field due to the quantum confined Stark effect, as does D VRS @filled diamonds, Fig. 4~b!# due to the decrease of exciton oscillator strength. 20 The magnitude of the Stark shift in Fig. 4~a! and the variation of D VRS are in good agreement with the results of solution of a Schro¨dinger equation for the quantum well ~QW! excitons, shown by the smooth solid lines in Figs. 4~a! and 4~b!.
Non-classical light sources offer a myriad of possibilities in both fundamental science and commercial applications. Single photons are the most robust carriers of quantum information and can be exploited for linear optics quantum information processing. Scale-up requires miniaturisation of the waveguide circuit and multiple single photon sources. Silicon photonics, driven by the incentive of optical interconnects is a highly promising platform for the passive optical components, but integrated light sources are limited by silicon’s indirect band-gap. III–V semiconductor quantum-dots, on the other hand, are proven quantum emitters. Here we demonstrate single-photon emission from quantum-dots coupled to photonic crystal nanocavities fabricated from III–V material grown directly on silicon substrates. The high quality of the III–V material and photonic structures is emphasized by observation of the strong-coupling regime. This work opens-up the advantages of silicon photonics to the integration and scale-up of solid-state quantum optical systems.
The previous scheme for shifting the frequency involved one AOM and a travelling wave EOM, which generated a sideband near 240 MHz [25, 26]. This sideband itself was used as the probe and its absolute frequency was tuned to the resonance of choice. The downside of this technique is that the carrier, albeit fairly far-detuned from the atom-cavity resonance, remains on continuously. This means that residual off-resonant light gets into the cavity, and experiments with Dan Stamper-Kurn in 2001 revealed that this was a very significant source of atomic heating. At that time we discovered that switching off the probe by eliminating the EOM sideband was insufficient, and that we also had to switch off the upstream AOM. This increased the trapping times from below 1 ms to several tens of ms. Unfortunately we never understood the discrepancy between these lifetimes and those of Ref.  (where the AOM was not switched off and a 28 ms trap lifetime was achieved). However, this concern alone does not explain the change to the two-DP-AOM configuration, since we seemingly resolved the early scheme’s main problem by switching off both the EOM and the AOM. The other concern that led to the change was that in the EOM scheme, the carrier still shines while the probe is on. This means that a known source of unwanted light gets into the cavity during experiments in which a probe is needed. It is a near certainty that we could not have done the experiments we eventually did (e.g., Chapter 4) without eliminating this problem.
Figure 2 shows the equilibrium distribution function under continuous pumping for a cavity having a normal-mode splitting of 5 meV containing a single QW, and for zero detuning of cavity and exciton modes. For all the curves the pump power absorbed by the single QW is set to be 4.2 W/cm 2 between k ¼ 3 10 6 and 5 10 6 cm 1 , roughly equivalent to an excess of energy of 20 meV. Taking into account only the acoustic phonon scattering (curve a in Fig. 2), a thermalised population is seen only beyond k ¼ 2 10 4 cm 1 (the bottleneck region) where the polaritons accumulate. Equilibrium