Simulation technique of quantum optical emission process from multiple two-level atoms based on classical numerical method.

In this paper, we report a numerical method for analyzing optical radiation from a two-level atom. The proposed method can consistently consider the optical emission and absorption process of an atom and also the interaction between atoms through their interaction with a radiation field. The numerical model is based on a damping oscillator description of a dipole current, which is a classical model of atomic transition and is implemented with a finite-difference time-domain method. Using the method, we successfully simulate the spontaneous emission phenomena in a vacuum, where the interaction between an atom and a radiated field plays an important role. We also simulate the radiation from an atom embedded in a photonic crystal (PhC) cavity. As a result, an atom-cavity field interaction is sucessfuly incorporated in the simulation, and the enhancement of the optical emission rate of an excited atom is explained. The method considers the effect of the interaction between atoms through the radiated field. We simulate the optical emission process of the multiple atoms and show that an enhancement of the emission rate can occur owing to an atom-atom interaction (superradiance) (R. H. Dicke, Phys. Rev. 93, 99 [1954]). We also show that the emission rate is suppressed by the effect of the destructive dipole-dipole interaction under an out-of-phase excitation condition (subradiance).

Room temperature continuous-wave nanolaser diode utilized by ultrahigh-Q few-cell photonic crystal nanocavities.

Few-cell point-defect photonic crystal (PhC) nanocavities (such as LX and H1 type cavities), have several unique characteristics including an ultra-small mode volume (Vm), a small device footprint advantageous for dense integration, and a large mode spacing advantageous for high spontaneous-emission coupling coefficient (ß), which are promising for energy-efficient densely-integratable on-chip laser light sources enhanced by the cavity QED effect. To achieve this goal, a high quality factor (Q) is essential, but conventional few-cell point-defect cavities do not have a sufficiently high Q. Here we adopt a series of modified designs of LX cavities with a buried heterostructure (BH) multi-quantum-well (MQW) active region that can achieve a high Q while maintaining their original advantages and fabricate current-injection laser devices. We have successfully observed continuous-wave (CW) lasing in InP-based L1, L2, L3 and L5 PhC nanocavities at 23°C with a DC current injection lower than 10 µA and a bias voltage lower than 0.9 V. The active volume is ultra-small while maintaining a sufficiently high confinement factor, which is as low as ~10-15 cm3 for a single-cell (L1) nanocavity. This is the first room-temperature current-injection CW lasing from any types of few-cell point-defect PhC nanocavities (LX or H1 types). Our report marks an important step towards realizing a nanolaser diode with a high cavity-QED effect, which is promising for use with on-chip densely integrated laser sources in photonic networks-on-chip combined with CMOS processors.

Design of nanowire-induced nanocavities in photonic crystal disks.

We propose a novel type of nanowire (NW)-induced nanocavity based on photonic crystal disks, and we investigate its design by three-dimensional finite-difference time-domain calculations. We detail the confinement principle used in such a cavity and discuss the influence of geometric and material parameters on the cavity performance. Finally, we report on an optimized design presenting a quality factor Q=7.2×104, a mode volume as small as Vm=2.2(λ/nrNW)3, and a large confinement factor of the electric field energy in the NW Γ=65%, which shows good prospects for the realization of efficient NW-based nanolasers operating in the ultraviolet and visible ranges.

Enhanced electron-hole droplet emission from surface-oxidized silicon photonic crystal nanocavities.

We have observed electron-hole droplet (EHD) emission enhanced by silicon photonic crystal (Si PhC) nanocavities with a surface oxide. The EHD is employed as a massive emitter that remains inside the nanocavity to achieve efficient cavity-emitter coupling. Time-resolved emission measurements demonstrate that the surface oxide greatly reduces the nonradiative annihilation of the EHDs and maintains them in the PhC nanocavities. It is found that the surface-oxidized Si PhC nanocavity enhances EHD emission in addition to the Purcell enhancement of the resonant cavity, which will contribute to works on Si light emission and the cavity quantum electrodynamics of electron-hole condensates.

Design of nanowire-induced nanocavities in grooved 1D and 2D SiN photonic crystals for the ultra-violet and visible ranges.

Nanowire-induced SiN photonic crystal (PhC) nanocavities specifically designed for the ultra-violet and visible range are investigated by three-dimensional finite-difference time-domain calculations. As opposed to their silicon PhC counterpart, we find that the formation of nanowire-induced two-dimensional (2D) SiN PhC nanocavities is more challenging because of the low refractive index of SiN. We thus discuss optimization strategies to circumvent such difficulties and we investigate the influence of critical design parameters such as PhC geometry, as well as nanowire geometry and position. We also propose a novel nanowire-induced cavity design based on one-dimensional (1D) nanobeam PhCs. We finally report on nanowire-induced nanocavity designs in 1D (resp. 2D) PhCs presenting quality factors as high as Qc = 5.1 x 104 (resp. Qc = 2.5 x 104 with a mode volume Vm=1.8(λ/nrNW)3 (resp. Vm=5.1(λ/nrNW)3), which show good prospects for light-matter interaction in the near-ultraviolet and visible ranges.

Optomechanical oscillator pumped and probed by optically two isolated photonic crystal cavity systems.

Optomechanical control of on-chip emitters is an important topic related to integrated all-optical circuits. However, there is neither a realization nor a suitable optomechanical structure for this control. The biggest obstacle is that the emission signal can hardly be distinguished from the pump light because of the several orders' power difference. In this study, we designed and experimentally verified an optomechanical oscillation system, in which a lumped mechanical oscillator connected two optically isolated pairs of coupled one-dimensional photonic crystal cavities. As a functional device, the two pairs of coupled cavities were respectively used as an optomechanical pump for the lumped oscillator (cavity pair II, wavelengths were designed to be within a 1.5 µm band) and a modulation target of the lumped oscillator (cavity pair I, wavelengths were designed to be within a 1.2 µm band). By conducting finite element method simulations, we found that the lumped-oscillator-supported configurations of both cavity pairs enhance the optomechanical interactions, especially for higher order optical modes, compared with their respective conventional side-clamped configurations. Besides the desired first-order in-plane antiphase mechanical mode, other mechanical modes of the lumped oscillator were investigated and found to possibly have optomechanical applications with a versatile degree of freedom. In experiments, the oscillator's RF spectra were probed using both cavity pairs I and II, and the results matched those of the simulations. Dynamic detuning of the optical spectrum of cavity pair I was then implemented with a pumped lumped oscillator. This was the first demonstration of an optomechanical lumped oscillator connecting two optically isolated pairs of coupled cavities, whose biggest advantage is that one cavity pair can be modulated with an lumped oscillator without interference from the pump light in the other cavity pair. Thus, the oscillator is a suitable platform for optomechanical control of integrated lasers, cavity quantum electrodynamics, and spontaneous emission. Furthermore, this device may open the door on the study of interactions between photons, phonons, and excitons in the quantum regime.

Systematic study of thresholdless oscillation in high-ß buried multiple-quantum-well photonic crystal nanocavity lasers.

Buried multiple-quantum-well (MQW) 2D photonic crystal cavities (PhC) achieve low non-radiative recombination and high carrier confinement thus making them highly efficient emitters. In this study, we have investigated the lasing characteristics of high-ß(spontaneous emission coupling factor) buried MQW photonic crystal nanocavity lasers to clarify the theoretically-predicted thresholdless operation in high-ß nanolasers. The strong light and carrier confinement and low non-radiative recombination in our nanolasers have enabled us to clearly demonstrate very smooth lasing transition in terms of the light-in vs light-out curve and cavity linewidth. To clarify the thresholdless lasing behavior, we carried out a lifetime measurement and a photon correlation measurement, which also confirmed the predicted behavior. In addition, we systematically investigated the dependence of ß on the detuning frequency, which was in good agreement with a numerical simulation based on the finite-difference time-domain method. This is the first convincing systematic study of nanolasers based on an MQW close to the thresholdless regime.

Movable high-Q nanoresonators realized by semiconductor nanowires on a Si photonic crystal platform.

Subwavelength semiconductor nanowires have recently attracted interest for photonic applications because they possess various unique optical properties and offer great potential for miniaturizing devices. However, realizing tight light confinement or efficient coupling with photonic circuits is not straightforward and remains a challenge. Here we show that a high-Q nanocavity can be created by placing a single III­V semiconductor nanowire with a diameter of under 100 nm in a grooved waveguide in a Si photonic crystal, by means of nanoprobe manipulation. We observe very fast spontaneous emission (91 ps) from nanowires accelerated by the strong Purcell enhancement in nanocavities, which proves that very strong light confinement can be achieved. Furthermore, this system enables us to move the nanocavity anywhere along the waveguide. This configuration provides a significant degree of flexibility in integrated photonics and permits the addition and displacement of various functionalities of III­V nanocavity devices in Si photonic circuits.

Fast calculation of the quality factor for two-dimensional photonic crystal slab nanocavities.

We developed a method that can accurately calculate the theoretical quality factor (Q) of a two-dimensional photonic crystal slab nanocavity at a very high speed. Because our method is based on a direct calculation of the out-of-slab radiation loss rate, it does not suffer from in-plane loss, and this allows us to obtain the same Q with 0.18 times less calculation volume. In addition, we can obtain the Q immediately after finishing the cavity excitation, because our method uses only a snapshot of the wavevector space distribution of the resonant mode in contrast to the conventional method, where we need to fit the electro-magnetic field with an exponential decay that requires a relatively long data set. For a width-modulated line defect cavity that has a Q of 8.5 × 10(7) we obtained the same value as with a conventional method but with 94% less computation time.

Systematic hole-shifting of L-type nanocavity with an ultrahigh Q factor.

We report simple systematic hole-shifting rules applicable to any Lx (x:2,3,4,5,…) nanocavity. The rules specify six sets of holes to be tuned with only two or three shift parameters. While keeping the same cavity wavelength and nearly the same mode volume, the new rule increases the Q factor by nearly one order of magnitude compared with an edge-hole-shifted Lx nanocavity. The Q factor of the high-order mode is also greatly increased. This merit is obvious from the maximum experimental Q factors of over 500,000 at L2 and of over 1,000,000 at L3, L4, and L5 achieved in Si photonic crystals.

Room-temperature continuous-wave operation of lateral current injection wavelength-scale embedded active-region photonic-crystal laser.

We have developed a wavelength-scale embedded active-region photonic-crystal laser using lateral p-i-n structure. Zn diffusion and Si ion implantation are used for p- and n-type doping. Room-temperature continuous-wave lasing behavior is clearly observed from the injection current dependence of the output power, 3dB-bandwidth of the peak, and lasing wavelength. The threshold current is 390 µA and the estimated effective threshold current is 9.4 µA. The output power in output waveguide is 1.82 µW for a 2.0-mA current injection. These results indicate that the embedded active-region structure effectively reduce the thermal resistance. Ultrasmall electrically driven lasers are an important step towards on-chip photonic network applications.

Narrow linewidth operation of buried-heterostructure photonic crystal nanolaser.

We investigate the spectral linewidth of a monolithic photonic crystal nanocavity laser. The nanocavity laser is based on a buried heterostructure cavity in which an ultra-small InGaAsP active region is embedded in an InP photonic crystal. Although it was difficult to achieve narrow linewidth operation in previously reported photonic crystal nanocavity lasers, we have successfully demonstrated a linewidth of 143.5 MHz, which is far narrower than the cold cavity linewidth and the narrowest value yet reported for nanolasers and photonic crystal lasers. The narrow linewidth is accompanied by a low power consumption and an ultrasmall footprint, thus making this particular laser especially suitable for use as an integrated multi-purpose sensor.

Finite-difference time-domain analysis of photonic crystal slab cavities with two-level systems.

In this paper, we report the numerical simulation of an atom-cavity interaction within photonic crystal nano-cavities. The numerical model is based on a damping oscillator description of a dipole current and it is implemented with a finite-difference time-domain method. Using the method, we successfully simulate the atom-cavity mode field interactions of a two-level system embedded in a photonic crystal cavity under several coupling strength conditions. We show that enhancement and suppression of optical emission rate from a two-level system are also shown by this model.

Slow light enhanced optical nonlinearity in a silicon photonic crystal coupled-resonator optical waveguide.

We demonstrate highly enhanced optical nonlinearity in a coupled-resonator optical waveguide (CROW) in a four-wave mixing experiment. Using a CROW consisting of 200 coupled resonators based on width-modulated photonic crystal nanocavities in a line defect, we obtained an effective nonlinear constant exceeding 10,000 /W/m, thanks to slow light propagation combined with a strong spatial confinement of light achieved by the wavelength-sized cavities.

20-Gbit/s directly modulated photonic crystal nanocavity laser with ultra-low power consumption.

We have demonstrated an ultracompact buried heterostructure photonic crystal (PhC) laser, consisting of an InGaAsP-based active region (5.0 x 0.3 x 0.15 µm3) buried in an InP layer. By employing a buried heterostructure with an InP layer, we can greatly improve thermal resistance and carrier confinement. We therefore achieved a low threshold input power of 6.8 µW and a maximum output power in the output waveguide of -10.3 dBm by optical pumping. The output light is effectively coupled to the output waveguide with a high external differential quantum efficiency of 53%. We observed a clear eye opening for a 20-Gbit/s NRZ signal modulation with an absorbed input power of 175.2 µW, resulting in an energy cost of 8.76 fJ/bit. This is the smallest reported energy cost for any type of semiconductor laser.

Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings.

We report designs for a silicon-on-insulator (SOI) one-dimensional (1D) photonic crystal (PhC) nanocavity with modulated mode-gap barriers based on the lowest dielectric band. These cavities have an ultrahigh theoretical quality factor (Q) of 10(7)-10(8) while maintaining a very small modal volume of 0.6-2.0 (lambda/n)(3), which are the highest Q for any nanocavities with SiO(2) under-cladding. We have fabricated these SOI 1D-PhC cavities and confirmed that they exhibited a Q of 3.6 x 10(5), which is also the highest measured Q for SOI-type PhC nanocavities. We have also applied the same design to 1D PhC cavities with air claddings, and found that they exhibit a theoretical quality factor higher than 10(9). The fabricated air-cladding 1D Si PhC cavities have showed a quality factor of 7.2 x 10(5), which is close to the highest Q value for 1D PhC cavities.

Electro-optic adiabatic wavelength shifting and Q switching demonstrated using a p-i-n integrated photonic crystal nanocavity.

We demonstrate adiabatic wavelength shifting by electro-optic modulation, using a p-i-n integrated high-Q photonic crystal nanocavity. The wavelength of the trapped light is adiabatically shifted by modulating the resonance of the cavity faster than the photon lifetime. The cavity resonance is changed by injecting electrons through a p-i-n junction to reduce the refractive index. In addition, we employ adiabatic wavelength shifting in a demonstration of dynamic Q tuning by electro-optic modulation.

On-demand ultrahigh-Q cavity formation and photon pinning via dynamic waveguide tuning.

We show that ultrahigh-Q wavelength-sized cavities can be reconfigurably formed by local refractive index tuning of photonic-crystal mode-gap waveguides. We have found that Q can be extraordinarily high (approximately 5 x 10(9)), which is much higher than that of structure-modulated mode-gap cavities. Furthermore, the required index modulation is extremely small (Deltan/n approximately 10(-3)), which enables dynamic cavity formation by fast optical nonlinearity. We numerically show that traveling photons in a waveguide can be pinned by fast local index tuning.

Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab.

We have presented a novel design of a photonic crystal slab (PCS) nanocavity, in which the electric field of the cavity mode is strongly localized in free space. The feature of the cavity is a linear air slot introduced to the center of the mode-gap confined PCS cavity. Owing to the discontinuity of the dielectric constant, the electric field of the cavity mode is strongly enhanced inside the slot, allowing strong matter-field coupling and large interaction volume in free space. Using finite-difference time-domain method, we calculate the properties of the cavity mode as a function of the slot width. The calculated quality factor is still as high as 2 x 10(5) and the mode volume is as small as 0.14 of a cubic wavelength in a vacuum, even if 200-nm-wide slot is introduced to the PCS.

Large pulse delay and small group velocity achieved using ultrahigh-Q photonic crystal nanocavities.

We systematically studied the spectral and temporal characteristics of wavelength-sized ultrahigh-Q photonic crystal nanocavities based on width-modulated line defects. By employing accurate measurements, we confirmed that the cavity exhibits an ultra-sharp resonance width (1.23 pm), an ultrahigh-Q (1.28x 10(6)), and an ultra-long photon lifetime (1.12 ns).We discussed the correlation between the spectral and temporal measurements for various cavities, and obtained extremely good agreement. In addition, we demonstrated photon trapping for the side-coupling configuration by employing ring-down measurement, which sheds light on another interesting aspect of this phenomenon. Finally, we performed pulse propagation experiments for samples with different waveguide-cavity coupling configurations, and achieved a smallest group velocity of about 4.6 km/s for a novel configuration. These results show that we can effectively trap and delay light by using ultra-small cavities, which can potentially increase the packing density of optical buffers and bit-shifters if applied to coupled-cavity waveguides.