Spontaneous emission from photonic crystals: full vectorial calculations

Polarization-sensitive photonic bandgaps in hybrid one-dimensional photonic crystals composed of all-dielectric elliptical metamaterials and isotropic dielectrics

Photonic bandgaps (PBGs) in conventional one-dimensional (1-D) photonic crystals (PhCs) composed of isotropic dielectrics are polarization-insensitive since the optical length within a isotropic dielectric layer is polarization-independent. Herein, we realize polarization-sensitive PBGs in hybrid 1-D PhCs composed of all-dielectric elliptical metamaterials (EMMs) and isotropic dielectrics. Based on the Bragg scattering theory and iso-frequency curve analysis, an analytical model is established to characterize the angle dependence of PBGs under transverse magnetic and transverse electric polarizations. The polarization-dependent property of PBGs can be flexibly controlled by the filling ratio of one of the isotropic dielectrics within all-dielectric EMMs. Assisted by the polarization-sensitive PBGs, high-performance polarization selectivity can be achieved. Our work offers a loss-free platform to achieve polarization-sensitive physical phenomena and optical devices.

Spontaneous Emission and Resonant Scattering in Transition from Type I to Type II Photonic Weyl Systems

Spontaneous emission and scattering behavior of an emitter or a resonant scatterer strongly depend on the density of states of the surrounding medium. It has been shown that the resonant scattering cross section (RSC) may diverge at the Weyl frequency of a type I Weyl system due to the diminishing density of states. Here we study the spontaneous emission (SE) and RSC in a photonic metacrystal across the critical transition between type I and type II Weyl systems. Theoretical results show that the SE rate of an emitter in a type I Weyl system diminishes to zero at the Weyl frequency. When the system is tuned towards the transition point between type I and type II Weyl point, the dip in the SE spectrum at the Weyl frequency becomes infinitely sharp. The dip vanishes at the critical transition, and transforms into a peak when the system changes into a type II Weyl system. We further show that the resonant scattering cross section also exhibits dramatically different spectral features across the transition. Our study demonstrates the ability to tune SE and RSC through altering the dispersion of the Weyl medium between type I and type II, which provides a fundamentally new route in manipulating light-matter interactions.

Manipulating Luminescence of Light Emitters by Photonic Crystals

The modulation of luminescence is essential because unwanted spontaneous-emission modes have a negative effect on the performance of luminescence-based photonic devices. Photonic crystals are promising materials for the control of light emission because of the variation in the local density of optical modes within them. They have been widely investigated for the manipulation of the emission intensity and lifetime of light emitters. Several groups have achieved greatly enhanced emission by depositing emitters on the surface of photonic crystals. Herein, the different modulating effects of photonic crystal dimensions, light-emitter positions, photonic crystal structure type, and the refractive index of photonic crystal building blocks are highlighted, with the aim of evaluating the fundamental principles that determine light propagation. The applications of using photonic crystals to manipulate spontaneous emission in light-emitting diodes and sensors are also reviewed. In addition, potential future challenges and improvements in this field are presented.

Breakdown of Bose-Einstein distribution in photonic crystals

In the last two decades, considerable advances have been made in the investigation of nano-photonics in photonic crystals. Previous theoretical investigations of photon dynamics were carried out at zero temperature. Here, we investigate micro/nano cavity photonics in photonic crystals at finite temperature. Due to photonic-band-gap-induced localized long-lived photon dynamics, we discover that cavity photons in photonic crystals do not obey Bose-Einstein statistical distribution. Within the photonic band gap and in the vicinity of the band edge, cavity photons combine the long-lived non-Markovain dynamics with thermal fluctuations together to form photon states that memorize the initial cavity state information. As a result, Bose-Einstein distribution is completely broken down in these regimes, even if the thermal energy is larger or much larger than the cavity detuning energy. In this investigation, a crossover phenomenon from equilibrium to nonequilibrium steady states is also revealed.

Terahertz photonic states in semiconductor-graphene cylinder structures

We propose a semiconductor-graphene cylinder that can serve as a terahertz (THz) photonic crystal. In such a structure, graphene plays a role in achieving a strong mismatch of the dielectric constant at the semiconductor-graphene interface due to its two-dimensional nature and relatively low value of the dielectric constant. We find that when the radius of the outer semiconductor layer is about ρ(1)~100 μm, the frequencies of the photonic modes are within the THz bandwidth and they can be efficiently tuned via varying ρ(1). Furthermore, the dispersion relation of the photonic modes shows that a semiconductor-graphene cylinder is of excellent light transport properties, which can be utilized for the THz waveguide. This study is pertinent to the application of graphene as THz photonic devices.

Lifetime distribution of spontaneous emission from emitter(s) in three-dimensional woodpile photonic crystals

Spontaneous emission lifetime distribution in the basic unit cell or on a plane of the excited emitters embedded in woodpile photonics crystals with low refractive index contrast are investigated. It is found that the spontaneous emission lifetime distribution strongly depends on the position and transition frequency of the emitters, and has the same symmetry as that of the unit cell. The lifetimes of emitters near the upper gap edge are longer than that in the center of the pseudo-gap, which is quite a contrast to the conventional concept. Furthermore, it is revealed that the polarization orientation of the emitters has significant influence on the lifetime distribution, and may result in a high anisotropy factor (defined as the difference between the maximum and minimum values of the lifetime) up to 4.2. These results may be supplied in probing the lifetime distribution or orientation-dependent local density of states in future experiments.

Spontaneous-emission rate in microcavities: application to two-dimensional photonic crystals

We present a simple, efficient procedure to compute the spontaneous-emission rate from short-time finite-difference time-domain (FDTD) data of the electromagnetic field energy in microcavities of arbitrary geometry. As an illustration, we apply this procedure to two-dimensional photonic crystals. For comparison, we calculate the local radiative density of states employing an unconditionally stable FDTD method, that is without solving the eigenvalue problem and integrating over the (first) Brillouin zone. We demonstrate that both methods yield the same predictions about the enhancement or suppression of the spontaneous-emission rate by photonic crystals.

Switching control of spontaneous emission by polarized atoms in two-dimensional photonic crystals

We calculate the lifetime distribution function of an assembly of polarized atoms in two-dimensional (2D) photonic crystals (PCs) at different polarization orientations of atomic dipole moments. We reveal a switching effect of atomic spontaneous emission (SE) and find a significant change of atomic lifetime, up to a factor of 33, by tuning the polarized orientation of the atoms. These observations suggest that the tuning of the polarized orientation of atoms provides a new way for the effective control of atomic SE processes in 2D PCs.

Doppler radiation emitted by an oscillating dipole moving inside a photonic band-gap crystal

We study the radiation emitted by an oscillating dipole moving with a constant velocity in a photonic crystal, and analyze the effects that arise in the presence of a photonic band gap. It is demonstrated through numerical simulations that the radiation strength may be enhanced or inhibited according to the photonic band structure, and anomalous effects in the sign and magnitude of the Doppler shifts are possible, both outside and inside the gap. We suggest that this effect could be used to identify the physical origin of the backward waves in recent metamaterials.

Spontaneous emission in one-dimensional photonic crystals

We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.

Two-dimensional treatment of the level shift and decay rate in photonic crystals

We present a comprehensive treatment of the level shift and decay rate of a model line source in a two-dimensional photonic crystal (2D PC) composed of circular cylinders. The quantities in this strictly two-dimensional system are determined by the two-dimensional local density of states (2D LDOS), which we compute using Rayleigh-multipole methods. We extend the critical point analysis that is traditionally applied to the 2D DOS (or decay rate) to the level shift. With this, we unify the crucial quantity for experiment--the 2D LDOS in a finite PC--with the band structure and the 2D DOS, 2D LDOS, and level shift in infinite PC's. Consistent with critical point analysis, large variations in the level shift are associated with large variations in the 2D DOS (and 2D LDOS), corroborating a giant anomalous Lamb shift. The boundary of a finite 2D PC can produce resonances that cause the 2D LDOS in a finite 2D PC to differ markedly from the 2D LDOS in an infinite 2D PC.

Three-dimensional Green's tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders

The three-dimensional local density of states (3D LDOS), which determines the radiation dynamics of a point-source, in particular the spontaneous emission rate, is presented here for finite two-dimensional photonic crystals composed of cylinders. The 3D LDOS is obtained from the 3D Green's tensor, which is calculated to high accuracy using a combination of a Fourier integral and the Rayleigh-multipole methods. A comprehensive investigation is made into the 3D LDOS of two basic types of PCs: a hexagonal cluster of air-voids in a dielectric background enclosed by an air-jacket in a fiberlike geometry, and a square cluster of dielectric cylinders in an air background. In the first of these, which has a complete in-plane band gap, the 3D LDOS can be suppressed by over an order of magnitude at the center of the air-voids and jumps sharply higher above the gap. In the second, which only has a TM gap in-plane, suppression is limited to a factor of 5 and occurs at the surface of the cylinders. The most striking band gap signature is the almost complete suppression of the radiation component of the 3D LDOS when the complete in-plane gap is sufficiently wide, accompanied by a burst into the radiation component above the gap.

Radiation pattern of a classical dipole in a photonic crystal: photon focusing

An asymptotic analysis of the radiation pattern of a classical dipole in a photonic crystal possessing an incomplete photonic bandgap is presented. The far-field radiation pattern demonstrates a strong modification with respect to the dipole radiation pattern in vacuum. Radiated power is suppressed in the direction of the spatial stop band and strongly enhanced in the direction of the group velocity, which is stationary with respect to a small variation of the wave vector. An effect of radiated power enhancement is explained in terms of photon focusing. A numerical example is given for a square-lattice two-dimensional photonic crystal. Predictions of asymptotic analysis are substantiated with finite-difference time-domain calculations, revealing a reasonable agreement.

Modified spontaneous emission from a two-dimensional photonic crystal

Decay kinetic properties of a two-level atom near the band edges of a two-dimensional photonic crystal are studied based on the Green's function expression for the evolution operator. Our calculations show that the decay kinetics can be controlled by changing the atomic parameters. We also find that there is a quite wide lifetime distribution in the spontaneous emission process.

Spontaneous-emission rates in finite photonic crystals of plane scatterers

The concept of a plane scatterer that was developed earlier for scalar waves is generalized so that polarization of light is included. Starting from a Lippmann-Schwinger formalism for vector waves, we show that the Green function has to be regularized before T matrices can be defined in a consistent way. After the regularization, optical modes and Green functions are determined exactly for finite structures built up of an arbitrary number of parallel planes, at arbitrary positions, and where each plane can have different optical properties. The model is applied to the special case of finite crystals consisting of regularly spaced identical planes, where analytical methods can be taken further and only light numerical tasks remain. The formalism is used to calculate position- and orientation-dependent spontaneous-emission rates inside and near the finite photonic crystals. The results show that emission rates and reflection properties can differ strongly for scalar and for vector waves. The finite size of the crystal influences the emission rates. For parallel dipoles close to a plane, emission into guided modes gives rise to a peak in the frequency-dependent emission rate.

Decay kinetic properties of atoms in photonic crystals with absolute gaps

Decay kinetic properties of a two-level atom near the band edges of photonic crystals (PCs) with absolute gaps are studied based on the Green's function expression for the evolution operator. The local coupling strength between the photons and an atom is evaluated by an exact numerical method. It is found that the decay behavior of an excited atom can be fundamentally changed by the variation of the atomic position: Weisskopf-Wigner and non-Weisskopf-Wigner decay phenomena occur at different atomic positions in the PCs as a result of a significant difference in the local coupling strength. Our finding implies that it is possible to engineer the luminescence spectrum by controlling the atomic position.

Conservative form of the density of states of a photonic crystal with a pseudogap

We show that the total number of states in a photonic crystal in the entire allowed frequency regime will be conserved, and it is equal to that of its corresponding effective medium, i.e., if the density of states (DOS) has a valley(s) in some range(s) of frequencies, it must be compensated for by increases over some other range(s). This rule is of importance in developing a model pseudogap in order to describe the mean emission characteristics of the system when there is a collection of dependently emitting atoms or molecules with essentially random dipole orientations in a large volume and the spectrum of the active atoms is wide enough. This is because, with this rule, the states-conservative model always results in DOS-induced suppression, absolute enhancement, narrowing, spectrum splits, and redshift or blueshift of spontaneous-emission spectra.

Three-dimensional local density of states in a finite two-dimensional photonic crystal composed of cylinders

The three-dimensional local density of states (LDOS), which determines the radiation dynamics of a point source, is presented here for a finite two-dimensional photonic crystal as a function of space and frequency. The LDOS is obtained from the dyadic Green's function, which is calculated exactly using the multipole method. Maximum suppression in the LDOS occurs at the high frequency edge of the complete two-dimensional band gap and varies smoothly about this frequency. Macroporous silicon is shown to suppress the LDOS by one order of magnitude at the center of its air pores.

Decay distribution of spontaneous emission from an assembly of atoms in photonic crystals with pseudogaps

Spontaneous decay behaviors from an assembly of atoms (or molecules) in 3D photonic crystals (PC's) with pseudogaps are investigated. Theoretically, a lifetime distribution function for these atoms or molecules is defined to reveal decay kinetics. Our calculations show that quite wide or narrow lifetime distributions can occur for different spread configurations of the atoms (or molecules). The pure PC effect may lead to coexistence of both accelerated and inhibited decay processes. These results provide theoretical clarification for substantial discrepancies in the recent reported experiments.

Dipole radiation in a one-dimensional photonic crystal: TE polarization

We study the power emitted by an oscillating dipole in a superlattice (SL) modeled by means of a periodic distribution of Dirac delta functions (Dirac comb SL). The radiation is permitted to propagate in all directions in space; however, it is restricted to the transverse electric (TE) polarization mode. The calculation is based on a classical theory of radiation in nonuniform dielectric media by Dowling and Bowden [Phys. Rev. A 46, 612 (1992)]. The emitted power is derived in terms of a single integral, with no approximations. A SL has no omnidirectional photonic band gaps, and therefore the power is always finite. The power spectrum exhibits slope discontinuities, which occur at the band edges for on-axis propagation. It also depends strongly on the dipole's position in the SL and on the grating strength that characterizes the Dirac comb model. The power peaks for low frequencies, and there can be large enhancement of emission as compared to free space. The closer the dipole is to a barrier (Dirac delta) and the greater the grating strength, the stronger the enhancement is. These conclusions are expected to be relevant for a real SL.

Two-dimensional Green's function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length

Using the exact theory of multipole expansions, we construct the two-dimensional Green's function for photonic crystals, consisting of a finite number of circular cylinders of infinite length. From this Green's function, we compute the local density of states (LDOS), showing how the photonic crystal affects the radiation properties of an infinite fluorescent line source embedded in it. For frequencies within the photonic band gap of the infinite crystal, the LDOS decreases exponentially inside the crystal; within the bands, we find "hot" and "cold" spots. Our method can be extended to three dimensions as well as to treating disorder and represents an important and efficient tool for the design of photonic crystal devices.