Photonic Crystal Band Edge Research Articles

Investigations of laser oscillation and switching using a resonance at the band edge crossover in an hetero-structure of one-dimensional photonic crystals

This paper presents a theoretical investigation of a laser oscillator and a laser switch, using a hetero-structure made of two one-dimensional photonic crystals with active materials and a period ratio of r ( r > 1). Lasing is achieved near frequencies where the upper and lower band edges of the adjacent photonic crystals overlap (i.e., band edge resonance). Near the band edge resonance, two modes of laser oscillations are found; mode A – the threshold gain increases with r and mode B – the threshold gain decreases with r. By assuming a homogenously broadened gain medium at any particular r, only one of the two modes is able to participate in lasing. We also found the lasing mode is switchable upon a very small alteration in the refractive index of the materials present in the photonic crystal. The results of the paper will be very useful for designing a new class of tunable lasers and high sensitivity sensors.

Enhancement of nonlinear effects at the degenerate band edge of two-dimensional photonic crystals

The ability of two-dimensional (2D) photonic crystals (PC) for high enhancements of nonlinear processes is analyzed in the case of a degenerate band edge when two symmetrical diffracted beams are generated by Bragg diffraction in the 2D-PC. Calculations are performed using the very simple Bragg-coupled wave theory which only involves three coupled waves (the incident wave and the two diffracted waves) for the linear interaction. The validity of the approximation is proved for wavelengths lying at the neighborhood of the band edges of 2D-PC. Very large local-field intensities are predicted around the band-edge wavelengths, in particular for the upper band edge. Nonlinear propagation is studied through the analysis of degenerate four-wave mixing. For counterpropagating pump beams orthogonally sent onto the 2D-PC huge improvement of the phase conjugate reflectivity are predicted at least for small incidence angles of the signal beam. These results represent an improvement by a factor of 20 when compared to the case of a one-dimensional PC of the same thickness made of the same materials. As three intense phase conjugate beams are generated in the four-wave mixing interaction, the 2D-PC could be very interesting for the purpose of dense parallel optical signal processing. Moreover, the simple theoretical analysis developed in the paper can be used for any kind of 2D-PC.

Goos–Hänchen shift in one‐dimensional photonic crystals containing uniaxial indefinite medium

AbstractWe study numerically the Goos–Hänchen (GH) shift of a light wave transmitted from one‐dimensional photonic crystals containing a uniaxial indefinite medium. It is found that the permittivity and permeability of the indefinite medium strongly affect the properties of the GH shift. The (positive or negative) GH shift is greatly enhanced near the band edge of photonic crystals, the sign of the GH shift in the low‐ and high‐frequency edges of the photonic bandgap can be different. In addition, the properties of the GH shift are also strongly dependent on the incident light frequency, incident angle and the orientation of the optical axis. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fiber-coupled surface-emitting photonic crystal band edge laser for biochemical sensor applications

We report on a refractive index sensor platform based on a surface-emitting photonic crystal (PC) Γ-point band edge laser (BEL). A simple butt-end fiber coupling makes the BEL system compact, while the translational symmetry of the PC pattern removes the necessity of fiber alignment. The laser wavelength shifts linearly to longer wavelengths as the refractive index of the environmental medium increases. Our BEL system had an index resolution of ∼10−3. Taking into account the alignment-free nature, as well as its ultracompactness and high fiber-coupled laser output, the BEL system is well suited to a label-free sensor platform for biochemical applications.

Spontaneous emission near the band edge of a three-dimensional photonic crystal: afractional calculus approach

We suggest a better mathematical method, fractional calculus, for studying the behavior ofthe atom–field interaction in photonic crystals. By studying the spontaneous emission of anatom in a photonic crystal with a one-band isotropic model, we found that the long-timeinducing memory of the spontaneous emission is a fractional phenomenon. This behaviorcould be well described by fractional calculus. The results show no steady photon–atombound state for the atomic resonant transition frequency lying in the proximity of theallowed band edge which was encountered in a previous study (Woldeyohannes and John2003 J. Opt. B: Quantum Semiclass. Opt. 5 R43). The correctness of this result is validatedby the ‘cut-off smoothing’ density of photon states (DOS) with fractional calculus. Byobtaining a rigorous solution without the multiple-valued problem for the system,we show that the method of fractional calculus has a logically concise property.

Time resolved nonlinear spectroscopy at the band edge of 1D photonic crystals

Large refractive index changes have been measured at the band edge frequency of 1D photonic crystals (PCs). Results concerning both thin and thick samples of high and low refractive index contrasts, respectively, are presented. The very large value of the refractive index changes obtained at moderate pump powers thanks to the strong enhancement of the local intensity inside the PC opens the way to very small volume devices for optical signal processing. However, time resolved experiments demonstrate the photo-generation of high free carrier densities through two- or even three-photon absorptions, which are shown to be also strongly enhanced at the band edge of the PC. This drawback may most probably be circumvented by using lower pump intensities in PCs showing narrower resonances.

Optofluidic tuning of photonic crystal band edge lasers

We demonstrate optofluidic tuning of polymer photonic crystal band edge lasers with an imposed rectangular symmetry. The emission wavelength depends on both lattice constant and cladding refractive index. The emission wavelength is shown to change 1nm with a cladding refractive index change of 10−2. The rectangular symmetry modification alters the emission characteristics of the devices and the relative emission intensities along the symmetry axes depend on cladding refractive index, suggesting a sensor concept based on detection of intensity rather than wavelength.

Quantum interference near a photonic band edge beyond the weak-field approximation

We investigate spontaneous emission and quantum interference effects involving a three-level atom in the vicinity of a photonic band edge beyond the weak-driving-field approximation. We consider two different three-level atoms, each subject to a probe field from the ground state and each embedded within a different photonic crystal (PhC). The first atom has the two excited states separated by a dipole transition in the optical frequency range, with this frequency being close to the surrounding PhC's band edge. The probe field couples the ground state and the highest excited state, and is well outside the PhC band gap. If a coupling field is applied between the two upper levels, electromagnetically induced transparency (EIT) may occur, depending on the position of the band edge. The second atom has the two upper levels each dipole-coupled to the ground state and close enough that the emissions from each can coherently interfere. This atom is embedded within a PhC whose band edge lies near the lower of the two excited states, and a probe field is applied that lies just beyond this band edge. This atom exhibits a quantum interference phenomenon related to EIT called field-induced transparency, again depending on the position of themore » band edge relative to the lower excited state.« less

Butt-end fiber coupling to a surface-emitting Γ-point photonic crystal band edge laser

The authors demonstrate a compact and efficient fiber coupling scheme for a surface-emitting photonic crystal laser by using a cleaved fiber tip connected to a wavelength-division-multiplexing 1×2 fiber coupler. Simultaneous optical excitation and laser light collection are achieved for a 1.55μm InGaAsP graphite-lattice Γ-point band edge laser. On comparing with the conventional microphotoluminescence setup based on an objective lens, their direct butt coupling setup is much simpler and yet offers the fiber-coupled output approximately ten times higher. Finite-difference time-domain simulations confirm that the Γ-point band edge laser exhibits the desired vertical emission property and that the fiber coupling efficiency can be as high as 30%.

Explicit solutions for the band edges of multi-layer photonic crystals with integer ratios of optical path lengths

The tangent formulation for photonic bandgap materials is used to derive explicit expressions for the energy eigenvalues at the centre and the edge of the Brillouin zone of multi-layer photonic bandgap materials with integer ratios of optical path lengths (e.g. any combination of quarter-wave, half-wave, etc., stacks). Unlike the transfer matrix formalism?in which such solutions are implicit functions of photon energy and require a root search?here, all the eigenfrequencies and wave amplitudes are found through a single diagonalization of a Hermitian eigenvalue problem. By reformulating the general nonlinear problem as an algebraic eigenvalue problem, the present solution replaces the search for resonance frequencies with a single eigenproblem, which considerably reduces the computational cost and provides a more accurate solution and a better insight for structure resonances.

Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons

The authors demonstrate how slow group velocities that are easily attainable at the band edge of photonic crystals can drastically enhance the electro-optical effect on tunable photonic crystal components. This property opens up the possibility of microsized nonlinear devices with low power requirement. In this letter we show how these possibilities for enhancement of nonlinear effects have been used to fabricate a 13×13μm2 sized lithium niobate photonic crystal intensity modulator that shows an enhanced electro-optic effect 312 times bigger than the one predicted by the classical Pockels effect for an equivalent device in bulk material.

Enhanced light extraction in Er3+ doped SiO2–TiO2 microcavity embedded in one-dimensional photonic crystal

Erbium doped silica–titania one-dimensional photonic crystal microcavities have been analyzed by solving the erbium rate equations and the Maxwell equations by means of an auxiliary differential equation finite difference time domain technique. The interaction time between light and matter is enhanced by the presence of microcavity, used to localize the light inside the PC and allows to achieve a significant gain. The investigation treats the influence of the pump signal power, the device length and the dopant concentration, on the optical amplification in correspondence of the defect resonance. A comparison between the erbium doped photonic crystal microcavities and erbium doped photonic crystal band edge amplifiers is reported as well, which shows a higher compactness of the erbium doped photonic crystal microcavities respect with the erbium doped photonic crystals.

Transfer-matrix modeling of four-wave mixing at the band edge of a one-dimensional photonic crystal

We present a modeling of a degenerate four-wave-mixing nonlinear process in one-dimensional photonic crystals. The model is based on the nonlinear extension of the transfer-matrix description of propagation in the structure. The influence of light localization, near the band edge of the structure, on the enhancement of the phase-conjugate reflectivity is studied. The phase-conjugate reflectivity is shown to increase as the eighth power of the number of layers with an additional large dependence on the index contrast of the structure. In both cases the enhancement is accompanied by a strong reduction of the resonance width, which may lead to some limitation of the enhancement when ultrashort pulses are used. A strong influence of the losses on the nonlinear efficiency of the structure is also predicted with a great importance of scattering losses at the multiple interfaces of the structure.

All-optical switching in silicon photonic crystal waveguides by use of the plasma dispersion effect

Silicon photonic crystals offer new ways of controlling the propagation of light as well as new tools for the realization of high-density optical integration on monolithic substrates. However, silicon does not possess the strong nonlinearities that are commonly used in the dynamic control of optical devices. Such dynamic control is nevertheless essential if silicon is to provide the higher levels of functionality that are required for optical integration. We demonstrate that the combination of the refractive index change caused by the presence of photoexcited carriers, or so-called plasma dispersion, and photonic crystal properties such as photonic bandgaps, constitutes a powerful tool for active control of light in silicon integrated devices. We show close to 100% modulation depth near the photonic crystal band edge.

Kerr and four-wave mixing spectroscopy at the band edge of one-dimensional photonic crystals

Kerr and four-wave mixing spectroscopy is shown to be a powerful technique to quantify the strong enhancement of the third-order optical nonlinear susceptibilities at the band edge of photonic crystals. Local field factors of about 5 are demonstrated for crossed Kerr effect and a narrow resonance peak observed for the conjugate reflectivity. Moreover, a reduction of the effective nonlinear susceptibility of the four-wave mixing process with increasing pump intensities is measured, which is due to different Kerr-induced blueshifts of the band edge for forward and backward pump beams and signal and conjugate beams. This observation definitely demonstrates the need for considering all the nonlinear processes for the optimization of nonlinear photonic crystals for a given application in optical signal processing.

Highly directional enhanced radiation from sources embedded inside three-dimensional photonic crystals

We have experimentally studied emission of microwave radiation from a monopole source embedded in a three-dimensional photonic crystal. We have demonstrated enhancement of microwave radiation at the band edge and cavity mode frequencies. Furthermore, we have shown that it is possible to obtain highly directive microwave radiation sources operating at the band edge of the three-dimensional photonic crystal. We have measured half power beam widths of 13 degrees for both E and H planes, corresponding to a maximum directivity of 245.

Planar Defect Modes Excited at the Band Edge of Three-dimensional Photonic Crystals

We experimentally and numerically studied planar defect modes excited at band-edge resonant mode frequencies in three-dimensional photonic crystals. We identified the observed peaks as the defect modes using the spectrum calculated at the defect layer. The spectrum also clarifies the difference between these modes and ordinary band-edge resonant modes. The calculated spatial distribution of the electric field in the defect modes shows that the defect modes have a characteristic field concentration in the band-edge resonant mode.

Organic Photonic Crystal Band Edge Laser Fabricated by Direct Nanoprinting

A direct nanoprinting technique is used to fabricate a pit arrangement on the surface of an organic amorphous emissive layer. A pit arrangement with a closely packed hexagonal pattern with a 400 nm pitch is successfully fabricated within 60 s. Pit depth is more than 70 nm and depends on press pressure. The fabricated structure is considered to be a photonic crystal band edge laser, and laser oscillation is confirmed by optical excitation. It is also confirmed that the oscillation threshold can be controlled simply by changing the press pressure used in the direct nanoprinting procedure. The results show that the use of the direct nanoprinting technique enables the fabrication of organic nanostructure devices such as photonic crystal band edge lasers with an organic emissive material.

Optical Bloch-mode-induced quasi phase matching of quadratic interactions in one-dimensional photonic crystals

We examine in detail the quasi-phase-matching process obtained as a stationary modulation of the fundamental field at the band edge of a finite one-dimensional photonic crystal. The treatment is carried out in terms of the structure Bloch waves and fully explains the behavior of second-harmonic generation in the grating. An integrated microstructured AlGaAs mesa waveguide is proposed that gives efficient second-harmonic and difference-frequency generation in virtue of the combined presence of a periodic modulation of the fundamental-field amplitude and of the photonic bandgap edge.

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.