Biomedical subjects

C Martijn de Sterke

Publications and source records attributed to C Martijn de Sterke.

At least 19 recordsLinked to original sources

PubMed2006

Wide-angle coupling into rod-type photonic crystals with ultralow reflectance.

We describe the surprising phenomenon of near-perfect coupling from free space into uniform two-dimensional rod-type photonic crystals over a wide range of incident angles. This behavior is shown to be a generic feature of many rod-type photonic crystal structures that is related to strong forward scattering resonances of the individual cylinders. We explain these results using both semianalytic analysis and two-dimensional numerical calculations and identify the conditions under which efficient, wide-angle coupling can occur. The results may lead to more efficient designs for in-band photonic crystal devices such as superprisms and self-collimation based photonic circuits.

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PubMed2006

Spontaneous emission suppression via quantum path interference in coupled microcavities.

We examine theoretically the spontaneous emission rate in optical microstructures with cavity resonances that overlap in both position and frequency. Using projection techniques, we show that the spontaneous emission in such structures can be accurately described by the direct emission and quantum path interference of emission into a few discrete resonant modes, even though the exact infinite-dimensional problem involves a coupling to the continuum of radiation states. Moreover, we obtain an efficient numerical time-domain method for determining the spontaneous emission rate that incorporates these effects, including the suppression of spontaneous emission into some modes.

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PubMed2005

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.

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PubMed2005

Analytic properties of photonic crystal superprism parameters.

We study the analytic properties of the photonic crystal superprism resolution parameters p , q , and r introduced previously by Baba and Matsumoto [Appl. Phys. Lett. 81, 2325 (2002)], which characterize the potential dispersive power of a superprism. We find closed form expressions for these quantities that greatly simplify their accurate evaluation and reveal significant insights about their behavior. The expressions imply general properties of the parameters which are true for all bands and all photonic crystals. In particular, we demonstrate that all photonic crystals exhibit infinite resolution as measured by the parameter r along particular contours in any photonic band.

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PubMed2005

Modeling of defect modes in photonic crystals using the fictitious source superposition method.

We present an exact theory for modeling defect modes in two-dimensional photonic crystals having an infinite cladding. The method is based on three key concepts, namely, the use of fictitious sources to modify response fields that allow defects to be introduced, the representation of the defect mode field as a superposition of solutions of quasiperiodic field problems, and the simplification of the two-dimensional superposition to a more efficient, one-dimensional average using Bloch mode methods. We demonstrate the accuracy and efficiency of the method, comparing results obtained using alternative techniques, and then concentrate on its strengths, particularly in handling difficult problems, such as where a mode is highly extended near cutoff, that cannot be dealt with in other ways.

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PubMed2005

Conductance of photons in disordered photonic crystals.

The conductance of photons in two-dimensional disordered photonic crystals is calculated using an exact multipole-plane wave method that includes all multiple scattering processes. Conductance fluctuations, the universal nature of which has been established for electrons in the diffusive regime, are studied for photons, in both principal polarizations and for varying disorder. Our simulations show that universal conductance fluctuations can be observed in H(||) (TE) polarization for weak and intermediate disorder while, for E(||) (TM) polarization, we show that the conductance variance is essentially independent of sample size but strongly dependent on disorder. The probability distribution of the conductance is also calculated in the diffusive and localized regimes, and also at their transition, for which the distributions for both polarizations are seen to be very similar.

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PubMed2004

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.

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PubMed2004

Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory.

We present a rigorous Bloch mode scattering matrix method for modeling two-dimensional photonic crystal structures and discuss the formal properties of the formulation. Reciprocity and energy conservation considerations lead to modal orthogonality relations and normalization, both of which are required for mode calculations in inhomogeneous media. Relations are derived for studying the propagation of Bloch modes through photonic crystal structures, and for the reflection and transmission of these modes at interfaces with other photonic crystal structures.

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PubMed2004

Bloch mode scattering matrix methods for modeling extended photonic crystal structures. II. Applications.

The Bloch mode scattering matrix method is applied to several photonic crystal waveguide structures and devices, including waveguide dislocations, a Fabry-Pérot resonator, a folded directional coupler, and a Y-junction design. The method is an efficient tool for calculating the properties of extended photonic crystal (PC) devices, in particular when the device consists of a small number of distinct photonic crystal structures, or for long propagation lengths through uniform PC waveguides. The physical insight provided by the method is used to derive simple, semianalytic models that allow fast and efficient calculations of complex photonic crystal structures. We discuss the situations in which such simplifications can be made and provide examples.

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PubMed2004

Modes of coupled photonic crystal waveguides.

We consider the modes of coupled photonic crystal waveguides. We find that the fundamental modes of these structures can be either even or odd, in contrast with the behavior in coupled conventional waveguides, in which the fundamental mode is always even. We explain this finding using an asymptotic model that is valid for long wavelengths.

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PubMed2003

Ultracompact resonant filters in photonic crystals.

A novel design for an ultracompact, high-Q notch-rejection filter is presented, and an analytic expression for the transmission properties is derived. This folded directional coupler shares the properties of a Fabry-Perot resonator and a directional coupler. We compare and contrast the device to high-Q Fabry-Perot cavities in photonic crystal waveguides.

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PubMed2003

Antisymmetric grating coupler: experimental results.

The principle of an antisymmetric grating coupler was recently proposed theoretically as a planar waveguide add-drop multiplexer. It has the potential to enhance significantly the functionality of an add-drop multiplexer based on grating-assisted coupling. Here we realize the concept experimentally in an all-fiber geometry. We show that conventional devices exhibit two high-reflection bands. In contrast, the antisymmetric grating coupler has only a single reflection band, thereby dramatically improving its filtering characteristics.

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PubMed2003

Semianalytic treatment for propagation in finite photonic crystal waveguides.

We present a semianalytic theory for the properties of two-dimensional photonic crystal waveguides of finite length. For single-mode guides, the transmission spectrum and field intensity can be accurately described by a simple two-parameter model. Analogies are drawn with Fabry-Perot interferometers, and generalized Fresnel coefficients for the interfaces are calculated.

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PubMed2003

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.

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PubMed2003

Diffusion and anomalous diffusion of light in two-dimensional photonic crystals.

The transport properties of electromagnetic waves in disordered, finite, two-dimensional photonic crystals composed of circular cylinders are considered. Transport parameters such as the transport and scattering mean free paths and the transport velocity are calculated, for the case where the electromagnetic radiation has its electric field along the cylinder axes. The range of the parameters in which the diffusion process can take place is specified. It is shown that the transport velocity upsilon(E) can be as much as 10(8) times less than its free space value, while just outside the cluster upsilon(E) can be 0.3c. The effects of weak and strong disorders on the transport velocity are investigated. Different regimes of the wave transport-ordered propagation, diffusion, and anomalous diffusion-are demonstrated, and it is inferred that Anderson localization is incipient in the latter regime. Exact numerical calculations from the Helmholtz equation are shown to be in good agreement with the diffusion approximation.

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PubMed2003

Optimal poling of nonlinear photonic crystals for frequency conversion.

Nonlinear photonic crystals formed by two-dimensional periodic poling of the quadratic susceptibility chi(2) can support quasi-phase-matched harmonic generation. The frequency-conversion efficiency depends on the photonic crystal's poling pattern through certain Fourier coefficients of the poling function. A procedure is described for finding those poling patterns that are most efficient for any specific quasi-phase-matched frequency-conversion scheme.

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PubMed2002

Symmetries and invariant solutions of the planar paraxial wave equation in photosensitive media.

We study the equations describing planar self-written waveguides through group theoretical methods. We show the equations are nonintegrable through Painlevé analysis. Using Lie group analysis we construct a class of exact solutions for this problem. We also show the previously reported modal ansatz solutions can be recovered from our present results as a special case.

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PubMed2002

Conditions for dynamic localization in generalized ac electric fields.

We examine the conditions for dynamic localization of electrons in a periodic potential due to an applied ac electric field. Using a general one-band model, we establish the surprising result that only electric fields that are discontinuous at all changes of sign can lead to exact dynamic localization. We also develop a general procedure for constructing ac fields that yield dynamic localization and derive an "area condition" for such fields. We confirm this result numerically in a multiband simulation.

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