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Dispersion Engineering: Negative Refraction and Designed Surface Plasmons in Periodic Structures
KTH, School of Information and Communication Technology (ICT), Microelectronics and Applied Physics, MAP.
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The dispersion property of periodic structures is a hot research topic in the last decade. By exploiting dispersion properties, one can manipulate the propagation of electromagnetic waves, and produce effects that do not exist in conventional materials. This thesis is devoted to two important dispersion effects: negative refraction and designed surface plasmons.

First, we introduce negative refraction and designed surface plasmons, including a historical perspective, main areas for applications and current trends.

Several numerical methods are implemented to analyze electromagnetic effects. We apply the layer-KKR method to calculate the electromagnetic wave through a slab of photonic crystals. By implementing the refraction matrix for semi-infinite photonic crystals, the layer-KKR method is modified to compute the coupling coefficient between plane waves and Bloch modes in photonic crystals. The plane wave method is applied to obtain the band structure and the equal-frequency contours in two-dimensional regular photonic crystals. The finite-difference time-domain method is widely used in our works, but we briefly discuss two calculation recipes in this thesis: how to deal with the surface termination of a perfect conductor and how to calculate the frequency response of high-Q cavities more efficiently using the Pad\`{e} approximation method.

We discuss a photonic crystal that exhibits negative refraction characterized by an effective negative index, and systematically analyze the coupling coefficients between plane waves in air and Bloch waves in the photonic crystal. We find and explain that the coupling coefficients are strong-angularly dependent. We first propose an open-cavity structure formed by a negative-refraction photonic crystal. To illuminate the physical mechanism of the subwavelength imaging, we analyze both intensity and phase spectrum of the transmission through a slab of photonic crystals with all-angle negative refraction. It is shown that the focusing properties of the photonic crystal slab are mainly due to the negative refraction effect, rather than the self-collimation effect.

As to designed surface plasmons, we design a structured perfectly conducting surface to achieve the negative refraction of surface waves. By the average field method, we obtain the effective permittivity and permeability of a perfectly conducting surface drilled with one-dimensional periodic rectangle holes, and propose this structure as a designed surface plasmon waveguide. By the analogy between designed surface plasmons and surface plasmon polaritons, we show that two different resonances contribute to the enhanced transmission through a metallic film with an array of subwavelength holes, and explain that the shape effect is attributed to localized waveguide resonances.

Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , xi, 74 p.
Series
Trita-ICT/MAP, 2007:11
Keyword [en]
photonic crystal, dispersion property, negative refraction, surface plasmon polariton, designed surface plasmon, negative index material, layer-KKR method, finite-difference time-domain method, plane wave method, subwavelength imaging, open cavity, enhanced transmission, slowing light
National Category
Telecommunications
Identifiers
URN: urn:nbn:se:kth:diva-4542OAI: oai:DiVA.org:kth-4542DiVA: diva2:12765
Public defence
2007-12-07, sal D, Forum, Isafjordsgatan 39, Kista, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20100817Available from: 2007-11-20 Created: 2007-11-20 Last updated: 2012-03-21Bibliographically approved
List of papers
1. Enhanced Transmission through Periodic Arrays of Subwavelength Holes: The Role of Localized Waveguide Resonances
Open this publication in new window or tab >>Enhanced Transmission through Periodic Arrays of Subwavelength Holes: The Role of Localized Waveguide Resonances
2006 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 96, no 23, 233901- p.Article in journal (Refereed) Published
Abstract [en]

By using the rigid full-vectorial three-dimensional finite-difference time-domain method, we show that the enhanced transmission through a metallic film with a periodic array of subwavelength holes results from two different resonances: (i) localized waveguide resonances where each air hole can be considered as a section of metallic waveguide with both ends open to free space, forming a low-quality-factor resonator, and (ii) well-recognized surface plasmon resonances due to the periodicity. These two different resonances can be characterized from electromagnetic band structures in the structured metal film. In addition, we show that the shape effect in the enhanced transmission through the Au film with subwavelength holes is attributed to the localized waveguide resonance.

Keyword
Finite difference method; Metallic films; Resonance; Time domain analysis; Wave transmission; Waveguide components; Electromagnetic band structures; Low-quality-factor; Subwavelength holes; Waveguide resonances; Waveguides
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-7663 (URN)10.1103/PhysRevLett.96.233901 (DOI)000238315600026 ()2-s2.0-33745048690 (Scopus ID)
Note
QC 20100817Available from: 2007-11-20 Created: 2007-11-20 Last updated: 2017-12-14Bibliographically approved
2. Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface
Open this publication in new window or tab >>Slow electromagnetic wave guided in subwavelength region along one-dimensional periodically structured metal surface
2007 (English)In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 90, no 20, 201906- p.Article in journal (Refereed) Published
Abstract [en]

A perfect electric conductor surface with one-dimensional periodic rectangle holes is proposed as a surface-plasmon-like waveguide, where designed surface plasmon modes with very low group velocity are confined in a subwavelength region. It is shown that the half maximum of electric field intensity of the mode can be confined in a 0.20 lambda x0.10 lambda subwavelength region on the transversal plane and the group velocity approaches to zeros, where lambda is the wavelength in vacuum.

Keyword
Electric conductors; Electromagnetic waves; One dimensional; Periodic structures; Surface plasmon resonance; Waveguides; Metal surface; Rectangle holes; Subwavelength region; Surface plasmon; Wavelength
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-7664 (URN)10.1063/1.2740174 (DOI)000246623500030 ()2-s2.0-34249006646 (Scopus ID)
Note
QC 20100817Available from: 2007-11-20 Created: 2007-11-20 Last updated: 2017-12-14Bibliographically approved
3. Negative refraction and sub-wavelength imaging through surface waves on structured perfect conductor surfaces
Open this publication in new window or tab >>Negative refraction and sub-wavelength imaging through surface waves on structured perfect conductor surfaces
2006 (English)In: Optics Express, ISSN 1094-4087, E-ISSN 1094-4087, Vol. 14, no 13, 6172-6177 p.Article in journal (Refereed) Published
Abstract [en]

We report that negative refraction can be achieved through surface waves on a metal surface with an array of drilled holes. Using a rigorous full-vectorial three-dimensional finite-difference time-domain method, we also demonstrate the sub-wavelength imaging of a point dipole source by a slab of such a structure.

Keyword
Finite difference method; Imaging systems; Refraction; Time domain analysis; Vector quantization; Conductor surfaces; Metal surface; Negative refraction; Point dipole; Wavelength imaging; Surface waves
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-7665 (URN)10.1364/OE.14.006172 (DOI)000238553200036 ()2-s2.0-33745505397 (Scopus ID)
Note
QC 20100817Available from: 2007-11-20 Created: 2007-11-20 Last updated: 2017-12-14Bibliographically approved
4. Open cavity formed by a photonic crystal with negative effective index of refraction
Open this publication in new window or tab >>Open cavity formed by a photonic crystal with negative effective index of refraction
2005 (English)In: Optics Letters, ISSN 0146-9592, E-ISSN 1539-4794, Vol. 30, no 17, 2308-2310 p.Article in journal (Refereed) Published
Abstract [en]

An open cavity formed by three 60 degrees wedges of a photonic crystal with negative effective index is designed and studied. The quality factor of the open cavity can be larger than 2000. The influence of the interface termination on the resonant frequency and the quality factor is studied.

Keyword
Natural frequencies; Photonic crystals; Quality factor; Refractive index
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-7666 (URN)10.1364/OL.30.002308 (DOI)000231436900040 ()
Note
QC 20100817Available from: 2007-11-20 Created: 2007-11-20 Last updated: 2017-12-14Bibliographically approved
5. Focusing properties of a photonic crystal slab with negative refraction
Open this publication in new window or tab >>Focusing properties of a photonic crystal slab with negative refraction
2004 (English)In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 70, no 11, 115113- p.Article in journal (Refereed) Published
Abstract [en]

A layered Korringa-Kohn-Rostoker method is exploited to study the subwavelength imaging through a slab of rods-in-air photonic crystal. Both the intensity and phase spectra of transmission are investigated. The high transmission of evanescent waves arises due to the excitation of some slab-guided bound modes and the high coupling between the incident evanescent field and some bulk-guided Bloch modes. Through a study of the phase spectrum of transmission, it is shown that the self-collimation effect occurs at smaller incident angles whereas the negative refraction effect occurs at relatively larger incident angles. The existence of imaging aberrations is also explained with the phase spectrum. The focusing properties of the photonic crystal slab are mainly due to the negative-refraction effect for large incident angles, rather than the self-collimation effect.

Keyword
article; collimator; crystal; mathematical analysis; mathematical model; photon; refraction index; technique
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-7667 (URN)10.1103/PhysRevB.70.115113 (DOI)000224209500033 ()2-s2.0-19744382128 (Scopus ID)
Note
QC 20100817 QC 20110923Available from: 2007-11-20 Created: 2007-11-20 Last updated: 2017-12-14Bibliographically approved
6. Coupling between plane waves and Bloch waves in photonic crystals with negative refraction
Open this publication in new window or tab >>Coupling between plane waves and Bloch waves in photonic crystals with negative refraction
Show others...
2005 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 71, no 4, 045111- p.Article in journal (Refereed) Published
Abstract [en]

A comprehensive analysis of the coupling coefficients between plane waves in conventional dielectric media and Bloch waves of photonic crystals with effective negative refractions is performed by the layer Korringa-Kohn-Rostoker method. Employing the infinite layers refraction operator, semi-infinite size photonic crystals are considered. Some special coupling properties are discussed. In particular, the strong angular dependence of coupling coefficients is found even for an interface between air (n=1) and a photonic crystal with effective refractive index (n(eff)=-1). Thus, a negative refractive index defined by the radius of a circular equal-frequency contour does not guarantee an isotropic behavior.

National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-7668 (URN)10.1103/PhysRevB.71.045111 (DOI)000226736200032 ()
Note
QC 20100817Available from: 2007-11-20 Created: 2007-11-20 Last updated: 2017-12-14Bibliographically approved

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