Photonic Metamaterials: Magnetism at Optical Frequencies
Summary (3 min read)
Introduction
- Electromagnetic metamaterials are artificial structures with inter-“atomic” distances (or “lattice constants”) that are still smaller than the wavelength of light.
- Similarly, the light field “sees” an effective homogeneous material for any given propagation direction (quite unlike in a photonic crystal).
- The authors also discuss the limits of size scaling.
II. PHYSICS OF SRRS AS “MAGNETIC ATOMS”
- It is well known from basic magnetostatics that a magnetic dipole moment can be realized by the circulating ring current of a microscopic coil, which leads to an individual magnetic moment given by the product of the current and the area of the coil.
- Authorized licensed use limited to: Universitatsbibliothek Karlsruhe.
- The SRR has also previously been discussed under the names “slotted-tube resonator” in 1977 [4] in the context of nuclear magnetic resonance (NMR) and “loopgap resonator” in 1996 [5].
- (4) Despite its simplicity and the crudeness of their derivation, this formula contains a lot of correct physics, as confirmed by the numerical calculations (see later): first, it tells us that the LCresonance wavelength is proportional to the linear dimension of the coil l, provided that the ratio w/d is fixed.
- Third, the dielectric environment influences the resonance via C , which is, e.g., modified by the presence of a dielectric substrate.
B. Limits of Size Scaling
- This question has been addressed in [7]–[9]: for an ideal metal, i.e., for an infinite electron density ne, hence an infinite metal plasma frequency, a finite current I flowing through the inductance is connected with zero electron velocity, hence, with a vanishing electron kinetic energy.
- The kinetic inductance adds to the usual inductance, L → L + Lkin in (3), and the authors immediately obtain the modified scaling for the magnetic resonance frequency ωLC ∝ 1√ size2 + constant .
- (8) Authorized licensed use limited to: Universitatsbibliothek Karlsruhe.
- For real metals in the optical regime, the interband transitions also often play a significant role.
C. Magnetic Permeability
- One can even obtain an explicit and a simple expression for the magnetic permeability µ(ω) from their simple circuit reasoning.
- The authors start by considering an excitation configuration where the electric field component of light cannot couple to the SRR (see later), and where the magnetic field is normal to the SRR plane.
- In contrast, interaction with rings from adjacent parallel planes tends to suppress F in (14).
- Indeed, it has already been pointed out in [11] that, alternatively, one can set µ̃ = 1 and describe the (meta)material response in terms of the spatial dispersion, i.e., via a wavevector dependence of the electric permittivity ̃(ω, k).
III. TOWARD MAGNETISM AT OPTICAL FREQUENCIES
- At this point, their experimental team entered this field—partly driven by the scepticism that similar materials would not be Authorized licensed use limited to: Universitatsbibliothek Karlsruhe.
- For normal incidence conditions, however, the light has zero magnetic field component perpendicular to the SRR plane.
- Thus, excitation via the magnetic field is not possible.
- Alternatively, the magnetic resonance can also be excited via the electric-field component of light if it has a component normal to the plates of the capacitor, i.e., if the incident light polarization is horizontal.
- This “selection rule” can be used to unambiguously identify the magnetic resonance.
A. SRR at Infrared Wavelengths
- Corresponding measured transmittance and reflectance spectra are shown in Fig. 2. Independent of the lattice constant axy , two distinct resonances are clearly visible.
- This also clearly shows that Bragg diffraction plays no major role.
- The constantF depends on the SRR volume filling fraction.
- The authors will come back to the Mie resonance in more detail later.
- Retrieving [16] the effective permittivity (ω) and magnetic permeability µ(ω) from the calculated spectra, indeed, reveals µ < 0 associated with the λLC = 3µm resonance for appropriate polarization conditions [6].
B. SRR at Near-Infrared Wavelengths
- Electron micrographs of miniaturized structures are shown in Fig. 3(a).
- 1) The corresponding measured spectra for horizontal incident polarization in Fig. 3(b) reveal the same (but blue-shifted) resonances as in Fig. 2(a).
- These arms are coupled via the SRR’s bottom arm (and via the radiation field).
- The red-shifted symmetric mode can be excited.
C. Cut-Wire Pairs
- The above discussion on the antisymmetric and symmetric eigenmodes of the two coupled vertical SRR arms makes one wonder whether the SRR bottom arm is necessary at all.
- This effectively reduces the total capacitance in the circuit; hence, it increases the magnetic resonance frequency for a given minimum feature size.
- On the other hand, this increased frequency at fixed lattice constant decreases the ratio between the wavelength λLC and the lattice constant axy , to about λLC /axy ≈ 2–3.
- The obvious polarization dependence of the cut-wire pairs may be undesired in certain cases.
- Authorized licensed use limited to: Universitatsbibliothek Karlsruhe.
IV. CONCLUSION
- In contrast to the “conventional textbook wisdom,” the magnetic permeability µ is no longer unity for all the optical materials.
- SRRs (and variations thereof) play the role of “magnetic atoms” and can lead to the local magnetic dipole moments.
- Other metals and/or other designs might allow for resonances with µ < 0 even in the visible range.
- Accounting for the “granularity” of the metamaterials and deviations from the strict case of n = −1 due to the real [30] and/or the imaginary [31] part of n, however, limits the performance of the “perfect lens.”.
- In any case, given today’s possibilities regarding the nanofabrication of tailored “atoms,” only their own imagination and creativity set the limits.
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Cites background from "Photonic Metamaterials: Magnetism a..."
...Examples of such structures are meta materials, photonic crystal devices, photolithographic m asks and nano-resonators [3, 6, 7, 10, 15]....
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Cites background from "Photonic Metamaterials: Magnetism a..."
...For small SRR, the kinetic inductance can add to L [35], [36]....
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"Photonic Metamaterials: Magnetism a..." refers background in this paper
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Frequently Asked Questions (11)
Q2. What future works have the authors mentioned in the paper "Photonic metamaterials: magnetism at optical frequencies" ?
The search for a negative real part of n itself is motivated by the fascinating possibility of a “ perfect lens ” [ 29 ] providing the subwavelength resolution. In any case, given today ’ s possibilities regarding the nanofabrication of tailored “ atoms, ” only their own imagination and creativity set the limits. Possibly, the real potential of the photonic metamaterials lies in other unexplored areas, for example, in chiral metamaterials or in nonlinear metamaterials.
Q3. What is the reason for the short-wavelength resonance between 1- and 2-m wavelength?
The additional short-wavelength resonance between 1- and 2-µm wavelength is due to the particle plasmon or Mie resonance, mainly exhibiting an electric permittivity, which follows a Lorentz oscillator form according to(ω) = 1 + Fω2plω2Mie − ω2 − iγω (15)with the metal Drude model damping γ.
Q4. What is the motivation for the search for a negative real part of n?
The search for a negative real part of n itself is motivated by the fascinating possibility of a “perfect lens” [29] providing the subwavelength resolution.
Q5. What is the real potential of the photonic metamaterials?
the real potential of the photonic metamaterials lies in other unexplored areas, for example, in chiral metamaterials or in nonlinear metamaterials.
Q6. What is the effect of the coupling of the two degenerate modes?
As usual, the coupling of the two degenerate modes leads to an avoided crossing with two new effec-tive oscillation modes, a symmetric and an antisymmetric one, which are frequency down-shifted and up-shifted as compared to the uncoupled resonances, respectively.
Q7. What is the way to ease the magnetic resonance of a metal?
This not only eases nanofabrication but also allows for the magnetic permeability µ(ω) for normal incidence conditions (the magnetic field can be perpendicular to the plane spanned by the two wire pieces, i.e., parallel to the magnetic dipole moment vector).
Q8. What is the simplest way to achieve a dipole moment?
It is well known from basic magnetostatics that a magnetic dipole moment can be realized by the circulating ring current of a microscopic coil, which leads to an individual magnetic moment given by the product of the current and the area of the coil.
Q9. How many atoms were arranged on a square lattice?
These “magnetic atoms” were arranged on a square lattice with axy = 450 nm ≈ 7 × λLC (and larger ones) and a total sample area of 25µm2.
Q10. What is the eigenfrequency of the LCresonance wavelength?
(4)Despite its simplicity and the crudeness of their derivation, this formula contains a lot of correct physics, as confirmed by the numerical calculations (see later): first, it tells us that the LCresonance wavelength is proportional to the linear dimension of the coil l, provided that the ratio w/d is fixed.
Q11. What is the oblique incidence of the Mie resonance?
An unexpected feature of the spectra in Fig. 4(a) is that the 950-nm wavelength Mie resonance at normal incidence splits into two resonances for oblique incidence.