Composite Medium with Simultaneously Negative Permeability and Permittivity
Physical Review Letters, 2000 · paper · Materials
Demonstrates a composite of split ring resonators and continuous wires with simultaneously negative effective permeability and permittivity in a microwave frequency range. This makes a "left-handed" medium, allowing microwave tests of predicted effects such as inverted Snell's law.
Checked: PDF from web.archive.org, fetched 5 Oct 2026. Page numbers are those of that PDF.
1 finding
Reference or label The Fig. 3 caption gives the noise floor as "instrumental noise floor (−52 dB)", but the main text gives it as "noise floor of the microwave detector (−52 dBm)" and the Fig. 3 y-axis is labelled "Transmitted Power (dBm)"; the caption unit should be dBm.
- p. 4 Fig. 3 caption
coincident with that of the instrumental noise floor (252 dB)
- p. 4 Main text, right column
detector (252 dBm)
- p. 4 Fig. 3 caption
coincident with that of the instrumental noise floor (252 dB).
- p. 4 Fig. 3 caption
instrumental noise floor (252 dB)
Judge's note: I checked the page 4 image (crops C004-a and C004-b). The caption reads "(−52 dB)". The right-column text reads "(−52 dBm)". The y-axis of Fig. 3 is labelled "Transmitted Power (dBm)". The '2' in the text layer is a minus sign lost in extraction; the image shows −52 in both places. A noise floor is an absolute power level, so it should be in dBm. The caption's "dB" is therefore a wrong unit label for the same quantity. Only the unit label is wrong; the data are unaffected.
Second check: another model agreed
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2 minor (typos and the like; most checked by the judge only)
Wording The symbol d is used for three quantities without redefinition: the SRR dimension "d = 0.2 mm" (Fig. 1 caption), the cell length in "phase advance per unit cell, or kd" (Fig. 2 caption, where the lattice parameter is elsewhere called a), and an undefined length in "ωp = (d²Lε0)^−1/2" (p. 3).
- p. 1 Fig. 1 caption
d 0.2 mm
- p. 2 Fig. 2 caption
cell, or kd, where k is the wave number
- p. 3 Plasma frequency formula
vp d2L´0
- p. 3 Plasma frequency formula
vp d2L´0212
Judge's note: Checked the Fig. 1 caption on page 1, the Fig. 2 caption crop and the ωp formula on page 3. d is defined only in Fig. 1, as a ring dimension. Its later uses as cell length and wire spacing are never defined. Context lets a reader infer the meaning, so this is a notation ambiguity rather than an error of fact.
Second check: another model agreed
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Wording Eq. (2), "k² = (ω² − ωp²)/c² · (ω² − ωb²)/(ω² − ω0²)", is printed with an equals sign. Combining ε = 1 − ωp²/ω² with Eq. (1) (Γ = 0) gives an additional prefactor (1 − F), which is not shown and not stated to be neglected.
- p. 3 Eq. (2)
we can derive the following expression for the dis- persion relation of the combined medium:
Only the authors can say what is right here.
Judge's note: Checked Eq. (1) on page 2 and Eq. (2) in crop C002-a. Re-derived: μ = 1 − Fω²/(ω² − ω0²) = (1 − F)(ω² − ωb²)/(ω² − ω0²), with ωb = ω0/√(1 − F). Then k² = ω²εμ/c² carries a factor (1 − F). Band edges and the sign of the group velocity are unaffected. Eq. (3) uses ≃, whereas Eq. (2) uses =, so the authors should say whether the factor was dropped as an approximation.
Second check: another model agreed