Table 2.
Definition of variables.
| Variable | Definition | Properties |
|
| ||
| a, b | junction length and width in (x, y) plane | a ≫ λJ, b ∼ λJ |
| α | quasiparticle damping factor | α = 1/ωpRQPC = 1/QQP(ωp) |
| C | junction capacitance | C = ε0εrab/d |
| c 0 | Swihart velocity |
|
| d, d1,2 | thicknesses of JJ interlayer and the two electrodes | d ≪ b ≪ a |
| Φ | flux in the junction | Φ = HyΛ*a |
| Φ0 | flux quantum | Φ0 = h/2e |
| Jc0, Ic0 | maximum critical current density and critical current | Ic0 = Jc0ab |
| k | field-induced phase gradient | k = 2πΦ/Φ0a |
| k n | wave number of a cavity mode | kn = (π/a)n |
| L*, L□ | inductance of JJ and inductance per square | L* = μ0Λa/b, L□ = μ0Λ |
| λL1,2 | London penetration depths of the two JJ electrodes | – |
| λ0 | wavelength in free space | – |
| λ | wavelength in the patch antenna | λ = λ0/
|
| λJ | Josephson penetration depth | λJ = [Φ0/2πμ0Jc0Λ]1/2 = c0/ωp |
| Λ | characteristic length associated with JJ inductance | Λ = d + λL1coth(d1/λL1) + λL2coth(d2/λL2) |
| Λ* | effective magnetic thickness of the JJ | Λ* = d + λL1tanh(d1/2λL1) + λL2tanh(d2/2λL2) |
| η | Josephson phase difference | – |
| ωp | Josephson plasma frequency | ωp = [2πIc0/Φ0C]1/2 |
| ωJ | angular Josephson frequency | ωJ = ∂η/∂t = 2πVdc/Φ0 |
| ωn | cavity mode angular frequency | ωn = c0kn |
| RQP, (rQP) | subgap quasiparticle resistance, (per unit area) | rQP = RQPab |
| R dis | net dissipative resistance | – |
| R surf | surface resistance of electrodes | – |
| R n | normal state resistance of the JJ | – |
| R TL | transmission line resistance | – |
| R rad | radiative resistance | – |
| R in | effective input resistance of the JJ | – |
| R tot | total load resistance of the JJ | – |