Surface plasmon polaritons (SPPs) in graphene are collective oscillations of electrons coupled to electromagnetic waves, confined to the surface of the material. Unlike conventional metal plasmons, graphene SPPs exhibit unique properties due to the two-dimensional nature of the material and its linear band structure near the Dirac point. These SPPs are highly confined and exhibit strong field enhancement, making them attractive for infrared (IR) and terahertz applications.

Graphene SPPs are tunable via electrostatic or chemical doping, which adjusts the Fermi level and carrier density. The dispersion relation of SPPs in graphene is given by:

\[ q_{sp} = \frac{\hbar \omega^2}{2 \alpha E_F} \left( 1 + \frac{4 \alpha E_F}{\hbar \omega} \right) \]

where \( q_{sp} \) is the plasmon wavevector, \( \omega \) is the angular frequency, \( E_F \) is the Fermi energy, and \( \alpha \) is the fine-structure constant. This relation shows that the plasmon frequency scales with \( \sqrt{E_F} \), allowing dynamic tuning via gating. For example, applying a gate voltage of a few volts can shift the plasmon resonance from mid-IR to terahertz frequencies.

In comparison, metal plasmons are less tunable due to fixed electron densities in bulk metals. Noble metals like gold and silver support SPPs primarily in the visible to near-IR range, with limited spectral adjustability. Graphene plasmons, in contrast, operate at lower energies and exhibit stronger field confinement, with wavelengths compressed by a factor of 10-100 compared to free-space radiation.

Infrared applications of graphene SPPs include enhanced sensing, subwavelength imaging, and optoelectronic devices. The strong light-matter interaction enables ultrasensitive molecular detection via surface-enhanced infrared absorption (SEIRA). Graphene plasmonic resonators can also be integrated into photodetectors, where localized plasmons enhance absorption in narrow spectral bands.

Nanoantenna designs leverage the tunability and confinement of graphene SPPs. Common geometries include ribbons, disks, and patterned arrays, where plasmon resonances are dictated by dimensions and doping levels. For instance, a graphene nanoribbon of width \( W \) supports a plasmon resonance at:

\[ \lambda_{res} \approx 2 \pi c \sqrt{\frac{\epsilon_{avg} W}{2 \alpha E_F}} \]

where \( \epsilon_{avg} \) is the average dielectric constant of the surrounding medium. By varying \( W \) and \( E_F \), resonances can be tailored across the IR spectrum. Coupled nanoantennas further enable directional emission and beam shaping, useful for compact photonic circuits.

Loss mechanisms in graphene plasmons include intrinsic damping from electron-electron and electron-phonon scattering, as well as radiative losses. The plasmon lifetime \( \tau \) is limited by impurity scattering and substrate interactions, with typical values in the range of 10-100 fs. Doped graphene exhibits lower losses compared to undoped graphene due to reduced intraband absorption. However, losses remain higher than in high-quality metals like silver, where SPP propagation lengths can exceed tens of micrometers in the visible range.

Metals suffer from ohmic losses at IR frequencies due to interband transitions, whereas graphene’s losses are dominated by Drude-like intraband processes. Despite higher losses, graphene’s tunability and extreme field confinement outweigh these drawbacks for many applications. Hybrid structures combining graphene with metallic elements can further mitigate losses while retaining tunability.

In summary, graphene SPPs offer unparalleled control over plasmonic response through electrostatic gating, enabling dynamic IR devices with subwavelength operation. While loss mechanisms pose challenges, advances in material quality and hybrid designs continue to improve performance. The contrast with metal plasmons highlights graphene’s unique advantages in tunability and confinement, driving innovations in nanophotonics and sensing.

The future of graphene plasmonics lies in optimizing loss-performance trade-offs and integrating these structures into scalable platforms. Emerging techniques such as hexagonal boron nitride encapsulation reduce substrate-induced losses, while novel antenna geometries enhance light-matter interaction. As fabrication methods mature, graphene-based plasmonic devices will play a pivotal role in next-generation IR technologies.