Optical Hawking Effect in Dielectrics

• Optical Hawking effect is a phenomenon where engineered nonlinear media create artificial horizons, leading to mode mixing and photon pair emission similar to black hole radiation.
• Experiments employ intense pump pulses in fibers or bulk glass to induce moving refractive-index perturbations, resulting in measurable Planckian spectra and Bogoliubov mode mixing.
• Key challenges include engineering steep index gradients and mitigating background nonlinear processes to reliably observe thermal Hawking radiation signatures.

The optical Hawking effect describes the spontaneous or stimulated emission of photons in optical media under conditions that mimic the causal structure of event horizons for light, in direct analogy with Hawking radiation from black holes. This phenomenon is realized using dispersive, typically nonlinear, dielectrics in which moving refractive-index perturbations (induced principally via the Kerr effect) generate artificial horizons for probe modes. The resulting physics is governed by the local mode structure, effective metric, and horizon kinematics, and is characterized by Bogoliubov-type mode mixing with associated Planckian or near-thermal spectra. Optical platforms provide an experimentally accessible analogue to quantum field theory on curved spacetime, and enable direct studies of fundamental processes such as quantum vacuum emission, mode conversion, and entanglement near horizons.

1. Effective Metric, Horizon Conditions, and Optical Analogue Gravity

The propagation of electromagnetic fields in a nonlinear dielectric medium with a space-time varying refractive index $n(x,t)$ can be recast in covariant form via the so-called Gordon metric. In an intense pump field, the Kerr effect induces a moving refractive-index perturbation (RIP),

$n(x) = n_0 + \delta n(x),$

where $\delta n \simeq n_2 |E(x)|^2$. In the laboratory frame, the effective (1+1)D metric for probe light is

$$ds^2_{\text{eff}} = [c^2/n^2(x) - V_p^2]\,dt^2 + 2V_p\,dx\,dt - dx^2 - dy^2 - dz^2,$$

with pump speed $V_p$. The horizon for a probe mode occurs where its local phase or group velocity equals $V_p$:

• Phase horizon: $v_{\text{ph}}(x_h) = c/n(x_h) = V_p$, or equivalently $\omega_{\text{lab}} - k V_p = 0$ in the comoving frame.
• Group horizon: $v_g(\omega) = d\omega/dk = V_p$.

This distinction is crucial: only the group horizon reproduces the exponential mode-mixing (“tearing”) and leads to the characteristic Hawking emission (Schützhold et al., 2010, Aguero-Santacruz et al., 2020). The surface gravity, which governs the effective Hawking temperature, is

$$\kappa = \left|\frac{\partial}{\partial x}\left(\frac{c}{n(x)} - V_p\right)\right|_{x=x_h}$$

with corresponding temperature

$$T_H = \frac{\hbar \kappa}{2\pi k_B} = \frac{\hbar}{2\pi k_B} \left| \frac{\partial}{\partial x}\frac{c}{n(x)} \right|_{x=x_h}.$$

(Schützhold et al., 2010, Aguero-Santacruz et al., 2020, Moreno-Ruiz et al., 2019, Ornigotti et al., 2017)

2. Mode Conversion, Bogoliubov Formalism, and Spontaneous Emission

At an optical horizon, quantized probe fields experience mode mixing between positive- and negative-norm modes. The "in" and "out" mode bases are related by a Bogoliubov transformation,

$$\phi_\omega^{\text{out}} = \sum_{j} \alpha_j(\omega)\,\phi_{\omega,j}^{\text{in}} + \sum_{j} \beta_j(\omega) \, \phi_{-\omega,j}^{\text{in}},$$

with $|\alpha|^2 - |\beta|^2 = 1$. The nonzero $\beta$ coefficients directly encode spontaneous photon-pair emission from vacuum fluctuations. For a stationary, dispersive-less horizon, the emission spectrum follows the Planck distribution,

$$\langle N_\omega \rangle = \frac{1}{e^{2\pi\omega/\alpha} - 1}, \quad T_H = \frac{\hbar\alpha}{2\pi k_B},$$

where $\alpha$ is the gradient of the “null ray” velocity at the horizon (Aguero-Santacruz et al., 2020, Belgiorno et al., 2014). In the presence of dispersion, the spectrum remains nearly thermal at low frequency, with frequency-dependent corrections described analytically and numerically (Moreno-Ruiz et al., 2019, Belgiorno et al., 2014).

Photon emission occurs dominantly in pairs with frequencies $\omega$ and $-\omega$ in the comoving frame, leading to output two-mode squeezed states and strong entanglement (Jacquet et al., 2020). Conditions for pure two-mode squeezing and maximal logarithmic negativity are met when only a single partner channel dominates (Jacquet et al., 2020).

3. Experimental Realizations and Stimulated Hawking Effect

Experiments have implemented the optical Hawking effect using ultrashort, intense pump pulses in optical fibers or bulk glass, generating a localized $\delta n(x)$ traveling at speed $V_p$ (Aguero-Santacruz et al., 2020, Drori et al., 2018, Bermudez et al., 2016). The probe field can be either vacuum (for spontaneous emission) or a classical seed (for stimulated emission). Stimulated Hawking radiation has been detected by coherently seeding one half of the Hawking partner pair and measuring amplification at the conjugate (negative-norm) frequency—a direct signature of Bogoliubov mixing (Drori et al., 2018, Aguero-Santacruz et al., 2020, Agullo et al., 2021).

Notably, only group-velocity horizons yield the full Hawking effect: the spontaneous emission spectrum is peaked around the group-horizon frequency, with vanishing output at the phase horizon (Bermudez et al., 2016, Schützhold et al., 2010). Soliton backgrounds in fibers or waveguides provide the required conditions, and the presence of four-wave mixing and modulation instability can lead to resonant enhancement of Hawking emission—boosting normally negligible spontaneous rates into the observable range (Robertson et al., 2019, Ornigotti et al., 2017). Planar or vortex geometries have been used to analogize rotating (Kerr) black holes and study superradiance alongside Hawking emission (Ornigotti et al., 2017).

Wave-optical analogues using time-varying gratings or topological photonic lattices (with synthetic horizons engineered via Dirac-cone tilting) offer stationary horizon realizations, prospects for high Hawking temperatures, and distinct emission signatures (Horsley et al., 2023, Kang et al., 2019).

4. Role of Dispersion, Stationarity, and Horizon Type

Dispersion fundamentally alters spectrum and kinematics. The group-velocity horizon under anomalous dispersion is identified as the locus of maximum Bogoliubov mixing and Hawking emission; dispersion also limits the allowed emission window and introduces cutoff frequencies (Aguero-Santacruz et al., 2020, Moreno-Ruiz et al., 2019, Bermudez et al., 2016). Analytical results show that for power-law or soliton-like $\delta n(\tau)$ profiles, the temperature becomes frequency-dependent; for low frequencies, deviations are small, but sharp or non-monotonic profiles yield pronounced non-thermal features (Moreno-Ruiz et al., 2019).

True Hawking emission requires stationary or slowly-evolving horizons on timescales longer than the characteristic $\kappa^{-1}$ (“Hawking time”). Fast, nonstationary, or short-lived index perturbations invalidate the stationary-horizon assumption and favor quantum vacuum emission characteristic of the dynamical Casimir effect rather than Hawking physics (Schützhold et al., 2010, Liberati et al., 2011). Only the group horizon leads to the characteristic “exponential tearing” (mode-mixing) underlying thermal Hawking radiation, whereas phase horizons allow at best a weaker Landau-type photon production (Schützhold et al., 2010).

5. Spectroscopy, Angular/Purity Signatures, and Distinction from Alternative Mechanisms

A genuine analogue Hawking process predicts:

• Planckian spectrum at $T_H$ without sharp lines or narrow bandwidth (Schützhold et al., 2010).
• Emission collimated in a narrow cone, typically forward-directed along the horizon normal.
• Strong polarization and entanglement correlations between Hawking partners.
• Pairwise quantum correlations robust under ideal detection but fragile to loss and background noise (Agullo et al., 2021, Jacquet et al., 2020).

By contrast, experiments reporting unpolarized, isotropic light in the transverse plane, or emission spectra inconsistent with Planckian scaling or collimation, are better explained by dynamical Casimir-type emission—i.e., quantum vacuum radiation instigated by rapid, nonstationary refractive-index modulations (Liberati et al., 2011, Schützhold et al., 2010). Quantitative estimates show that for pulse parameters typical of reported bulk-glass experiments, the true Hawking flux (thermal) is vastly insufficient to explain observed photon rates, further undermining direct Hawking claims (Schützhold et al., 2010).

Coincidence detection and second-order correlation measurements targeting Hawking-pair entanglement, as well as noise-resilient stimulation protocols (e.g., seeding with squeezed light), are essential for robust identification of the genuine Hawking mechanism (Agullo et al., 2021, Burkhard et al., 15 Nov 2025).

6. Extensions, Resonance Enhancement, and Theoretical Implications

Resonant enhancement in optical analogues can be realized in vortex geometries or by engineering topological transitions in photonic lattices (Dirac cones), leading to significant amplification of otherwise exponentially weak Hawking signals at resonance frequencies (e.g., where quasinormal modes overlap the emission window) (Ornigotti et al., 2017, Burkhard et al., 15 Nov 2025, Kang et al., 2019). In polariton fluids, detailed numerical simulations have identified “sonic horizons” supporting both spontaneous and stimulated Hawking emission, and the interplay with quasinormal-mode resonances is a current frontier (Jacquet et al., 2022, Burkhard et al., 15 Nov 2025).

More generally, optical Hawking analogues explore and test the universality of quantum field theory in curved spacetimes. They yield practical insights into the robustness of Hawking thermality under dispersion, the trans-Planckian problem (ultraviolet completion), and the impact of dissipative, out-of-equilibrium, and topological effects on quantum emission (Aguero-Santacruz et al., 2020, Kang et al., 2019, Belgiorno et al., 2014).

7. Limitations, Challenges, and Future Prospects

Key challenges include:

• Achieving sufficient stationarity and horizon area for detectable fluxes (Schützhold et al., 2010).
• Engineering steep index gradients (surface gravity) to raise $T_H$ into optical regimes.
• Suppressing backgrounds from Raman, four-wave mixing, or other nonlinear processes.
• Ensuring detection sensitivity to correlated quantum pairs amid losses and ambient thermal noise (Agullo et al., 2021, Aguero-Santacruz et al., 2020).

Current directions involve exploiting resonance enhancement, topological photonic structures, and improved quantum optics protocols to observe both stimulated and spontaneous emission in table-top settings. Realization of stationary horizons by static index engineering, such as in topological phase transitions, offers a pathway to long-lived, robust Hawking analogues (Kang et al., 2019). The optical Hawking effect thus remains a vibrant test-bed for both fundamental and applied investigations of quantum field phenomena in artificial curved geometries.