Cavity-Enhanced SPDC

• Cavity-enhanced SPDC is a nonlinear optical process using resonant cavities to control mode structure, narrow emission linewidths, and enhance spectral brightness.
• It employs χ(2) interactions with phase matching and cavity transmission (Airy functions) to produce entangled signal and idler photons in defined temporal and spectral modes.
• Implementations range from bulk crystal setups to nanofilm metasurfaces, enabling quantum state engineering and efficient coupling to atomic systems.

Cavity-enhanced spontaneous parametric down-conversion is SPDC performed in a resonant structure so that the cavity selects and enhances specific optical modes of the down-converted fields and, in some regimes, the pump. In standard notation, a pump photon at frequency $\omega_p$ is converted into signal and idler photons satisfying $\omega_p=\omega_s+\omega_i$ and, for quasi-phase matching, $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$. The cavity replaces the broad free-space mode continuum with resonant longitudinal and, in some platforms, transverse or orbital-angular-momentum modes, thereby narrowing linewidths, increasing spectral brightness per mode, and reshaping the joint spectral and temporal structure of the emitted biphoton state (Jeronimo-Moreno et al., 2010).

1. Nonlinear interaction and resonant regimes

In the undepleted-pump picture, SPDC is governed by a $\chi^{(2)}$ interaction Hamiltonian of the form

$$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$

or equivalent frequency-domain formulations in which the biphoton state is written as

$$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$

with

$$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$

In cavity-enhanced SPDC, the free-space joint spectral structure is multiplied by cavity transmission functions, which in the Fabry–Perot description are Airy functions. Jeronimo-Moreno, Rodriguez-Benavides and U’Ren distinguish singly-resonant cavities, where the signal and idler modes are resonant, from doubly-resonant cavities, where the pump mode is also resonant, and derive

$$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$

and

$$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$

The cavity linewidth and free spectral range obey

$$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$

so increasing finesse narrows the emission bandwidth while shorter cavities enlarge mode spacing (Jeronimo-Moreno et al., 2010).

Below threshold, cavity-enhanced SPDC is also naturally described by Bogoliubov transformations. In the arbitrary-gain, arbitrary-finesse theory of a two-sided ring cavity with a nonlinear crystal, the output field is written as

$\omega_p=\omega_s+\omega_i$0

with coefficients determined by round-trip time, mirror transmissions, losses, and single-pass squeezing parameter. That theory predicts increased coherence due to stimulated SPDC in the high-gain but sub-threshold regime, while preserving an analytic description of multimode cavity output and of correlation functions such as $\omega_p=\omega_s+\omega_i$1 (Zielińska et al., 2014).

2. Mode structure, clustering, and temporal correlations

A defining feature of type-II cavity-enhanced SPDC is the mismatch between the signal and idler free spectral ranges. In a doubly resonant type-II OPO, only subsets of signal and idler longitudinal modes overlap, producing the cluster effect. The cluster spacing is

$\omega_p=\omega_s+\omega_i$2

and, for a cavity containing both an SPDC crystal and an additional birefringent tuning crystal, it becomes

$\omega_p=\omega_s+\omega_i$3

A single cluster within the SPDC bandwidth requires

$\omega_p=\omega_s+\omega_i$4

and effective single-longitudinal-mode operation further requires

$\omega_p=\omega_s+\omega_i$5

These conditions formalize how birefringence and finesse can suppress multimode longitudinal emission without external mode filters (Moqanaki et al., 2018).

The temporal structure is the Fourier dual of the cavity-shaped spectral response. For continuous-wave pumped cavity-enhanced SPDC,

$\omega_p=\omega_s+\omega_i$6

and the signal-signal correlation is

$\omega_p=\omega_s+\omega_i$7

In multimode cavities these correlations form a comb in time, with peak spacing set by the cavity round-trip time and an envelope set by the cavity decay rates; the complete theory further predicts the signal-signal-idler correlation surface

$\omega_p=\omega_s+\omega_i$8

together with stripe-like contributions from uncorrelated multi-pair events (Müller et al., 2020).

Monolithic type-II Fabry–Perot cavities provide a particularly transparent example of the cluster condition. In a submillimeter PPKTP cavity designed for telecom photons, the measured values were $\omega_p=\omega_s+\omega_i$9 GHz, $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$0 GHz, cavity bandwidths $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$1 MHz and $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$2 MHz, and a residual mismatch $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$3 GHz, which exceeds $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$4 MHz. Under that inequality, only the central orthogonal mode pair is doubly resonant, yielding single-longitudinal-mode operation (Li et al., 2019).

3. Architectures and representative devices

Conventional cavity-enhanced SPDC sources are commonly realized with bulk periodically poled crystals inside linear, bow-tie, ring, or semi-hemispherical resonators. One implementation uses a linear high-finesse cavity around a type-II PPKTP crystal pumped at $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$5 to generate non-degenerate photons with signal at $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$6, resonant with the cesium $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$7 line. In that source the cavity is double-resonant for signal and idler, the pump is not resonant, and the heralded single-photon linewidth is $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$8 (Tseng et al., 2020).

A distinct route to intrinsic single-mode operation is the introduction of an additional birefringent crystal into the cavity. In a linear semi-hemispherical cavity containing a 30 mm PPKTP crystal and a 15 mm BBO tuning crystal, a source at $\mathbf{k}_p=\mathbf{k}_s+\mathbf{k}_i+\mathbf{G}$9 compatible with the Cs $\chi^{(2)}$0 line achieved a bandwidth of $\chi^{(2)}$1, a photon-pair generation rate of approximately $\chi^{(2)}$2 at $\chi^{(2)}$3 pump power, an auto-correlation value $\chi^{(2)}$4, and heralded $\chi^{(2)}$5 at the bright operating point (Moqanaki et al., 2018).

Monolithic cavities collapse the resonator and nonlinear medium into a single element. A type-II PPKTP Fabry–Perot cavity with dimensions $\chi^{(2)}$6 and dielectric coatings on the crystal faces produced single-longitudinal-mode time-energy entangled photons at $\chi^{(2)}$7. In that device the measured Glauber cross-correlation FWHM was about $\chi^{(2)}$8, and a Michelson-interference fit gave a Lorentzian linewidth of $\chi^{(2)}$9, in close agreement with the cavity transmission linewidth (Li et al., 2019).

Bow-tie resonators with auxiliary birefringent tuning elements and external Fabry–Perot filters enable independent signal and idler tuning. A 610 mm cavity containing a 20 mm PPKTP crystal and an unpoled KTP tuning crystal produced photon pairs around the Rb $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$0 line with filters such that over 97% of the correlated photons are in a single mode of $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$1 bandwidth. The measured mean free spectral range was $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$2 MHz, the cavity decay rate was $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$3, and the cluster spacing was $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$4 GHz (Prakash et al., 2019).

Cavity-enhanced SPDC has also been extended beyond Gaussian transverse modes. A flat–concave cavity with a 5-mm-long type-II PPKTP crystal, operating at the Rb $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$5 line $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$6, supported degenerate high-order Laguerre–Gaussian modes $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$7. With cavity length $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$8 mm, finesse $$\hat{H}_\text{int} = \epsilon_0 \int d^3 r\; \chi^{(2)}(\mathbf{r}) E_p(\mathbf{r}) \hat{E}_s^{(-)}(\mathbf{r}) \hat{E}_i^{(-)}(\mathbf{r}) + \text{h.c.},$$9, and average free spectral range $$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$0 GHz, the measured photon linewidth was $$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$1 MHz after single-longitudinal-mode filtering by an external Fabry–Pérot etalon (Wan et al., 8 Feb 2025).

4. Quantum-state engineering and entanglement control

The cavity does not merely narrow the spectrum; it can also fix the mode structure in which entanglement is produced. In the monolithic telecom Fabry–Perot source, Franson interferometry with two all-fiber unbalanced Michelson interferometers yielded raw visibilities $$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$2 and $$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$3, and net visibilities $$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$4 and $$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$5, demonstrating high-quality time-energy entanglement in a single-longitudinal-mode source (Li et al., 2019).

A long-standing issue for narrow-band cavity sources was that the direct cavity output was often not itself entangled, so entanglement had to be created outside the cavity by postselection. A recent solution uses orbital angular momentum (OAM) as the intracavity degree of freedom. In a cavity supporting the four resonant modes $$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$6, OAM conservation in type-II SPDC directly generates the state

$$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$7

with no external postselection. The measured fidelity of the directly generated OAM-entangled state was $$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$8. Deterministic OAM-to-polarization transfer produced

$$|\Psi\rangle = \int d\omega_s \int d\omega_i\, f(\omega_i,\omega_s)\, a_s^\dagger(\omega_s)\,a_i^\dagger(\omega_i)\,|\text{vac}\rangle,$$9

with fidelity $$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$0, and a PBS-based extension yielded OAM–polarization hyperentanglement with fidelity $$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$1 (Wan et al., 8 Feb 2025).

The same cavity-shaped biphoton spectrum also modifies interference without induced emission. In a Zou–Wang–Mandel interferometer fed by singly resonant OPOs below threshold, the cavity-enhanced signal spectrum becomes a comb of Lorentzian lines,

$$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$2

and the visibility of the $$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$3-th comb line is

$$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$4

This places induced coherence in a narrow-band, cavity-defined regime and makes the sample transmissivity directly visible in mode-resolved single-photon interference (Cho et al., 2024).

5. Interfaces with atoms, memories, and spectroscopy

One of the main motivations for cavity-enhanced SPDC is spectral matching to narrow atomic transitions. A cavity-enhanced type-II PPKTP source resonant with the cesium $$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$5 line generated heralded single photons with linewidth $$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$6, close to the atomic natural linewidth $$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$7. Interfaced to an EIT memory in a cold cesium MOT, this source achieved storage-and-retrieval efficiency $$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$8 at short storage time, $$f(\omega_i,\omega_s)=\alpha(\omega_s+\omega_i)\,\phi(\omega_i,\omega_s)\,F_s(\omega_s)\,F_i(\omega_i).$$9 efficiency at $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$0, and $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$1 efficiency at $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$2. The corrected fidelity for stored polarization qubits was $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$3, while the heralded photons retained nonclassical statistics with $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$4 and source-side peak $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$5 (Tseng et al., 2020).

Cavity-enhanced SPDC is equally effective as a spectroscopic tool. Around the Rb $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$6 line, a bow-tie CE-SPDC source with tuneable birefringence resonator and tunable Fabry–Perot filters achieved independent signal and idler tuning with MHz resolution. Difference-frequency generation was used to map the CE-SPDC spectrum and locate emission clusters, and CE-SPDC driven atomic spectroscopy demonstrated that the generated photon pairs efficiently interact with neutral rubidium. In that system the single-mode linewidth was $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$7, and the measured brightness was $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$8 coincidences/s/mW at the detectors, corresponding to approximately $$S_{\text{SR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,|f(\omega_i,\omega_s)|^2$$9 pairs/s/mW in fiber after correcting for APD quantum efficiency (Prakash et al., 2019).

At the Cs $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$0 line, the birefringence-tuned single-mode source at $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$1 provides a complementary benchmark for hybrid light-matter systems. Its bandwidth of $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$2, photon-pair generation rate exceeding $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$3 kHz at $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$4 mW, and four-photon generation rate of $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$5 Hz at $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$6 mW place it directly in the regime of hybrid quantum systems and long-coherence-time photonic interfaces (Moqanaki et al., 2018).

The architectural significance is that cavity enhancement narrows the SPDC spectrum at the source, rather than by lossy post-generation filtering alone. In memory-oriented work this enables photons narrower than or comparable to the atomic linewidth; in spectroscopy-oriented work it enables independent control of signal and idler detunings around hyperfine structure. Both capabilities are central to quantum repeaters, quantum memories, and light–matter interfaces (Tseng et al., 2020).

6. Limits, misconceptions, and emerging directions

A persistent limitation of cavity-enhanced SPDC is multimode longitudinal emission. In narrow-band OPO sources this was identified as a major drawback, and a substantial part of the literature is devoted to suppressing it by cavity design, birefringent tuning, or auxiliary filters. In another direction, the usual purity–yield trade-off of heralded SPDC can be attacked by adding strong intracavity photon–photon interaction. A cavity-SPDC proposal based on photon blockade predicts that, by introducing a strong photon-photon interaction into the intracavity medium and increasing the pump power, the available single-photon yield can be larger than $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$7 while maintaining a high purity of $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$8, with $$S_{\text{DR}}(\omega_i,\omega_s)=\mathscr{A}_s(\omega_s)\,\mathscr{A}_i(\omega_i)\,\mathscr{A}_p(\omega_s+\omega_i)\,\mathscr{P}(\omega_i,\omega_s)\,|f(\omega_i,\omega_s)|^2.$$9 and $$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$0 for $$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$1, and $$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$2 and $$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$3 for $$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$4 (Tang et al., 2021).

Another common misconception is that cavity enhancement must involve an external mirror cavity around a bulk crystal. Subwavelength nonlinear films can exhibit cavity-like enhancement through their own Fabry–Perot resonances. In GaP nanofilms, the resonant enhancement occurs for the vacuum fluctuations seeding SPDC, not for an externally fed radiation, and the measured spectrum shows about $$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$5 times enhancement of SPDC efficiency at resonant wavelengths. This is not a conventional cavity-SPDC experiment, but it directly demonstrates that a low-$$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$6 Fabry–Perot microcavity can shape the vacuum field and the SPDC spectrum in an ultrathin nonlinear medium (Santiago-Cruz et al., 2020).

That idea has been pushed further in nonlinear metasurfaces. A lithium-niobate metasurface with a lateral guided-mode cavity formed by two distributed Bragg reflectors was predicted, using quasi-normal-mode theory, to reach an SPDC rate up to $$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$7, about $$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$8 times higher than the corresponding metasurface without a cavity, with high-$$\delta\omega=\frac{2c}{\ell\,n(\omega_0)+(L-\ell)}\,\mathscr{F}^{-1/2}, \qquad \Delta\omega=\frac{\pi c}{\ell\,n(\omega_0)+(L-\ell)},$$9 resonances $\omega_p=\omega_s+\omega_i$00–950 across a broad angular bandwidth. In that platform, the cavity dispersion allows all-optical tuning of photon-pair emission directions by controlling the pump wavelength (Fan et al., 21 May 2025).

The concept has also been extended beyond biphotons. In a flux-pumped superconducting parametric cavity, direct three-photon SPDC was observed with flux densities exceeding $\omega_p=\omega_s+\omega_i$01 photon/s/Hz and strongly non-Gaussian output, including the triangular “star state” generated by a cubic Hamiltonian. A later experiment on a superconducting three-photon SPDC source reported genuine tripartite non-Gaussian entanglement in the steady-state output field, with a maximum violation of the witness bound by $\omega_p=\omega_s+\omega_i$02 standard deviations of the statistical noise (Chang et al., 2019, Jarvis-Frain et al., 6 Oct 2025).

Taken together, these developments show that cavity-enhanced SPDC now spans bulk Fabry–Perot and ring cavities, monolithic cavities, OAM-supporting resonators, superconducting parametric cavities, and metasurface or nanofilm microcavities. Across these platforms, the unifying theme remains the same: the cavity engineers the density of optical states, the spectral response, and the spatiotemporal mode structure in which spontaneous parametric down-conversion occurs.