Second-Order Nonlinear Microcavity Design

• Second-order nonlinear microcavities are optical resonators that harness the quadratic susceptibility of materials like GaN to boost frequency conversion processes.
• They use precisely engineered GaN/AlGaN layers and quarter-wavelength DBRs to achieve optimal phase matching and resonant enhancement, increasing SHG efficiency by up to three orders of magnitude.
• These microcavities are pivotal for on-chip frequency conversion, UV light generation, and quantum photonics by enabling low-threshold, highly efficient nonlinear interactions.

A second-order nonlinear microcavity is an optical microresonator system engineered to exploit the quadratic nonlinear susceptibility χ^2 of suitable materials, enabling efficient nonlinear processes such as second-harmonic generation (SHG), sum-frequency generation (SFG), and related frequency-conversion effects. These structures combine the intrinsic material nonlinearity with photonic design elements that localize and enhance optical fields, resulting in substantially increased efficiency for desired nonlinear interactions compared to their bulk material counterparts. Careful attention to material growth, interface quality, cavity design, and phase-matching is necessary to fully realize the enhancement potential of such microcavities.

1. Fundamentals of Second-Order Nonlinearity and Microcavity Design

In non-centrosymmetric materials, such as wurtzite-structured GaN, the second-order susceptibility χ^2 is nonzero. The interaction of a fundamental electromagnetic field E(ω) at frequency ω with such a medium induces a nonlinear polarization at 2ω according to

$$P^{(2)}(2\omega) = \epsilon_0 \chi^{(2)} E^2(\omega)$$

This nonlinear polarization serves as the source for processes such as SHG.

A canonical second-order nonlinear microcavity comprises a nonlinear layer (such as GaN) embedded between two high-reflectivity distributed Bragg reflectors (DBRs), typically formed by alternating layers of materials with different refractive indices (e.g., GaN/AlGaN). The DBRs are engineered with quarter-wavelength (λ/4) thicknesses tuned to the second-harmonic wavelength, forming a stop band and confining the electromagnetic field within the cavity.

The resonant enhancement of intracavity intensity is critical, as the generated second-harmonic intensity scales as

$$I^{(2\omega)} \propto |\chi^{(2)}|^2\, |E(\omega)|^4$$

Thus, the microcavity effect dramatically amplifies the nonlinear interaction relative to the bulk.

2. Distributed Bragg Reflectors and Field Enhancement Mechanisms

The DBRs play a dual role: they enforce spectral selectivity at the target nonlinear wavelength and spatially confine the optical field within the cavity region, both for the fundamental and second-harmonic frequencies. The reflectors are constructed from repeated GaN/Al₀.₅Ga₀.₅N pairs, usually on the order of 5 periods for each DBR as demonstrated in GaN/AlGaN microcavities (Tasco et al., 2011).

The field enhancement associated with the cavity resonance can be approximated by

$E_\text{cavity} \propto \sqrt{Q}$

where $Q$ is the quality factor of the cavity. Maximizing $Q$ and ensuring optimal layer thicknesses and interface abruptness are essential for maximizing the nonlinear response.

Sharp, well-defined interfaces—characterized by minimal roughness (e.g., 0.6 nm measured via AFM)—are crucial to maintaining both the optical quality of the DBRs and the phase-matching conditions for nonlinear conversion. High-resolution analysis by SEM, AFM, and HRXRD are standard characterizations to verify these parameters.

3. Experimental Implementation and Performance Benchmarking

The nonlinear response of such microcavities is often assessed via second-harmonic generation experiments. In one implementation, a noncollinear Maker fringe setup using a femtosecond Ti:Sapphire laser (λ ≈ 830 nm) and transmission detection geometry is employed:

• Pump pulses are split into two beams with controlled polarization and recombined at a defined angle (e.g., 18°) inside the microcavity.
• The angular and polarization dependence of the SH signal is mapped by rotating and translating the sample.
• Temporal overlap is maintained via an active delay line.

Compared to a bulk GaN slab (e.g., 300 nm thick on sapphire), a GaN/AlGaN microcavity demonstrates:

• Narrower angular emission profile due to resonant feedback.
• Brighter SH signal at half the pump power, confirming field localization and enhanced nonlinear interaction.
• Polarization selectivity reflecting the anisotropy of GaN's χ^2.

These observations quantify the degree of enhancement attributable to both photonic and material engineering.

4. Material and Interface Engineering Constraints

Achieving maximal second-order nonlinear response requires highly crystalline epitaxial growth of GaN and AlGaN with low defect densities and controlled orientation (c-axis alignment). Dislocations, mosaic spread, and interface roughness degrade the effective nonlinear susceptibility by compromising phase-matching and increasing scattering.

Material stacks are typically grown via MOCVD or MBE, and growth evolution is monitored with in situ and ex situ crystallographic and morphological tools to ensure abrupt compositional transitions and minimal interface roughness.

Phase matching is further enforced by precise optical thickness control of DBR and cavity layers, leveraging the high refractive index contrast to tune the resonance to the desired SH wavelength (∼400 nm in prototypical implementations).

5. Mechanisms of Nonlinear Enhancement and Theoretical Considerations

The enhancement in microcavity-based SHG is fundamentally due to the interaction length and field localization afforded by both the cavity resonance and the phase-matched DBR environment. Considering a distributed structure with gain G (reflectivity-induced enhancement), the field inside the cavity can be expressed as: $E(\omega) = E_0\, G$ where $G$ is determined by the DBR reflectivities, absorption, and spatial overlap of the optical modes.

From the scaling behavior,

$I^{(2\omega)} \propto Q^2\, |E_0|^4$

Since even moderate $Q$ enhancements (for example, $Q > 10^3$) are achievable in such heterostructures, two to three orders of magnitude increase in SHG efficiency relative to bulk is typical, assuming comparable crystalline quality.

6. Applications and Implications

Second-order nonlinear microcavities based on GaN/AlGaN are promising for on-chip frequency conversion (e.g., visible-to-UV or NIR-to-visible), parametric processes, and quantum photonics applications including sources of entangled photons and quantum frequency conversion. Their operation in the near-UV (∼400 nm) makes them suitable for integration with UV emitters, detectors, and quantum optical platforms. The resonant enhancement effect enables low-threshold nonlinear devices and facilitates exploration of nonlinear dynamics at lower pump powers.

These microcavities further provide a testbed for studying cavity quantum electrodynamics (QED) in nonlinear regimes, exploring the interplay of resonance-enhanced nonlinear processes with quantum emitter coupling, and advancing photonic integration with III–V semiconductors.

7. Summary Table: Key Parameters and Enhancement Strategies

Design Aspect	Implementation Detail	Function
Nonlinear Material	GaN (non-centrosymmetric wurtzite)	Provides high χ^2 for SHG (10–100 pm/V)
Microcavity Structure	GaN layer between GaN/AlGaN DBRs	Resonant field enhancement, spectral selectivity
DBR Construction	5 GaN/Al₀.₅Ga₀.₅N periods, λ/4 thick	High reflectance at SH wavelength, phase matching
Quality Factor (Q)	Controlled by interface roughness, DBR	Higher Q → greater field buildup and SHG enhancement
Growth and Interface Assessment	SEM, AFM, HRXRD	Validates crystallinity and abruptness (e.g., 0.6 nm RMS)
SHG Performance Metric	I^2ω ∝	χ^2

The combination of high intrinsic χ^2, optimized multilayer engineering, and stringent interface control in GaN/AlGaN microcavities enables a robust platform for highly efficient second-order nonlinear optical processes, with direct impact on the evolution of integrated frequency conversion and nonlinear photonics technologies (Tasco et al., 2011).