[Paper Review] Deterministic relation between optical polarization and lattice symmetry revealed in ion-doped single microcrystals

Peng Li, Yaxin Guo+6 more|arXiv (Cornell University)|Mar 17, 2022

Quantum optics and atomic interactions67 references37 citations

TL;DR

This study establishes a deterministic link between optical polarization and lattice symmetry in ion-doped microcrystals by showing that the c/a lattice constant ratio quantitatively determines the linear polarization degree of emitted light. Using polarization-resolved microspectroscopy, the authors derive the 3D orientation of single microcrystals from emission polarization, enabling precise, non-invasive optical orientation mapping via electric and magnetic dipole transitions with unequal polarization degrees.

ABSTRACT

Rare-earth ions doped crystals are of great significance for micro-sensing and quantum information, whilst the ions in the crystals emit light with spontaneous partial polarization, which is, though believed to be originated from the crystal lattice structure, still lacking a deterministic explanation that can be tested with quantitative accuracy. We report the experimental evidence showing the profound physical relation between the polarization degree of light emitted by the doped ion and the lattice symmetry, by demonstrating, with unprecedented precision, that the lattice constant ratio c/a directly quantifies the macroscopic effective polar angle of the electric and magnetic dipoles, which essentially determines the linear polarization degree of the emission. Based on this discovery, we further propose a pure optical technology to identify the three-dimensional orientation of a rod-shaped single microcrystal using the polarization-resolved micro-spectroscopy. Our results, revealing the physical origin of light polarization in ion-doped crystals, open the way towards on-demand polarization control with crystallography, and provide a versatile platform for polarization-based microscale sensing in dynamical systems.

Motivation & Objective

• To establish a quantitative, deterministic relationship between optical polarization and lattice symmetry in ion-doped single microcrystals.
• To resolve the long-standing ambiguity in the physical origin of partial linear polarization in rare-earth ion-doped crystals.
• To develop a pure optical method for determining the three-dimensional orientation of rod-shaped microcrystals using polarization-resolved microspectroscopy.
• To provide a versatile platform for polarization-based microscale sensing and on-demand polarization control in nanomaterials.

Proposed method

• Employed polarization-resolved micro-photoluminescence (μ-PL) spectroscopy with half-wave, quarter-wave plates, and a linear polarizer to measure Stokes parameters (S1, S2, S3) across multiple polarization bases.
• Combined Poincaré sphere (PS) and polarization fitting (PF) methods to ensure robust analysis, excluding circular polarization and enhancing accuracy of linear polarization degree (LDOP) and angle (φ).
• Derived dipole orientation from crystal symmetry using point group theory (P63/m space group) and confirmed that dipoles align along the composite vector of c- and a-axes.
• Developed mathematical models using intensity ratios (I∥/I⊥) and orthogonal emission intensities (Iz′x′, Iz′y′) at 90° polarization angles to calculate 3D orientation (θ′, φ′) from two magnetic, two electric, or one magnetic and one electric transition peaks.
• Formulated analytical solutions (Eqs. S7–S8, S13–S14, S17–S18) that relate measured intensities to the tilt (θ′) and azimuthal (φ′) angles of the microcrystal’s c-axis relative to the detection axis.
• Validated the method by requiring unequal LDOPs for selected transitions to avoid singularities and ensure solvability of the orientation equations.

Experimental results

Research questions

• RQ1 What is the quantitative relationship between the lattice symmetry (c/a ratio) and the linear polarization degree of light emitted by doped ions in single microcrystals?
• RQ2 How can the three-dimensional orientation of a single microcrystal be determined solely from polarization-resolved optical measurements?
• RQ3 What is the physical origin of the partial linear polarization in ion-doped microcrystals, and how is it linked to the crystal field direction?
• RQ4 Can the orientation of a microcrystal be retrieved without repositioning it, using only emission intensity data from orthogonal polarization states?
• RQ5 What conditions must be met for the mathematical inversion of orientation from polarization data to yield a unique and stable solution?

Key findings

• The linear polarization degree (LDOP) of emission from Eu3+ ions in NaYF4:Eu3+ microcrystals is quantitatively determined by the c/a lattice constant ratio, establishing a deterministic link between macroscopic optical polarization and microscopic lattice symmetry.
• The electric and magnetic dipole transitions of Eu3+ ions are found to oscillate precisely along the composite vector of the c- and a-axes, defining the generalized crystal field direction.
• The 3D orientation (θ′, φ′) of a single microcrystal can be uniquely determined using polarization-resolved measurements from two magnetic, two electric, or one magnetic and one electric transition peaks with unequal LDOPs.
• The method achieves high-precision orientation retrieval without repositioning the sample, relying only on emission intensity ratios and known LDOP values from prior in-plane measurements.
• Theoretical models (Eqs. S7–S8, S13–S14, S17–S18) provide a complete analytical framework for solving the orientation from orthogonal intensity measurements, with singularities avoided when LDOPs are unequal and non-1.
• Experimental validation confirms that circular polarization is negligible, supporting the use of linear polarization models and enabling robust extraction of LDOP and polarization angle with sub-degree accuracy.