[Paper Review] Coherently superposed efficient second harmonic generation by domain wall series in ferroelectrics

Huaijin Ren, Xuewei Deng+1 more|arXiv (Cornell University)|Oct 8, 2010

Photorefractive and Nonlinear Optics4 citations

TL;DR

This paper proposes a novel mechanism for efficient second harmonic generation (SHG) in periodically poled ferroelectrics based on coherent superposition of Cherenkov second harmonics (CSH) emitted from discrete domain walls. By angle-tuning a continuous 1064 nm laser beam, phase-matched constructive interference across dozens of domain walls achieves a record single-pass conversion efficiency of 5%/W, significantly exceeding conventional quasi-phase-matching (QPM) in efficiency per cycle.

ABSTRACT

A novel mechanism of efficient second harmonic generation in domain wall series is reported. By employing angle modulation, obvious intensity peaks of second harmonic appear at specific incident angles utilizing the continuous laser source of 200mW, and the single-pass conversion efficiency comes up to 5%/W only through dozens of domain walls. It can be shown that the phenomenon is caused by coherent superposition of Cherenkov second harmonics (CSH) generated by different domain walls, which is a novel mechanism totally distinguished from Quasi-phase-matching (QPM).

Motivation & Objective

• To investigate the role of ferroelectric domain walls in generating efficient second harmonic generation beyond traditional quasi-phase-matching (QPM).
• To determine whether coherent superposition of Cherenkov second harmonics (CSH) from multiple domain walls can lead to enhanced SHG efficiency.
• To demonstrate that domain wall series can act as discrete, phase-coherent sources for complete phase-matched SHG.
• To establish a new mechanism for high-efficiency frequency conversion that avoids temperature or precise phase-matching control.

Proposed method

• Employed a 200 mW continuous-wave 1064 nm laser incident at variable angles relative to the y-axis of periodically poled LiNbO3 (PPLN) crystals with 30 μm period and 1:1 duty ratio.
• Measured second harmonic intensity as a function of incident angle, observing distinct intensity peaks at specific angles.
• Theoretical modeling based on phase-matching condition: k₂cosθ = 2k₁cosα, where α and θ are internal angles of fundamental and second harmonic waves relative to the y-axis.
• Derived a condition for coherent superposition: ΔΦ = 2πm, where m is an integer, ensuring in-phase addition of CSH from adjacent domain walls.
• Used Snell’s law to convert internal angles to external emergence angles for comparison with experimental data.
• Calculated normalized conversion efficiency per cycle (two domain walls) and compared it to state-of-the-art QPM results.

Experimental results

Research questions

• RQ1 Can coherent superposition of Cherenkov second harmonics (CSH) from multiple domain walls lead to enhanced second harmonic generation in ferroelectrics?
• RQ2 Does angular tuning of the incident beam enable complete phase matching in a domain wall series, distinct from quasi-phase-matching (QPM)?
• RQ3 What is the achievable conversion efficiency of this CSH-based mechanism compared to conventional QPM in periodically poled ferroelectrics?
• RQ4 Can this mechanism operate efficiently under continuous-wave (CW) excitation, unlike prior reports limited to ultrashort pulses?
• RQ5 What is the physical origin of the observed intensity peaks in the second harmonic signal at specific incident angles?

Key findings

• A peak single-pass conversion efficiency of 5%/W was achieved in PPLN with only 20 domain walls traversed, corresponding to 0.5%/W per cycle.
• The highest efficiency occurred at an incident angle of 6.15°, where the phase difference ΔΦ between CSH contributions from adjacent domain walls was exactly 2π, enabling full constructive interference.
• The observed intensity peaks were attributed to coherent superposition of CSH from domain walls, not to QPM, as confirmed by the absence of reciprocal vector matching along the x-axis.
• The mechanism operates under continuous-wave excitation (200 mW), enabling milliwatt-level second harmonic output—unprecedented in CSHG under CW conditions.
• The efficiency (0.5%/W per cycle) exceeds that of the highest reported QPM efficiency (0.37%/W per cycle) after normalization.
• The method enables high-efficiency frequency conversion without temperature stabilization or precise phase-matching control, relying only on angular tuning.