Tailoring focal plane component intensities of polarization singular fields in a tight focusing system
Bibliographic record
Abstract
Abstract The scientific community studies tight focusing of radially and azimuthally-polarized vector beams as it is a versatile solution for many applications. We offer a new method to produce tight focusing that ensures a more uniform intensity profile in multiple dimensions, providing a more versatile and stable solution. We manipulate the polarization of the radially and azimuthally polarized vector beams to find an optimal operating point. We examine in detail optical fields whose polarization states lie on the equator of the relevant Poincaré spheres namely, the fundamental Poincaré sphere, the hybrid order Poincaré sphere (HyOPS), and the higher order Poincaré sphere. We find via simulation that the fields falling on these equators have focal plane intensity distributions characterized by a single rotation parameter $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> determining the individual state of polarization. The strengths of the component field distributions vary with $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and can be tuned to achieve equal strengths of longitudinal ( z ) and transverse ( x and y ) components at the focal plane. Without control of this parameter (e.g., using $$\alpha =0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in radially and $$\alpha =\pi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> in azimuthally-polarized vector beams) intensity in x and y components are at 20% of the z component. In our solution with $$\alpha =\pi /2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , all components are at 80% of the maximum possible intensity of z . In examining the impact of $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> on a tightly focused beam, we also found that a helicity inversion of HyOPS beams causes a rotation of 180 degree in the axial intensity distribution.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".