Vector Optical Bullets in Dielectric Media: Polarization Structures and Group-Velocity Effects
<p>(<b>a</b>) Angular dispersion of the optical bullet inside the BK7 glass, when <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>1.25</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>: <math display="inline"><semantics> <mrow> <mn>0.7</mn> </mrow> </semantics></math> (1), <math display="inline"><semantics> <mrow> <mn>0.75</mn> </mrow> </semantics></math> (2), <math display="inline"><semantics> <mrow> <mn>0.85</mn> </mrow> </semantics></math> (3), 1 (4), <math display="inline"><semantics> <mrow> <mn>1.4</mn> </mrow> </semantics></math> (5). (<b>b</b>) Angular dispersion of the optical bullet within the BK7 glass, when <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>: <math display="inline"><semantics> <mrow> <mn>0.629</mn> </mrow> </semantics></math> (1), <math display="inline"><semantics> <mrow> <mn>0.63685</mn> </mrow> </semantics></math> (2), <math display="inline"><semantics> <mrow> <mn>0.645</mn> </mrow> </semantics></math> (3), <math display="inline"><semantics> <mrow> <mn>0.65495</mn> </mrow> </semantics></math> (4), <math display="inline"><semantics> <mrow> <mn>0.685</mn> </mrow> </semantics></math> (5), (<b>c</b>) Angular dispersion of the optical bullet within the BK7 glass, when <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mo>−</mo> <mn>1.2</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mi>γ</mi> </semantics></math>: <math display="inline"><semantics> <mrow> <mn>6</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> (1), <math display="inline"><semantics> <mrow> <mn>7</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> (2), <math display="inline"><semantics> <mrow> <mn>8</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> (3), <math display="inline"><semantics> <mrow> <mn>9</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> (4), <math display="inline"><semantics> <mrow> <mn>10</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> (5). The frequency is normalized to the value of <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.7716</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 2
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of transverse electric (TE) linearly polarized optical bullets and their individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)) in the transverse plane. The white arrows in (<b>b</b>) represent the orientation of the electric field. The frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 3
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of transverse magnetic (TM) linearly polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)). The white arrows in (<b>b</b>) represent the orientation of the electric field. Frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 4
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of azimuthally polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)) in the transverse plane. The white arrows in (<b>b</b>) represent the orientation of the electric field. Frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 5
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of radially polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)) in the transverse plane. The white arrows in (<b>b</b>) represent the orientation of the electric field. Frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 6
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of transverse electric (TE) linearly polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)) in the transverse plane. The white arrows in (<b>b</b>) represent the orientation of the electric field. The frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 7
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of transverse magnetic (TM) linearly polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)) in the transverse plane. The white arrows in (<b>b</b>) represent the orientation of the electric field. The frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 8
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of azimuthally polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)) in the transverse plane. The white arrows in (<b>b</b>) represent the orientation of the electric field. Frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 9
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of radially polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)) in the transverse plane. The white arrows in (<b>b</b>) represent the orientation of the electric field. Frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 10
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of higher polarization order optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)) in the transverse plane. The white arrows in (<b>b</b>) represent the orientation of the electric field. The frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 11
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of higher polarization order optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)) in the transverse plane. The white arrows in (<b>b</b>) represent the orientation of the electric field. The frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>1.6</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 12
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of transverse electric (TE) linearly polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)). The white arrows in (<b>b</b>) represent the orientation of the electric field. Frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mo>−</mo> <mn>1.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>6</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 13
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of transverse magnetic (TM) linearly polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)). The white arrows in (<b>b</b>) represent the orientation of the electric field. Frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mo>−</mo> <mn>1.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>6</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 14
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of azimuthally polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)). The white arrows in (<b>b</b>) represent the orientation of the electric field. Frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mo>−</mo> <mn>1.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>6</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 15
<p>Intensity distributions in the longitudinal (<b>a</b>) and transverse (<b>b</b>) planes of radially polarized optical bullets and its individual components (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>c</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>d</b>), <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>e</b>)). The white arrows in (<b>b</b>) represent the orientation of the electric field. Frequency <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi>fs</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs, <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mo>−</mo> <mn>1.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>6</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 16
<p>Dependencies of FWHM (<b>a</b>) and second-moment (<b>b</b>) pulse widths in BK7 glass for different values of frequency <math display="inline"><semantics> <msub> <mi>ω</mi> <mi>c</mi> </msub> </semantics></math> for linear, azimuthal and radial polarizations. The red color represents <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, and the blue color <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mo>−</mo> <mn>1.2</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>6</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs.</p> "> Figure 17
<p>Normalized intensities of individual components of FWM pulses (<math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>—blue, <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>—red, <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>—orange). Topological charge <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, pulse duration <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> fs. For the cases: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mn>0.63685</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mo>−</mo> <mn>0.628</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>/</mo> <mi>c</mi> <mo>=</mo> <mo>−</mo> <mn>1.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>6</mn> <mi>π</mi> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. The solid line represents the linear polarization of TE, the dashed line represents the linear polarization of TM, the dotted line represents the azimuthal polarization, and the dashed-dotted line represents the radial polarization.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
3. Vector Optical Bullets in Dielectric Material
4. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
FWM | Focus Wave Modes |
TE | Transverse Electric |
TM | Transverse Magnetic |
FWHM | Full-Width Half Maximum |
GVD | Group-Velocity Dispersion |
References
- Rubinsztein-Dunlop, H.; Forbes, A.; Berry, M.V.; Dennis, M.R.; Andrews, D.L.; Mansuripur, M.; Denz, C.; Alpmann, C.; Banzer, P.; Bauer, T.; et al. Roadmap on structured light. J. Opt. 2016, 19, 013001. [Google Scholar] [CrossRef]
- Shvedov, V.; Davoyan, A.R.; Hnatovsky, C.; Engheta, N.; Krolikowski, W. A long-range polarization-controlled optical tractor beam. Nat. Photonics 2014, 8, 846–850. [Google Scholar] [CrossRef]
- Mitri, F.; Li, R.; Guo, L.; Ding, C. Optical tractor Bessel polarized beams. J. Quant. Spectrosc. Radiat. Transf. 2017, 187, 97–115. [Google Scholar] [CrossRef]
- Friese, M.E.; Nieminen, T.A.; Heckenberg, N.R.; Rubinsztein-Dunlop, H. Optical alignment and spinning of laser-trapped microscopic particles. Nature 1998, 394, 348–350. [Google Scholar] [CrossRef]
- Milione, G.; Dudley, A.; Nguyen, T.A.; Chakraborty, O.; Karimi, E.; Forbes, A.; Alfano, R.R. Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams. J. Opt. 2015, 17, 035617. [Google Scholar] [CrossRef]
- Vettenburg, T.; Dalgarno, H.I.; Nylk, J.; Coll-Lladó, C.; Ferrier, D.E.; Čižmár, T.; Gunn-Moore, F.J.; Dholakia, K. Light-sheet microscopy using an Airy beam. Nat. Methods 2014, 11, 541–544. [Google Scholar] [CrossRef] [PubMed]
- Ren, Y.X.; He, H.; Tang, H.; Wong, K.K. Non-diffracting light wave: Fundamentals and biomedical applications. Front. Phys. 2021, 9, 698343. [Google Scholar] [CrossRef]
- Akhmanov, S.A.; Nikitin, S.Y. Physical Optics; Oxford University Press: Oxford, UK, 1997. [Google Scholar]
- Vesperinas, M.N. Scattering and Diffraction in Physical Optics; World Scientific Publishing Company: Singapore, 2006. [Google Scholar]
- Bennett, C.A. Principles of Physical Optics; John Wiley & Sons: Hoboken, NJ, USA, 2022. [Google Scholar]
- Durnin, J. Exact solutions for nondiffracting beams. I. The scalar theory. JOSA A 1987, 4, 651–654. [Google Scholar] [CrossRef]
- Gori, F.; Guattari, G.; Padovani, C. Bessel-gauss beams. Opt. Commun. 1987, 64, 491–495. [Google Scholar] [CrossRef]
- Gutiérrez-Vega, J.C.; Iturbe-Castillo, M.; Chávez-Cerda, S. Alternative formulation for invariant optical fields: Mathieu beams. Opt. Lett. 2000, 25, 1493–1495. [Google Scholar] [CrossRef]
- López-Mariscal, C.; Bandres, M.A.; Gutiérrez-Vega, J.C.; Chávez-Cerda, S. Observation of parabolic nondiffracting optical fields. Opt. Express 2005, 13, 2364–2369. [Google Scholar] [CrossRef] [PubMed]
- Siviloglou, G.; Broky, J.; Dogariu, A.; Christodoulides, D. Observation of accelerating Airy beams. Phys. Rev. Lett. 2007, 99, 213901. [Google Scholar] [CrossRef] [PubMed]
- Gutiérrez-Vega, J.C.; Bandres, M.A. Helmholtz–gauss waves. JOSA A 2005, 22, 289–298. [Google Scholar] [CrossRef] [PubMed]
- Shen, Y.; Zhan, Q.; Wright, L.G.; Christodoulides, D.N.; Wise, F.W.; Willner, A.E.; Zou, K.h.; Zhao, Z.; Porras, M.A.; Chong, A.; et al. Roadmap on spatiotemporal light fields. J. Opt. 2023, 25, 093001. [Google Scholar] [CrossRef]
- Orlov, S.; Gajauskaite, A.; Juršėnas, A. Propagation of vector nondiffracting and nondispersive pulsed beams through an air-dielectric planar interface. Procedia CIRP 2018, 74, 585–588. [Google Scholar] [CrossRef]
- Hodgson, J.N. Optical Absorption and Dispersion in Solids; Springer Science & Business Media: Berlin, Germany, 2012. [Google Scholar]
- Orlov, S.; Piskarskas, A.; Stabinis, A. Localized optical subcycle pulses in dispersive media. Opt. Lett. 2002, 27, 2167–2169. [Google Scholar] [CrossRef] [PubMed]
- Orlov, S.; Stabinis, A. Angular dispersion of diffraction-free optical pulses in dispersive medium. Opt. Commun. 2004, 240, 1–8. [Google Scholar] [CrossRef]
- Saari, P.; Sõnajalg, H. Pulsed bessel beams. Laser Phys. 1997, 7, 32–39. [Google Scholar]
- Reivelt, K.; Saari, P. Optical generation of focus wave modes. JOSA A 2000, 17, 1785–1790. [Google Scholar] [CrossRef]
- Porras, M.A.; Valiulis, G.; Di Trapani, P. Unified description of Bessel X waves with cone dispersion and tilted pulses. Phys. Rev. E 2003, 68, 016613. [Google Scholar] [CrossRef]
- Zapata-Rodríguez, C.J.; Porras, M.A. X-wave bullets with negative group velocity in vacuum. Opt. Lett. 2006, 31, 3532–3534. [Google Scholar] [CrossRef] [PubMed]
- Salem, M.A.; Bağcı, H. Reflection and transmission of normally incident full-vector X waves on planar interfaces. JOSA A 2012, 29, 139–152. [Google Scholar] [CrossRef] [PubMed]
- Kondakci, H.E.; Abouraddy, A.F. Diffraction-free space–time light sheets. Nat. Photonics 2017, 11, 733–740. [Google Scholar] [CrossRef]
- Yessenov, M.; Hall, L.A.; Schepler, K.L.; Abouraddy, A.F. Space-time wave packets. Adv. Opt. Photonics 2022, 14, 455–570. [Google Scholar] [CrossRef]
- Davila-Rodriguez, J.; Gutiérrez-Vega, J.C. Helical Mathieu and parabolic localized pulses. JOSA A 2007, 24, 3449–3455. [Google Scholar] [CrossRef] [PubMed]
- Butkus, R.; Orlov, S.; Piskarskas, A.; Smilgevicius, V.; Stabinis, A. Phase matching of optical X-waves in nonlinear crystals. Opt. Commun. 2005, 244, 411–421. [Google Scholar] [CrossRef]
- Orlov, S.; Stabinis, A.; Smilgevicius, V.; Valiulis, G.; Piskarskas, A. Parametric excitation of X-waves by downconversion of Bessel beams in nonlinear crystals. Opt. Lett. 2007, 32, 68–70. [Google Scholar] [CrossRef] [PubMed]
- Dorn, R.; Quabis, S.; Leuchs, G. Sharper focus for a radially polarized light beam. Phys. Rev. Lett. 2003, 91, 233901. [Google Scholar] [CrossRef] [PubMed]
- Dorn, R.; Quabis, S.; Leuchs, G. The focus of light—Linear polarization breaks the rotational symmetry of the focal spot. J. Mod. Opt. 2003, 50, 1917–1926. [Google Scholar]
- Orlov, S.; Peschel, U.; Bauer, T.; Banzer, P. Analytical expansion of highly focused vector beams into vector spherical harmonics and its application to Mie scattering. Phys. Rev. A 2012, 85, 063825. [Google Scholar] [CrossRef]
- Orlov, S.; Berškys, J. Vector-spherical-harmonics representation of vector complex source beams carrying vortices. Phys. Rev. A 2020, 102, 063532. [Google Scholar] [CrossRef]
- Gonoskov, I.; Aiello, A.; Heugel, S.; Leuchs, G. Dipole pulse theory: Maximizing the field amplitude from 4 π focused laser pulses. Phys. Rev. A 2012, 86, 053836. [Google Scholar] [CrossRef]
- Orlov, S.; Peschel, U. Complex source beam: A tool to describe highly focused vector beams analytically. Phys. Rev. A 2010, 82, 063820. [Google Scholar] [CrossRef]
- Orlov, S.; Banzer, P. Vectorial complex-source vortex beams. Phys. Rev. A 2014, 90, 023832. [Google Scholar] [CrossRef]
- Mitri, F. Superposition of nonparaxial vectorial complex-source spherically focused beams: Axial Poynting singularity and reverse propagation. Phys. Rev. A 2016, 94, 023801. [Google Scholar] [CrossRef]
- Gutiérrez-Cuevas, R.; Moore, N.J.; Alonso, M.A. Lorenz-Mie scattering of focused light via complex focus fields: An analytic treatment. Phys. Rev. A 2018, 97, 053848. [Google Scholar] [CrossRef]
- Bauer, T.; Orlov, S.; Peschel, U.; Banzer, P.; Leuchs, G. Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams. Nat. Photonics 2014, 8, 23–27. [Google Scholar] [CrossRef]
- Oron, R.; Blit, S.; Davidson, N.; Friesem, A.A.; Bomzon, Z.; Hasman, E. The formation of laser beams with pure azimuthal or radial polarization. Appl. Phys. Lett. 2000, 77, 3322–3324. [Google Scholar] [CrossRef]
- Machavariani, G.; Lumer, Y.; Moshe, I.; Meir, A.; Jackel, S. Spatially-variable retardation plate for efficient generation of radially-and azimuthally-polarized beams. Opt. Commun. 2008, 281, 732–738. [Google Scholar] [CrossRef]
- Beresna, M.; Gecevičius, M.; Kazansky, P.G.; Gertus, T. Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass. Appl. Phys. Lett. 2011, 98, 201101. [Google Scholar] [CrossRef]
- Wang, Z.Y.; Zhou, Z.; Zhang, H.; Wei, Y.; Yu, H.G.; Hu, W.; Chen, W.; Dai, H.T.; Ma, L.L.; Qiu, C.W.; et al. Vectorial liquid-crystal holography. eLight 2024, 4, 5. [Google Scholar] [CrossRef]
- Mazanov, M.; Yermakov, O.; Deriy, I.; Takayama, O.; Bogdanov, A.; Lavrinenko, A.V. Photonic spin Hall effect: Contribution of polarization mixing caused by anisotropy. Quantum Rep. 2020, 2, 489–500. [Google Scholar] [CrossRef]
- Fedorov, F.I. K teorii polnogo otrazheniya. Dokl. Akad. Nauk. SSSR 1955, 105, 465–468. [Google Scholar]
- Imbert, C. Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam. Phys. Rev. D 1972, 5, 787. [Google Scholar] [CrossRef]
- Bouchal, Z.; Olivík, M. Non-diffractive vector Bessel beams. J. Mod. Opt. 1995, 42, 1555–1566. [Google Scholar] [CrossRef]
- Stratton, J.A. Electromagnetic Theory; John Wiley & Sons: Hoboken, NJ, USA, 2007; Volume 33. [Google Scholar]
- Morse, P.; Feshbach, H. Methods of theoretical physics, number 2 tom. In International Series in Pure and Applied Physics; McGraw-Hill: New York, NY, USA, 1953. [Google Scholar]
- Salem, M.A.; Bağcı, H. Energy flow characteristics of vector X-waves. Opt. Express 2011, 19, 8526–8532. [Google Scholar] [CrossRef] [PubMed]
- Ornigotti, M.; Conti, C.; Szameit, A. Universal form of the carrier frequency of scalar and vector paraxial X waves with orbital angular momentum and arbitrary frequency spectrum. Phys. Rev. A 2015, 92, 043801. [Google Scholar] [CrossRef]
- Diouf, M.; Harling, M.; Yessenov, M.; Hall, L.A.; Abouraddy, A.F.; Toussaint, K.C. Space-time vector light sheets. Opt. Express 2021, 29, 37225–37233. [Google Scholar] [CrossRef] [PubMed]
- Yessenov, M.; Chen, Z.; Lavery, M.P.; Abouraddy, A.F. Vector space-time wave packets. Opt. Lett. 2022, 47, 4131–4134. [Google Scholar] [CrossRef]
- Gotovski, P.; Orlov, S. Parabolic Vector Focus Wave Modes. J. Laser Micro Nanoeng. 2019, 14, 25–31. [Google Scholar]
- Vosylius, V.; Orlov, S. Vector Focus Wave Modes with Elliptic Cross-Section. J. Laser Micro Nanoeng. 2019, 14, 74–80. [Google Scholar]
- Meier, M.; Romano, V.; Feurer, T. Material processing with pulsed radially and azimuthally polarized laser radiation. Appl. Phys. A 2007, 86, 329–334. [Google Scholar] [CrossRef]
- Kraus, M.; Ahmed, M.A.; Michalowski, A.; Voss, A.; Weber, R.; Graf, T. Microdrilling in steel using ultrashort pulsed laser beams with radial and azimuthal polarization. Opt. Express 2010, 18, 22305–22313. [Google Scholar] [CrossRef] [PubMed]
- Bhuyan, M.; Courvoisier, F.; Lacourt, P.; Jacquot, M.; Salut, R.; Furfaro, L.; Dudley, J. High aspect ratio nanochannel machining using single shot femtosecond Bessel beams. Appl. Phys. Lett. 2010, 97, 081102. [Google Scholar] [CrossRef]
- Duocastella, M.; Arnold, C.B. Bessel and annular beams for materials processing. Laser Photonics Rev. 2012, 6, 607–621. [Google Scholar] [CrossRef]
- Laurinavičius, K.; Orlov, S.; Gajauskaitė, A. Azimuthally and Radially polarized pulsed Bessel-X vortices. Optik 2022, 270, 169998. [Google Scholar] [CrossRef]
- Zamboni-Rached, M.; Recami, E.; Hernández-Figueroa, H.E. New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies. Eur. Phys. J. D-At. Mol. Opt. Plasma Phys. 2002, 21, 217–228. [Google Scholar] [CrossRef]
- Valtna, H.; Reivelt, K.; Saari, P. Methods for generating wideband localized waves of superluminal group velocity. Opt. Commun. 2007, 278, 1–7. [Google Scholar] [CrossRef]
- Kondakci, H.E.; Abouraddy, A.F. Optical space-time wave packets having arbitrary group velocities in free space. Nat. Commun. 2019, 10, 929. [Google Scholar] [CrossRef]
- Li, H.; Liu, J.; Bai, L.; Wu, Z. Deformations of circularly polarized Bessel vortex beam reflected and transmitted by a uniaxial anisotropic slab. Appl. Opt. 2018, 57, 7353–7362. [Google Scholar] [CrossRef]
- Fu, S.; Gao, C. Vector Beams and Vectorial Vortex Beams. In Optical Vortex Beams: Fundamentals and Techniques; Springer Nature Singapore: Singapore, 2023; pp. 277–333. [Google Scholar] [CrossRef]
- Nikogosyan, D.N. Properties of Optical and Laser-Related Materials: A Handbook; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2003. [Google Scholar]
- Porras, M.A.; Parola, A.; Di Trapani, P. Nonlinear unbalanced O waves: Nonsolitary, conical light bullets in nonlinear dissipative media. JOSA B 2005, 22, 1406–1413. [Google Scholar] [CrossRef]
- Stabinis, A.P.; Valiulis, G. Ultratrumpųjų Šviesos Impulsų Netiesinė Optika; Vilniaus Universitetas: Vilnius, Lithuania, 2008. [Google Scholar]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Laurinavičius, K.; Orlov, S.; Gajauskaitė, A. Vector Optical Bullets in Dielectric Media: Polarization Structures and Group-Velocity Effects. Appl. Sci. 2024, 14, 3984. https://doi.org/10.3390/app14103984
Laurinavičius K, Orlov S, Gajauskaitė A. Vector Optical Bullets in Dielectric Media: Polarization Structures and Group-Velocity Effects. Applied Sciences. 2024; 14(10):3984. https://doi.org/10.3390/app14103984
Chicago/Turabian StyleLaurinavičius, Klemensas, Sergej Orlov, and Ada Gajauskaitė. 2024. "Vector Optical Bullets in Dielectric Media: Polarization Structures and Group-Velocity Effects" Applied Sciences 14, no. 10: 3984. https://doi.org/10.3390/app14103984