Table 1 Calculated ratios of the mean intensity of the diffraction order to the mean intensity of the incident beam for the diffraction patterns illustrated in Fig. 2.

From: An azimuthally-modified linear phase grating: Generation of varied radial carpet beams over different diffraction orders with controlled intensity sharing among the generated beams

s=

−5

−4

−3

−2

−1

0

1

2

3

4

5

\(\tfrac{{\sum }_{{\boldsymbol{s}}=-{\bf{5}}}^{+{\bf{5}}}\,{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{s}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{s}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{-{\bf{5}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{-{\bf{4}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{-{\bf{3}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{-{\bf{2}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{-{\bf{1}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{{\bf{0}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{{\bf{1}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{{\bf{2}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{{\bf{3}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{{\bf{4}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

\(\tfrac{{\bar{{\boldsymbol{I}}}}_{{\bf{5}}}}{{\bar{{\boldsymbol{I}}}}_{{\boldsymbol{i}}}}\)%

γ=

π/2

0.00

0.02

0.47

6.21

32.07

22.28

32.19

6.25

0.48

0.02

0.00

99.99

2.4048

0.02

0.42

3.94

18.58

26.90

0.00

27.00

18.70

3.98

0.42

0.02

99.98

π

0.27

2.28

11.07

23.49

8.09

9.26

8.12

23.64

11.17

2.30

0.27

99.96

3.8317

1.27

6.51

17.60

16.17

0.00

16.22

0.00

16.27

17.75

6.55

1.29

99.63

3π/2

4.93

13.66

16.40

2.13

7.92

7.07

7.95

2.15

16.54

13.77

5.01

97.53

5.1356

7.68

15.68

11.48

0.00

11.52

1.75

11.56

0.00

11.59

15.80

7.82

94.88

5.5201

10.34

15.62

6.27

1.51

11.56

0.00

11.60

1.52

6.32

15.73

10.52

90.99

2π

13.77

9.92

0.08

8.26

4.50

4.85

4.52

8.31

0.09

10.00

14.01

78.31

  1. The red numbers show the maximum values of the intensity sharing in each row. By increasing the value of γ, the maximum values shift toward the higher orders.
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