Abstract

This paper presents a novel design for broadband zero-order half-wave plates to eliminate the first-order or up to second-order wavelength-dependent birefringent phase retardation (BPR) with 2 or 3 different birefringent materials. The residual BPRs of the plates increase monotonously with the wavelength deviation from a selected wavelength, so the plates are applicable to the broadband light pulses which gather most of the light energy around their central wavelengths. The model chooses the materials by the birefringent dispersion coefficient and evaluates the performances of the plates by the weighted average of the absolute value of residual BPR in order to emphasize the contributions of the incident spectral components whose possess higher energies.

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References

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  1. M. Emam-Ismail, “Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal,” Opt. Commun. 283(22), 4536–4540 (2010).
    [CrossRef]
  2. P. Hariharan, “Broad-band superachromatic retarders,” Meas. Sci. Technol. 9(10), 1678–1681 (1998).
    [CrossRef]
  3. I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5-fs pulses from a Ti:sapphire laser,” Opt. Lett. 22(13), 1009–1011 (1997).
    [CrossRef] [PubMed]
  4. S. Ghimire, B. Shan, C. Wang, and Z. Chang, “High-Energy 6.2-fs Pulses for Attosecond Pulse Generation,” Laser Phys. 15, 838–842 (2005).
  5. J. Zhu, P. Wang, H. Han, H. Teng, and Z. Wei, “Experimental study on generation of high energy few cycle pulses with hollow fiber filled with neon,” Sci. China, Ser. G G50, 507–511 (2007).
  6. C. J. Koesrter, “Achromatic Combinations of Half-Wave Plates,” J. Opt. Soc. Am. 49(4), 405–409 (1959).
    [CrossRef]
  7. J. M. Beckers, “Achromatic linear retarders,” Appl. Opt. 10(4), 973–975 (1971).
    [CrossRef] [PubMed]
  8. P. Hariharan, “Broad-band apochromatic retarders: choice of materials,” Opt. Laser Technol. 34(7), 509–511 (2002).
    [CrossRef]
  9. P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng. 35(11), 3335–3337 (1996).
    [CrossRef]
  10. M. Emam-Ismail, “Spectral variation of the birefringence, group birefringence and retardance of a gypsum plate measured using the interference of polarized light,” Opt. Laser Technol. 41(5), 615–621 (2009).
    [CrossRef]

2010 (1)

M. Emam-Ismail, “Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal,” Opt. Commun. 283(22), 4536–4540 (2010).
[CrossRef]

2009 (1)

M. Emam-Ismail, “Spectral variation of the birefringence, group birefringence and retardance of a gypsum plate measured using the interference of polarized light,” Opt. Laser Technol. 41(5), 615–621 (2009).
[CrossRef]

2007 (1)

J. Zhu, P. Wang, H. Han, H. Teng, and Z. Wei, “Experimental study on generation of high energy few cycle pulses with hollow fiber filled with neon,” Sci. China, Ser. G G50, 507–511 (2007).

2005 (1)

S. Ghimire, B. Shan, C. Wang, and Z. Chang, “High-Energy 6.2-fs Pulses for Attosecond Pulse Generation,” Laser Phys. 15, 838–842 (2005).

2002 (1)

P. Hariharan, “Broad-band apochromatic retarders: choice of materials,” Opt. Laser Technol. 34(7), 509–511 (2002).
[CrossRef]

1998 (1)

P. Hariharan, “Broad-band superachromatic retarders,” Meas. Sci. Technol. 9(10), 1678–1681 (1998).
[CrossRef]

1997 (1)

1996 (1)

P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng. 35(11), 3335–3337 (1996).
[CrossRef]

1971 (1)

1959 (1)

Beckers, J. M.

Chang, Z.

S. Ghimire, B. Shan, C. Wang, and Z. Chang, “High-Energy 6.2-fs Pulses for Attosecond Pulse Generation,” Laser Phys. 15, 838–842 (2005).

Emam-Ismail, M.

M. Emam-Ismail, “Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal,” Opt. Commun. 283(22), 4536–4540 (2010).
[CrossRef]

M. Emam-Ismail, “Spectral variation of the birefringence, group birefringence and retardance of a gypsum plate measured using the interference of polarized light,” Opt. Laser Technol. 41(5), 615–621 (2009).
[CrossRef]

Ghimire, S.

S. Ghimire, B. Shan, C. Wang, and Z. Chang, “High-Energy 6.2-fs Pulses for Attosecond Pulse Generation,” Laser Phys. 15, 838–842 (2005).

Han, H.

J. Zhu, P. Wang, H. Han, H. Teng, and Z. Wei, “Experimental study on generation of high energy few cycle pulses with hollow fiber filled with neon,” Sci. China, Ser. G G50, 507–511 (2007).

Hariharan, P.

P. Hariharan, “Broad-band apochromatic retarders: choice of materials,” Opt. Laser Technol. 34(7), 509–511 (2002).
[CrossRef]

P. Hariharan, “Broad-band superachromatic retarders,” Meas. Sci. Technol. 9(10), 1678–1681 (1998).
[CrossRef]

P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng. 35(11), 3335–3337 (1996).
[CrossRef]

Jung, I. D.

Kärtner, F. X.

Keller, U.

Koesrter, C. J.

Matuschek, N.

Morier-Genoud, F.

Scheuer, V.

Shan, B.

S. Ghimire, B. Shan, C. Wang, and Z. Chang, “High-Energy 6.2-fs Pulses for Attosecond Pulse Generation,” Laser Phys. 15, 838–842 (2005).

Sutter, D. H.

Teng, H.

J. Zhu, P. Wang, H. Han, H. Teng, and Z. Wei, “Experimental study on generation of high energy few cycle pulses with hollow fiber filled with neon,” Sci. China, Ser. G G50, 507–511 (2007).

Tilsch, M.

Tschudi, T.

Wang, C.

S. Ghimire, B. Shan, C. Wang, and Z. Chang, “High-Energy 6.2-fs Pulses for Attosecond Pulse Generation,” Laser Phys. 15, 838–842 (2005).

Wang, P.

J. Zhu, P. Wang, H. Han, H. Teng, and Z. Wei, “Experimental study on generation of high energy few cycle pulses with hollow fiber filled with neon,” Sci. China, Ser. G G50, 507–511 (2007).

Wei, Z.

J. Zhu, P. Wang, H. Han, H. Teng, and Z. Wei, “Experimental study on generation of high energy few cycle pulses with hollow fiber filled with neon,” Sci. China, Ser. G G50, 507–511 (2007).

Zhang, G.

Zhu, J.

J. Zhu, P. Wang, H. Han, H. Teng, and Z. Wei, “Experimental study on generation of high energy few cycle pulses with hollow fiber filled with neon,” Sci. China, Ser. G G50, 507–511 (2007).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Laser Phys. (1)

S. Ghimire, B. Shan, C. Wang, and Z. Chang, “High-Energy 6.2-fs Pulses for Attosecond Pulse Generation,” Laser Phys. 15, 838–842 (2005).

Meas. Sci. Technol. (1)

P. Hariharan, “Broad-band superachromatic retarders,” Meas. Sci. Technol. 9(10), 1678–1681 (1998).
[CrossRef]

Opt. Commun. (1)

M. Emam-Ismail, “Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal,” Opt. Commun. 283(22), 4536–4540 (2010).
[CrossRef]

Opt. Eng. (1)

P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng. 35(11), 3335–3337 (1996).
[CrossRef]

Opt. Laser Technol. (2)

M. Emam-Ismail, “Spectral variation of the birefringence, group birefringence and retardance of a gypsum plate measured using the interference of polarized light,” Opt. Laser Technol. 41(5), 615–621 (2009).
[CrossRef]

P. Hariharan, “Broad-band apochromatic retarders: choice of materials,” Opt. Laser Technol. 34(7), 509–511 (2002).
[CrossRef]

Opt. Lett. (1)

Sci. China, Ser. G (1)

J. Zhu, P. Wang, H. Han, H. Teng, and Z. Wei, “Experimental study on generation of high energy few cycle pulses with hollow fiber filled with neon,” Sci. China, Ser. G G50, 507–511 (2007).

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Figures (2)

Fig. 1
Fig. 1

The residual BPR ΔΦ vs. wavelength of some zero-order half-wave plates based on 2 (a) or 3(b) birefringent materials

Fig. 2
Fig. 2

The residual BPR vs. wavelength of the zero-order half-wave plates composed of the birefringent crystal combinations: Quartz/calcite/ADP, Quartz/calcite/KDP and MgF2/sapphire/ADP

Tables (3)

Tables Icon

Table 1 Birefringent Dispersion Coefficient σ, Thicknesses, and ΔΦ of 2 Different Material-based Zero-order Half Waveplates from 6 Candidate Birefringent Crystals: Quartz, MgF2, Sapphire, Calcite, ADP, and KDP

Tables Icon

Table 2 Birefringent Dispersion Coefficient σ, Thicknesses, and ΔΦ of the 3-Material–Based Zero-order Half-wave Plates from 6 Candidate Birefringent Crystals: Quartz, MgF2, Sapphire, Calcite, ADP, and KDP

Tables Icon

Table 3 WAAVRB of Half-wave Plates Based on All Combinations Listed in Tables 1 and 2 for an Incident Field with 100 nm Gaussian Bandwidth from 400 to 700nm Window

Equations (12)

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η ( λ ) = n o ( λ ) n e ( λ ) ,
φ ( λ ) = 2 π λ [ η A ( λ ) d A + η B ( λ ) d B ] .
φ ( λ ) = φ ( λ 0 ) + φ ( 1 ) ( λ 0 ) 1 ! ( λ λ 0 ) + φ ( 2 ) ( λ 0 ) 2 ! ( λ λ 0 ) 2 + φ ( 3 ) ( λ 0 ) 3 ! ( λ λ 0 ) 3 + ... ,
{ η A ( λ 0 ) d A + η B ( λ 0 ) d B = λ 0 2 , η A ( 1 ) ( λ 0 ) d A + η B ( 1 ) ( λ 0 ) d B = 1 2 .
φ ( λ ) = φ ( 2 ) ( λ 0 ) 2 ( λ λ 0 ) 2 = π λ 0 [ η A ( 2 ) ( λ 0 ) d A + η B ( 2 ) ( λ 0 ) d B ] ( λ λ 0 ) 2 = σ ( λ λ 0 ) 2 .
σ = π 2 λ 0 η A ( λ 0 ) η B ( 2 ) ( λ 0 ) η B ( λ 0 ) η A ( 2 ) ( λ 0 ) + λ 0 [ η A ( 2 ) ( λ 0 ) η B ( 1 ) ( λ 0 ) η B ( 2 ) ( λ 0 ) η A ( 1 ) ( λ 0 ) ] η A ( λ 0 ) η B ( 1 ) ( λ 0 ) η B ( λ 0 ) η A ( 1 ) ( λ 0 ) .
[ η A ( λ 0 ) η B ( λ 0 ) η C ( λ 0 ) η A ( 1 ) ( λ 0 ) η B ( 1 ) ( λ 0 ) η C ( 1 ) ( λ 0 ) η A ( 2 ) ( λ 0 ) η B ( 2 ) ( λ 0 ) η C ( 2 ) ( λ 0 ) ] [ d A d B d C ] = [ λ 0 / 2 1 / 2 0 ] .
φ ( λ ) = π 3 λ 0 [ η A ( 3 ) ( λ 0 ) d A + η B ( 3 ) ( λ 0 ) d B + η C ( 3 ) ( λ 0 ) d C ] ( λ λ 0 ) 3 = σ ( λ λ 0 ) 3 ,
σ = π 3 λ 0 M [ η A ( 3 ) ( λ 0 ) M A + η B ( 3 ) ( λ 0 ) M B + η C ( 3 ) ( λ 0 ) M C ] ,
M = | η A ( λ 0 ) η B ( λ 0 ) η C ( λ 0 ) η A ( 1 ) ( λ 0 ) η B ( 1 ) ( λ 0 ) η C ( 1 ) ( λ 0 ) η A ( 2 ) ( λ 0 ) η B ( 2 ) ( λ 0 ) η C ( 2 ) ( λ 0 ) | ,     M A = | λ 0 / 2 η B ( λ 0 ) η C ( λ 0 ) 1 / 2 η B ( 1 ) ( λ 0 ) η C ( 1 ) ( λ 0 ) 0 η B ( 2 ) ( λ 0 ) η C ( 2 ) ( λ 0 ) | , M B = | η A ( λ 0 ) λ 0 / 2 η C ( λ 0 ) η A ( 1 ) ( λ 0 ) 1 / 2 η C ( 1 ) ( λ 0 ) η A ( 2 ) ( λ 0 ) 0 η C ( 2 ) ( λ 0 ) | ,           M C = | η A ( λ 0 ) η B ( λ 0 ) λ 0 / 2 η A ( 1 ) ( λ 0 ) η B ( 1 ) ( λ 0 ) 1 / 2 η A ( 2 ) ( λ 0 ) η B ( 2 ) ( λ 0 ) 0 | .
Δ ψ = 1 λ 2 λ 1 λ 1 λ 2 | φ ( λ ) 180 | E ( λ λ 0 ) d λ .
E ( λ λ 0 ) = exp [ 4 ln 2 ( λ λ 0 Δ λ ) 2 ] ,

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