Abstract

A new device for producing order-sortable echelle spectra by use of consecutive diffractions in several echelle grating surfaces is described. This echelle emulating device (EED) comprises a prism placed in the path between a pair of echelle grating surfaces. The refractive angle of the prism is fixed through a simple relation. The device reproduces all the main properties of a single virtual echelle, obtained from a simple grating equation describing the combined action of the gratings and the prism. The spectral order of the EED is the sum of the spectral orders of the individual gratings. A spectrograph that utilizes the device is described, and several applications are discussed.

© 2003 Optical Society of America

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References

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  1. G. R. Harrison, “The production of diffraction gratings: the design of echelle gratings and spectrographs,” J. Opt. Soc. Am. 39, 522–528 (1949).
    [CrossRef]
  2. S. Engman, P. Lindblom, “Multiechelle grating mountings with high spectral resolution and dispersion,” Appl. Opt. 21, 4363–4367 (1982).
    [CrossRef] [PubMed]
  3. P. Lindblom, “Diffraction of light,” Swedish patent application0200627-8 (1March2002).
  4. P. Lindblom, “New compact echelle spectrographs with multichannel time-resolved recording capabilities,” Anal. Chim. Acta 380, 353–359 (1999).
    [CrossRef]
  5. P. Lindblom, “Apparatus for carrying out spectral analysis of an optical light source using image detection and separation of spectral orders,” U.S. patent5,859,702 (12January1999).
  6. S. Engman, P. Lindblom, “Blaze characteristics of echelle gratings,” Appl. Opt. 21, 4356–4362 (1982).
    [CrossRef] [PubMed]
  7. P. Lindblom, F. Stenman, “Resolving power of multigrating spectrometers,” Appl. Opt. 28, 2542–2549 (1989).
    [CrossRef] [PubMed]
  8. A. D. Sappey, G. Murphy, “Echelle grating dense wavelength division multiplexer/demultiplexer,” U.S. patent6,415,080 (2July2002).

1999

P. Lindblom, “New compact echelle spectrographs with multichannel time-resolved recording capabilities,” Anal. Chim. Acta 380, 353–359 (1999).
[CrossRef]

1989

1982

1949

Engman, S.

Harrison, G. R.

Lindblom, P.

P. Lindblom, “New compact echelle spectrographs with multichannel time-resolved recording capabilities,” Anal. Chim. Acta 380, 353–359 (1999).
[CrossRef]

P. Lindblom, F. Stenman, “Resolving power of multigrating spectrometers,” Appl. Opt. 28, 2542–2549 (1989).
[CrossRef] [PubMed]

S. Engman, P. Lindblom, “Blaze characteristics of echelle gratings,” Appl. Opt. 21, 4356–4362 (1982).
[CrossRef] [PubMed]

S. Engman, P. Lindblom, “Multiechelle grating mountings with high spectral resolution and dispersion,” Appl. Opt. 21, 4363–4367 (1982).
[CrossRef] [PubMed]

P. Lindblom, “Diffraction of light,” Swedish patent application0200627-8 (1March2002).

P. Lindblom, “Apparatus for carrying out spectral analysis of an optical light source using image detection and separation of spectral orders,” U.S. patent5,859,702 (12January1999).

Murphy, G.

A. D. Sappey, G. Murphy, “Echelle grating dense wavelength division multiplexer/demultiplexer,” U.S. patent6,415,080 (2July2002).

Sappey, A. D.

A. D. Sappey, G. Murphy, “Echelle grating dense wavelength division multiplexer/demultiplexer,” U.S. patent6,415,080 (2July2002).

Stenman, F.

Anal. Chim. Acta

P. Lindblom, “New compact echelle spectrographs with multichannel time-resolved recording capabilities,” Anal. Chim. Acta 380, 353–359 (1999).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

Other

A. D. Sappey, G. Murphy, “Echelle grating dense wavelength division multiplexer/demultiplexer,” U.S. patent6,415,080 (2July2002).

P. Lindblom, “Diffraction of light,” Swedish patent application0200627-8 (1March2002).

P. Lindblom, “Apparatus for carrying out spectral analysis of an optical light source using image detection and separation of spectral orders,” U.S. patent5,859,702 (12January1999).

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Figures (13)

Fig. 1
Fig. 1

Schematic sketch of two gratings with coacting dispersion, defining the notations used in this paper.

Fig. 2
Fig. 2

(a) Two gratings with parallel grating surfaces and (b) the analogous mounting with double pass of a single grating. As any diffraction angle of the first grating equals the angle of incidence of the second with opposite sign, the final diffraction will depend on the sum of the spectral orders of the gratings only, meaning that diffractions with the sum m 1 + m 2 = constant will emerge from the second grating in exactly the same direction. This is illustrated for gratings with 13.25 grooves/mm that have angles of incidence α1 = 79°, diffracting the wavelength 0.74085 μm. The central ray in spectral order 100 is diffracted at β0 = 0°. The blaze angle of the gratings would thus need to be 39.5°. Diffraction in orders m 1 = 100 + i and m 2 = 100 - i with i = -3, -2, … 3 is shown. The two gratings in (a) correspond to one echelle grating in a Littrow mounting with a blaze angle of 79° diffracting the wavelength 0.74085 nm in spectral order 200.

Fig. 3
Fig. 3

(a) Two coacting gratings in a symmetrical mounting (A = 2β0) with the angle of incidence of the first grating equal to the central angle of diffraction of the second and (b) the corresponding mounting of a single grating in double pass. The way in which diffractions of a wavelength with a constant sum M of their diffraction orders m 1 and m 2 emerge from the second grating is shown. α1 = 79°, β0 = 60°, and the groove density is 24.94 grooves/mm. The rays represent the diffraction of the wavelength 0.74085 nm in spectral orders m 1 = 100 + i and m 2 = 100 - i, with i = -3, 2, … 3. As can be seen, the emerging rays are far from parallel.

Fig. 4
Fig. 4

Two coacting gratings in mountings with an intermediate Bk7 prism that has refractive angle P calculated from Eq. (13). In (a) and (c) the gratings are mounted symmetrically (A = 2β0); (b) shows the double-pass mounting of a single grating corresponding to (a) by use of a Littrow prism with refractive angle P/2. In (a)–(c) β0 = 60°, P = 72.54°, and wavelength 0.74085 nm is diffracted in spectral orders m 1 = 100 + i and m 2 = 100 - i, with i = -3, -2, … 3. The groove density is 24.94 grooves/mm, and α1 = 79° for (a) and (b); the groove density is 15.183 grooves/mm and α1 = 15° for (c). As for the mounting in Fig. 2, the diffracted rays are now parallel because of the action of the prism. The collective diffraction properties of the EED can, to a high degree of accuracy, be described by grating equation (16) and a single order number, M = 200.

Fig. 5
Fig. 5

EED solutions that use (a) transmission gratings and (b) GRISMs. For the transmission EED with zero deviation in (a) the same prism, diffraction angle, wavelength, and spectral orders (M = 200 with m 1 = 100 + i and m 2 = 100 - i, with i = -3, -2, … 3) as in Fig. 4 were chosen, giving a groove density of 4.3735 grooves/mm. In the GRISM EED of (b) the air prism between the glass surfaces is used, and prism angle P has been determined from Eq. (14). The data for the GRISM EED shown are as follows: α1 = 78.103°; β0 = 51.103°; groove density, 35.86 grooves/mm; GRISM material, Bk7. The rays represent the diffraction of the wavelength 0.74085 nm in spectral orders m 1 = 100 + i and m 2 = 100 - i, with i = -3, -2, … 3. The angle of the air prism calculated from Eq. (14) is P = 86.7°.

Fig. 6
Fig. 6

Schematic of a four-grating EED assembled from two pairs of EEDs as shown in Fig. 4(a). These pairs are coupled through a third prism, satisfying Eq. (13) for the diffraction-incidence angle of the second and third gratings, respectively.

Fig. 7
Fig. 7

Efficiency curves calculated from Eq. (38) for α1 > θ as a function of the variable x = MΔλ/λ0, i.e., the wavelength in units of the free spectral range, compared to the corresponding efficiency curve for a single grating with α < θ. There are two pairs of calculated curves; each pair represents different values of the quantity F =cos(β0)/cos(α). Despite the fact that the central blaze efficiency is lower for an EED than for its single-grating analog, the efficiencies at the order edges are the same. However, the gain in dispersion and resolution offered by the EED may well compensate for the lower central blaze efficiency.

Fig. 8
Fig. 8

Experimental EED order-sorted spectrograph. Light from the input fiber is collimated and conducted through a folding mirror to the first grating of the EED. The Bk7 prism used satisfies Eq. (13). After the second grating the light is conducted to a cross-dispersion grating order sorter that folds the light into the focusing lens. A CCD camera records the final order-sorted spectrum (Figs. 9 and 10).

Fig. 9
Fig. 9

Images showing the EED orders M of a tungsten light source recorded with a digital CCD camera. Each horizontal band represents the subspectrum associated with a collective order number M. The action of the cross-dispersion element (Fig. 8) separates the bands from one another in the focal plane. From image (a) the structure caused by interference of the intermediate orders can be seen. Image (b) shows the same spectrum after a slight tilt of the groove orientation has been applied, almost completely eliminating the interference structure.

Fig. 10
Fig. 10

EED spectral image of a low-pressure discharge containing oxygen, recorded under the same conditions as for Fig. 9(b). The image shows some of the characteristic lines of the oxygen atom that appear in two EED orders. The expanded view shows the intensity profile of the three oxygen lines at 777 nm extracted from the digital image.

Fig. 11
Fig. 11

Schematic view of a double-pass EED applied in a tunable laser. Using a Littrow prism instead of a mirror could considerably improve efficiency.

Fig. 12
Fig. 12

Schematic view of an EED arrangement of the type shown in Fig. 5(a) applied for splitting an incident laser beam into several parallel beams. A schematic arrangement for application in a coupler for fiber-optic communications is shown.

Fig. 13
Fig. 13

Schematic view of an EED used in a component of the type discussed in Ref. 8 for dense wavelength-division multiplexing-demultiplexing. Through the EED, the size of such a component can be reduced further compared that those of components that use single echelle-type gratings.8

Equations (42)

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Md λ=sinα1+sinα2,
m10λ0d1=sinα1+sinβ0, m20λ0d2=sinA-β0+sinα20
m1λd1=sinα1+sinβ0+Δβ, m2λd2=sinA-β0-Δβ+sinα2
cm1+m2d2 λ=sinα1+2 sinA2cosA2-β0-Δβ+sinα2.
cm1+m2d2 λ=sinα1+sinα2.
m10+nλ0d1=sinα1+sinβ0+Δβn, m20-nλ0d2=sinA-β0+Δβn+sinα20+δn,n.
cn-nλ0d2=cosβ0Δβn-½ sinβ0Δβn2- cosβ0Δβn3++cosA-β0Δβn-½ sinA-β0Δβn2- cosA-β0Δβn3++sinα20+δn,n-sinα20,
cn-n=0,
Δβn=a1Δβn+a2Δβn2+a3Δβn3+.
cosβ0+a1 cosA-β0=0, 2a2 cosA-β0-a12 sinA-β0-sinβ0=0, 6a1a2 sinA-β0-a3 cosA-β0+a13×cosA-β0+cosβ0=0.
a1=-1, a2=tanβ0, a3=-tan2β0=-a22.
±Δβn=±Δβn+BΔβn2±B2Δβn3+, B=tanφN2-1N2-sin2φ, sinφ=N sinP/2.
tanβ0=tanφN2-1N2-sin2φ.
tanβ0=tanφN2-11-N2 sin2φ, sinP2=N sinφ,
m1λ0+Δλd=sinα1+sinβ0+Δβ, m2λ0+Δλd=sinβ0+Δβ+sinα2,
Mλd=sinα1+2 sinβ0+sinα2+OΔβ4,
Mλd=2k-1sinα1+2k sinβ0+sinα2k, M=12 · k mi.
Δβn=a1Δβn+b1ΔN+a2Δβn2+b11ΔNΔβn+b2ΔN2+,
b1=2Ntanφ, b11=2Ntan2P2-tan2φ.
sinα20+δn,n-sinα20=b1 cosβ0ΔN+12cosβ02b2-b12×tanβ0ΔN2+cosβ0b11+b1 tanβ0ΔNΔβn,
δΔN2 sinP/2cosφcosβ0cosα20 ΔN.
b11+b1 tanβ0=2Ntan2P2-tan2φ+tanφtanβ0=0.
dα2dλ=Md cosα2,
Fλ=λ/M,
R=MNg,
mmin=RΔlDFPA-12,
tanθ=RΔl/2feff1+RΔl/2fefftanθ-α,
λmaxmmin=2d sinθcosθ-α1+12mmin+1,
Mmin=RΔl2kDFPA-12,
tanθ=RΔl/4kfeff1+RΔl/4kfefftanθ-α,
λmaxMmin=4kd sinθcosθ-α1+12Mmin+1,
Eir=Sig sin c2κi,
κ1=πdλsin2θ-β-sinα, S1g=cosαcosβ0,
κ2=πdλsin2θ-α-sinβ, S2g=cosβ0cosα.
κ1,nπ cosαcosβ0m0Δλλ0+n,
κ2,nπm0Δλλ0+n.
-cosβ0cosαncosβ0cosα,
β=β0+Δβn+Δβλβ0+λ0d cosβ0Δλλ0m+n+n.
α2=α20+Δα2α+Md cosα Δλ.
β=β0-Δβn-Δβλβ0-λ0d cosβ0Δλλ0m+n+n.
Ex=F2kj=-nnsin cπFix2+j×sincπFix21+F-1+j2,
F=cosαcosβ0k, x=MΔλλ0, k=2i-1, i=1, nF-1case1α>θ0, n=0case2α<θ,

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