Abstract

Diode lasers can be tuned by simultaneous rotation and translation of an external grating. This can be achieved by rotating the grating about a displaced pivot point. We derive the tuning range as a function of pivot point position for various extended cavity geometries. In each case, the geometric problem reduces to the solution of a quadratic equation. For near-infrared wavelengths, placement of the pivot is relatively noncritical for tuning ranges of the order of 10 GHz, but requires millimeter accuracy for a tuning range >100 GHz.

© 1999 Optical Society of America

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References

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  1. C. E. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
    [CrossRef]
  2. K. Liu, M. G. Littman, “Novel geometry for single-mode scanning of tunable lasers,” Opt. Lett. 6, 117–118 (1981).
    [CrossRef] [PubMed]
  3. P. McNicholl, H. J. Metcalf, “Synchronous cavity mode and feedback wavelength scanning in dye laser oscillators with gratings,” Appl. Opt. 24, 2757–2761 (1985).
    [CrossRef] [PubMed]
  4. W. R. Trutna, L. F. Stokes, “Continuously tuned external cavity semiconductor laser,” J. Lightwave Technol. 11, 1279–1286 (1993).
    [CrossRef]
  5. A. E. Siegman, “Axial modes in a grating-dispersed laser cavity,” Appl. Phys. B 42, 165–166 (1987).
    [CrossRef]

1993 (1)

W. R. Trutna, L. F. Stokes, “Continuously tuned external cavity semiconductor laser,” J. Lightwave Technol. 11, 1279–1286 (1993).
[CrossRef]

1991 (1)

C. E. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
[CrossRef]

1987 (1)

A. E. Siegman, “Axial modes in a grating-dispersed laser cavity,” Appl. Phys. B 42, 165–166 (1987).
[CrossRef]

1985 (1)

1981 (1)

Hollberg, L.

C. E. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
[CrossRef]

Littman, M. G.

Liu, K.

McNicholl, P.

Metcalf, H. J.

Siegman, A. E.

A. E. Siegman, “Axial modes in a grating-dispersed laser cavity,” Appl. Phys. B 42, 165–166 (1987).
[CrossRef]

Stokes, L. F.

W. R. Trutna, L. F. Stokes, “Continuously tuned external cavity semiconductor laser,” J. Lightwave Technol. 11, 1279–1286 (1993).
[CrossRef]

Trutna, W. R.

W. R. Trutna, L. F. Stokes, “Continuously tuned external cavity semiconductor laser,” J. Lightwave Technol. 11, 1279–1286 (1993).
[CrossRef]

Wieman, C. E.

C. E. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

A. E. Siegman, “Axial modes in a grating-dispersed laser cavity,” Appl. Phys. B 42, 165–166 (1987).
[CrossRef]

J. Lightwave Technol. (1)

W. R. Trutna, L. F. Stokes, “Continuously tuned external cavity semiconductor laser,” J. Lightwave Technol. 11, 1279–1286 (1993).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

C. E. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–20 (1991).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Simplified Littrow geometry. The pivot point (x, y) lies in the plane of the grating. The cavity length L is defined by the intersection of the grating plane and the x axis.

Fig. 2
Fig. 2

Contour plot showing the tuning range as a function of pivot point position (x, y) for λ0 = 780 nm and d = 1/1200 mm. The laser is positioned at the origin and the grating plane is a line passing through the point (x, y) with slope cot θ. Infinite tuning range occurs at the intersection between the grating plane and the y axis. The tuning range has been set to zero in the region above the line y = -cot θx as this would correspond to a negative cavity length. There are ten equally spaced contours between 10 and 100 GHz.

Fig. 3
Fig. 3

Generalized Littrow cavity geometry. The laser is positioned at (0,0) and the pivot point at (x, y). The grating plane is displaced a distance u from the pivot point.

Fig. 4
Fig. 4

Contour plot showing the tuning range of an extended cavity laser of length L 0 = 0.05 m, center wavelength λ0 = 780 nm, and grating spacing d = 1/1200 mm as a function of the pivot location (x, y). The maximum tuning range occurs at the intersection of the grating plane (indicated by a dotted line) and the y axis. The contours run from 10 to 100 GHz in 10-GHz intervals.

Fig. 5
Fig. 5

Tuning range in the vicinity of the optimum point as a function of the pivot point error in the x (lower) and y (upper) directions. Note that the scale on the upper graph is expanded by a factor of 10.

Fig. 6
Fig. 6

Contour plot showing the tuning range near the intersection between the grating plane (dotted line) and the y axis. The contours run from 10 to 100 GHz in 10-GHz intervals.

Fig. 7
Fig. 7

Geometry for the general grazing-incidence cavity. The grating is mounted at the grazing incidence, a distance L 1 from the laser. The first-order diffraction is retroreflected by a mirror, positioned at distance L 2 from the grating.

Fig. 8
Fig. 8

Geometry for the simplified grazing-incidence cavity.

Fig. 9
Fig. 9

Contour plot showing the tuning range as a function of the pivot point position (x, y) for a grazing-incidence cavity with λ0 = 780 nm, d = 1/1800 mm, θ = 60°, and L 1 = 0.092 m. The upper dotted line indicates the grating plane. The solid line shows the mirror plane passing through the optimum point. The lower dotted line (parallel to the mirror plane) separates the physical and nonphysical regions of the plot. There are ten equally spaced contours between 10 and 100 GHz.

Equations (36)

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Lα=x-y tanθ-α
λg=2d sinθ-α=λ0sinθ-αsin θ.
mαλm2=Lα,
Δmα=y/cos θ-y/cosθ-αd.
mα=m0+Δmα=2L0λ0+2y sin θλ01cos θ-1cosθ-α=2λ0x-y sin θcosθ-α.
λm=λ0x-y tanθ-αx-y sin θ/cosθ-α.
λm=λ0sinθ-αsin θ,
|νg-νm|=12c2Lα.
Δν=|νmα+-νmα-|=c1λmα+-1λmα-,
±1λgα1λmα=14Lα.
±sin θsinθ-αx-y sin θ/cosθ-αx-y tanθ-α=λ04x-y tanθ-α.
±4x sin θ1+v2=λ0±4xv,
v1,2=16x2 sin2 θλ02±8λ0x+16x2 cos2 θ1/2,
Δνx, y=cλ0x-y sin θ1+v12x-yv1-x-y sin θ1+v22x-yv2,
u=x-L0cos θ-y sin θ.
Lα=x-y tanθ-α-ucosθ-α.
mα=2λ0x-y sin θcosθ-α-u cos θ-u sin θ tanθ-α.
λmλ0=x-y tanθ-α-u/cosθ-αx-y sin θ/cosθ-α-ucos θ+sin θ tanθ-α=x cosθ-α-y sinθ-α-ux cosθ-α-y sin θ-u cos α.
λgλ0=1-cot θ α-12 α2+Oα3,
λmλ0=1+yL0 α+L0+2y tan θL0-x2L02 α2+Oα3.
y=-L0 cot θ,
y=-L0 cot θ1-x/2L01-x/L0.
±4x sin θ1+v2=λ0±4x4u cos θv±4u sin θ,
λ0=dsin θ+sin ϕ.
λg=dsin θ+sinϕ+α,
λg=λ0sin θ+sinϕ+αsin θ+sin ϕ.
Lα=L1+L1-xcosϕ+α-θ-y sinϕ+α-θ.
λmλ0=LαL0=L1+L1-xcosϕ+α-θ-y sinϕ+α-θL1+L1-xcosϕ-θ-y sinϕ-θ.
λgλ0=1+cos ϕsin θ+sin ϕ α-12sin ϕsin θ+sin ϕ α2+Oα3,  λmλ0=1-1LL1-xsinϕ-θ+y cosϕ-θα-12LL1-xcosϕ-θ-y sinϕ-θα2+Oα3.
y=-L1 cot θ+cot θ+sinϕ-θ1+cosϕ-θ x,
y=-L1 cot θ+cotϕ-θx.
x=0,
y=-L1 cot θ,
Δν=c1λmα+-1λmα-=cL0λ01Lα+-1Lα-,
a12+a22w2-2a1a3w+a32-a22=0,
a1=-λ04L04y cos θ-L1-xsin θsin θ+sin ϕ,  a2=4L1-xcos θ+y sin θsin θ+sin ϕ,  a3=λ0±4L0sin θ4L1sin θ+sin ϕ.

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