DE1514639C - Optical resonator delimited by spherical concave mirrors for optical transmitters (laser) - Google Patents

Description

The invention relates to an optical resonator for optical, limited by spherical concave mirrors Transmitter (laser), whose at least one concave mirror is covered by a lens that is partially transparent on one side is formed.

As a resonator mirror in general, unless they are directly on the stimulable medium, z. B. a Crystal, are attached, plano-concave glass body use, which for the laser beam to be coupled out act as a divergent lens.

The invention is based on the object of creating a "parallel" laser beam that only diffracts diverges, to be coupled out of the optical resonator, whose beam waist assumes a fixed position regardless of the distance between the resonator mirrors.

In the case of an optical resonator of the type mentioned at the outset, this object is achieved according to the invention solved in that for the purpose of decoupling a coherent divergent solely by diffraction The lens as meniscus-shaped Converging lens is formed whose focal point located within the optical resonator with the The center of curvature of their concave mirror coincides.

Further features and details of the invention emerge from the explanations below and from the description of an exemplary embodiment with reference to the figure.

A diffraction-limited light beam is characterized by its beam waist. The beam waist is characterized by the smallest beam cross-section, ie by the smallest beam circumference, i.e. by the smallest bundle radius vv ₀ . For a wavelength / the light spot radius w (2) and the radius of curvature R (2) of the phase front on the optical axis at a distance ζ from the waist radius vv "depend in the following way:

vv (γ) = W ₀ / I + (■■■ '-—,) = light spot radius, V VT »vr. /

K (r) - ζ

40

Radius of curvature of the phase front,
whereby

■ τ tV ₍ )

is the angle of diffraction of the beam.

From the above relationship one can see that the radius of curvature of the phase front at the point ζ --- () becomes infinitely large, ie that the phase front is flat in the beam waist.

With a given light spot radius vv (z) and the radius of curvature R (z), the waist radius iv "and the distance ζ can also be determined from the above formulas:

Waist radius,

/ I Λ

.1 VV "

λ R

I 1

R. λ R

: ι VV "

(see e.g. also R. L. Fork, D. R. Herriott and H. Kogelnik, Applied Optics, 3, 12, p. 1471 to 1484 [1964]).

Rays of this type exist within every optical resonator. The radius of curvature R (.2) of the phase fronts at the resonator mirrors is equal to the radius of curvature of the resonator mirror, that is to say of the partially transparent mirrored lens surfaces. In particular, the curvature of the wavefronts before and after the refraction at the lens is obtained by mapping the centers of curvature Ic according to geometrical optics.

At the resonator mirror the shaft has the radius of curvature R (z). This radius of curvature R (r) largely coincides with the radius of curvature η of the concave, ie hollow-curved, partially transparent mirrored lens surface 1 (see figure) on the converging lens serving as resonator delimitation and for coupling out. In this context, partially transmissive reflective coating is to be understood as meaning that part of the coherent radiation generated in the optical transmitter is reflected on this surface 1, while the other part of the radiation passes through the lens surface, that is to say is coupled out.

If, according to the invention, instead of a flat surface, a convex, ie raised, curved surface 2 is ground on the rear of the lens so that the image of the center of curvature k of the concave lens surface 1 lying on the optical axis is at infinity, the wave occurs with a plane phase front out of the resonator. The center of curvature k of the lens surface 1 must therefore be the focal point F, of the lens.

The radius vv "of the beam waist, the distance ζ from the beam waist to the partially transparent mirrored

Lens area 1, the diffraction angle of the beam

in the resonator and the spot radius vv on the lens surface 1 depend both on the radii of curvature of the two lens surfaces and on the distance between the partially mirrored lenses of the resonator arrangement. But if you have the rear lens surface 2 after

l'i -

I I

1
/ il

dimensioned or with a corresponding correction for thick lenses, the beam occurs with the waist tv,

· * "And the angle of diffraction! 'From the resonator

out. (It means in the above relation:; · _, - ■ = radius of curvature of the convex surface 2; / ·, - radius of curvature of the concave surface I; η - refractive index of the lens material used). The larger one makes .w _L , for example by moving the mirrors apart close to the concentric case, the smaller the diffraction angle becomes. In any case, one always has a diffraction limiter

available in the beam.

For spherical mirrors and paraxial rays, i.e. for rays with such a small opening angle that the Replaced sine and tangent functions with the angles in radians without sacrificing accuracy

(15, the following condition for the radius of curvature r, the outer, convex lens areas 2, the radius of curvature r, the inner, concave lens areas 1, the refractive index / 1 des

the lens material used and the thickness d of the lens apply:

= Oi

«0-4)

By means of a concave-convex lens designed in this way, a beam emerges from the optical transmitter, the divergence angle Θ of which is determined only by diffraction, ie the spot diameter D on the concave lens surface 1, which is partially reflective. The divergence angle Θ of such a "parallel ray" due to diffraction is

Further details of the invention can be found in the following description of what is shown in the figure Embodiment.

The figure shows a concavo-convex lens that is partially transmissive mirrored on its inner, concave surface 1, which acts as a resonator delimitation for the coherent radiation generated in the optical transmitter and for coupling out a diffraction-limited radiation "Parallel" laser beam from the resonator arrangement should be used.

By grinding a spherical, convex surface with the radius of curvature r ₂ on the rear side 2 of the lens, a beam emerges from the optical transmitter whose divergence angle is only determined by diffraction, ie by the spot diameter D.

Furthermore, the figure shows the optical axis 0 of the arrangement and the two main planes H ₁ and H _{2 of} the converging lens, which are to the right of the apex A _{1 of} the first lens surface 1 at a distance Zi ₁ = d and Zj ₂ = dh + - ^ - J , drawn. D the lens thickness is bezeich.net.

35

According to the invention, the center of curvature k of the lens surface 1, which has the radius of curvature T ₁ , coincides with the focal point F _{1 of} the lens. The center of curvature of the convex lens surface 2 with the radius of curvature r ₂ is Ic ₂

designated. The two focal lengths measured from the main planes H ₁ and H ₂ are marked with /, the corresponding focal points with F ₁ and F ₂ . The focal length / is equal to / = r _x + d.

Claims (2)

Patent claims: 1. Optical resonator, limited by spherical concave mirrors, for optical transmitters (laser), the at least one concave mirror of which is formed by a partially transparent mirrored lens on one side, characterized in that the lens (1 , 2) is designed as a meniscus-shaped converging lens whose focal point (F ₁ ) located within the optical resonator coincides with the center of curvature of its concave mirror (1). 2. Optical resonator according to claim 1, characterized in that the radius of curvature of the outer, convex lens surface? ₂ , the radius of curvature of the inner, concave lens surface r ,, the refractive index η of the lens material used and the thickness d of the lens for spherical lens surfaces and paraxial rays of the condition r, = suffice. 1 sheet of drawings