EP0000810B1

EP0000810B1 - Method of and apparatus for forming focusing diffraction gratings for integrated optics

Info

Publication number: EP0000810B1
Application number: EP78300156A
Authority: EP
Inventors: Ping King Tien
Original assignee: Western Electric Co Inc
Current assignee: AT&T Corp
Priority date: 1977-07-14
Filing date: 1978-07-17
Publication date: 1981-10-07
Also published as: JPS5434846A; JPS6048003B2; CA1102593A; EP0000810A1; DE2861133D1; US4140362A

Description

The invention relates to methods and apparatus for producing holographic diffraction gratings and the like. Gratings that have substantially equal spacing between their lines are referred to as being unchirped. They are especially useful for focusing as well as diffracting light in integrated optical devices.
Gratings have been incorporated in integrated optics devices for several purposes, including the fabrication of distributed feedback lasers, light-wave couplers, and band-rejection filters. Integrated-optics gratings known to the prior art were composed of straight lines, and therefore could not focus the light being processed. Gratings that combine focusing and diffraction were known to be desirable, but the prior art was unable to produce them.
U.S. Patent 3,578,845 discloses a method and apparatus for producing curved-line holographic gratings that have unequally spaced, or chirped, lines. This patent teaches the production of gratings that focus light that propagates into and out of the plane of the grating. It does not teach the relative orientation of laser beams and focal lines that are required in order to produce curved-line gratings that will function in integrated optics devices.
With the invention as claimed one of two coplanar beams which form an interference pattern on a planar surface perpendicular to the plane of the beams is focused to a focal line in the plane of the beams so that the interference pattern comprises substantially equispaced curved fringes. The other beam may be focused to infinity or it may also be focused to a focal line in the plane of the beams.
The invention is particularly applicable to. the production of unchirped, curved-line, holographic diffraction gratings in thin films, which gratings will focus as well as diffract light that is confined to the film in which the grating is formed. (In integrated optics, the film containing the light is called optical waveguide, and the waveguide with a grating in it is called a corrugated waveguide.) The gratings are made by forming an interference pattern in a photosensitive material, photographically processing the interference pattern so formed such as by developing and fixing, and then using the fixed pattern as a mask for ion or chemical etching processes of conventional type to form corrugated waveguides.
In one embodiment of the invention two cylindrically focused beams of coherent optical radiation are provided for writing holographic diffraction gratings. The focal lines of the beams are oriented in a predetermined manner with respect to each other and with respect to the grating being written. The focal lines of the two beams are coplanar and are oriented so that the plane which contains the focal lines also contains the axis of the grating, thereby providing uniform spacing between the grating lines.
Some embodiments of the invention will now be described by way of example with reference to the accompanying drawings, in which

FIGS. 1 A, 1B and 1 C show apparatus for forming gratings according to an embodiment of the invention and
FIGS. 2A to 2L show different gratings according to embodiments of the invention and the methods employed in forming these gratings.

An optical system used to form curved-line gratings is shown in FIG. 1A. It involves two oblique coherent light beams 1 and 2, generated by conventional means not shown, focused by two cylindrical lenses 3 and 4, respectively. A curved-line grating is formed by recording the interference pattern of the two light beams on a photoresist plate 5. Plate 5 is in the (x, z) vertical plane with y = 0. Lenses 3 and 4 are centered in a horizontal plane at z = 0, and the beams are also horizontal. Lines bc and aC,along the center of the two beams are thus also horizontal, and planes adce and bdce are vertical. Note that in this invention, lines f-f and g-g, the focal lines of beams 1 and 2 respectively, are horizontal and are not necessarily parallel to the plate. This is in contrast with the prior art apparatus of U.S. Patent 3,578,845 referred to above in which focal lines would be oriented in the vertical direction and parallel to the photosensitive plate (see FIGS. 4 and 6 of Patent 3,578,845). The relative orientation of these focal lines and their relationship with the plate 5 determine the form of grating that will be formed and are the key to the invention.
In FIG. 1A, the beams are shown as being centered in a horizontal plane at z = 0. The particular value of z and the choice of a horizontal plane are, of course, arbitrarily chosen in order to make the illustration more comprehensible. The essential point is that the two incident beams are coplanar, i.e. they are centered about the same plane (the "beam plane"), and that plane is substantially perpendicular to the plane of the photosensitive material. Since the focal lines f-f and g-g and lenses 3 and 4 are centered in their respective beams, they lie in the "beam plane" also. The above remarks hold true even if one or more of the beams is collimated and the corresponding focal line is theoretically at infinity. If one focal line lies at a great distance from the photosensitive plate, the beam plane is still unambiguously defined by the centers of the beams, the centers of the lenses and the other focal line.
In designing a grating, the curvature of each fringe and the spacing between fringes on the x axis must be specified. The curvature is specified by the formula:

C(incident) + C(reflection) = 2C(fringe), (1) where incident and reflection refers to the light being processed. The inter-fringe spacing is specified by the Bragg-reflection condition:
where
d is the inter-fringe spacing, X is the unit vector in the positive x-direction, m is an integer specifying the diffraction order, and λ is the wavelength of the light beams 1 and 2.

The curvature of the fringe may also be expressed in terms of the beams 1 and 2 used to write the grating. In FIG. 1 B, which shows a view looking down on the x, y plane of FIG. 1 A, ac is the distance along the direction of propagation of beam 1 from focal line f-f to the x axis, and be is the corresponding distance for beam 2.
The curvature of the fringes may be expressed in terms of the wavefront curvatures of the two beams.
(4) where x = o at G, A = the distance F-G, and α is the angle between the direction of propagation of beam 1 and the x-axis. Equations 1 through 4 permit the design of gratings to accomplish the various tasks disclosed above.
FIG. 1 C shows a plan view looking down on the x, y plane of the apparatus shown in FIG. 1 A, further including the source of beams 1 and 2. For ease of illustration, the particular case where the beams intersect the x-axis at an angle α of 45 degrees is shown. Other configurations of beam angle and therefore of mirror position will be required to form gratings for various purposes and may be readily calculated by those skilled in the art from the information disclosed in this application.
In FIG. 1 C, laser 9 generates a parallel beam of coherent optical radiation. It may be desired to employ a mask 10 to define the shape of the beam envelope (rectangular, square, et cetera). The beam from laser 9 is split by beam splitter 8, forming beams 1 and 2. These two beams are reflected by mirrors 6 and 7 into lenses 3 and 4 respectively. The position of all these elements will, of course, be adjusted to give the angles between beams 1 and 2 and plate 5 and the positions of focal lines f-f and g-g that are required by Equations 1 to 4 to provide the grating parameters that are desired.
In the first example of gratings design, shown in FIG. 2A, a grating is used to reflect and focus light emitting from a point source G in a waveguide back to that same point. FIG. 2B illustrates the optics used, looking down on the x-y plane. In this and the following cases, the first figure shows the grating in operation, and the next figure shows the parameters used to write the grating. Beam 1, focused at infinity, crosses the x axis at an angle α. Beam 2 is focused at line g-g, which crosses the x axis at point G, the same point as the focus, at an angle β_B. In general, line g-g is not at right angles to the direction of propagation of beam 2, which is 180 - α. Note that in FIG. 2B, the lines 1 and 2 illustrate the center lines of the beams 1 and 2, respectively. The beams are wide and they overlap one another as they are projected to the plate forming an interference pattern.
In the second grating, a plane parallel beam in a waveguide is focused to a point, at G in the same waveguide (FIG. 2C). In FIG. 2D, we see that beam 1 (plane-parallel) is oriented as before, and that g-g is at right angles to the x axis, passing through point G. Beam 2 has the same direction of propagation as in FIG. 2B.
In the third grating as shown in FIG. 2E, we use the grating to form a lens-like medium, in which all the grating lines have the same curvature. To produce the grating of FIG. 2E, we place the focal line g-g parallel to the x axis as shown in FIG. 2F. The other parameters of the two beams are the same as in the previous examples of FIGS. 2B and 2D.
In the fourth grating (FIG. 2G), light in a waveguide is focused from point G on the x axis to point F, also on the x axis. To produce the grating of FIG. 2G, both beams 1 and 2 are focused at finite distances, both focal lines being perpendicular to the x axis as shown in FIG. 2H. Line f-f intersects the axis at point F, the image point, and line g-g intersects the axis at point G, the object point.
In addition to the above, embodiment gratings may be used to form resonators in diode-lasers. Consider a Hermite-Gaussian beam propagating in a waveguide along the x axis, the curvature of the wave front varies in x as
where N is the mode index of the waveguide,
and a_o is the radius of the beam at x = 0. A requirement for the formation of a grating resonator for such a beam is that the curvatures of the incident and reflected waves, given by Equation 5 as well as the curvatures of the fringes in the grating, agree with Equation 4.
As an illustration, we consider a resonator for an AI Ga As Sb Bragg-reflector laser shown in FIG. 21. The gratings used as left and right reflectors are each 100 µm long. The center of the left reflector is located at x = 0, where C = 0, and the center of the right reflector is located at x = D = 600 µm. The two reflectors are formed separately, the parameters of the right reflector being shown for purposes of illustration. Putting x = D + Ax in Equation 5, and taking D = 600 µm, N = 3.6, A = 1.3 µm and a_o= 4 µm, we find
C≈ -1.37 x 10^-3 (1-0.93 x 10^-3Δx) µm^-1. This curvature may be realized by the arrangement shown in FIG. 2J. Here, C_A= 0, α = 40.13, β_B = 28.53, and G is located 931 ,um from D.
FIG. 2K shows another grating-resonator designed for a distributed feedback laser. The grating is 350 ,um long and centered at x = 0. Two cylindrically focused beams are used, as shown in FIG. 2L. The parameters that match the requirements of Equation 4 satisfactorily are: N = 3.6, A = 1.3 µm, a_o = 5 ,um, a = 40.1, β_A = -156.33, β_B = -23.67, and G and F are located at x = -583.33 ,um and +583.33 µm.
The method discussed above applies equally well to forming unstable resonators, in which the light being reflected travels along a different path on each pass between the two ends of the grating.
One practical problem that may be overcome arises from the distortions that are introduced in the cylindrical wavefront by placing the focal line at an angle other than normal to the direction of propagation. The use of only the center portion of the grating reduces this effect. Secondly, the intensities of the beams vary somewhat along the x axis, tending to overexpose parts of the photoresist plate. This effect may be reduced by the use of spatially varied neutral density filters that may be empirically adjusted to provide a uniform exposure.

Claims

1. A method of forming an interference pattern with curved fringes in a planar piece of photosensitive material wherein a first beam (2) and a second beam (1) of coherent optical radiation, the centres of the beams being coplanar and defining a first plane (X, Y) are directed onto the piece of photosensitive material (5) lying in a second plane (X, Z) perpendicular to the first plane to form the interference pattern, the first beam being focused to a focal line (g-g) characterised in that the focal line lines in the first plane so that the interference pattern comprises substantially equispaced curved fringes.

2. A method as claimed in claim 1 wherein the second beam is focused to infinity.

3. A method as claimed in claim 1 wherein the second beam is focused towards a second focal line (f-f) lying in the first plane.

4. A method as claimed in claim 2 or claim 3 wherein the or each focal line is perpendicular to the second plane.

5. A method as claimed in any of the preceding claims wherein the or each focal line lies in front of the photosensitive material.

6. A method as claimed in any of claims 1 to 4 wherein the or each focal line lies behind the photosensitive material.

7. Apparatus for forming an optical interference pattern with curved fringes in a planar piece of photosensitive material comprising means arranged to provide a first beam (2) and a second beam (1) of coherent optical radiation such that the centres of the beams are coplanar and define a first plane (X, Y) and the first beam is focused to a focal line (g-g) and means arranged to support the photosensitive material (5) in a second plane (X, Z perpendicular to the first plane so that the beams form an interference pattern in the material characterised in that the focal line lies in the first plane so that the interference pattern comprises substantially equispaced curved fringes.

8. Apparatus as claimed in claim 7 wherein the beam-providing means are arranged so that the second beam is focused to infinity.

9. Apparatus as claimed in claim 7 wherein the beam-providing means are arranged so that the second beam is focused to a second focal line (f-f) lying in the first plane.

10. Apparatus as claimed in claim 8 or 9 wherein the or each focal line is perpendicular to the second plane.

11. Apparatus as claimed in any of claims 7 to 10 wherein the or each focal line lies in front of the second plane.

12. Apparatus as claimed in any of claims 7 to 10 wherein the or each focal line lies behind the second plane.