Curved grating surface-emitting distributed feedback laser

Surface-emitting distributed feedback (SEDFB) lasers having a curved grating with a shape that produces good beam quality. A preferred shape is one for which the grating curves away from the center of the gain region of the laser. The use of the curved grating of the present invention produces good beam quality from broad area SEDFB lasers with high power and high efficiency. The present invention overcomes self-induced filament formation and dynamic instabilities that limit achievable beam quality. The present invention provides for a holographic method for fabricating curved gratings for the SEDFB lasers that is consistent with laser batch processing.

BACKGROUND 
The present invention relates to distributed feedback lasers, and more 
particularly, to a surface-emitting distributed feedback (SEDFB) laser 
having curved gratings and a holographic method for fabricating such 
gratings that is consistent with batch processing of lasers. 
The prior art for which the present invention is an improvement is a broad 
area surface-emitting distributed feedback (SEDFB) laser with chirped or 
straight gratings. Surface-emitting distributed feedback laser with 
chirped gratings are described in U.S. Pat. No. 5,241,556, issued to 
Macomber et al. entitled "Chirped Grating Surface-Emitting Distributed 
feedback Lasers", and U.S. Pat. No. 5,238,531 issued to Macomber et al. 
entitled "Apparatus and Method for Fabricating a Chirped Grating in a 
Surface-Emitting Distributed Feedback Semiconductor Laser Diode Device", 
both of which are assigned to the assignee of the present invention. 
Surface-emitting distributed feedback laser with straight gratings are 
described in "Surface emitting distributed feedback semiconductor laser", 
by S. H. Macomber et al., Appl. Phys. Lett., vol. 51, pp. 472-474, 
1987,"AlGaAs surface emitting distributed feedback semiconductor laser", 
by S. H. Macomber et al., Proc. SPIE, vol. 893, pp. 188-194, 1988, 
"Two-dimensional surface emitting distributed feedback laser arrays", IEEE 
Photon. Lett. vol. 1, pp. 202-204, 1989, by J. S. Mott et al., "Analysis 
of grating surface emitting lasers", IEEE J. Quant. Electron., vol. 26, 
pp. 456-465 (1990), by R. J. Noll et al., "Non-linear analysis of surface 
emitting lasers distributed feedback lasers", IEEE J. Quant. Electron., 
vol. 26, pp. 2065-2074, 1990, by S. H. Macomber et al., and Recent 
developments in surface-emitting distributed feedback arrays", Proc. SPIE, 
vol. 1219, pp. 228-232, 1990, by S. H. Macomber et al. 
Although the prior art has demonstrated high power, high efficiency, and 
good longitudinal beam quality, the lateral beam quality is generally very 
poor. This problem has limited the usable range in imaging laser radar 
systems, limited the spot size and depth of focus in applications 
requiring focusing, and limited the minimum core size of fiber optics into 
which the laser can be coupled. 
The maximum achievable power from a semiconductor laser can be increased by 
increasing the width of the stripe. However, it has long been known that 
the beam quality of wide stripe semiconductor lasers is usually many times 
the diffraction limit. This is described in "A GaAsAl.sub.x Ga.sub.1-x As 
double-heterostructure planar stripe laser", H. Yonezu et al., in Japan. 
J. Appl. Phys., vol. 12., pp. 1585-1592, 1973, for example. This problem 
is caused by self-induced waveguiding that arises from a combination of 
spatial hole burning and index antiguiding (i.e., the index of refraction 
of the medium tends to decrease when the local carrier density increases) 
forming self-guiding filaments. This is described in "Observation of 
self-focusing in stripe geometry semiconductor lasers and the development 
of a comprehensive model of their operation", by P. A. Kirby et al., IEEE 
J. Quant. Electron., vol. QE-13, pp. 705-719, 1977. An initially flat 
wavefront propagating along a uniform wide stripe tends to break up into 
self-perpetuating filaments that lead to poor beam quality. This is 
described in "Spatial evolution of filaments in broad area laser 
amplifiers", Appl. Phys. Lett., by R. J. Lang et al., vol. 62, pp. 
1209-1211, 1993. This problem worsens as the drive current increases, 
usually with a progressively more aberrated output beam. In comparison, an 
expanding wavefront should be much less susceptible to this problem. 
Unstable resonators have been used with a variety of high power lasers. 
They produce a high degree of lateral mode selectivity with a mode that 
fills a large gain region and are relatively insensitive to intracavity 
index aberrations. This is described in "Unstable optical resonators", by 
A. E. Siegman, in Appl. Opt., vol. 13, pp. 353-367, 1974. These 
characteristics combined with curved (expanding) internal wavefronts that 
can suppress filamentation makes the unstable resonator approach 
well-suited to the problem of lateral mode control in broad area 
semiconductor lasers. Unstable resonator Fabry-Perot devices have 
demonstrated good lateral beam quality. This is described in "High power, 
nearly diffraction limited output from a semiconductor laser with an 
unstable resonator", by M. L. Tilton et al., IEEE J. Quant. Electron., 
vol. QE-27, pp. 2098-2108, 1991, and "Fabrication of unstable resonator 
diode lasers", by C. Largent et al., Proc. SPIE, vol. 1418, pp. 40-45, 
1991. However, fabrication of curved mirrors with required surface 
smoothness has been problematic. 
Presently copending patent application Ser. No. 07/974,775, filed Nov. 12, 
1992, entitled "Curved Grating Surface-Emitting Distributed Feedback 
Semiconductor Laser", assigned to the assignee of the present invention, 
generally describes curved grating SEDFB lasers. However, this invention 
only relates to a constant radius grating shape as an example. It was not 
clear at that time what the optimum shape would be since analysis was not 
yet available. In the present invention, a curved grating approach is 
described for achieving lateral mode control in wide stripe SEDFB lasers 
that is analogous to an unstable resonator. Furthermore, in a second 
copending patent application Ser. No. 07/975,303, filed Nov. 12, 1992, 
entitled "Apparatus and Method of Fabricating a Curved Grating in a 
Surface-Emitting Distributed Feedback Semiconductor Laser Diode Device", 
also assigned to the assignee of the present invention, a method is 
described for fabricating a constant radius grating using the Talbot 
effect but not the more general types of curved gratings described herein. 
U.S. Pat. No. 5,307,183 and U.S. Pat. No. 5,345,466 are incorporated 
herein. 
Therefore, it is an objective of the present invention to provide for a 
surface-emitting distributed feedback (SEDFB) laser having curved gratings 
that overcomes the problems associated with conventional surface-emitting 
distributed feedback lasers, and to provide for a holographic method for 
fabricating such gratings that is consistent with batch processing of 
lasers 
SUMMARY OF THE INVENTION 
In order to meet the above and other objectives, the present invention 
provides for a surface-emitting distributed feedback (SEDFB) laser with a 
curved grating having a shape that produces good beam quality. A preferred 
shape is one for which the grating curves away from the center of the gain 
region. The use of the curved grating of the present invention produces 
good beam quality from broad area SEDFB lasers with high power and high 
efficiency. 
The curved grating may comprise a variable radius grating that curves away 
from the center of the gain region or from a central point near a center 
of the gain region. The curved grating typically has a grating curvature 
that is represented by a deformation function L(y, z) whose dominant term 
has a form corresponding to -zy.sup.2. The grating deformation function 
may have additional terms that improve output beam quality of the laser, 
that include chirp (z.sup.2) and aberration correction terms (z.sup.3 
y.sup.2). 
The present invention overcomes a fundamental problem in semiconductor 
lasers, namely self-induced filament formation and dynamic instabilities 
that limit achievable beam quality. In addition, the present invention 
provides for a holographic method for fabricating curved gratings that is 
consistent with batch processing of lasers. The method provides for 
fabricating a curved grating in a surface-emitting distributed feedback 
laser that comprises a substrate having a gain region formed adjacent a 
surface thereof. The method comprising the steps of providing a prism, 
disposing the surface of the substrate adjacent a selected surface of the 
prism, and irradiating the surface of the substrate with two laser beams 
to holographically form the curved grating in the substrate, wherein one 
beam is planar and the other beam has a varying phase that generates a 
predetermined grating distortion function.

DETAILED DESCRIPTION 
Referring to the drawing figures, FIG. 1a shows a partial cross sectional 
perspective view of a portion of a surface-emitting distributed feedback 
(SEDFB) laser 10 having a curved grating 30 in accordance with the 
principles of the present invention. FIG. 1b illustrates a perspective 
cutaway view of a bottom portion of the surface-emitting distributed 
feedback laser 10 of FIG. 1a showing details of the curved grating 30 in 
accordance with the principles of the present invention. The present 
invention is referred to herein as a curved grating surface-emitting 
distributed feedback laser 10. In general, surface-emitting distributed 
feedback lasers are well known in the art as is evidenced by the 
references cited herein. 
The curved grating surface-emitting distributed feedback laser 10 is 
comprised of an n-type gallium arsenide substrate 24 and a curved grating 
30 (FIG. 1b) is formed therein subsequent to the formation of additional 
material layers. A zinc diffusion layer 15 is formed in the layer 16 
subsequent to formation of the curved grating 30. The zinc diffusion layer 
15 forms the gain region 31 or gain stripe 31 of the laser 10. The gain 
region 31 is shown more clearly in FIG. 1b. 
As set forth in the co-pending patents, U.S. Pat. No. 5,307,183 and U.S. 
Pat. No. 5,345,466, the curved grating surface-emitting distributed 
feedback laser is fabricated on the GaAs substrate 24 in the inverse order 
of the disposition of the layers on the heat sink 11 as described below. 
On top of a heat sink 11 the plurality of material layers are disposed as 
follows. A layer of gold (Au) 12 is disposed on the heat sink 11. A layer 
of platinum (Pt) 13 is disposed on the layer of gold 12. A second layer of 
gold (Au) 14 is disposed on the layer of platinum 13. The second layer of 
gold 14 forms the curved grating 30 of the present invention, which is 
formed in the a p-type cladding layer 16 which is disposed over the second 
layer of gold 14 and the zinc diffusion layer 15. An active layer 17 is 
disposed over the p-type cladding layer 16. An n-type confinement layer 18 
is disposed over the active layer 17. An n-type cladding layer 21 is 
disposed over the n-type confinement layer 18. An n-type GaAs layer 22 is 
disposed over the n-type cladding layer 21. A stop etch layer 23 is 
disposed over the n-type GaAs layer 22 which is used to form an output 
window 19. An n-type GaAs layer 24 is disposed over the stop etch layer 
23. Finally, a gold-germanium-nickel (Au--Ge--Ni) layer 25 is disposed 
over the n-type GaAs layer 24. The output window 19 is disposed at the 
bottom of an etched well 20. 
FIG. 1b illustrates a perspective cutaway inverted view of a bottom portion 
of the surface-emitting distributed feedback laser 10 of FIG. 1a showing 
the curved grating 30 in accordance with the principles of the present 
invention. The bottom-most layers illustrated in FIG. 1a are shown that 
include the gold, platinum and second gold layers 12, 13, 14. The other 
layers, 16, 17, 18, 21, 22 and 23 are not shown separately from the 
substrate 24 in FIG. 1a. The gain region 31 or gain stripe 31 is formed by 
the zinc diffusion layer 15. The design and construction of 
surface-emitting distributed feedback lasers is well-known in the art and 
will not be further described herein except for the improvements provided 
by the present invention. 
The basic idea behind the present invention is to use a curved grating 30 
having particular shapes in a broad area SEDFB laser 10 with an otherwise 
standard type of design, such as are described in the above-cited articles 
or patents. As shown by the examples in FIGS. 2a-2f, there are many 
possible shapes for the curved grating 30 that may be used. FIGS. 2a-2f 
illustrate different curved grating patterns that may be employed in the 
laser 10 of FIG. 1. All these grating designs have a nearly constant 
grating periodicity that satisfy the grating resonance condition: 
EQU .lambda.=n.LAMBDA. (1) 
where .lambda. is vacuum wavelength, n is an effective index of a 
waveguide, and .LAMBDA. is grating periodicity. 
Of all the grating shapes illustrated in FIGS. 2a-2f, a numerical model of 
the laser 10 has shown that a variable radius grating 30 that curves away 
from the center of the lasers stripe 31, as is shown in FIG. 2e, has the 
best lateral mode stability and beam quality. This shape is analogous to 
an unstable resonator in a Fabry-Perot diode laser. 
Curved grating shapes may be described mathematically by a function L(y,z) 
that deforms a linear grating into the curved grating 30. If y and z are, 
respectively, the lateral and longitudinal coordinates of an undeformed 
grating then a transformation to a new coordinate system (y, 
z).fwdarw.(y', z') 
EQU z'=z+L(Y, Z) (2) 
EQU y'=y (3) 
is such that deformed grating grooves lie on lines of constant z'. The 
grating shape shown in FIG. 2(e) is described by a dominant term 
EQU L(y, z) .alpha. zy.sup.2 (4) 
where (y, z)=(0, 0) is at (or near) the center of the gain stripe 31. 
Results from the numerical simulation are presented below. Numerical 
simulation results were obtained for several types of curved grating SEDFB 
lasers 10. Of all the curved grating designs that were modeled, the design 
in FIG. 2(e) produced the most stable solutions at high antiguiding. A 
generalization of equation (4) that includes a z.sup.2 term for grating 
chirp as well as a z.sup.3 y.sup.2 term that was found to correct for 
astigmatism is given by: 
EQU L(y, z) .alpha. c.sub.20 z.sup.2 +c.sub.12 zy.sup.2 +c.sub.32 z.sup.3 
y.sup.2. (5) 
In the particular case that was modeled, the gain stripe 31 was 1200 .mu.m 
long by 50 .mu.m wide where the grating function given in (5) had a 
coefficient such that grating phase deviation at the corners corners of 
the gain stripe 31 from the three terms was 
______________________________________ 
Term Magnitude 
______________________________________ 
c.sub.20 z.sup.2 
0.25 waves 
c.sub.12 zy.sup.2 
-1 waves 
c.sub.32 z.sup.3 y.sup.2 
0.1 waves. 
______________________________________ 
The magnitude of the chirp term was typical of that used in experiments 
with non-curved SEDFB lasers that produce a single-lobed longitudinal far 
field. 
The optimum value of these terms vary with the dimensions of the gain 
stripe 31, but are of the same order of magnitude as the example case 
above. Additional higher order terms may be used to reduce aberrations in 
the output beam of the laser 10. 
Thus, in a preferred embodiment of the curved grating surface-emitting 
distributed feedback laser 10, the curved grating 30 is a variable radius 
grating 30 that curves away from the center of the laser stripe 31 or gain 
region 31. Use of such a variable radius grating 30 achieves lateral mode 
control in a wide stripe SEDFB laser 10 that is analogous to an unstable 
resonator. 
FIGS. 3a-3d illustrate graphs of numerical analysis performed on the 
preferred embodiment of the laser 10 of FIG. 1. A cross-section of the 
center of the near field is shown in FIG. 3a. The intensity is relatively 
smooth while the phase has an overall quadratic lateral phase profile that 
corresponds to approximately 5 .mu.m virtual waist located approximately 
0.3 mm behind the device near field plane as shown in FIG. 3b. The lateral 
far field for this case, shown in FIG. 3c, is consistent with the 
divergence from a nearly diffraction limited source at the virtual waist. 
The longitudinal field in FIG. 3d shows a profile that is typical of past 
chirp lasers. 
These results stand out from all other types of SEDFB lasers that were 
tested using the same computer program. Linear arrays, offset arrays, 
tilted arrays, Talbot spatial filter and broad stripes were simulated and 
found to be numerically unstable at even low levels of antiguiding. This 
results parallels the results from comprehensive dynamical models of 
Fabry-Perot diode lasers for which all but narrow stripe and unstable 
resonator designs were dynamically unstable, such as are described in 
"Spatiotemporal chaos in broad area semiconductor lasers", by H. 
Adachihara et al., J. Opt. Soc. Am., vol. B10, pp. 658-665, 1993, and in 
U.S. Pat. No. 4,803,696 entitled "Laser with Grating Feedback Unstable 
Resonator", assigned to the assignee of the present invention. 
For comparative purposes, U.S. Pat. No. 4,803,696 cited above discloses 
that a partially reflecting facet, in addition to a grating, participates 
in establishing the lasing mode. The present invention does not use any 
reflectors but instead relies completely on the grating 16. Four of the 
five embodiments disclosed in U.S. Pat. No. 4,803,696 use separate gain 
and grating regions, whereas the present invention provides for for 
colocation of the gain region 31 and grating 20. The one embodiment in 
U.S. Pat. No. 4,803,696 that does colocate the gain region and grating has 
a different grating shape than the present invention. 
A method of fabricating a curved grating 30 for the curved grating 
surface-emitting distributed feedback laser 10 in accordance with the 
principles of the present invention will now be described. To be 
cost-effective, fabrication of the laser 10 must be compatible with wafer 
level batch processing. The grating pattern must be repeated over the gain 
stripe 31 of each laser 10 on a wafer. The present method uses a 
holographic grating fabrication technique as is described below, although 
non-holographic techniques may also be employed, but are not considered to 
be as practical. 
A prism contact technique currently used by the assignee of the present 
invention may be used with the addition of two lenses 51, 52 and a phase 
plate 53 as shown in FIG. 4. The prism contact technique is described in 
detail in U.S. Pat. No. 5,241,556 cited above. FIG. 4 illustrates grating 
exposure apparatus 50 employed in making the curved grating 30 in the 
laser 10 of FIG. 1 in conjunction with the prism contact technique. The 
grating exposure apparatus 50 includes a phase plate 53, two lenses 51, 
52, a spatial filter 54 disposed between the lenses 51, 52, a baffle 55, a 
prism 57 and a wafer 56 (substrate 11) masked with photoresist arranged as 
shown in FIG. 4. Two-beam interference at a surface of the wafer 56 is 
employed where one beam is planar and the second beam has a varying phase 
.PHI.(y, z) that generates a grating distortion function given by 
EQU L(y, z)=.PHI.(y, z)/K.sub.0 (6) 
where K.sub.0 =2.pi./.LAMBDA. is the grating vector. A glass (or fused 
silica) phase plate 53 has a height profile h(y, z) that produces a phase 
profile given by 
##EQU1## 
The phase plate 53 may be comprised of any optically transparent material 
in which the surface height pattern is stepped and repeated over a large 
area such that it aligns with a stripe mask used to fabricate the lasers 
10. A variety of conventional methods are available for fabricating such 
phase plates 53. 
The behavior of the imaging optics employed in the grating exposure 
apparatus 50 is shown in FIGS. 5a and 5b. Referring to FIG. 5a, the two 
lenses 51, 52, each of focal length F, are spaced a distance 2F apart such 
that a plane wave images to a plane wave and a point images to a point. 
The image and object planes are tilted as shown since the wafer exposure 
surface, or wafer plane, unfolded from the prism 57, is also tilted. The 
opposing tilts ensure that, to first order, the image and object distances 
satisfy the lens equation. The lenses 51, 52 have one edge cut down or 
truncated to prevent shadowing of a plane wave input beam. The phase plate 
tilt angle is nominally 34 degrees, depending on the exact index of 
refraction of the prism 57 and the prism angle. The coarse spatial filter 
54 centrally located between the lenses 51, 52 removes unwanted high 
spatial frequencies (e.g., spatial period less than 10 .mu.m) that may 
arise from a phase plate 53 made using binary optics or imperfections in 
an analog plate. The same principle of relaying the image of the phase 
plate 53 may be adapted to any other two-beam holographic system such as 
those that use ultraviolet lasers and do not necessarily use a prism. The 
same principle of relaying the image of a phase plate 53 may be adapted to 
any other two-beam holographic system such as those that use ultraviolet 
lasers and do not necessarily use a prism. Moreover, the focal lengths of 
the lenses 51, 52 do not necessarily have to be equal as long as they are 
confocal. Also, the phase plate 53 may be used in reflection instead of in 
transmission. The phase pattern may also be impressed in the form of a 
gradient index, for example, as fabricated by masking and ion exchange in 
glass. 
There are numerous commercial and military applications for the present 
laser 10. Examples of identified commercial applications include laser 
gingivectomy, medical laser surgery, photo-dynamic therapy, materials 
micro-joining, ignition of jet fuel, pump sources for solid state lasers, 
color laser printers, soldering systems, and frequency-doubled blue 
lasers. Examples of military applications include laser initiated 
ordinance for ejection seats, jet engine ignition, wide field imaging 
laser radar for ground search, narrow field of view forward-looking 
imaging laser radar systems for missile guidance, free space optical 
communications systems, illuminators for night visions systems, and 
medical hand-held lasers for tracheotomy or wound cauterization. 
Thus there has been described a new and improved surface-emitting 
distributed feedback laser having curved gratings and a holographic method 
for fabricating such gratings that is consistent with batch processing of 
lasers. It is to be understood that the above-described embodiment is 
merely illustrative of some of the many specific embodiments which 
represent applications of the principles of the present invention. 
Clearly, numerous and other arrangements can be readily devised by those 
skilled in the art without departing from the scope of the invention.