A computer model has been developed that simulates light propagating through an optical data storage system. A model of a laser beam that originates at a laser diode, propagates through an optical system, interacts with a optical disk, reflects back from the optical disk into the system, and propagates to data and servo detectors is discussed

Flagello, D. G.

Milster, T. D.

Treptau, J. P.

English

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Appendix I / 187
Laser Beam Modeling in Optical Storage S_tems . ; _:
f _
J.r,. or,ti-I U,iv r i ,of "r  on. 8572 2
"r.o.Milster,OpticalSciencesCenter,Universityof  izona, tucson, 857za , i,
D.G. F'lageilo, T.J. Watson Research Center, IBM, Yorktown Heights, N'Y', 10598 [ f '
Abstract / . _eZ_ " /
A computer model has been developed that simulates light propagating thrbugia an optical
data storage system. This paper will discuss a model of a laser beam that originates at a laser diode,
propagates through an optical system, interacts with a optical disk, reflects back from the optical disk
into the system, and propagates to data and servo detectors.
Introduction
The field of optical data storage technology has rapidly advanced in the recent past. Several
different types of optical disks have been developed, each with different capabilities and different
methods of storing information. One form of optical disk used for data storage is the CD-ROM,
which is a read only device. The write-once read-many (WORM) medium was developed after the
CD-ROM, and it has the increased functionality of allowing the user to write information to the disk.
A drawback of WORM devices is that they are not erasable. Most recently, the erasable optical disk
has been developed, which has the full functionality of magnetic disk media, in that data may be
written, read back, and erased from the disk if desired. This paper will discuss a system model of an
erasable optical disk system. A number of system models analyzing various components of an optical
disk system have already been completed (1)(2)(3). In contrast to those models, this model is a
complete, end-to-end system model instead of an analysis that deals with only specific components
of an optical data storage system.
There are several types of erasable optical disks, each with a different technique to write,
read, and erase data. The most common type of erasable media is magneto-optic. The read operation
in magneto-optic media aecomplithed through polarization modulation. Light incident on the disk is
reflected, and the reflected light has its polarization rotated due to the data pattern on the disk. The
polarization rotation of the reflected light is known as the polar Kerr effect (4). The system model
discussed in this paper will consider the disk to be an erasable, magneto-optic medium.
Modelini the Laser Beam
The source of light in a magneto-optic (M-O) disk system is a laser diode. A physical optics
analysis is accomplished through modeling the amplitude and phase of the laser beam's electric field.
Beam propagation it simulated through the use of Fresnel diffraction calculations (5). In this model,
a scalar diffraction approach is used. A vector diffraction analysis is certainly valid, but it is very
computationally expensive. In the system model, the beam is represented by a matrix of complex
values, where each matrix element repretents a different sample point in the wavefront. The complex
values represent the amplitude and phase of the wavefront at a given point. Fresnel diffraction
calculations are computed through the use of Fast Fourier Transforms.
Consideration must be given to the type of beam a laser diode generates. Among others, there
are two characteristics of a typical laser diode used for optical data storage that are discussed. A
diagram for a typical laser diode is shown in Figure 1. The cavity is rectangular in shape, which causes
https://ntrs.nasa.gov/search.jsp?R=19920005693 2020-03-17T14:13:34+00:00Z
v188 Appendix I
the far-field pattern of the
beam to have an elliptical
shape. This necessitates, as
far as optical data storage is
concerned, circularizing
optics in the system.
Secondly, the cavity is index
guided perpendicular to the
diode junction, and gain
guided parallel to the
junction. This has three
effects on the emitted beam:
(1) The far-field intensity
pattern has a Lorentzian
profile in the direction
perpendicular to the
junction (6); (2) The far-
field intensity pattern has a
Gaussian profile in the
direction parallel to the
junction (7); and (3) the
beam contains astigmatism (7).
Generic laser diode
• J-------_--lOOiAm B
In_i_
[/_ Profile e_,,
pw
Figure I Generic Laser Diode
Modeling the Optical System
The laser beam propagates from the diode and eventually is incident on the entrance pupil
of the optical system. A geometrical optics analysis of the system is a vafid method of characterizing
the optical system. Ray-trace calculations may be performed in order to quantify aberrations in the
system. Figure 2 shows a portion of a generic M-O optical data storage system. The light from the
diode is collimated, circularized, focused down to a spot on the disk, and the reflected light containing
information is delivered to
data and servo detectors. The
following paragraphs describe
a method of modeling the
entrance pupil to exit pupil
mapping of the optical system.
The wavefront is
propagated to the entrance
pupil of the system with scalar
diffraction. The optical system
maps the wavefront incident
on the entrance pupil to the
exitpupilof the system.Then,
thewavefrontispropagated to
thediskwithscalardiffraction.
This modeling of the pupilto
pupilmapping isaccomplished
ina two pronged approach as
shown inFigure 3.
MO storage device (laser to disk)
Om¢_
CoIlimang
Lens
Circuladzi_
F'llplm2 Schematic of an Optical System for M-O Data
Storage
Append/x I 189
To begin, we
compute the ideal
diffraction mapping of the
entrance pupil to the exit
pupil. We calculate a
paraxial system quantifier,
the ABCD matrix. An
ABCD matrix is developed
for all the elements in the
system, and the resulting
system ABCD matrix is
simply the product of all
component matrices: :'N
Figure 3 Diagram of Entrance Pupil to Exit Pupil mapping
technique
ABCD,,:**m --- IX ABCD,,
n-I
In the above equation, the optical system has i elements. Once the system ABCD matrix has been
found, that information is placed into the Huygens' integral for wave propagation (8). In the
following equation, xz = entrance pupil plane, x, = exit pupil plane, and ta_(x_)is the wavefront at the
given plane. Computation of the integral will map the wavefront from entrance to exit pupil, that is,
a2(x2) I o-_*L,f f lc(xl,xt)t_t(xl)d.xt
The Huygens' kernel in one transverse dimension is given by:
The abertltions in the optical system must now be considered. To compute the aberrations,
a ray-trace of the system is performed. An ideal lens may be placed at the exit pupil, and that lens
will focus the ray1 to an image plane. At the arbitrary image plane, the two-dimensional transverse
ray fan is calculated. If that ray fan is integrated, the result is the optical path difference (OPD) in
the exit pupil due to the aberrations in the system.
The ideal diffraction imaging wavefront and the OPD in the exit pupil due to aberrations are
cnmbined to give the total exit pupil wavefront. This is simply the addition of the two component
phase fronts. The OPD due to aberrations, plus the ideal diffraction phase front equals the exit pupil
phase front. The amplitude of the beam at the exit pupil is given by the ideal diffraction propagation
of the amplitude of the E-field incident on the entrance pupil.
.... +.+-+:_.+ +;_++r+eIS
OF ?- +-,R
190 Ap/_nd/x I
The wavefront that is now at the exit pupil is propagated to the optical disk using scalar
diffraction calculations. The light interacts with the disk, and it is reflected from the disk back into
the optical system. The reflected light propagates to detectors where the data is converted into an
electrical signal.
Modelin_ Disk Interaction
Jones calculus is utilized in the analysis of the disk-laser beam interaction (2). The following
column vector represents an arbitrary E-field, where _ and E r symbolize two orthogonal polarization
components:
and F.v are the matrices of complex values that model the wavefront. The light that is incident on
the disk is linearly polarized, and the direction of polarization is defined as the x direction. The
following column vector represents the incident light:
This light interacts with the disk. The disk may be described using the following Jones matrix:
/9-_"
where 1' is the bulk reflectivity of the medium, K is a matrix which contains information about the
tangent of the Kerr angle at sampled positions on the disk, and 6 is the phase shift between the x
and y components on reflection from the medium (2). The reflected light is the product of the disk
matrix and the incident fight:
_'+' - 1/I, 01 _',++_+'
_¢contains the information about the data marks on the disk. Marks, which correspond to logical ones
have a vahm equal to +tan(Kerr angle). Spaces between the marks, which correspond to logical
zeros, have a value equal to -tan(Kerr angle). Figure 4 graphically depicts the matrix elements in a
sample K matrix.
The two polarization components in the reflected field are separately propagated back
through the optical system using of Fresnel diffraction calculations. The methods described in the
sections above are used to model propagation of the reflected light back through the system to data
and servo detectors, which convert the information contained in the reflected beam into an electrical
signal.
Appendix I 191
Implementation
This model is
implemented on a 386
computer, running at 25 MHz.
The modeling environment is
the MATLAB programming
language. MATLAB is an
interactive mathematics
programming environment that
allows a user to perform a
variety of calculations, including
those necessary for the scalar
diffraction model of the light
propagating through the system.
Figure 4
!,l_t'l<
--&- -- ,'C -&-
Example of a K matrix
Conclusion
Light that travels through an optical data storage system can be modeled using the techniques
discussed above. We can treat the modeling of light differently according to the functional subsystems
interacting with the light. As discussed above, these subsystems are the laser diode, the optical system,
and the optical disk. The model of the laser beam in the system is a combined physical optics analysis
and geometrical optics analysis. The model uses Fresnel diffraction calculations and ray-trace
calculations in order to simulate the propagation of the laser beam through the system.
Acknowledgements
The authors wish to thank Ken Moore of the Optical Sciences Center for suggesting the
combination of ray-trace and diffraction calculations necessary to find the exit pupil wavefront. This
work was supported by NASA grant no. NGT-50579.
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,, ,. :31;¢i _'_Z
192 Appendix I


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