Magnetooptic multilayered memory structure with abirefringent superstrate: a rigorous analysis

R. Stephen Weis and Thomas K. Gaylord

A novel interference enhanced magnetooptic multilayered memory structure with a birefringent superstratethat converts incident linear polarization to rotated linear polarization on reflection is introduced. Thisstructure employs a birefringent superstrate; several different ways of implementing a birefringnet super-strate are proposed. The structure is analyzed using a rigorous method described previously [J. Opt. Soc. Am.A 4, 1720 (1987)]. The reflection characteristics of the structure as functions of incident angle are given.

1. Introduction

Since multilayered structures containing a magne-tooptic layer exhibit desirable reflection characteris-tics, they have been investigated for use as magnetoop-tic computer memories.1 In magnetooptic memoriesinformation is recorded and erased thermomagnetical-ly using a laser. The information is read out by ob-serving the change of the incident (reading) wave'spolarization on reflection from the multilayered struc-ture.

Magnetooptic effects that occur on reflection arecollectively referred to as magnetooptic Kerr effects.2These Kerr effects are exhibited as changes in thepolarization of light on reflection from a magnetostati-cally biased material. When the magnetization vectorM is normal to the material's reflecting surface, theeffect is known as the polar Kerr effect. High density,erasable computer memory disk systems that employthe polar Kerr effect are now commercially available.3The polarization of light reflected from a magnetoop-tic layer exhibiting the polar Kerr effect with the mag-netization (M) in a given direction (into or out of thesurface) can be described by its ellipticity (e) andazimuth (0); if the direction of M is reversed, the re-flected polarization state parameters become -e and1800 - 0 as depicted in Fig. 1.

Steve Weis is with U.S. Naval Academy, Electrical EngineeringDepartment, Annapolis, Maryland 21402, and Thomas Gaylord iswith Georgia Institute of Technology, School of Electrical Engineer-ing, Atlanta, Georgia 30332-0250.

Received 29 August 1988.0003-6935/89/101926-05$02.00/0.C 1989 Optical Society of America.

The transmission and reflection characteristics of amagnetooptic material can be calculated rigorously(without approximation) by including the magnetoop-tic effects in the dielectric permittivity tensor andtaking the relative magnetic permeability to be unity.4The appropriate permittivity tensor () for the polarKerr effect for the coordinate system used in this work(shown in Fig. 2) is

XX JExy 0

e= JExy 6YY 0 ,

[ 0 0 EZzJ

(1)

where j = \/-T. The time and spatial dependence ofthe electromagnetic plane wave is taken to be expj(cot- k r)], where o is the angular frequency, t is the time,k is the wavevector in the medium, and r is the vectorfrom the origin to the point being described.5

As depicted in Fig. 2, the azimuth angle () and theangle of incidence (inc) characterize the linearly po-larized incident wave. The azimuth angle of an inci-dent transverse electric (TE) polarized wave is 0,whereas the azimuth of an incident transverse magnet-ic (TM) polarized wave is 900. For normal incidence,the reference direction of the reflected TM componentof E is taken to be antiparallel to the reference direc-tion of the incident TM component of E.5

Section II describes structures previously used forthe interference enhancement of Kerr rotation andthen introduces an interference enhanced magnetoop-tic multilayered memory device that converts incidentlinear polarization to rotated linear polarization onreflection. In Sec III, the parameters for two specificimplementations of the new structure are given andtheir reflection characteristics as functions of incidentangle are rigorously analyzed using the method pre-sented in Ref. 6. Finally, Sec. IV concludes with abrief summary.

1926 APPLIED OPTICS / Vol. 28, No. 10/ 15 May 1989

Ba~~~~~~Ia

Fig. 2. Geometry of the N-layered structure analyzed. The planeof incidence is chosen, without loss of generality, to be the x-z plane.

The azimuth angle (00) of the polarization of the incident wave andthe angle of incidence (t9jc) are defined as shown.

Fig. 1. Depiction of the polar Kerr effect illustrating the change in

the reflected light's ellipticity (e) and azimuth (0) on reversal of the

direction of the magnetization (M).

11. Interference Enhancement of Kerr Rotation

The use of interference effects to enhance the azi-muth rotation (Orot = 0 - o) produced by a magnetoop-tic layer exhibiting the polar Kerr effect (Kerr rota-tion) has been investigated by several authors.7-10

Connell 9 proposed the structure shown in Fig. 3 in1982. In Connell's structure, the center dielectric lay-er thickness is adjusted so that for incident TE polar-ization (E 11 y), the power in the reflected TE polariza-tion is minimized while the power in the orthogonalTM polarization (H It y) is maximized. For normalincidence and reasonable material parameters, Con-nell's Kerr rotation enhancement structure yields aKerr reflectance (IEx/EincI2) of 10 to 100 times greaterthan that of a magnetooptic film on a semi-infinitesubstrate.9 A similar structure, proposed by Tomitaand Yoshino, 7 is shown in Fig. 4. In their structure,the dielectric superstrate is the phase adjusting layerand the quarterwave dielectric multilayers serve as thereflector. Both of these interference enhanced mag-netooptic multilayered structures have been impor-tant components in improving magnetooptic readoutsystems.7 ' 8

For readout systems that employ a differential de-tection scheme, the Kerr rotation angle and the signal-to-noise ratio are both maximized by converting thereflected elliptical polarization to linear polarizationfor one of the two allowed magnetization states. 8 11

The readout systems that employ the above interfer-ence enhanced structures as the memory media use aphase plate to convert the reflected elliptical polariza-tion to linear polarization by eliminating the phasedifference between the reflected TE and TM polarizedcomponents of the wave.7' 8

PrimaryIncident Reflected WavesWave , (Elly Polarization)

PrimaryReflected Waves(HI y Polarization)

Subtraction Addition

Magneto-Optic Mt

Layer V\/ |Y xDieletric

Reflector (Z

Fig. 3. Multilayered structure of Connell 9 for the interference en-

hancement of the polar Kerr rotation.

Incident Wave

(1

EightQuarter-Wave

Layers

Fig. 4. Multilayer structure of Tomita and Yoshino7 for the inter-ference enhancement of the polar Kerr rotation.

15 May 1989 / Vol. 28, No. 10/ APPLIED OPTICS 1927

\1,

As proposed here, the effect of the external phaseplate can be incorporated directly into the interferenceenhanced magnetooptic multilayered structure by us-ing a birefringent superstrate. The birefringent su-perstrate converts the elliptical polarization to linearpolarization and simultaneously serves as a phase ad-justing layer to produce linear polarization on reflec-tion.

Since the present novel multilayered structure con-verts incident linear polarization to rotated linear po-larization on reflection, a large extinction ration can beachieved by placing only a polarizer in the path of thereflected wave and orienting it so that a minimum isdetected for one of the two allowed magnetizationstates (Mout or Mi.). The transmission axis of thepolarizer is then perpendicular to the reflected linearpolarization for that M state. For the opposite Mstate, a nonzero fraction of the power incident on thestructure will be detected. The fraction of the reflect-ed power that is transmitted through the polarizer isproportional to [sin(Ort)] 2, where rot is the azimuthrotation produced by the polar Kerr effect. In thisideal case, the minimum detected would be a null, thusproducing an infinite extinction ratio.

The magnetooptic structure with a birefringent su-perstrate shown in Fig. 5 converts a normally incidentlinear polarization (either x- or y-polarized) to reflect-ed linear polarization with a rotated azimuth. With-out loss of generality, the incident wave may be chosento be y-polarized (TE) . This structure can be de-signed by simultaneously satisfying all the followingconditions for a normally incident wave of a given free-space wavelength:

(1) The birefringent superstrate's optic axis mustbe in the plane of incidence so that the y-polarizedincident light remains y-polarized until it is incidenton the magnetooptic layer.

(2) The reflected x-polarized waves (generated bythe polar Kerr effect) should be in phase. This iscontrolled by the glass phase adjusting layer (thirdlayer) thickness (t3 ).

(3) The amplitude of reflected y-polarized waves(Iri) should be minimized. For Kerr spectroscopy thiswould be zero amplitude, however for tracking andfocusing of a computer memory readout head rsI2should be between 10 and 20%.11,12 This is controlledby the superstrate thickness (t1) and the magnetoopicfilm thickness (t 2 ).1 1

(4) The reflected x- and y-polarized waves shouldbe in phase. This is controlled by the effective bire-fringence of the superstrate.

Several factors must be considered in the determi-nation of the magnetooptic film thickness (t2). First,the magnitude of the complex TE-to-TM amplitudereflectance (r8p) should be maximized. Next, for suit-able tracking and focusing 0.10 < Ir812 < 0.20. Alsosince a high numerical aperture lens is frequently usedto focus the light onto the desired location, 1'1 3 thereflection characteristics as functions of incident angle(up to as large as 500) must be satisfactory. Increasingt2 increases r and makes the reflection characteristicsmore uniform as functions of incident agle. 1

Incident | t Reflected

Birefringent Layer ex = 1.63Cy = C = 2.25

MnBi Layer ex = =C = -1.42 - j28.27

-Cyx = C = 1.29+ jO.27

Glass Layer Fig= 2.25

Aluminum Layer C = -46.4 -j28.4

Glass Substrate E = 2.25

Iv

Iv

Iv

t i

t2

t3

t4

V x

Fig. 5. Novel interference enhanced magnetooptic multilayeredstructure, introduced in this work, that converts incident linearpolarization to rotated reflected linear polarization. This is accom-plished by making the superstrate birefringent. The birefringentsuperstrate converts the elliptical polarization to linear and simulta-neously serves as a phase adjusting plate for each of the component

polarized (TE and TM) waves.

The procedure used to determine the layer thick-nesses (t, and t3 ) and the effective birefringence of thesuperstrate is:

(1) The reflection characteristics of the structureare calculated as a function of t3 (varying it over at leastone optical half-wavelength). The optimum thicknessis that which produces the maximum r.

(2) The reflection characteristics of the structureare calculated as a function of t (varying it over at leastone optical half-wavelength). The optimum thicknessis that which produces the minimum r (which corre-sponds to the maximum azimuth rotation).

(3) The phase difference between the x-polarizedand y-polarized waves (5) corresponding to the chosent, is used to calculate the superstrate's effective bire-fringence.

There are several different ways of making a super-strate with the desired effective birefringence. Thebirefringent superstrate could be:

a high spatial frequency binary grating whose effec-tive form birefringence is controlled by changing thegrating's filling factor,14

an obliquely deposited thin film layer whose effec-tive form birefringence is controlled by changing theangle of deposition, 15 or

1928 APPLIED OPTICS / Vol. 28, No. 10/ 15 May 1989

a plastic overcoat layer (e.g., a polycarbonate layersimilar to those currently used for compact disk sub-strates) whose photoelastically induced effective bire-fringence is controlled by changing the strain in thelayer. 16

III. Analysis

Several different methods have been used to analyzethe reflection characteristics of magnetooptic struc-tures. The first matrix methods were applied bySmith.17"18 Reiterative formulas were used by Man-suripur et al.

8 and Gamble et al.19 Analyses thatemploy a 4 X 4 matrix method have also been used byseveral authors.2 021 The analysis method used in thiswork is a 4 X 4 matrix method described previously. 6

A comparison of the different analysis methods is pre-sented in Ref. 21.

Closed-form expressions for the reflectance of thesestructures for normally incident light have been ana-lytically derived.7 The reflectances have also beennumerically calculated.8 Multilayered structureswhich maximize the change in the polarization statefor normally incident light have been proposed.7 8 Re-flection characteristics as functions of incident anglefor some magnetooptic multilayered structures werecalculated by Sprokel20 in 1984. Sprokel's analysismethod is based on the rigorous 4 X 4 matrix method ofBerreman.22 The structures Sprokel analyzed werelimited to those composed of isotropic layers and asingle magnetooptic layer exhibiting the polar Kerreffect. The reflection characteristics of an isotropic-magnetooptic interface for the case of a polar Kerreffect magnetooptic region were calculated and mea-sured by Ruane et al.13 in 1986.

To demonstrate the effect of t2 on the reflectioncharacteristics as functions of incident angle, two four-layer magnetooptic structures of the type depicted inFig. 5 were designed using the procedure described inthe previous section. For the structure with the thin-ner magnetooptic layer, designated the thinner struc-ture, t2 = 17 nm, tj = 688 nm, and t 3 = 120 nm; whereasfor the thicker structure, t2 = 21 nm, tj = 679 nm, and t3

= 106 nm. The magnetooptic layer in both isMnBi(ec, = cyy = c, = -1.4 - j28.3 and ey = 1.29 +jO.27 = -er, where e is the relative permittivity givenby c/EO, where EO is the permittivity of free space),8 andthe incident free-space wavelength is 840 nm. For thetwo structures, the superstrate has an effective bire-fringence of 0.22, and the aluminum layer thickness(t4 ) is 60 nm.

As shown in Fig. 6, both Orot and e are more nearlyconstant for the thicker structure. But 6 rot for normalincidence for the thinner structure is -150% of that forthe thicker structure.

IV. Summary

In summary, a novel interference enhanced magne-tooptic multilayered memory device that converts in-cident linear polarization to rotated linear polarizationon reflection was introduced. This novel structureemploys a birefringent superstrate; several possibleimplementations of the birefringent superstrate were

i o t = 17 nm

X

o (a)o- I I I i

0 10 20 30 40 50

INCIDENT ANGLE. l3ine (degree.)

' N =2nm

o \7 nm

o (b)_ I I i

0 10 20 30 40 50

INCIDENT ANGLE, Orc (degrees)

Fig. 6. Reflectance characteristics of two structures of the type

shown in Fig. 5 as functions of incident angle (t9 ic) for a TE polarized

incident plane wave with X0 = 840 nm. The solid lines depict the

characteristics for a structure with a magnetooptic layer thickness(t2) equal to 17 nm. The dashed lines depict the characteristics for astructure with t2 = 21 nm; (a) azimuth rotation angle (Orot = 0 - 00)

and (b) ellipticity (e).

proposed. Finally, the effect of the magnetooptic lay-er thickness on the reflection characteristics as func-tions of incident angle for the proposed structures wasdiscussed.

This work was supported by a National ScienceFoundation Fellowship (to RSW) and by the JointServices Electronics Program under contractDAAG29-84-K-0024.

References1. Y. Togami, "Magneto-Optic Disk Storage," IEEE Trans. Magn.

MAG-18, 1233 (1982).2. M. J. Freiser, "A Survey of Magnetooptic Effects," IEEE Trans.

Magn. MAG-4, 152 (1968).3. Laser Focus/Electro-Optics Staff, "Sony Announces Erasable

Optical Memory," Laser Focus/Electro-Optics 23,8 (July 1987).4. P. S. Pershan, "Magneto-Optical Effects," J. Appl. Phys. 38,

1482 (1967).5. R. H. Muller, "Definitions and Conventions in Ellipsometry,"

Surf. Sci. 16, 14 (1969).6. R. S. Weis and T. K. Gaylord, "Electromagnetic Transmission

and Reflection Characteristics of Anisotropic MultilayeredStructures," J. Opt. Soc. Am. A 4, 1720 (1987).

7. Y. Tomita and T. Yoshino, "Optimum Design of Multilayer-

Medium Structures in a Magneto-Optical Readout System," J.Opt. Soc. Am. A 1, 809 (1984).

15 May 1989 / Vol. 28, No. 10/ APPLIED OPTICS 1929

8. M. Mansuripur, G. A. N. Connell, and J. W. Goodman, "Signaland Noise in Magneto-Optical Readout," J. Appl. Phys. 53,4485(1982).

9. G. A. N. Connell, "Interference Enhanced Kerr Spectroscopy forVery Thin Absorbing Films," Appl. Phys. Lett. 40, 212 (1982).

10. K. Balasubramanian, A. S. Marathay, and H. A. Macleod, "De-sign Technique for Anisotropic Multilayer Thin-Film Systems,"in Techical Digest of the 1987 Annual Meeting of the OpticalSociety of America, (Optical Society of America, Washington,DC, 1987), p. 134.

11. M. N. Deeter and D. Sarid, "Effects of Incident Angle on Read-out in Magnetooptic Storage Media," Appl. Opt. 27,713 (1988).

12. A. E. Bell, "Antireflection Structures for Magneto-Optic Recor-ding," in Technical Digest of Topical Meeting on Optical DataStorage (Optical Society of America, Washington, DC, 1987),paper ThD2.

13. M. Ruane, M. Mansuripur, and R. Rosenvold, "Measurement ofReflectivities for Magnetooptical Media," Appl. Opt. 25, 1946(1986).

14. T. K. Gaylord, W. E. Baird, and M. G. Moharam "Zero-Reflec-tivity High Spatial-Frequency Rectangular-Groove DielectricSurface-Relief Gratings," Appl. Opt. 25, 4562 (1986).

15. I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, and J.J. Wharton, "Measurement of the Principal Refractive Indicesof Thin Films Deposited at Oblique Incidence," J. Opt. Soc. Am.A 2, 1693 (1985).

16. S. Ohsawa, M. Tsuge, A. Takatsu, T. Okunishi, J. Tanaka, and S.Mikami, "Thermosetting Resin Substrate for Computer-UseOptical Memory Disk," Appl. Opt. 25, 4027 (1986).

17. D. 0. Smith, "Magneto-Optical Scattering from MultilayerMagnetic and Dielectric Films," Opt. Acta 12, 13 (1965).

18. D. 0. Smith, "Optical Scattering from Cubic Electro-OpticalFilms," Opt. Acta 13, 195 (1966).

19. R. Gamble, P. H. Lissberger, and M. R. Parker, "A SimpleAnalysis for the Optimization of the Normal Polar Magneto-Optical Kerr Effect in Multilayer Coating Containing a Magnet-ic Film," IEEE Trans. Magn. MAG-21, 1651 (1985).

20. G. J. Sprokel, "Reflectivity, Rotation, and Ellipticity of Magne-tooptic Film Structures," Appl. Opt. 23, 3983 (1984).

21. Z. Li, B. T. Sullivan, and R. R. Parsons, "Use of the 4 X 4 MatrixMethod in the Optics of Multilayer Magnetooptic RecordingMedia," Appl. Opt. 27, 1334 (1988).

22. D. W. Berreman, "Optics in Stratified and Anisotropic Media:4 X 4-Matrix Formulation," J. Opt. Soc. Am. 62, 502 (1972).

NASA continued from page 1909

used. Similar choices have been made in remote sensing of theearth. Gas correlation spectroscopy is particularly appropriate formeasurements of the atmosphere of Mars because radiation origi-nating from airborne dust can be distinguished from that originatingfrom the gas of interest. Pressure modulation radiometry is a noveluse of gas correlation spectroscopy in which radiation from theemission lines of a specific constituent gas is detected during modu-lation of the pressure of the same gas in a cell placed in the opticalpath of the instrument. The transmission of the pressure modula-tor cell (PMC), and hence the intensity of atmospheric radiationincident on the detector, varies at the frequency of modulation onlynear absorption spectral lines of the gas in question. Therefore, thesignal at the modulation frequency, selected by electronic process-ing, quantifies emission in spectral regions in and near the absorp-tion lines in the PMC, which match the emission lines of the same gasin the atmosphere.

The spectral response of a pressure-modulator radiometer can bedesigned to fit the shapes of atmospheric spectral lines by varyingthe length, mean pressure, and depth of modulation of a cell. Oncechosen, the length is fixed, but the pressure and the depth of modula-tion can be altered in flight.

In addition to its atmospheric observations, the PMIRR will alsoobtain data on the polar radiative balance, deposits of CO2 frost, andthermal inertia of the surface. The PMIRR provides accurate sur-face brightness temperatures on the day and night sides in thewavelength range from 6.8 to 50 jum at high spatial resolution andwith simultaneous measurements of broadband solar reflectanceand the properties of the overlying atmosphere. The spectral re-sponse at 0.3 to 3.0 am of the PMIRR solar channel encompassesover 97% of the incident solar flux, and its observations are used toconstruct hemispheric bidirectional reflection plots and determinealbedos on a daily basis for the core regions of the north and southpermanent caps.

This work was done by D. J. McCleese, J. T. Schofield, R. W.Zurek, J. V. Martonchik, R. D. Haskins, D. A. Paige, R. A. West, D. J.Diner, J. R. Locke, M. P. Chrisp, and W. Willis of Caltech; C. B.Leovy of the University of Washington; and F. W. Taylor of theUniversity of Oxford for NASA's Jet Propulsion Laboratory. Referto NPO 17353.

Thermographic inspection of coatingsThe use of infrared thermography has been proposed for the

inspection of some kinds of coatings, especially those intended to

provide thermal protection. By the use of commercially availableinfrared thermographic equipment, it may be possible to identifydefects, including areas of poor adhesion.

A source of heat would be placed behind the sample to be inspect-ed, and the sample would be viewed through the thermographicequipment (see Fig. 7). Depending on the specific thicknesses andtypes of material in the sample, it may be preferable for the camerato view the coating side or the substrate side of the sample. Defectswould be seen on the monitor as islands of different temperature.This inspection technique could be executed by remote scanning orby robotic scanning with automatic electronic detection of anoma-lies.

Sample

Source ofLow Heat

Substrate CoatingAdhesive

InfraredCanera or

/ Sensor

Video DisplayShowing Infrared Scene

Fig. 7. Sample heated radiantly from behind would be viewed byinfrared thermography. Defects in the coating would be visible at

infrared wavelengths.

This work was done by W. A. Riehl and P. W. Hayes of UnitedTechnologies for Marshall Space Flight Center. Inquiries concern-ing rights for the commercial use of this invention should be ad-dressed to the Patent Counsel, L. D. Wofford, Jr., Mail Code CC01,Marshall Space Flight Center, AL 35812. Refer to MFS-28258.

continued on page 1948

1930 APPLIED OPTICS / Vol. 28, No. 10/ 15 May 1989