• Dionne, Allen, Haddad, Ross, and Lax Circular and Nonreciprocal Propagation in Magnetic Media and Nonreciprocal Propagation in Magnetic Media Gerald F. Dionne, Gary A. Allen, Pamela R. Haddad, Caroline A. Ross, and Benjamin Lax n The polarization of electromagnetic signals is an important feature in the design of modern radar and telecommunications. Standard electromagnetic theory readily shows that a linearly polarized plane wave propagating in free space consists of two equal but counter-rotating components of circular polarization. In magnetized media, these circular modes can be arranged to produce the nonreciprocal propagation effects that are the basic properties of isolator and circulator devices. Independent phase control of right-hand (+) and left-hand (–) circular waves is accomplished by splitting their propagation velocities through differences in the e±m± parameter. A phenomenological analysis of the permeability m and e in dispersive media serves to introduce the corresponding magnetic- and electric-dipole mechanisms of interaction length with the propagating signal. As an example of permeability dispersion, a Lincoln Laboratory quasi-optical Faraday- rotation isolator circulator at 35 GHz (l ~ 1 cm) with a garnet-ferrite rotator element is described. At infrared wavelengths (l = 1.55 mm), where fiber-optic laser sources also require protection by passive isolation of the Faraday-rotation principle, e rather than m provides the dispersion, and the frequency is limited to the quantum energies of the electric-dipole atomic transitions peculiar to the molecular structure of the magnetic garnet. For optimum performance, bismuth additions to the garnet chemical formula are usually necessary. Spectroscopic and molecular theory models developed at Lincoln Laboratory to explain the bismuth effects are reviewed. In a concluding section, proposed advances in present technology are discussed in the context of future radar and telecommunications challenges.

he polarization of an electromagnetic its plane of polarization either vertical or horizontal, wave is an important aspect of its propagation depending on the specific application. Linear polar- Tcharacteristics. In applications that involve ra- ization is also readily transmitted through flexible co- diated beams, such as radar, polarization concerns are axial cable or rigid waveguides in radio frequency (RF) critical in the design of the antennas for optimum and systems. In recent years the frequency performance. Factors that influence the choice of range of electromagnetic communication technology polarization include the nature of the target and the has been extended to the infrared (IR) region in the features of the propagation environment, such as ir- form of polarized signals emitted by semiconductor la- regular ground terrain or open water that can corrupt sers and transmitted through optical-fiber networks. the signal by introducing unwanted reflections. Linear Less familiar uses of polarization occur in the func- polarization emerges as a natural result of the radia- tion of passive isolators that protect signal sources or tion from an oscillating dipole and is transmitted with other components from potentially harmful reflec-

VOLUME 15, NUMBER 2, 2005 LINCOLN LABORATORY JOURNAL 323 • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media tions, and circulator versions that can direct the return where w is the angular frequency and E denotes the signals into the appropriate receiver channels. For RF instantaneous electric-field vector, while E corresponds applications, the magnetic vectors of the two counter- to its phasor form. Any time variation of an electro- rotating circular-polarization modes of the linear wave, magnetic wave can be expressed as a superposition of and the way they are affected by the dispersive perme- harmonic solutions according to Fourier theory. ability of a magnetized medium (usually a ferrite), are Polarization is an inherent property of an electro- the keys to the operation of these devices. When the magnetic wave that describes the orientation of its waves are propagating in the direction of magnetiza- electric-field vector as the wave propagates in time. tion, the individual phase velocities of the counter-ro- The simplest polarization case is that of linear polar- tating modes are split from the unmagnetized value in ization in which the electric-field vector traces out a a positive and negative sense. As a consequence, the line over time. An example of this polarization is a differing velocities cause the plane of polarization of transverse electromagnetic (TEM) plane wave propa- the resultant linear wave to undergo a progressive Far- gating along z in free space with phasor electric- and aday-rotation effect that is nonreciprocal. magnetic-field components along the xˆ and yˆ unit Nonreciprocal propagation effects of magnetic ma- vector axes given by terials also provide isolation functionality in photonic β E()z= xˆE e −i0 z (2) systems. Analogously to the RF circuit applications, 0 isolator devices are necessary in optical communica- and tion systems to protect the laser sources from power H()z= yˆH e −iβ0 z . (3) instabilities. Although the wavelength band is in the 0 near-IR region where the interaction of the electric E0 and H0 are the amplitudes in free space, and the vector with the dispersive permittivity determines the propagation constant b0 is the ratio of angular fre- propagation properties, the phenomenological theory quency to the velocity of (w/c). The phasor form of Faraday rotation for both RF and optical cases is of the given by Equation 2 shows the almost identical. To understand the operation of these electromagnetic wave to be linearly polarized along xˆ. devices in terms of plane-wave propagation, we begin The instantaneous TEM traveling waves derived from with a review of polarization fundamentals, followed Equations 1 through 3 are by an explanation of in magnetized me-  z, t =xEˆ cos ωt − β z dia, and continue with the development of key rela- () 0 ()0 tions between Faraday rotation and the medium’s and permeability and permittivity. We conclude with de- ()z, t =yHˆ 0 cos()ωt − β0 z . scriptions of device applications that continue to be of interest to Lincoln Laboratory and the broader scien- A snapshot of the TEM field at time t = 0 is illustrated tific community. by the orthogonal sinusoidal functions of z in Figure 1, in which the electric-field vector is aligned in the x Polarization direction. As time advances, this snapshot effectively An electromagnetic wave consists of time-varying elec- moves forward in the z direction corresponding to tric and magnetic fields that jointly satisfy Maxwell’s wave propagation. equations [1]. The electric and magnetic fields are vec- Linear polarization is commonly referred to as tor quantities that are functions of time and spatial horizontal or vertical, which describes its orientation position. In electromagnetic analyses, a harmonic time within a given reference frame such as relative to a flat variation is usually assumed so that the field E (or H) earth surface or within a local target coordinate sys- can be represented via a phasor quantity according to tem. Linear polarization oriented horizontally with respect to the earth is often used for upward-looking iω t (,x y,,z t)(= Real{}E x,, y z), e (1) radar systems performing air surveillance, since this

polarization is well matched to the horizontal metal

324 LINCOLN LABORATORY JOURNAL VOLUME 15, NUMBER 2, 2005 • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media

x Electromagnetic wave There are two senses of circular polarization, right- hand circular polarization (RHCP) and left-hand cir- cular polarization (LHCP). In Figure 2, these modes y λ are revealed as counter-rotating spirals that sum to form a linearly polarized wave. The handedness prop- erty describes the rotation of the electric-field vector (clockwise or counterclockwise) relative to the direc- Electric field tion of propagation. If the fingers in a person’s right z hand curl in the same direction as the rotation of the electric-field vector while the thumb is pointing in the propagation direction, then the wave is right-hand cir- Horizontal linear Vertical linear cularly polarized. Similarly, a circularly polarized wave for air surveillance for over-water looking up surveillance is left handed if the fingers on a person’s left hand curl in the direction of electric vector rotation while the thumb points in the direction of propagation.

Left-Hand Circular Right-Hand Circular Polarization (LHCP) Polarization (RHCP)

x x FIGURE 1. Instantaneous (t = 0) sinusoidal trace of an elec- tromagnetic signal of wavelength l directed along the z-axis. The orthogonal electric- and magnetic-field components are z z shown oscillating along the respective x- and y-axes. The lower two figures show the appropriate electric-field linear polarization for two specific measurement conditions.

y y structure of an airplane. Vertical polarization in an earth-reference frame is used for over-water surveil- lance, since it suffers less multipath loss than horizon- Sum tal polarization. The polarization for a radar applica- Linear polarization tion needs to be matched to both the target and the propagation environment. x The orientation of the electric-field vector can change with time as the wave propagates. Two simple TEM plane waves consisting of both x and y electric- z field components can be combined to yield a vector that rotates in the x-y plane as the wave propagates forward with time. In the most general case, this elec- tric-field vector traces out an ellipse. However, if the amplitudes and phases of the x and y components sat- y isfy certain conditions, then the electric-field vector can be made to trace out a circle, thereby producing circular polarization. Circular polarization is used in FIGURE 2. Anatomy of the linearly polarized wave shown propagating along the z-axis. The electric-field vectors of radar applications for polarization diversity and target two equal-amplitude counter-rotating circularly polarized discrimination, and is used in communications sys- waves sum to form a parent linear wave of twice the ampli- tems to mitigate rain attenuation. tude.

VOLUME 15, NUMBER 2, 2005 LINCOLN LABORATORY JOURNAL 325 • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media

Mathematically, the electric-field phasors for RHCP z (+) and LHCP (–) plane waves propagating along z are described respectively by λ /2

1 β E ()z= E xˆ − iy ˆ e −i0 z (4) + 2 0 () and

1 −iβ0 z E− ()z= E ()xˆ + iy ˆ e . 2 0 (5) Equations 4 and 5 show that circular polarization is ϕ achieved when the x and y components of the electric + field assume equal amplitudes and are separated in ϕ phase by 90°. It is instructive to examine the instan- – taneous form of these waves. The time-varying electric x fields for RHCP and LHCP are given by

1 y ± ()z, t = E0 { xˆ cos()ωt− β0 z 2 (6) 0 ±yˆ sin()ω t − β0z . } In the z = 0 plane, Equation 6 reduces to FIGURE 3. Snapshots at t = 0 of E± in the x-y plane at suc- cessive l/8 stages in a medium of propagation 1 constant b. The rotation angles ϕ+ and ϕ− of the respective ± ()0,t= E0 {xˆ cos()ω t ± yˆ sin() ω t } , (7) 2 RHCP and LHCP vectors are equal in magnitude because b+ = b– = b. In situations where b+ and b– differ, nonreciprocal which describes a circle in the x-y plane that is traced action will occur that can be utilized for isolation or modula- out clockwise (RHCP) or counterclockwise (LHCP) tion purposes. versus time, when the plane is viewed from the nega- tive z direction. ent velocities, creating an effect called magnetic circu- To understand device operations based on the mag- lar birefringence (MCB). Birefringence is the property netic control of individual circular-polarization phases of a medium with two distinct propagation constants in a dielectric or magnetic medium, we must recog- [1, 2] that result from the arrangement of internal di- nize how the rotation angles vary with path length. In pole moments in a dielectric or magnetic medium.*

Figure 3, snapshots of the E± vectors at time t = 0 are In a magnetic medium, MCB is caused by a differ- sketched at regular intervals over a half cycle. As the ence in the product of the permittivity and permeabil- waves progress from zero along the z-axis, the rotation ity, i.e., e±m±, between the two circular components. In angles ϕ± of the two vectors increase according to bz, the permeability case the magnetic dipoles from the consistent with the images of the counter-rotating spi- combined quantum orbital and spin angular momenta rals of Figure 2 that make up a linearly polarized wave of the individual ions produce the interaction with the advancing with velocity w/b. This concept is used to propagating signal. It is important to remember the explain Faraday rotation of linear polarization and the dual nature of orbital angular momentum, whereby origin of nonreciprocal effects in microwave and opti- an orbiting electron creates both a magnetic- and an cal systems.

Nonreciprocal Birefringence * In the pure dielectric case, magnetic moments have no influence on propagation. The material is usually a single crystal with a defined The importance of the two circular-polarization com- axis of symmetry, e.g., calcite or quartz, that presents a different ponents arise in magnetized media where the propa- permittivity, depending on whether the electric field of the linearly polarized TEM wave is parallel or perpendicular to the symmetry gation constants are not equal. In this situation, the axis. In this case, the effects on signal polarization are reciprocal, i.e., spiraling modes shown in Figure 2 propagate at differ- independent of entry or exit port.

326 LINCOLN LABORATORY JOURNAL VOLUME 15, NUMBER 2, 2005 • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media electric-dipole moment. In the permittivity case, the Reflector electric-dipole aspect of the orbital momentum pro- 45° Faraday duces the interaction, but the essential alignment of rotator the individual dipoles for a collective result is accom- plished by magnetic alignment. 45° In the pure magnetic-dipole case, the optimum in- teraction between the magnetic field H of the propa- gating TEM wave and the magnetic medium occurs when H is transverse to the axis of the magnetization vector M in the material, i.e., when the propagation is along the M axis. To create a resultant M, the indi- M 90° vidual magnetic-dipole moments must be aligned in a static magnetic bias field H. What is most significant, however, is that the effects are nonreciprocal; i.e., they are reversed when either FIGURE 4. Basic demonstration of nonreciprocal action for signal isolation. The polarization of a reflected linear wave the entry and exit ports of the medium are reversed is rotated through 90° from the transmitted wave by two suc- or alternatively, the direction of M is reversed. This cessive 45° rotations in passage through a magnetized Fara- feature of MCB creates the nonreciprocal propagation day-rotation medium. If the rotator had reciprocal propaga- action of microwave and optical isolators and circula- tion properties, the two 45° rotations would cancel and the tors that are often essential for radar and communica- polarization of the return signal would be unchanged. tion systems. A common application of the nonreciprocal charac- teristic of these magnetized media for RF and optical Permeability and Permittivity Relations transmission is illustrated in Figure 4, where a linearly For a medium with permeability tensor m and permit- polarized wave propagating parallel to M undergoes tivity tensor e transmitting a TEM wave of angular a polarization rotation of 45°. Note that the polariza- frequency w along the positive z axis—described ear- tion angle of the return signal increases to 90° instead lier and illustrated with its counter-rotating circular of being restored to zero. This property allows for the modes in Figure 2 and 3—the relevant Maxwell rela- creation of two-port isolators, and three- and four- tions [1, 2] at a fixed value of z can be written in elec- port circulators that are described later in the section tromagnetic units (emu) as entitled “Microwave and Optical Beam Isolators.” In ∇ × ∇ ×  =ω2 [] ε ⋅[]µ ⋅ a TEM wave, the rotation of the axis of polarization 2 is called Faraday rotation, and the basic mechanisms ∇ × ∇ ×  =ω[] ε ⋅[]µ ⋅ . that cause it are dipole transitions—magnetic for RF wavelengths and electric in the optical bands. The combined permeability/permittivity tensor can be Frequency-dependent permeability and permittiv- expressed as ity arising from respective magnetic- and electric-di-  ε−i ε 0   µ−i κ 0  pole interactions with a propagating electromagnetic 0 1 []ε⋅ µ =  +iε ε 0  ⋅ +iκ µ 0  , signal are the basis for the nonreciprocal effects. Al- []  1 0     0 0 ε   0 0 µ  though the wavelength regimes of the two phenom-  z   z  ena are the microwave bands for permeability and the near-IR/visible for permittivity, the electromagnetic where the symbols e0, e1, m, and k are adopted to con- phenomenology is almost identical in both cases. The form to accepted conventions. If all of the dipole mo- physical origins, however, differ in ways that require ments are aligned with the z-axis, the eigenfunction separate explanations. We first review the standard solutions of the diagonalized matrix are the two or- classical theory. thogonal RHCP (+) and LHCP (–) modes of circular

VOLUME 15, NUMBER 2, 2005 LINCOLN LABORATORY JOURNAL 327 • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media

polarization from Equations 4 and 5. The correspond- ϕ−+ ϕ +  β−− β +  θ = =   z ing eigenvalues appear on the diagonal after the x-y-z F 2 2  coordinates are rotated about the z-axis, according to ω ε ω ε =0 µ − µ z ≈ − 0 κ z , (11) ()− + µ  ε+ µ + 0  2c 2c []ε⋅[] µ = , (8)  0 ε µ  − − where κ µ and qF is the Faraday-rotation angle for a distance z. Rotation of the optical E can be treated in where e±m± = (e0m + e1k) ± (e0k + e1m) and ezmz is the same manner by assuming m = 1 and k = 0. From dropped because it is presumed that there is no active Equations 10 and 11 the off-resonance Faraday rota- signal field component in the z direction. Note that tion can be as approximated by ezmz reduces to em when the off-diagonal elements ω µ are zero, which is consistent with no splitting of the θF =ε− − ε + z 2c () circular modes. We show later in the section entitled ω µ “Resonance Dispersion Effects” that the permeabil- ≈ − ε z , 2c ε 1 ity elements m and k are dependent on the density of 0 magnetic moments, i.e., M. The permittivity elements where ε1 ε 0 , the dielectric constant, which is as- e0 and e1 also depend on the density of electric dipoles. sumed to be constant over the frequency range of in- Since the RF and near-IR frequency regimes are far terest [4]. enough apart to be considered independent, the sepa- Resonance Dispersion Effects rate solutions m± = (m ± k) and e± = (e0 ± e1) become key analytical expressions for the present discussion. Because m and e resonate in different frequency re- After rearrangement of Equation 8, gimes, the frequency dependence of m can be analyzed 1 with e = e as the dielectric constant, and then the re- µ=() µ + µ 0 2 + – 1 κ=() µ − µ 2 + – Circular Faraday components rotation angle and θ 1 F ε0 =() ε+ + ε – 2 H+ H– 1 ε=() ε − ε . (9) ϕ ϕ 1 2 + – + – ϕ+ ϕ For both M and the propagation directed parallel to Propagation – axis the z-axis in a semi-infinite medium, the propagation M = 0 M > 0 constant (with attenuation ignored) can be generalized H for the (+) and (–) modes, and ϕ = – β z z + + ω ϕ = z − β− β± =()ε0 µ + ε 1 κ ±()ε0 κ + ε 1 µ . (10) c y

When b+ and b– are different, the clock-face images of Figure 3 serve to illustrate the origin of Faraday ro- FIGURE 5. Schematic diagram of Faraday rotation in a ferrite tation of the polarization axis in the x-y plane, which magnetized along the z-axis of propagation. Phase angles ϕ and ϕ of the corresponding H and H circular com- occurs when the medium is magnetically biased, as + − + – ponents are equal in magnitude and opposite in sign when shown in Figure 5. the magnetization M is zero, thereby canceling the two field In the RF case, e1 = 0, and the resultant H of the components along the y-axis. When M is not zero, ϕ+ < ϕ− , RHCP (+) and LHCP (–) vectors is rotated by [3] and the resultant H undergoes a net Faraday rotation qF.

328 LINCOLN LABORATORY JOURNAL VOLUME 15, NUMBER 2, 2005 • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media sults applied by analogy to the e case with m = 1. For in simplest terms as [7, 8] low power conditions in the absence of damping ef- µ=1 + ω ρ , (12) fects, the respective resonance and nonresonance re- ± M ± lations for the (+) and (–) circular permeabilities are where derived from classical theory. ω± ω ρ 0 ± = 2 2 2 Magnetic-Dipole Resonance ω0 − ω + Γ From the general case of a fixed magnetization M are the Lorentzian line shape functions for use as (usually a collection of aligned spin moments each la- building blocks for combining polarization modes. beled by its quantum operator S) coupled to a static The parameter wM = g 4pM is the symbol used to field H along the z-axis, the basic theory of magnetic represent the magnetization as an effective frequency. resonance is derived from the equation of motion Note that only r+ is resonant at w = w0, but that r– be- dM comes comparable away from resonance. In Figure 7, =γ ()MH × , the m curves are sketched as a function of w . Because dt ± 0 it is presumed that signal loss would be minimized in where the vector M × H is normal to the plane con- any practical situation, the damping parameter, i.e., taining M and H. Consequently, the resulting torque half-linewidth Γ , is assumed to be negligible under causes M to precess about H. The Larmor precession the conditions of interest. For the discussion that fol- −1 frequency is derived in most standard textbooks [5, 6], lows, the approximation ρ± = ( ω0  ω ) is used. and is given by Electric-Dipole Resonance ω= γ H , 0 Nonreciprocal propagation can also occur in magnetic where the gyromagnetic constant g = 2.8 GHz/kOe materials beyond the microwave and millimeter-wave when w is expressed in cycles/sec. bands where magnetic-dipole interactions prevail. In Magnetic resonance therefore occurs where an alter- the optical bands, electric-dipole transitions driven by nating (usually microwave or millimeter wave) mag- circularly polarized E± field components can produce netic H field is applied perpendicular to H. Because a magneto-optical Faraday rotation that is of major im- linearly polarized signal can be decomposed into two portance for fiber-optical and photonics technology. circularly polarized modes, the physical situation re- The physics that creates the birefringence involves sembles that depicted in Figure 6(a). Only the circular transitions between atomic quantum states with or- component that rotates in the sense of the precessing bital angular momentum split by spin-orbit coupling. moment is capable of continuously influencing the The basic interactions are between rotating electric angle of M relative to the z-axis by creating a second fields and a collection of electric dipoles with quan- torque M × H normal to the M × H direction. By set- tum states of frequency and polarization compatible ting the frequency of the alternating field at w = w0, with those of the stimulating radiation field. Since H will synchronize with the precession and apply a the individual dipole effects result from coupling of constant torque that will cause the cone half-angle to the momenta of orbiting electrons and magnetic spins oscillate from full alignment with H to its opposite within each dipole, the full combined effects of the limit of p radians. The rotation of M away from H electric dipoles can be achieved only by the collective represents the dispersion and absorption of the signal. alignment of each ionic spin, which usually requires a In ferrimagnetic systems where M comprises mul- saturating magnetic field. The most general theoreti- tiple individual atomic moments, only small fractions cal formalism must account for multiple contributing of them complete this full rotation from the z-axis, spectral pairs and their respective intensities. For the and M departs only slightly from the z-axis under a present purposes, we consider only one such spectral low-amplitude H signal. For these spontaneously transition pair [9]. magnetic systems, the permeabilities can be expressed In the magnetic dipole case, the off-diagonal ele-

VOLUME 15, NUMBER 2, 2005 LINCOLN LABORATORY JOURNAL 329 • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media

Larmor precession ization mode. Therefore, a second set of permittivity z solutions is required. For separate from H Sx+iSy this energy-level splitting, each counter-rotating orbit- y a b al angular momentum state separated by ()ω0 − ω0 x Sz S must interact with the E± of the appropriate circular µ± Linearly polarized mode.* The quantum wave functions for the electric field comprising both dipoles that carry the opposing senses L = ±1 of or- circular modes z

H ± iH bital angular momentum correspond to the split en- x y ergy levels of a 2P orbital quantum term, as illustrated (a) in Figure 6(b). Since the line shape factors are identical for both magnetic and dielectric resonances, the magnetic res- Circularly polarized p electrons x,y onance results can be adopted directly for each elec- z tric-dipole transition stimulated by circular polariza- pz forms oscillating dipole ez (Lz = 0) tion without loss of generality. The tensor elements p form rotating dipoles y x,y e0 and e1 can be readily obtained by a reverse process. e(x ± iy) in x-y plane (L = ±1) 2 x z For dual transitions arising from split P levels, indi- ε± vidual mode permittivities e± corresponding to states Linearly polarized field labeled a and b are determined first from an extension comprising both circular † of Equation 12: modes Ex ± iEy (b) a a b b ε± =1 + ωEρ± + ωEρ (13) FIGURE 6. Rotating angular momentum diagrams: (a) spin a  1  b  1  angular momentum S precessing at the Larmor frequency =1 + ωE   + ωE   .  ωa  ω   ω b ± ω  about a z-axis magnetic field H, and driven by circularly po- 0 0 larized modes H in the x-y plane. Magnetic resonance oc- ± ω curs when signal frequency equals the Larmor precession The quantum theory origin of E is compared with its magnetic counterpart ω in the Appendix. frequency of the S vector; and (b) split px,y orbital states of M a magnetic molecule with orbital angular momentum Lz that rotates with the electric field E± circular-polarization modes Tensor Element Functions in the x-y plane. The z-axis orbital state pz does not respond The real-part solutions for the tensor elements of per- to the circular polarization. Optical transition frequencies correspond to the particular quantum state energies of the meability and permittivity for various cases can now electric dipoles. Note that the amplitudes of H and E rotat- be constructed with the aid of Equations 9, 12, and ing with frequency w in the x-y plane at z = 0 are expressed 13. The magnetic-dipole single transition solution is in complex scalar form to be consistent with the correspond- ing quantum wavefunctions of the transition states shown in 1 ωM ω 0 µ=1 + ωM []ρ++ ρ − =1 + Equation 7. 2 ω2− ω 2 0 (14) 1 ω ω κ ω ρ ρ M =M []+ − − = 2 2 . ment k emerges directly from the solution of the clas- 2 ω0 − ω sical Larmor model in the form of a spin-flip transi- tion, as shown in Figure 6(a). A magnetic field creates a quantum energy splitting ω and determines which 0 * In magneto-optical materials in which electric rather than magnetic circular-polarization mode experiences resonance and dipoles provide the agents for splitting the (+) and (–) modes, the which is unaffected, as defined by the m± relations of magnetic spin components of the dipoles must still be aligned in a Equation 12 and illustrated in Figure 7. By contrast, magnetic field to produce the necessary alignment for a collective a b effect on a macroscopic scale. there are two transition energies ω0 and ω0 in the birefringent electric-dipole case, one for each polar- † Planck's constant, , is absorbed into the w terms for brevity.

330 LINCOLN LABORATORY JOURNAL VOLUME 15, NUMBER 2, 2005 # & ("0 !") ("0 +") ! = 1+" % + ( 0 E 2 2 2 2 $%("0 !") !" ("0 +") !" '( # 1 1 & ! = !" !% ! (, 1 E 2 2 2 2 $%("0 "") !" ("0 +") !" '( • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media

2 reaches 27 dB over a fractional bandwidth of 2 GHz. 2 4 Applications of this principle have also been demon- strated at 16 and 95 GHz, where large amplitude sig- 1 3 nals produce high power densities in the quasi-optical 45° Polarization beam. 4 filter In the near-IR telecommunication wavelength band centered at 1.55 mm, optical isolators for semi- Samarium-cobalt Polarization magnet conductor laser sources are also commonly made as filter Ferrite disk discrete components for insertion with fiber-optical circuits (networks). These devices involve 45° polariza- tion rotation that is accomplished in the same manner 3 High-power 1 as the microwave device, and have a rotator element path (1-2) that is also a magnetic garnet, but with electric-dipole transitions at the appropriate frequency. However, un- FIGURE 9. Diagram of the Lincoln Laboratory four-port like the microwave rotator that operates with an en- quasi-optical Faraday-rotation circulator based on Figure 4. The device comprises a ferrite rotator disk magnetized in ergy splitting ω0 that can be adjusted directly by the an external magnetic field supplied by a samarium-cobalt applied magnetic field, the optical rotator cannot be (SmCo) donut magnet, and two appropriately oriented linear polarization filters. The antireflection impedance-matching plates on either face of the ferrite are not shown. Samarium-cobalt magnet

Ferrite material signal source and the circulator function of directing Aluminum the return signal into a receiver channel. For the de- nitride sign of the ferrite rotator element, Equations 11 and 14 are combined to give a total Faraday rotation: H ω ε ω ω ε θ 0 M 0 γ π F = − 2 2 d≈4 M ⋅d , 2c µ ω0 − ω 2c where ω ω0 and µ → 1. As a consequence, the basic variables involved in the design of the ferrite element Boron nitride are M, the magnitude of the fixed magnetization M, (a) and the element thickness d required for a 45° rota- 0.2 dB tion angle. Reference A previous article by W.D. Fitzgerald described the insertion of this device in the Kiernan Reentry Mea- surements Site (KREMS) Ka-band Millimeter Wave Radar [16]. Figure 10(a) shows a cross section of the Faraday rotator unit with ferrite and dielectric anti-re- 34 GHz 35 GHz 36 GHz flection disks stacked inside the donut-shaped samar- (b) ium-cobalt (SmCo) permanent magnet that provides the field necessary to saturate the magnetic state of FIGURE 10. Details of the ferrite rotator element: (a) cross section of the dual-ferrite-disk design, which has a half- the ferrite. For this application, a temperature-insensi- wavelength heat sink inserted between the ferrite halves: (b) tive ferrite derived from yttrium-iron garnet Y3Fe5O12 measured insertion loss over the 34 to 36 GHz band. The only (YIG) is used. Measured transmission characteristics cooling is an air flow directed at the outer-face boron nitride are presented in Figure 10(b), where the isolation quarter-wavelength impedance matching plates.

332 LINCOLN LABORATORY JOURNAL VOLUME 15, NUMBER 2, 2005 • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media

Bi Each of the magnetically opposed iron sublattices Bi covalent bonds of the garnet ferrite has its own set of spectral parame- ters. Calculated values of the off-diagonal permittivity

e1 are obtained by subtraction of the computed con- tributions from the tetrahedral and octahedral oxy- gen-coordinated sites. An example of the accuracy of Fe O Fe oct oct theory fit to measurement is given in Figure 12. For this exercise, Equation 15 (with the damping param- 3P eter Γ included) was used for the sublattice transitions ω tet oct 4 Bi at energies  0 = 2.6 eV, ω0 = 3.15 eV, and a sec- P tet 4P ond ω0 = 3.9 eV, respectively, for the compound Y2.75Bi0.25Fe5O12 (BiYIG). We must remark that the Feoct m Fetet actual operating energy for the 1.55 m wavelength is 6S 1S 6S only 0.8 eV, which is far into the low-energy tails of the resonance lines and cannot be adjusted by external

FIGURE 11. Molecular bonding source of the bismuth-en- fields. hanced electric-dipole transitions in the iron-garnet struc- With single-crystal rotator disks, these devices ture. The iron ions occupy oxygen sites of octahedral and tet- have excellent performance, offering isolation ratios rahedral coordination and interact with each other through exceeding 40 dB and insertion losses below 0.5 dB the oxygen ions (magnetic superexchange). When bismuth is present, its excited 3P orbital state couples to the excited over a range of wavelengths centered on the 1.55 mm 4 telecommunications wavelength. Although YIG has a P states of the neighboring Feoct and Fetet ions to enhance the spin-orbit splitting and produce a larger e1. The energy- relatively low Faraday-rotation parameter (0.084°/mm level model illustrates how these split transitions can pro- duce the major magneto-optical lines of the Y2.75Bi0.25Fe5O12 9 (BiYIG) family. Y2.75Bi0.25Fe5O12 Fetet = 3.15 eV 6 tuned magnetically. Optimization of design is there- fore dependent on the compatibility of quantum tran- 3

sition energies of matching semiconductor laser source ) 3 – and magnetic rotator. Furthermore, because of the 10 0 × (

microscopic dimensions dictated by the infrared wave- 1 ε lengths, purity of transmission cannot be obtained by –3 polycrystalline (ceramic) media. Fe = 2.6 eV Fe = 3.9 eV To magnify the splitting of the excited 2P term, the tet tet –6 conventional yttrium-iron-garnet composition were Theory modified with the addition of bismuth Bi3+ ions in the Experiment Y3+ site, shown schematically as a molecule together –9 2 3 4 5 with an abbreviated energy-level diagram in Figure ω (eV) 11. In a project sponsored by the Lincoln Laboratory Innovative Research Committee, the physical mecha- FIGURE 12. Comparison of theory to measurement data for 3+ nism for the splitting by Bi ions was explained in the compound Y2.75Bi0.25Fe5O12. Energy splittings w0 are ex- journal articles [17, 18], culminating in an MIT De- pressed in electron volts (eV) and indicate that the main magneto-optical transition at 3.15 eV originates from the oc- partment of Physics doctoral thesis [19]. The resulting tahedral Fe site. Two other transitions at 2.6 and 3.9 eV are theoretical models have become the standard for in- attributed to Fe in the magnetically opposed tetrahedral sub- terpreting the magneto-optical properties of bismuth lattice. In fiber-optical transmission systems, the IR energy magnetic garnet isolators. band is below 1 eV.

VOLUME 15, NUMBER 2, 2005 LINCOLN LABORATORY JOURNAL 333 • Dionne, Allen, Haddad, Ross, and Lax Circular Polarization and Nonreciprocal Propagation in Magnetic Media at 0.633 mm wavelength [20]), the substitution of Magnetic field Quarter-wave bismuth into the yttrium sites increases the Faraday plate (quartz) 45° polarization rotation dramatically, so that the fully substituted rotation Bi3Fe5O12 (BiIG) has a Faraday rotation of 7.8°/mm at 0.633 mm [21]. In practice, the garnet ferrite is a film deposited on a dielectric substrate by liquid-phase epitaxial (LPE) growth with the properties of a single crystal.

Present and Future Challenges Magnetized Metal mirror Because of their intrinsic nonreciprocal property, mag- ferrite netic components remain as the only passive solution to isolation and circulation in RF or optical transmis- FIGURE 13. Generic concept of the 45° Faraday rotator. Angle of incidence narrows by inside the sion systems. As a consequence, efforts are continuing magnetized ferrite disk. Because the wave passes through to attain improvements in terms of greater power han- the ferrite twice (each passage producing a 22.5° rotation) dling and efficiency, lower cost and, most significantly the thickness can be halved and only one quarter-wavelength for photonic applications, integration with the ever- impedance-matching plate is needed. The metal reflector plate can also serve as part of the external magnetic struc- shrinking size of microelectronic circuitry. ture. The net result is a geometry that offers advantages of more efficient heat removal and a simpler magnetizing circuit High-Power Reflection Circulator capable of higher fields. With the development of increasingly higher-power microwave- and millimeter-wave sources, the demands for greater efficiency of passive isolator and circulator as well as a more efficient heat-removal configuration. components have also accelerated. Future require- A further advance could utilize a magnetically self-bi- ments for advanced radar will challenge the power ased uniaxial type of ferrite (hexagonal structure) that handling limits of the transmission concept described can function at millimeter wavelengths without re- in the preceding section. Heat generated by absorption quiring an external magnetizing structure [26]. of the incident Gaussian-profiled signal beam localized at the center of the outer face of the ferrite element is Integrated Photonics the main issue. For pulsed-microwave operation, peak The interest in integrated photonics has made it im- powers can in theory exceed 100 kW at millimeter portant to develop thin-film isolators that can be in- wavelengths before nonlinear spin-wave thresholds corporated into a planar photonic circuit [27, 28]. Ac- are reached [22]. However, average heat dissipation of tive magneto-optical devices such as modulators have only a few kW will cause temperature increases that also been proposed, based on the ability to change can degrade the ferrite-rotator performance by reduc- the Faraday-rotation angle by varying the magnetiza- ing the value of M. A more serious problem arises tion M through a time-dependent magnetic bias field when thermal shock at the rotator surface can fracture H(t) [29]. Magnetic garnet films have been grown by the ceramic and lead to catastrophic failure. using chemical vapor deposition [30] and sputtering In a second Lincoln Laboratory Innovative Research [31–33], but the most work has been in producing Program project [23–25], a novel modification of the thin-film isolators by using LPE-grown garnet films quasi-optical concept was described, where the path on nonferrimagnetic garnet substrates [34–37]. The length through the ferrite could be halved by design- key element of these thin-film isolators is a ridge wave- ing a reflection configuration, as illustrated in Figure guide formed in the BiYIG film. A permanent magnet 13. This arrangement also permits simplification of film may be overlaid to magnetize the waveguide, and the biasing magnet structure to allow for higher mag- a sequence of cladding layers and overlayers confine netization ferrite, and consequently thinner elements, the light within the waveguide, control the birefrin-

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gence of the structure, and tune the wavelength-de- from magnetic ions. Maghemite (gFe2O3) and magne- pendent response. A basic structure is sketched in Fig- tite (Fe3O4), both with spinel crystal structures, can be ure 14. Dielectric birefringence, which originates both grown relatively easily by vapor processes such as sput- from the asymmetry of the rectangular shape of the tering or laser ablation, and have high Faraday rota- waveguide and from effects such as growth-induced tion, but their optical absorption is too high for them anisotropy and film internal stress, leads to elliptical to make practical isolator materials [38]. Barium hexa-

polarization that must be minimized to obtain a high ferrite (BaFe12O19) films have also been studied [39]. isolation ratio. Devices with up to 35 dB isolation ra- Orthoferrites, with the generic formula ABO3, have tios have been demonstrated [33–35, 37]. been extensively studied in the bulk form for their However, for integration with conventional mi- Faraday rotation [11], but there have been few stud- croelectronics, the deposition of garnet-based mag- ies of their properties as thin films [40], especially in neto-optical materials onto non-garnet substrates such the near-IR region. Another approach is to magneti-

as silicon has presented problems because of crystal- cally dope a material such as barium titanate, BaTiO3, lographic incompatibility. BiYIG compounds have which has excellent optical transparency. Substitution lattice parameters much larger than that of common of Fe for Ti leads to the development of dilute ferro- substrate materials. To overcome this difficulty, we magnetism that provides weak Faraday rotation [41].

have investigated other magnetic oxides. In any of As an example, BaTi0.8Fe0.2O3 showed a rotation of these materials there is a trade-off between absorp- only 0.02°/mm thickness at 1.55 mm, but its low ab- tion and Faraday rotation, both of which depend on sorption gives it a figure of merit (i.e., ratio of rotation the spectral location of the electric-dipole transitions to loss) that is much higher than that of materials such as maghemite [42]. Finally, magnetically doped semi- conductors, although usually paramagnetic, may be promising as isolator materials for integrated photonic SmCo devices for certain wavelengths [43]. magnet Acknowledgments The authors are grateful for the contributions of Dr. Jerald A. Weiss to the invention of the quasi-optical GdGaG millimeter-wave circulators. Engineering design infor- mation on the KREMS operational version was sup- Buffer layers plied by William D. Fitzgerald and David S. Rogers. for lattice match Dr. Ashok Rajamani of MIT is acknowledged for his Silicon or GaAs work on magneto-optical films for photonic-electronic BiYIG circuit design, sponsored by the MIT Microphotonics Consortium. We also wish to recognize Dr. Hans P. Jenssen and Prof. Mildred S. Dresselhaus of MIT, and Vincent Vitto and the Innovative Research Program Committee at Lincoln Laboratory for their unyielding Optical fiber support and encouragement during the early stages of FIGURE 14. Generic concept of a magneto-optical planar the magneto-optical part of this work. structure with Faraday-rotation capability. An infrared signal is introduced from a fiber into a thick bismuth-yttrium-garnet- ferrite film, which is patterned in the shape of a waveguide grown epitaxially on a gadolinium-gallium garnet (GGG) substrate and clad to confine the propagating lightwave. The SmCo top layer is magnetized appropriately to generate a magnetic field along the axis of the BiYIG waveguide.

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17. G.F. Dionne and G.A. Allen, “Spectral Origins of Giant Fara- day Rotation and Ellipticity in Bi-Substituted Magnetic Gar- R e f e r e n c e s nets,” J. Appl. Phys. 73 (10), 1993, pp. 6127–6129. 18. G.F. Dionne and G.A. Allen, “Molecular-Orbital Analysis of 1. D.M. Pozar, Microwave Engineering, 2nd ed. (John Wiley, Magneto-Optical Bi-O-Fe Hybrid Excited States,” J. Appl. New York, 1998). Phys. 75 (10), 1994, pp. 6372–6377. 2. B. Lax and K.J. Button, Microwave Ferrites and Ferrimagnetics 19. G.A. Allen, “The Magneto-Optic Spectra of Bismuth-Sub- (McGraw-Hill, New York, 1962). stituted Iron Garnets,” Ph.D. Thesis, Dept. of Physics, MIT, 3. Lax and Button, Microwave Ferrites and Ferrimagnetics, p. Cambridge, Mass., 1994. 299. 20. P. Hansen and J.-P. Krumme, “Magnetic and Magneto-Opti- 4. J.F. Dillon, Jr., “Magneto-Optical Properties of Magnetic Gar- cal Properties of Garnet Films,” Thin Solid Films 114 (1/2), nets,” Physics of Magnetic Garnets: Proc. Int. School of Physics 1984, pp. 69–107. “Enrico Fermi” Course LXX, Varenna on Lake Como, Italy, 27 21. N. Adachi, V.P. Denysenkov, S.I. Khartsev, A.M. Grishin, and June–9 July 1977, pp. 379–416. T. Okuda, “Epitaxial Bi3Fe5O12 (001) Films Grown by Pulsed 5. A.H. Morrish, The Physical Principles of Magnetism (IEEE Laser Deposition and Reactive Ion Beam Sputtering Tech- Press, New York, 2001), chap. 3. niques,” J. Appl. Phys. 88 (5), 2000, pp. 2734–2739. 6. G.E. Pake, Paramagnetic Resonance (W.A. Benjamin, New 22. E. Schlömann, J.J. Green, and U. Milano, “Recent Develop- York, 1962), chap. 2. ments in Ferromagnetic Resonance at High Powers,” J. Appl. 7. Lax and Button, Microwave Ferrites and Ferrimagnetics, p. Phys. 31 (supp. 5), 1960, pp. S386–S395. 156. 23. B. Lax, J.A. Weiss, N.W. Harris, and G.F. Dionne, “Quasi- 8. Pozar, Microwave Engineering, p. 504. Optical Reflection Circulator,” IEEE Trans. Microw. Theory 9. G.F. Dionne, “Simple Derivation of Four-Level Permittivity Tech. 41 (12), 1994, pp. 2190–2197. Relations for Magneto-Optical Applications,” J. Appl. Phys. 97 24. J.A. Weiss, N.W. Harris, B. Lax, and G.F. Dionne, “Quasi- (10), 2005, pp. 10F103-1–3. Optical Ferrite Reflection Circulator Progress in Theory and 10. N. Blömbergen, “Magnetic Resonance in Ferrites,” Proc. IRE Millimeter-Wave Experiments,” SPIE 2250, 1994, pp. 365– 44 (Oct.), 1956, pp. 1259–1269. 366. 11. F.J. Kahn, P.S. Pershan, and J.P. Remeika, “Ultraviolet Mag- 25. N.W. Harris, G.F. Dionne, J.A. Weiss, and B. Lax, “Char- neto-Optical Properties of Single-Crystal Orthoferrites, Gar- acteristics of the Quasi-Optical Reflection Circulator,” IEEE nets and Other Ferric Oxide Compounds,” Phys Rev. 186 (3), Trans. Magn. 30 (6, pt.1), 1994, pp. 4521–4523. 1969, pp. 891–918. 26. M.R. Webb, “A mm-Wave Four-Port Quasi-Optical Circula- 12. G.A. Allen and G.F. Dionne, “Application of Permittivity Ten- tor,” Int. J. Infrared Millimeter Waves 12 (1), 1991, pp 45–63. sor for Accurate Interpretation of Magneto-Optical Spectra,” 27. M. Levy, “The On-Chip Integration of Magnetooptic Wave- J. Appl. Phys. 73 (10), 1993, pp. 6130–6132. guide Isolators,” IEEE J. Sel. Top. Quantum Electron. 8 (6), 13. Lax and Button, Microwave Ferrites and Ferrimagnetics, chap. 2002, pp. 1300–1306. 12. 28. D.C. Hutchings, “Prospects for the Implementation of Mag- 14. G.F. Dionne, J.A. Weiss, G.A. Allen, and W.D. Fitzgerald, neto-Optic Elements in Optoelectronic Integrated Circuits: “Quasi-Optical Ferrite Rotator for Millimeter Waves,” 1988 A Personal Perspective,” J. Phys. D 36 (18), 2003, pp. 2222– IEEE MTT-S Int. Microwave Symp. Dig. 1, New York, 25–27 2229. May 1998, pp. 127–130. 29. W.E. Ross, D. Psaltis, and R.H. Anderson, “Two-Dimension- 15. G.F. Dionne, J.A. Weiss, and G.A. Allen, “Nonreciprocal al Magneto-Optical Spatial Light Modulator for Signal Pro- Magneto-Optics for Millimeter Waves,” IEEE Trans. Magn. cessing,” Opt. Eng. 22 (4), 1998, pp. 485–490. 24 (6), 1988, pp. 2817–2819. 30. B. Stadler, K. Vaccaro, P. Yip, J. Lorenzo, Y.-Q. Li, and M. 16. W.D. Fitzgerald, “A 35-GHz Beam Waveguide System for the Cherif, “Integration of Magneto-Optical Garnet Films by Millimeter-Wave Radar,” Linc. Lab. J. 5 (2), 1992, pp. 245– Metal–Organic Chemical Vapor Deposition,” IEEE Trans. 272. Magn. 38 (3), 2002, pp. 1564–1567.

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31. M. Gomi, S. Satoh, and M. Abe, “Giant Faraday Rotation of Ce-Substituted YIG Films Epitaxially Grown by RF Sputter- ing,” Jpn J. Appl. Phys. 27 (8), 1988, L1536. 32. B.J.H. Stadler and A. Gopinath, “Magneto-Optical Garnet Films Made by Reactive Sputtering,” IEEE Trans. Magn. 36 (6), 2000, pp. 3957–3967. 33. T. Shintaku, “Integrated Optical Isolator Based on Nonrecip- rocal Higher-Order Mode Conversion,” Appl. Phys. Lett. 73 (14), 1998, pp. 1946–1948. 34. M. Levy, R.M. Osgood, H. Hegde, F.J. Cadieu, R. Wolfe, and V. Fratello, “Integrated Optical Isolators with Sputter-Depos- ited Thin-Film Magnets,” IEEE Photonics Technol. Lett. 8 (7), 1996, pp. 903–905. 35. R. Wolfe, J.F. Dillon, Jr., R.A. Lieberman, and V.J. Fratello, “Broad-Band Magneto-Optic Waveguide Isolator,” Appl. Phys. Lett. 57 (10), 1990, pp. 960–962. 36. N. Sugimoto, H. Terui, A. Tate, Y. Katoh, Y. Yamada, A. Su- gita, A. Shibukawa, and Y. Inoue, “A Hybrid Integrated Wave- guide Isolator on a Silica-Based Planar Waveguide Circuit,” J. Lightwave Technol. 14 (11), 1996, pp. 2537–2546. 37. R. Wolfe, R.A. Lieberman, V.J. Fratello, R.E. Scotti, and N. Kopylov, “Etch-Tuned Ridged Waveguide Magneto-Optic Isolator,” Appl. Phys. Lett. 56 (5),1990, pp. 426–428. 38. T. Tepper, C.A. Ross, and G.F. Dionne, “Microstructure and Optical Properties of Pulsed-Laser-Deposited Iron Oxide Films,” IEEE Trans. Magn. 40 (3), 2004, 1685–1690. 39. Z. Šimša, R. Gerber, T. Reid, R. Tesarˇ, R. Atkinson and P. Papakonstantinou, “Optical Absorption and Faraday Rotation of Barium Hexaferrite Films Prepared by Laser Ablation De- position,” J. Phys. Chem. Solids 59 (1), 1998, pp. 111–119. 40. D.S. Schmool, N. Keller, M. Guyot, R. Krishnan, and M. Tes- sier, “Magnetic and Magneto-Optic Properties of Orthoferrite Thin Films Grown by Pulsed-Laser Deposition,” J. Appl. Phys. 86 (10), 1999, pp. 5712–5717. 41. R. Maier and J.L. Cohn, “Ferroelectric and Ferromagnetic Iron-Doped Thin-Film BaTiO3: Influence of Iron on Physical Properties,” J. Appl. Phys. 92 (9), 2002, pp. 5429–5436. 42. A. Rajamani, G.F. Dionne, D. Bono, and C.A. Ross, “Fara- day Rotation, Ferromagnetism, and Optical Properties in Fe- Doped BaTiO3,” J. Appl. Phys. 98, 063907, 2005. 43. H. Shimizu and M. Tanaka, “Magneto-Optical Properties of Semiconductor-Based Superlattices Having GaAs with MnAs Nanoclusters,” J. Appl. Phys. 89 (11, pt 2), 2001, pp. 7281– 7286.

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APP e n D I X : Q u a n t u m O ri g i n s o f ω M a n d ω E

ransition probabilities for magnetic and elec- Zeeman splitting (partial) Ttric-dipole interactions with plane-wave radiation Sz 1 are explained by quantum mechanical time-dependent + /2 perturbation theory. Figure A shows semi-classical |e¯ 2S models for the resonance mechanisms. The parameter W0 $ Szp1 wM for a Zeeman-split S = 1 2 case is expressed as |g¯ 1 g m  /2 ω= γ 4π M = e B 4πNg m S Increasing H M    e B 4πN 2 FIGURE A. Energy level diagrams corresponding to the = gge m BS+ e (1) physical mechanism diagrams of Figure 6 in the main text.  The splitting shown corresponds to the wave functions in 2 4πN 1 1 Equation 1 for partial Zeeman splitting dipole energy states. ωM = + ge m B ()Sx± iS y − ,  2 2 where g m is the magnetic-dipole moment of the e BS+ Spin-orbit multiplet Lz right-hand circular polarized signal mode, mB is the p-state splitting moment of the electron spin (the Bohr magneton), 1 (x – iy) and the spectroscopic splitting factor g = 2 for an a,b 2P e |e ¯ 2$  z electron spin.* For the pair of electric-dipole transitions between 1 (x + iy) the ground state and the a and b split excited state shown in Figure B, the dipole energy of the orbital an- $L 1 W a W b zp gular momentum operator for the right-hand and left- 0 0 2 | S hand circular-polarization modes is expressed as erL±. g¯ 0 A parameter ω a,b is defined analogously to Equation 1 E FIGURE B. Spin-orbit p-state splitting diagram correspond- above, according to ing to Equation 2. Splitting of these states is independent 2 of H. The use of w to represent energy assumes that the a,b 4πN a,b ωE = gerL± e Planck’s constant multiplier  is implicit. Only the split excit-  (2) ed state (diamagnetic) case is shown. 2 4πN z x+ iy = er() Lx± iL y ..  r r

* The use of w to represent energy assumes that the Planck’s constant multiplier  is implicit. Only the split excited state (diamagnetic) case is shown.

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gerald f. dionne gary a. allen pamela r. haddad is a consultant for the Analog is a staff engineer in the Com- is an assistant group leader in Device Technology group. He ponents Research group at the Advanced Sensor Tech- received a B.Sc. degree from Intel Corporation in Hillsboro, niques group within the Sensor the University of Montreal Oregon. He has worked in the Systems division. She received (Loyola College), a B.Eng. field of microlithography since a B.S. degree from the Univer- from McGill University, an joining Intel in 1996, and he is sity of Massachusetts, an M.S. M.S. degree from Carnegie- currently engaged in identify- degree from the University of Mellon University, and a ing and developing advanced Michigan, and a Ph.D. degree Ph.D. degree from McGill lithography techniques for from the University of Mas- University with a thesis on semiconductor manufacturing. sachusetts, all in electrical electron paramagnetic reso- He joined Lincoln Labora- engineering. Her doctoral work nance and relaxation. Before tory as a cooperative educa- focused on the electromagnetic joining MIT, he was a member tion student in 1985 in the analysis of microstrip antennas of the Department of Physics Radar Measurements division. using numerical techniques. faculty at McGill, worked on He maintained a part-time She joined Lincoln Laboratory semiconductor device develop- position with the Laboratory in 1995 where she specialized ment at IBM and the Sylvania until starting his thesis work in the design of antennas and Division of GTE, and inves- in investigating the magneto- arrays for air defense radar tigated electron emission and optic effects of iron garnet systems. In August 2000, she cesium vapor ionization for materials, which was sponsored moved to the Ballistic Missile thermionic energy conversion by Lincoln Laboratory. He Defense (BMD) Technol- at Pratt & Whitney Aircraft. received a B.S. degree in phys- ogy division to lead a team Since 1966 he has carried out ics from Worcester Polytechnic of analysts in the evaluation research at Lincoln Laboratory Institute, and a Ph.D. degree of discrimination algorithms in the fields of fundamental in physics from MIT. and architectures for future magnetism in solids, ferri- BMD systems. She joined the magnetic materials for micro- Advanced Sensor Techniques wave, millimeter-wave, and group in January 2004 to con- magneto-optical applications, centrate on radar technology millimeter- and submillimeter- and algorithm development for wave radiometry, and electron the surface surveillance mission emission. He pioneered in the area. She is a member of the development of ferrite devices Lincoln Laboratory Advanced that utilize the low resistance Concepts Committee, and has properties of superconductors served as a part-time instruc- for use in microwave phase tor in the graduate school at shifters and high-Q tunable Northeastern University. filters. He served as materials advisor to the DARPA-spon- sored Ferrite Development Consortium in the 1990s. He is a fellow of the IEEE, the American Physical Society, and a member of the Materials Re- search Society and the Society of Sigma Xi.

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caroline a. ross benjamin lax is the Merton C. Flemings is a consultant for the Optical Career Development Professor Fabrication Facility in the Solid of Materials Science and Engi- State Division working on laser neering at MIT. She received and millimeter-wave radar. He B.A. and Ph.D. degrees from is also Professor Emeritus and Cambridge University, U.K. Director Emeritus at MIT. She was a post-doctoral fel- He received a B.M.E. degree low at Harvard University and in mechanical engineering an engineer at Komag before from Cooper Union and a coming to MIT in 1997. Her Ph.D. degree in physics from research interests are directed MIT. Prior to his arrival at towards magnetic properties of Lincoln Laboratory, he taught thin films and small structures, electronics at Harvard, served particularly for data storage as a radar officer at the MIT applications. Her group studies Radiation Laboratory and as fabrication using sputtering, radar consultant to Sylvania pulsed laser deposition, evapo- Electric Company. In 1951, ration and electrodeposition he joined the Solid State group combined with nanolithogra- at Lincoln Laboratory where, phy and self-assembly meth- in 1953, he became the head ods, and measuring and mod- of the Ferrite group. In 1955 eling the magnetic behavior of he was appointed the head of the resulting films and nano- the Solid State group, which structures. She is a fellow of the later became the Solid State American Physical Society and division under his leadership. the Institute of Physics. He was an associate director of Lincoln Laboratory, a professor of physics at MIT, and a mem- ber of the National Academy of Science. He founded the MIT Francis Bitter National Magnet Laboratory and served as its director until 1981. His scientific activities include microwave ferrites, plasma physics, magnetospectroscopy of solids, nonlinear optics, semiconductor and x-ray lasers, and quantum electronics. He has received numerous awards and citations, including the Buckley Prize of the American Physical Society, a Guggen- heim Fellowship, and an award from the IEEE for his contri- bution to the development of the semiconductor laser.

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