Abstract: The lack of optical isolators has limited the serial integrationof components in the development of photonic integrated circuits. Isolatorsare inherently nonreciprocal and, as such, require nonreciprocal opticalpropagation. We propose a class of integrated photonic devices that makeuse of electrically-generated electron spin polarization in semiconductorsto cause nonreciprocal TE/TM mode conversion. Active control over thenon-reciprocal mode coupling rate allows for the design of electrically-controlled isolators, circulators, modulators and switches. We analyze theeffects of waveguide birefringence and absorption loss as limiting factors todevice performance.
References and links1. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics
3, 91–94 (2009).2. H. Shimizu, S. Goto, and T. Mori, “Optical isolation using nonreciprocal polarization rotation in Fe-
InGaAlAs/InP semiconductor active waveguide optical isolators,” Appl. Phys. Express 3, 072201 (2010).3. X. Guo, T. Zaman, and R. J. Ram, “Magneto-optical semiconductor waveguides for integrated isolators,” Proc.
SPIE 5729, 152–159 (2005).4. Tauhid R. Zaman, Xiaoyun Guo and Rajeev J. Ram, “Semiconductor waveguide isolators,” J. Lightwave Technol.
26, 291–302 (2008).5. N. Sugimoto, T. Shintaku, A. Tate, J. Terui, M. Shimokozono, E. Kubota, M. Ishii and Y. Inoue, “Waveguide
polarization-independent optical circulator,” IEEE Photon. Technol. Lett. 11, 355–357 (1999).6. G. T. Reed, G. Z. Mashanovich, W. R. Headley, B. Timotijevic, F. Y. Gardes, S. P. Chan, P. Waugh, N. G. Emer-
son, C. E. Png, M. J. Paniccia, A. Liu, D. Hak, and V. M. N. Passaro, “Issues associated with polarizationindependence in silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1335–1344 (2006).
7. T. R. Zaman, X. Guo, and R. J. Ram, “Faraday rotation in an InP Waveguide,” Appl. Phys. Lett. 90, 023514(2007).
8. Vadym Zayets, Mukul C. Debnath, and Koji Ando, “Optical isolation in Cd1−xMnxTe magneto-optical waveguidegrown on GaAs substrate,” J. Opt. Soc. Am. B 22, 281–285 (2005).
9. T. R. Zaman, X. Guo and R. J. Ram, “Proposal for a polarization-independent integrated optical circulator,” IEEEPhoton. Technol. Lett. 18, 1359–1361 (2006).
10. J. Fujita, M. Levy, R. M. Osgood, Jr., L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158–2160 (2000).
11. Y. Nishikawa, A. Tackeuchi, S. Nakamura, S. Muto, and N. Yokoyama, “All-optical picosecond switching of aquantum well etalon using spin-polarization relaxation,” Appl. Phys. Lett. 66, 839–841 (1995).
#147312 - $15.00 USD Received 10 May 2011; revised 28 Jun 2011; accepted 8 Jul 2011; published 18 Jul 2011(C) 2011 OSA 1 August 2011 / Vol. 19, No. 16 / OPTICS EXPRESS 14845
12. D. Marshall, M. Mazilu, A. Miller, and C. C. Button “Polarization switching and induced birefringence in In-GaAsP multiple quantum wells at 1.5μm,” J. Appl. Phys. 91, 4090 (2002).
13. T. Mizumoto and Y. Naito, “Nonreciprocal propagation characteristics of YIG thin film,” IEEE Trans. Microw.Theory Tech. MTT-30, 922–925 (1982).
14. H. Shimizu and Y. Nakano, “Fabrication and characterization of an InGaAsP/InP active waveguide optical isola-tor with 14.7dB/mm TE mode nonreciprocal attenuation.” J. Lightwave Technol. 24, 38–43 (2006).
15. Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transi-tions,” Appl. Phys. Lett. 94, 171116 (2009).
16. F. Meier and B. P. Zakharchenya, Optical Orientation (Elsevier Science Ltd., 1984).17. Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, “Current-induced spin polarization in strained
semiconductors,” Phys. Rev. Lett. 93, 176601 (2004).18. A. Yu. Silov, P. A. Blajnov, J. H. Wolter, R. Hey, K. H. Ploog, and N. S. Averkiev, “Current-induced spin polar-
ization at a single heterojunction,” Appl. Phys. Lett. 85, 5929-5931 (2004).19. V. Sih, R. C. Myers, Y. K. Kato, W. H. Lau, A. C. Gossard, and D. D. Awschalom, “Spatial imaging of the spin
Hall effect and current-induced polarization in two-dimensional electron gases,” Nat. Phys. 1, 31 (2005).20. C. L. Yang, H. T. He, Lu Ding, L. J. Cui, Y. P. Zeng, J. N. Wang, and W. K. Ge, “Spectral dependence of spin
photocurrent and current-induced spin polarization in an InGaAs/InAlAs two-dimensional electron gas,” Phys.Rev. Lett. 96, 186605 (2006).
21. W. F. Koehl, M. H. Wong, C. Poblenz, B. Swenson, U. K. Mishra, J. S. Speck, and D. D. Awschalom, “Current-induced spin polarization in gallium nitride,” Appl. Phys. Lett. 95, 072110 (2009).
22. N. P. Stern, S. Ghosh, G. Xiang, M. Zhu, N. Samarth, and D. D. Awschalom, “Current induced polarization andthe spin hall effect at room temperature,” Phys. Rev. Lett. 97, 126603 (2006).
23. D. Culcer and R. Winkler, “Steady states of spin distributions in the presence of spin-orbit interactions,” Phys.Rev. B 76, 245322 (2007).
24. H.-A. Engel, E. I. Rashba, and B. I. Halperin, “Out-of-plane spin polarization from in-plane electric and magneticfields,” Phys. Rev. Lett. 98, 036602 (2007).
25. B. M. Norman, C. J. Trowbridge, J. Stephens, A. C. Gossard, D. D. Awschalom, and V. Sih, “Mapping spin-orbitsplitting in strained (In,Ga)As epilayers,” Phys. Rev. B 82, 081304 (2010).
26. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).27. C. Weisbuch and C. Hermann, “Optical detection of conduction-electron spin resonance in GaAs, Ga1−xInxAs,
and Ga1−xAlxAs,” Phys. Rev. B 15, 816–822 (1977).28. B. A. Bernevig and S.-C. Zhang, “Spin splitting and spin current in strained bulk semiconductors,” Phys. Rev. B
72, 115204 (2005).29. J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki, “Gate control of spin-orbit interaction in an inverted
In0.53Ga0.47As/In0.52Al0.48As heterostructure,” Phys. Rev. Lett. 78, 1335–1338 (1997).30. A. T. Hanbicki, B. T. Jonker, G. Itskos, G. Kioseoglou, and A. Petrou, “Efficient electrical spin injection from a
magnetic metal/tunnel barrier contact into a semiconductor,” Appl. Phys. Lett. 80, 1240 (2002).
1. Introduction
Increasing demand for high speed data transmission is driving the proliferation of optical fibernetworks and the integration of optoelectronic components at the optical-electronic interface.Simultaneously, the emergence of nanophotonics has increased interest in the development ofall-optical chips [1]. Monolithically integrated isolators and circulators have remained chal-lenging and are needed to protect components from feedback in optical paths with serially ar-ranged components [2–10]. In addition, the performance of planar photonic devices is typicallypolarization dependent, which underscores the need for on-chip polarization control [6].
In an effort to develop integrated optical isolators and circulators based on nonreciprocalmode conversion (NRMC), DC Faraday rotation has been measured in magnetically-dopedInP, InGaAlAs on GaAs [2–4], (Ga,La):YIG on GGG [5], and CdMnTe on GaAs [8] waveg-uides. These devices require an applied magnetic field and do not offer electrical control. Anoptical switch using Faraday rotation from a transient, optically-pumped spin population haspreviously been proposed for bulk optical elements [11,12]. Nonreciprocal phase shift, result-ing from the application of a magnetic field perpendicular to the direction of light propagationin a magneto-optic medium, has also been explored as a means to achieve integrated isolation[3,5,10,13]. While this technique has the advantage that waveguide birefringence has no effecton the isolation ratio, generating a polarization-independent isolator would require a magnetic
#147312 - $15.00 USD Received 10 May 2011; revised 28 Jun 2011; accepted 8 Jul 2011; published 18 Jul 2011(C) 2011 OSA 1 August 2011 / Vol. 19, No. 16 / OPTICS EXPRESS 14846
field with carefully balanced in-plane and out-of-plane components and the interferometric na-ture of proposed designs limits the isolation bandwidth. Nonreciprocal loss integrated isolatorshave been demonstrated with 14.7 dB mm−1 isolation in the TE mode [14]. This device ispolarization-dependent, and a semiconductor optical amplifier must be used to compensate forloss in the forward direction. However, larger isolation ratios may be achieved by increasing thedevice length. Recently, isolators based on optical inter-band transitions resulting from spatiallyand temporally modulated index materials have been proposed [1,15], though no devices haveyet been demonstrated. In Ref. [1], nonreciprocal frequency shifts would be used in conjunctionwith an optical filter to achieve isolation, while Ref. [15] would rely on a non-reciprocal phaseshift with a Mach-Zehnder interferometer.
In this paper, we propose a class of semiconductor waveguide devices which make use ofnon-reciprocal mode conversion resulting from an electrically-generated spin polarization innon-magnetic materials. By using electrically-generated spin polarization, no external magneticfield is required, vastly simplifying the design of integrated systems. Devices of this nature areintrinsically electrically controlled and could be used for polarization control, modulation andswitching, in addition to realizing optical circulators and isolators. We describe the design fora spin-based optical isolator, modulator, and switch. In order to evaluate how well such devicescould perform, we consider the effects of waveguide birefringence and absorption and quantifythe Faraday rotation due to an electrically-generated spin polarization near the band edge ofInGaAs.
2. Basic Operating Principles of a Spin-Based Optoelectronic Device
The spin-based optoelectronic devices proposed here would operate based on controlling thepolarization of light. In the context of a waveguide, orthogonal modes (TE and TM) take theplace of orthogonal polarization vectors, so that a rotation of the polarization vector manifestsas a coupling between orthogonal modes. The presence of an electron spin polarization alignedwith the propagation of light gives rise to a non-reciprocal rotation of linearly polarized light forphoton energies near the band gap. This effect has its origin in the selection rules for circularlypolarized light in zincblende materials [16]. In the presence of a spin polarization along thedirection of light propagation, state filling in the conduction band causes the absorption edge ofone circular polarization to occur at a higher energy than the other. This differential absorptiongives rise to a circular birefringence and Faraday rotation of the linearly-polarized light.
Recent measurements have shown that an electron spin polarization can be generated even inthe absence of magnetic fields and magnetic materials by causing a current to flow in particulardirections with respect to the crystal axes in conventional non-magnetic semiconductors [17–22]. The electrically-generated spin polarization can be generated along an in-plane direction,which would result in NRMC for waveguides aligned along the direction of the spin polariza-tion. While the process which generates this spin polarization is not yet fully understood, itis believed to be related to spin-orbit effects [23,24]. This effect has been observed in a widevariety of materials, including InGaAs [17], ZnSe [22] and GaN [21]. Electrically-generatedspin polarization was found to persist to room temperature in ZnSe [22].
With control over the mode in which light is found after passing through the active region ofthe device, many optical components become possible. For instance, mode-selective couplingbetween two waveguides would allow for the construction of an electrically-controlled opticalswitch. After traveling through an electrically-controlled NRMC region, light would enter awaveguide coupler in which a single mode is transferred to an adjacent waveguide. Incominglight could then be rapidly switched between the two output waveguides based on its polariza-tion after the NRMC region. For polarization control, incoming light of arbitrary polarizationcould be actively placed into a chosen mode with the use of a feedback circuit before propa-
#147312 - $15.00 USD Received 10 May 2011; revised 28 Jun 2011; accepted 8 Jul 2011; published 18 Jul 2011(C) 2011 OSA 1 August 2011 / Vol. 19, No. 16 / OPTICS EXPRESS 14847
gating to further optical circuitry. This arrangement would help to compensate for optical fiberwhich is not, in general, polarization preserving.
A number of potential device designs have been put forth which would use NRMC alongwith reciprocal mode conversion to achieve isolation and circulation. Two such designs, basedon buried core and high mesa waveguide architectures, are summarized in Ref. [4]. In additionto NRMC regions, integrated half wave plates are used to decrease the total Faraday rotationneeded to achieve isolation to 45°.
While our proposed device operates in a similar manner to those that use magnetic dopantsand an externally applied magnetic field to generate a Faraday rotation [9], it does not requirethe application of an external magnetic field or the use of magnetic materials since an electricfield can be used to generate the Faraday effect. In addition, electric fields have the advan-tage that they can be controlled locally using patterned contacts and more rapidly than appliedmagnetic fields.
Fig. 1. Experimental geometry for measurement of Faraday rotation due to current inducedspin polarization. In-plane magnetic field B causes spins aligned along −ex to precess outof the sample plane, leading to a rotation of the polarization angle of the probe beam whichtravels along ez.
3. Faraday Rotation and Absorption Measurements
For spin-based optoelectronic devices to be useful, it must be possible to generate a sufficientpolarization rotation without significant loss of power to material absorption and scattering.Since the spin-based Faraday effect is largest near the absorption edge, material absorption lossis expected to dominate. Measurements were carried out in a 500 nm n-doped In0.04Ga0.96Asepilayer with a doping density of 3×1016 cm−3. 100 μm wide channels connecting ohmic con-tacts were photolithographically defined and oriented along the [110] direction. For more detailson the sample and device, see Ref. [25]. The measurement geometry is summarized in Fig. 1.Current flows through the channel in the ey direction between the two contacts, generating aspin polarization in the plane of the sample. The applied magnetic field �B in the −ey direction
#147312 - $15.00 USD Received 10 May 2011; revised 28 Jun 2011; accepted 8 Jul 2011; published 18 Jul 2011(C) 2011 OSA 1 August 2011 / Vol. 19, No. 16 / OPTICS EXPRESS 14848
causes the ex component of the initial spin polarization to undergo Larmor precession, whichgives rise to an out-of-plane component. As the spins precess they dephase with a coherencetime T ∗
2 . The optical probe traveling in the ez direction then undergoes Faraday rotation, withthe angle of rotation proportional to the ez component of the spin polarization per unit area. Thelinearly polarized probe beam was generated by a mode-locked Ti:Sapphire laser with a repeti-tion rate of 76 MHz and has a FWHM of 15 nm. An AC square wave voltage was applied acrossthe channel for lock-in detection. Assuming a constant rate of spin alignment and subsequentprecession around the applied magnetic field, the Faraday rotation signal is odd-Lorentzian inapplied field [17], as shown in Fig. 2(a). These data were taken at a temperature of 30 K withan electric field of 5 mV·μm−1 applied along the length of the channel. The data were fit toextract the amplitude of the odd Lorentzian, which is proportional to the product of the rate ofspin alignment γ and the coherence time T ∗
2 [17].In this experiment, the externally applied magnetic field is required to cause spins initially
aligned in-plane to precess out-of-plane so that the spin polarization may be measured using aprobe beam that is perpendicular to the sample plane. An applied magnetic field would not benecessary for devices in which light is propagating in waveguides in the sample plane as themaximum Faraday rotation would occur for zero applied field.
To characterize the wavelength dependence of the Faraday rotation and absorption, the wave-length of the probe beam was varied near the absorption edge. At each wavelength magneticfield scans were fit to determine the amplitude of Faraday rotation, and absorption measure-ments were taken with an optical power meter. Results are shown in Fig. 2(b). Note that sincethe measurements were taken using a mode-locked laser, the data is a convolution of the truewavelength-dependent signal and the laser power spectrum. Maximum Faraday rotation of 1.7°cm−1 at 848 nm was measured, with corresponding absorption of 23.4 dB μm−1.
a) b)
Applied Field (T)
θ F (μR
ad)
Wavelength (nm)
θ F /E
ext (
μRad
μm
mV
-1)
Abs
orpt
ion
Fig. 2. (a) Faraday rotation as a function of applied magnetic field for an applied electricfield along [110] of 5 mV/μm at 30 K (solid red line: fit to data). (b) Faraday rotationamplitude per applied electric field (black) and device absorption (red) as a function ofwavelength.
In considering the usefulness of spin polarization as a basis for optical isolation, a figure ofmerit FOM has been introduced in Ref. [5] as:
FOM =θα
(1)
where θ is the Faraday rotation per unit length and α is the absorption loss in dB per unit length.Therefore, a FOM of 45 would correspond to a loss of 1 dB over the course of a rotation of 45°.
#147312 - $15.00 USD Received 10 May 2011; revised 28 Jun 2011; accepted 8 Jul 2011; published 18 Jul 2011(C) 2011 OSA 1 August 2011 / Vol. 19, No. 16 / OPTICS EXPRESS 14849
Large absorption due to the small detuning of the probe beam from the band gap severely limitsthe FOM in our InGaAs sample. The largest observed FOM was 7.73× 10−6 at a wavelengthof 848 nm.
By comparing Faraday rotation in the case of electrically generated spin polarization to thatof optically injected spin polarization it is possible to estimate the degree of polarization in theformer case [17]. In the presence of a near-resonant left (right) circularly polarized pump beam,optical carriers will be generated in the ratio of n↑/n↓ = 3 ( 1
3 ) when the pump linewidth is largecompared to the heavy hole/light hole splitting. Averaging over pump powers ranging from 172μW to 485 μW the rate of Faraday rotation per areal spin density was found to be 1.24×10−14
cm2·spin−1 with the pump tuned to λ = 848 nm. This indicates a current-induced degree ofspin polarization of 1.3×10−3.
4. Limitations Imposed by Waveguide Birefringence
In addition to material absorption, nonreciprocal devices based on mode coupling suffer fromanother design challenge. Polarization mode birefringence in the active region limits the amountof power that can be transferred from one mode to the other. In the presence of birefringence,the normalized intensity of light I in an undriven mode which is coupled to a driven mode withinitialintensity I0 is given by:
II0
=4
4+(Δ/k)2 sin2(
12[4+{Δ/k}2]1/2kz
)(2)
where k is the mode coupling constant, Δ is the mismatch in phase velocities, kTE − kTM , and zis the position along the waveguide in the direction of propagation [26]. The maximum achiev-able fractional power transfer is plotted in Fig. 3(a) as a function of Δ/k. Figure 3(b) showsEq. (2) plotted as a function of the dimensionless parameters kz and Δ/k. To achieve a powertransfer between modes of 95%, in the case of the highest observed FOM above the waveguidebirefringence must be limited to 1.3×10−2 cm−1.
Nor
mal
ized
Inte
nsity
I/I 0 1
0
a) b)
Max
. Tra
nsfe
r I/I 0
Δ/k
Δ/k
kzπ 2π 3π
Fig. 3. (a) Maximum normalized power transfer between modes as a function of Δ/k. Apower transfer of 95% requires Δ/k < 0.459. (b) Intensity in an undriven mode coupled to adriven mode at rate k, with phase velocity splitting Δ, plotted as a function of dimensionlessparameters Δ/k and kz, where z is the position along the waveguide.
Despite the high absorption and low Faraday rotation observed in the InGaAs device pre-sented here, there are reasons to be optimistic about the use of electrically generated spin polar-ization in integrated nonreciprocal devices. There has yet to be a thorough search of available
#147312 - $15.00 USD Received 10 May 2011; revised 28 Jun 2011; accepted 8 Jul 2011; published 18 Jul 2011(C) 2011 OSA 1 August 2011 / Vol. 19, No. 16 / OPTICS EXPRESS 14850
materials for those with a high degree of current-induced spin polarization. It has been pre-dicted that the magnitude of the electrically-generated spin polarization is proportional to thespin splitting [23,24]. The spin splitting can be modified by varying material composition orstrain and by the application of a gate voltage [27–29]. By maximizing the spin splitting, the de-gree of spin polarization, along with the rate of Faraday rotation and FOM, may be improved. Inaddition, for devices where ferromagnetic contacts can be used, larger spin polarizations havealready been achieved. Recently, a spin injection efficiency of 30% has been demonstrated us-ing ferromagnetic contacts [30]. Such a spin polarization would give rise to a Faraday rotationof 391° cm−1 and an increase in the FOM by a factor of 230 under the assumption that Faradayrotation is directly proportional to the areal spin density.
5. Conclusion
In this paper, we have considered the use of current induced spin polarization as a means toachieve nonreciprocal mode coupling in integrated optoelectronic devices. In principle, thesedevices could provide benefits over competing technologies, including electronic control, sim-ple integration, operation without an externally applied magnetic field and room temperatureoperation in the proper materials. However, in the InGaAs samples used in absorption and Fara-day rotation measurements, we find that absorption far outweighs Faraday rotation. This is aresult of the fact that spin polarization induced Faraday rotation is largest near the absorptionedge. Further study into the mechanism of current induced spin polarization, potential materi-als, and device design is warranted given the potential benefits of these devices.
Acknowledgments
This material is based in part upon work supported by the National Science Foundation underGrants No. ECCS-0844908 and No. DMR-0801388 and the Horace H. Rackham School ofGraduate Studies. Sample fabrication was performed at the Lurie Nanofabrication Facility, partof the NSF funded NNIN network.
#147312 - $15.00 USD Received 10 May 2011; revised 28 Jun 2011; accepted 8 Jul 2011; published 18 Jul 2011(C) 2011 OSA 1 August 2011 / Vol. 19, No. 16 / OPTICS EXPRESS 14851
