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The lack of optical isolators has limited the serial integration of components in the development of photonic integrated circuits. Isolators are inherently nonreciprocal and, as such, require nonreciprocal optical propagation. We propose a class of integrated photonic devices that make use of electrically-generated electron spin polarization in semiconductors to cause nonreciprocal TE/TM mode conversion. Active control over the non-reciprocal mode coupling rate allows for the design of electrically-controlled isolators, circulators, modulators and switches. We analyze the effects of waveguide birefringence and absorption loss as limiting factors to device performance.
©2011 Optical Society of America
1. Introduction
Increasing demand for high speed data transmission is driving the proliferation of optical fiber networks and the integration of optoelectronic components at the optical-electronic interface. Simultaneously, the emergence of nanophotonics has increased interest in the development of all-optical chips [1]. Monolithically integrated isolators and circulators have remained challenging and are needed to protect components from feedback in optical paths with serially arranged components [2–10]. In addition, the performance of planar photonic devices is typically polarization dependent, which underscores the need for on-chip polarization control [6].
In an effort to develop integrated optical isolators and circulators based on nonreciprocal mode conversion (NRMC), DC Faraday rotation has been measured in magnetically-doped InP, InGaAlAs on GaAs [2–4], (Ga,La):YIG on GGG [5], and CdMnTe on GaAs [8] waveguides. These devices require an applied magnetic field and do not offer electrical control. An optical switch using Faraday rotation from a transient, optically-pumped spin population has previously been proposed for bulk optical elements [11, 12]. Nonreciprocal phase shift, resulting from the application of a magnetic field perpendicular to the direction of light propagation in 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 effect on the isolation ratio, generating a polarization-independent isolator would require a magnetic field with carefully balanced in-plane and out-of-plane components and the interferometric nature of proposed designs limits the isolation bandwidth. Nonreciprocal loss integrated isolators have been demonstrated with 14.7 dB mm−1 isolation in the TE mode [14]. This device is polarization-dependent, and a semiconductor optical amplifier must be used to compensate for loss in the forward direction. However, larger isolation ratios may be achieved by increasing the device length. Recently, isolators based on optical inter-band transitions resulting from spatially and temporally modulated index materials have been proposed [1, 15], though no devices have yet been demonstrated. In Ref. [1], nonreciprocal frequency shifts would be used in conjunction with an optical filter to achieve isolation, while Ref. [15] would rely on a non-reciprocal phase shift with a Mach-Zehnder interferometer.
In this paper, we propose a class of semiconductor waveguide devices which make use of non-reciprocal mode conversion resulting from an electrically-generated spin polarization in non-magnetic materials. By using electrically-generated spin polarization, no external magnetic field is required, vastly simplifying the design of integrated systems. Devices of this nature are intrinsically electrically controlled and could be used for polarization control, modulation and switching, in addition to realizing optical circulators and isolators. We describe the design for a spin-based optical isolator, modulator, and switch. In order to evaluate how well such devices could perform, we consider the effects of waveguide birefringence and absorption and quantify the Faraday rotation due to an electrically-generated spin polarization near the band edge of InGaAs.
2. Basic Operating Principles of a Spin-Based Optoelectronic Device
The spin-based optoelectronic devices proposed here would operate based on controlling the polarization of light. In the context of a waveguide, orthogonal modes (TE and TM) take the place of orthogonal polarization vectors, so that a rotation of the polarization vector manifests as a coupling between orthogonal modes. The presence of an electron spin polarization aligned with the propagation of light gives rise to a non-reciprocal rotation of linearly polarized light for photon energies near the band gap. This effect has its origin in the selection rules for circularly polarized light in zincblende materials [16]. In the presence of a spin polarization along the direction of light propagation, state filling in the conduction band causes the absorption edge of one circular polarization to occur at a higher energy than the other. This differential absorption gives 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 in the absence of magnetic fields and magnetic materials by causing a current to flow in particular directions 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 polarization. While the process which generates this spin polarization is not yet fully understood, it is believed to be related to spin-orbit effects [23,24]. This effect has been observed in a wide variety of materials, including InGaAs [17], ZnSe [22] and GaN [21]. Electrically-generated spin 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 of the device, many optical components become possible. For instance, mode-selective coupling between two waveguides would allow for the construction of an electrically-controlled optical switch. After traveling through an electrically-controlled NRMC region, light would enter a waveguide coupler in which a single mode is transferred to an adjacent waveguide. Incoming light could then be rapidly switched between the two output waveguides based on its polarization after the NRMC region. For polarization control, incoming light of arbitrary polarization could be actively placed into a chosen mode with the use of a feedback circuit before propagating to further optical circuitry. This arrangement would help to compensate for optical fiber which is not, in general, polarization preserving.
A number of potential device designs have been put forth which would use NRMC along with reciprocal mode conversion to achieve isolation and circulation. Two such designs, based on buried core and high mesa waveguide architectures, are summarized in Ref. [4]. In addition to NRMC regions, integrated half wave plates are used to decrease the total Faraday rotation needed to achieve isolation to 45°.
While our proposed device operates in a similar manner to those that use magnetic dopants and an externally applied magnetic field to generate a Faraday rotation [9], it does not require the application of an external magnetic field or the use of magnetic materials since an electric field can be used to generate the Faraday effect. In addition, electric fields have the advantage that they can be controlled locally using patterned contacts and more rapidly than applied magnetic fields.
3. Faraday Rotation and Absorption Measurements
For spin-based optoelectronic devices to be useful, it must be possible to generate a sufficient polarization 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 loss is expected to dominate. Measurements were carried out in a 500 nm n-doped In0.04Ga0.96As epilayer with a doping density of 3×1016 cm−3. 100 μm wide channels connecting ohmic contacts were photolithographically defined and oriented along the [11̄0] direction. For more details on the sample and device, see Ref. [25]. The measurement geometry is summarized in Fig. 1. Current flows through the channel in the e y direction between the two contacts, generating a spin polarization in the plane of the sample. The applied magnetic field B⃗ in the –e y direction causes the e x component of the initial spin polarization to undergo Larmor precession, which gives rise to an out-of-plane component. As the spins precess they dephase with a coherence time . The optical probe traveling in the e z direction then undergoes Faraday rotation, with the angle of rotation proportional to the ez component of the spin polarization per unit area. The linearly polarized probe beam was generated by a mode-locked Ti:Sapphire laser with a repetition rate of 76 MHz and has a FWHM of 15 nm. An AC square wave voltage was applied across the channel for lock-in detection. Assuming a constant rate of spin alignment and subsequent precession around the applied magnetic field, the Faraday rotation signal is odd-Lorentzian in applied field [17], as shown in Fig. 2(a). These data were taken at a temperature of 30 K with an electric field of 5 mV·μm−1 applied along the length of the channel. The data were fit to extract the amplitude of the odd Lorentzian, which is proportional to the product of the rate of spin alignment γ and the coherence time [17].
Fig. 1 Experimental geometry for measurement of Faraday rotation due to current induced spin polarization. In-plane magnetic field B causes spins aligned along −ex to precess out of the sample plane, leading to a rotation of the polarization angle of the probe beam which travels along ez.
Fig. 2 (a) Faraday rotation as a function of applied magnetic field for an applied electric field along [11̄0] of 5 mV/μm at 30 K (solid red line: fit to data). (b) Faraday rotation amplitude per applied electric field (black) and device absorption (red) as a function of wavelength.
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 a probe beam that is perpendicular to the sample plane. An applied magnetic field would not be necessary for devices in which light is propagating in waveguides in the sample plane as the maximum Faraday rotation would occur for zero applied field.
To characterize the wavelength dependence of the Faraday rotation and absorption, the wavelength of the probe beam was varied near the absorption edge. At each wavelength magnetic field scans were fit to determine the amplitude of Faraday rotation, and absorption measurements were taken with an optical power meter. Results are shown in Fig. 2(b). Note that since the measurements were taken using a mode-locked laser, the data is a convolution of the true wavelength-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.
In considering the usefulness of spin polarization as a basis for optical isolation, a figure of merit FOM has been introduced in Ref. [5] as:
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°. Large absorption due to the small detuning of the probe beam from the band gap severely limits the FOM in our InGaAs sample. The largest observed FOM was 7.73 × 10−6 at a wavelength of 848 nm.By comparing Faraday rotation in the case of electrically generated spin polarization to that of optically injected spin polarization it is possible to estimate the degree of polarization in the former case [17]. In the presence of a near-resonant left (right) circularly polarized pump beam, optical carriers will be generated in the ratio of when the pump linewidth is large compared to the heavy hole/light hole splitting. Averaging over pump powers ranging from 172 μW 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 of spin polarization of 1.3 × 10−3.
4. Limitations Imposed by Waveguide Birefringence
In addition to material absorption, nonreciprocal devices based on mode coupling suffer from another design challenge. Polarization mode birefringence in the active region limits the amount of 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 with initialintensity I 0 is given by:
where k is the mode coupling constant, Δ is the mismatch in phase velocities, k TE – k TM, and z is the position along the waveguide in the direction of propagation [26]. The maximum achievable fractional power transfer is plotted in Fig. 3(a) as a function of Δ/k. Figure 3(b) shows Eq. (2) plotted as a function of the dimensionless parameters kz and Δ/k. To achieve a power transfer between modes of 95%, in the case of the highest observed FOM above the waveguide birefringence must be limited to 1.3 × 10−2 cm−1.Fig. 3 (a) Maximum normalized power transfer between modes as a function of Δ/k. A power transfer of 95% requires Δ/k < 0.459. (b) Intensity in an undriven mode coupled to a driven mode at rate k, with phase velocity splitting Δ, plotted as a function of dimensionless parameters 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 presented here, there are reasons to be optimistic about the use of electrically generated spin polarization in integrated nonreciprocal devices. There has yet to be a thorough search of available materials for those with a high degree of current-induced spin polarization. It has been predicted that the magnitude of the electrically-generated spin polarization is proportional to the spin splitting [23,24]. The spin splitting can be modified by varying material composition or strain and by the application of a gate voltage [27–29]. By maximizing the spin splitting, the degree of spin polarization, along with the rate of Faraday rotation and FOM, may be improved. In addition, for devices where ferromagnetic contacts can be used, larger spin polarizations have already been achieved. Recently, a spin injection efficiency of 30% has been demonstrated using ferromagnetic contacts [30]. Such a spin polarization would give rise to a Faraday rotation of 391° cm−1 and an increase in the FOM by a factor of 230 under the assumption that Faraday rotation 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 to achieve nonreciprocal mode coupling in integrated optoelectronic devices. In principle, these devices could provide benefits over competing technologies, including electronic control, simple integration, operation without an externally applied magnetic field and room temperature operation in the proper materials. However, in the InGaAs samples used in absorption and Faraday rotation measurements, we find that absorption far outweighs Faraday rotation. This is a result of the fact that spin polarization induced Faraday rotation is largest near the absorption edge. Further study into the mechanism of current induced spin polarization, potential materials, 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 under Grants No. ECCS-0844908 and No. DMR-0801388 and the Horace H. Rackham School of Graduate Studies. Sample fabrication was performed at the Lurie Nanofabrication Facility, part of the NSF funded NNIN network.
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