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Although it is well accepted that the ultrafast manipulation of spins or magnetization in solid promises potential applications in coherent terahertz (THz) radiation source, spintronics and quantum information processing, their performance is significantly limited by the weak coupling between radiation field and magnetic dipole oscillation. For such ‘weak’ magnetic system, we propose an effective and simple route based on the cavity-based phase modulation technique towards the efficient energy extraction, demonstrated via controlling the magnetic dipole THz radiation generated in the nonlinear Raman process from antiferromagnetic (AFM) NiO. An asymmetric coupled Fabry-Pérot (FP) cavity is constituted by simply placing a metallic planar mirror in the vicinity of a NiO slab. The energy-extraction (THz radiation) can be effectively manipulated by changing the NiO-mirror distance to modulate the phase relation between the magnetic wave and the induced magnetization in NiO. The distinct radiation control can be observed and the experiments are well explained by numerically analyzing the radiation dynamics that highlights the role of phase modulation during the radiation process.
©2011 Optical Society of America
1. Introduction
Magnetic light-matter interaction has recently attracted much attention due to the promising unprecedented optical behaviors. In particular, the ultrafast manipulation of light-spin interaction in solid has triggered intense pursuits not only for the coherent light sources, but also for the future information technologies such as spintronics and quantum computation [1–6]. The manipulation of magnetic resonance at higher frequency have been challenged quite recently, and beautiful results have been demonstrated in antiferromagnetic (AFM) NiO based on the nonlinear Raman conversion process, e.g., the highly coherent terahertz (THz) radiation generated from the ultrafast induced magnetization [7] and the effective coherent control of magnetization benefited from its long coherence time [8,9]. In addition, such magnetic response at close to the optical frequency region also invokes the insightful discussion to reconstruct the framework of conventional electrodynamics [10]. Whereas the tremendous advances, the performance of its further applications is often limited by the weak output power of the induced magnetic oscillation [11]. For such ‘weak’ magnetic system, it is desirable to find an effective and simple route to realize the efficient conversion for the future applications. One strategy of addressing the low-efficiency issue is to engineer the electromagnetic boundary to tune relative phases between the magnetic field and the nonlinear magnetization.
For the efficient conversion with nonlinear process, in bulk crystal, it is required to satisfy the phase matching condition between the electromagnetic (EM) fields and the nonlinear polarization [12], which can be achieved by engineering the refractive-index matching state between the ‘pump’ and ‘output’ beams [13–16]. In the THz regime, the scale of crystal geometry is comparable with or even smaller than the wavelength, therefore the conversion efficiency is sensitive to the crystal geometry, i.e., the position of boundaries, in affecting the phase relation between the EM field and the induced magnetic polarization. Thus, we can expect that, through actively engineering the system geometries, the phase of EM field can be effectively tailored to optimize the phase relation, leading to the efficient energy extraction from the λ-comparable nonlinear media.
Given the Fabry-Pérot (FP) effect induced by the crystal boundaries, changing the crystal thickness is the most straightforward route of phase tuning to obtain optimum output. Unfortunately, the ambition of thickness design often suffers from the emerging issues of absorption loss and the crystal strength. In addition, changing the thickness of prepared-crystal always denotes the complicated additional processing and the high expense. Therefore, it is desirable to seek an effective and simple route to manipulate the relative phases between the EM field and the polarization (or magnetization) for the efficient energy extraction.
In this work, we demonstrate the cavity-based phase modulation towards the efficient energy extraction, via controlling the magnetic dipole (MD) THz radiation generated in the nonlinear Raman process from AFM NiO. An asymmetric Fabry-Pérot cavity is constituted by simply placing a metallic planar mirror in the vicinity of a NiO slab. The manipulation of energy-extraction (radiation) is realized by changing the NiO-mirror distance to tune the phase relation between the magnetic wave and the induced magnetization in NiO. The dynamics of the THz radiation process in the cavity is analyzed to evidence the role of phase modulation in the process of radiation control. This work offers a strong support for the future applications of NiO. Moreover, it provides a clear picture of THz radiation dynamics in a cavity, offering an effective and simple route to extract energy from the intrinsically inefficient nonlinear media based on the cavity-based phase modulation. It also provides deeper understanding for the previous study concerning about the electric dipole cases [17,18]. More importantly, the results demonstrate a direct magnetic dipole coupling to cavity modes. The controlled magnetic light-matter interaction opens a new avenue of enabling the efficient quantum processing by optimizing the coupling between the spin ensembles in magnetic solid and light from designed optical resonators.
2. Experiment
The FP cavity is constituted by simply placing a planar silver mirror in the vicinity of a 100μm thick NiO slab (Fig. 1(b) ). This structure works as a coupled FP cavity, by taking into account the cavity effects from the NiO slab itself and the air gap between the Ag mirror and the lower-boundary of NiO crystal. The separation distance between the NiO and the planar mirror is tuned by using a micro-transition stage. In practice, a piece of powder paper with the thickness of ~30μm is covered on silver mirror to rule out the effect from the reflected laser beam on the NiO radiation. As is shown in Fig. 1(a), THz radiation is measured by free-space electro-optic (EO) sampling technique [19]. A regenerative amplified Ti:Sapphire laser with the central wavelength of 800 nm, pulse duration of 100 fs and repetition rate of 1 kHz is used as the light source. The horizontally polarized laser pulses normally illuminate on the NiO to generate THz radiation and the reflected THz waves from the structure are detected. All of the measurements are performed at room temperature.
Fig. 1 (a) Schematic of the setup for detecting the THz radiation. (b) Schematic of the asymmetric Fabry-Pérot cavity with the tunable distance between NiO and silver mirror; z=z0 is the NiO/air boundary where THz waves emit into free space. (c) Measured time-domain waveform of the radiated THz electric field at different distances of the mirror, forward-radiation of the bare NiO is also plotted for the comparison. The time dependences are vertically shifted for better clarity. (d) Frequency-domain radiation spectra with the various NiO-mirror distances, normalized by the radiation spectrum of bare NiO. Green arrows denote the radiation enhancement when cavity modes overlap with the magnetic resonance of NiO.
Figure 1(c) shows the typical measured time-domain waveform of the radiation THz electric field at different NiO-mirror distances. Spectrum from the forward-radiation of bare NiO is also plotted for the comparison. The structured NiO exhibits the typical oscillations from the cavity effect at the beginning of the radiation pulse, which shifts with the various distances. Importantly, after ~15ps, all of the spectra exhibit the feature oscillation period of ~1ps (~1THz), which can be accounted for the MD radiation from the excitation of magnetization in NiO [7]. One can see that the amplitude of radiated field is strongly dependent on the change of separation distance, the enhancement and inhibition of the THz radiation compared with the bare NiO can both be observed. Based on the Fourier analysis of the time-domain spectra, the frequency-domain THz radiation spectra with the distance varying from 68 μm to 314 μm, normalized by the bare NiO is shown in Fig. 1(d). More clearly, all of the radiation spectra show the fixed radiation peaks at ~1THz, originating from the excitation of magnetization [7]. On the other hand, some small radiation bumps due to the cavity effect can also be seen. It can be anticipated that such cavity modes will shift when the distance is changed. Interestingly, the intensity at ~1THz is found to be dependent on the position of these bump modes, i.e., intensity is enhanced when the small bump modes are tuned to approach the magnetic resonance at 1THz and exhibits the strongest intensity at exactly overlapping, while it is inhibited when the bump modes are tuned to depart from ~1THz. The enhancement ratio of strongest intensity from the cavity structure is ~9 compared with the weakest cavity and is ~3.5 compared with the forward radiation of bare NiO. It should be noted that there is no anti-crossing of the magnetic and FP resonances, because we are in the case of weak coupling here.
3. FDTD calculations
To verify the experimental observation, the dynamics of the ultrafast laser induced magnetization M(z,t), the electric E(z,t) and magnetic B(z,t) fields were calculated by the one-dimensional finite-difference time-domain (FDTD) method. The equations of motion are:
where χ0(z) is the static magnetic susceptibility, Γ(z) the damping coefficient, ω0/2π=1 THz the AFM resonance frequency, ε(z) the permittivity, and μ0 the vacuum permeability. JMNL(z, t) is the magnetization current induced by the stimulated Raman process, and its amplitude is proportional to the incident laser intensity. The refractive index n for this laser is 2.3 and the penetration depth is 60μm. The crystal is assumed to be a slab with χ0 = 4.4×10−4, Γ=40 GHz and ε= 12.25ε0. Outside the slab, χ0 and Γ are zero, and ε=ε0. One end of the computational region at z=0 is set to be a perfect metal to represent the mirror. For the other end at z=zend, non-reflecting boundary condition is used. The parameters used for calculation are from ref [20]. Figures 2(a) and 2(b) show the calculated time- and frequency-domain radiation spectra where the distance between the mirror and the slab is changed. The calculations agree well with the experimental results. Note that the calculation does not take inhomogeneity of the resonant frequency in the crystal and heating process followed by thermal relaxation into account, which can explain the slight discrepancy from the experiments.More calculations are performed to unveil the origin of the radiation control. In fact, the magnetic field strength H(t)=B(t)/µ0-M(t) in such FP cavity structure can be directly evaluated from the classical Maxwell’s equations. For Eq. (1), when we integrated it in a small volume across the interface, the components of H parallel to the boundary is continuous. Therefore, calculations of H with the values of magnetic field B and induced magnetization M at the boundary will help to identify how the THz radiation is extracted from the cavity structure and evaluate how much radiation power goes out from the cavity. Here, the time-domain B(t), M(t) and magnetic field strength H(t) are calculated at the NiO boundary (z = z0 plane, indicated in Fig. 1(b)), where THz waves emit into free space. Two NiO-mirror distances of 156 µm and 114 µm are chosen to represent the on- and off-resonance conditions, respectively.
The temporal lines are plotted in Fig. 3 . As can be seen, the induced magnetization M(z0, t) shows almost the same profile for different NiO-mirror distances, denoting the fixed excitation condition of the coherent magnetic oscillation and we are in the weak-coupling regime. On the other hand, the magnetic field B(z0, t) is highly dependent on the NiO-mirror distance, i.e., for d = 156 µm where we have the emission enhancement, B(z0, t) oscillates out-of-phase with the magnetization M(z0, t), whereas for weaker emission case of d = 114 µm, B(z0, t) and M(z0, t) are in phase. Consequently, the emission control can be described as, when distance is tuned to make the cavity modes couple with magnetic resonance, the magnetic field B(z0, t) is tuned to be out of phase with the induced magnetization M(z0, t) at the NiO boundary, resulting in the stronger magnetic field strength H(z0, t), more energy extraction from the cavity structure and the resulted enhanced emission intensity. The in-phase situation, oppositely, gives the weaker emission intensity. The above calculations directly demonstrate how emitted field is extracted from the cavity structure, illustrating that the radiation field can be modified by tuning the phase relation between the induced magnetization and magnetic field in the process of magnetic coupling. Such mechanism provides a more direct route for the coherent radiation modification, on the basis of its predictable phase of the optically induced magnetization (or polarization in case of electric dipoles).
Fig. 3 Temporal spectra lines of magnetic field (B), magnetization (M) and (H) at NiO boundary with the NiO-mirror distances of 114µm and 156 µm.
To further identify the significance of the cavity-based phase-modulation, FDTD calculations are performed to compare the radiation intensity at 1THz from NiO with various structure characteristics: NiO crystal thickness and NiO-mirror distance. For reference, in Fig. 4(a) , the linear analytical calculation is also performed to identify the on- and off-resonance conditions of this coupled FP cavity by using the following equation obtained based on the transfer matrix method:
where nTHz=3.5 is the refractive index of NiO at 1THz, L the thickness of NiO and d the distance between NiO and mirror. As can be seen in Fig. 4(b), the radiation intensity mapping exhibits a strong dependence on the crystal thickness and the NiO-mirror distance. The profile and locus of the radiation enhancement and inhibition match well with the on- and off-resonance FP modes from the analytical calculation, evidencing the cavity effect on the radiation mediation. For each crystal thickness, we can find the appropriate cavity structures to realize the maximum radiation enhancement or inhibition. The reason of continuously decrease of radiation intensity at thicker crystal is THz-wave absorption in NiO. Together with the intensity of bare NiO, the cavity-induced strongest and weakest intensity at different crystal thickness are extracted and plotted in Fig. 4(c). One can see that bare NiO exhibits the distinct intensity fluctuation with the different thickness, evidencing the effect of cavity-based phase-modulation on the energy out-coupling. It is natural that radiation intensity can be enhanced when cavity length is optimized. However, even in the case of a non-optimized bare crystal, e.g., 100 μm thick crystal in this work, simply placing a planar mirror at a proper distance from the crystal helps to optimize the phase relation and push the out-put coupling efficiency to a high level.Fig. 4 (a) Analytical calculation of on- and off-resonance conditions of the coupled FP cavity. This calculation is performed with the assumption that the permeability of NiO equal to 1. (b) FDTD calculation of the radiation intensity as the function of slab thickness and the NiO-mirror distance, normalized by the intensity of 100 μm thick NiO. (c) Normalized radiation intensity extracted from the best and worst cavity structures at different crystal thickness, forward and backward radiation from bare crystals are also plotted for comparison.
4. Conclusions
In summary, the intensity of coherent THz radiation generated from the excitation of magnetization in AFM NiO has been modified by tuning the separation distance between a NiO slab and a planar metallic mirror. The dynamics analysis evidences the magnetic coupling as the cavity-based phase modulation between the coherently induced magnetization and the propagating magnetic wave. The present work offers a general strategy based on the geometry-based phase modulation for extracting energy from intrinsically inefficient crystal, leading to the novel high efficient THz optoelectronic devices. Besides, in the other frequency regions, this technique also promises the possible utility in ultrashort pulse generation by employing the chirped mirrors which enable the frequency-dependent phase manipulation of reflected beams. Most importantly, this work spurs the quantum information tasks, by the deterministic coupling of spin ensembles in the magnetic solids with light from optical resonators.
Acknowledgments
We thank the valuable discussions with H. Tamaru. This research was supported by the Photon Frontier Network Program, Global COE Program ‘the Physical Sciences Frontier’, Special Coordination Funds for Promoting Science and Technology of the Ministry of Education, Culture, Sports, Science and Technology, Japan, KAKENHI (20104002). N. Kanda and T. Higuchi also thank the Research Fellowships for Young Scientists from the Japan Society for the Promotion of Science.
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