Accurate measurement of the residual birefringence ... - OSA Publishing

Accurate measurement of the residual birefringence in VECSEL: Towards understanding of the polarization behavior under spin-polarized pumping Julien Frougier,1 Ghaya Baili,2,∗ Isabelle Sagnes,3 Daniel Dolfi,2 Jean-Marie George,1 and Mehdi Alouini2,4 1 Unit´ e

Mixte de Physique CNRS-Thales and Université Paris Sud 11, 1 av. Fresnel, 91767 Palaiseau, France 2 Thales Research & Technology, 1 av. Fresnel, 91767 Palaiseau, France 3 Laboratoire de Photonique et de Nanostructures, Route de Nozay, 91460 Marcoussis, France 4 Institut de Physique de Rennes, 263 Avenue G´ enéral Leclerc, 35042 Rennes, France ∗ [email protected]

Abstract: In this paper we report birefringence measurements of an optically pumped (100)-oriented InGaAs/GaAsP multiple quantum well (MQWs) Vertical External Cavity Surface Emitting Laser (VECSEL) in oscillating conditions. The proposed technique relies on the measurement in the microwave domain of the beatnote between the oscillating mode and the amplified spontaneous emission of the cross-polarized non-lasing field lying in the following longitudinal mode. This technique is shown to offer extremely high sensitivity and accuracy enabling to track the amount of residual birefringence according to the laser operation conditions. The experience fits within the broader framework of polarization selection in spin-injected lasers. © 2015 Optical Society of America OCIS codes: (140.7260) Vertical cavity surface emitting lasers; (120.0120) Instrumentation, measurement, and metrology.

References and links 1. I. Zutić, R. Oszwaldowski, J. Lee and C. Gothgen, Handbook of Spin Transport and Magnetism, Chap. 38 “Semiconductor Spin-Lasers,” p. 731–745 (CRC, 2011). 2. M. Holub and P. Bhattacharya, “Spin-polarized light-emitting diodes and lasers,” J. Phys. D: Appl. Phys. 40, R179 (2007). 3. N. C. Gerhardt and M. R. Hofmann, “Spin-controlled vertical-cavity surface-emitting lasers,” Adv. Opt. Tech, Article ID 268949, doi:10.1155/2012/268949 (2012). 4. J. Rudolph, D. Hagele, H. M. Gibbs, G. Khitrova, and M. Oestreich, “Laser threshold reduction in a spintronic device,” Appl. Phys. Lett. 82, 4516 (2003). 5. H. Fujino, S. Koh, S. Iba, T. Fujimoto and H. Kawaguchi, “Circularly polarized lasing in a (110)-oriented quantum well vertical-cavity surface-emitting laser under optical spin injection,” Appl. Phys. Lett. 94, 131108 (2009). 6. S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, “Room temperature circularly polarized lasing in an optically spin injected vertical-cavity surface-emitting laser with (110) GaAs quantum wells,” Appl. Phys. Lett. 98, 081113 (2011). 7. H. Hopfner, M. Lindemann, N. C. Gerhardt and M. R. Hofmann, “Controlled switching of ultrafast circular polarization oscillations in spin-polarized vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 104, 022409 (2014). 8. D. Basu, D. Saha and P. Bhattacharya, “Optical Polarization Modulation and Gain Anisotropy in an electrically injected spin Laser,” Phys. Rev. Lett. 102, 093904 (2009).

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Received 8 Dec 2014; revised 14 Mar 2015; accepted 19 Mar 2015; published 6 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.009573 | OPTICS EXPRESS 9573

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1.

Introduction

In the past decade, a continuous interest and a research effort have been dedicated to the study of spin-injection into semiconductor lasers with vertical geometry [1–12]. In such devices, the spin information carried by the injected electrons is encoded into circular polarization information carried by the emitted photons. This information transfer happens through the optical quantum selection rules for dipole radiation associated with the conservation of angular momentum zprojections mz occurring in confined strained active medium or Quantum Wells (QWs) [13]. Spin-Lasers could provide interesting properties for next-generation optical communication systems such as enhanced bandwidth [14], fast modulation dynamics [15,16], polarization control [17, 18] as well as higher performances with laser threshold reduction [18–20], improved laser intensity and polarization stability. The ideas emerging from spin-lasers and polarization switching may also motivate original device concepts such as spin interconnects [21] or spin information amplifiers [22, 23]. Tremendous accomplishments have been achieved using opti-

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Spin-injector: (2,5nm) MgO/(1,2nm) CoFeB/(5nm) Ta Two switchable perpendicular magnetic states at RT and B=0 T: Bottom Ti/Au electrode

or

Electrical pumping

e-

+ -

σ+

Top Ti/Au electrode

σ+

SWITCH

λ

SWITCH

σDBR

σ-

QWs (l)

External laser cavity (L)

Output mirror

Fig. 1. Conceptual illustration of an electrically spin-injected VECSEL operating at room temperature and magnetic remanence. The external laser cavity (L) is fixed between the bottom Distributed Bragg Reflector (DBR) and the output mirror. We deposit on top of the semiconductor 1/2-VCSEL, close to the active medium, a Magnetic-Tunnel-Junction (MTJ) spin-injector with perpendicular magnetization at magnetic remanence. The role of this spin-injector (here MgO(2.5nm)/CoFeB(1.2nm)/Ta(5nm)) is to spin-polarize the electrons which are electrically injected in the system through a top annular Ti/Au electrode. The spin-polarized electrons then drift from the spin-injector toward the active medium based on multiple quantum wells (QWs). In the QWs, the electrons-holes recombinations are driven by the conservation of angular momentum according to the optical selection rules [13]. Spin-up and spin-down electrons generate left (σ − ) and right (σ + ) circularly-polarized photons respectively. Accordingly, by switching the spin-polarization of the injected electrons, one can control the polarization emitted by the VECSEL.

cally spin-injected monolithic Vertical-Cavity Surface-Emitting Lasers (VCSEL) [4–6]. However, despite impressive technological effort [8, 24], highly efficient electrical spin-injection in VCSEL at room temperature and magnetic remanence remains to be demonstrated. During the last years, we investigated the possibility of spin-injection in Vertical External Cavity Surface Emitting Lasers (VECSEL) based on 1/2-VCSELs. The external cavity of VECSEL enables to deposit an ultra-thin electrical spin-injector perpendicularly magnetized at magnetic remanence [25, 26] close to the active medium (QWs) (≈ 100-200 nm) as illustrated in Fig. 1 [27]. As opposed to previously proposed designs [8, 24], this architecture reduces the distance between the spin-injector and the active medium. Hence, this geometry minimizes the impact of the spin-relaxation mechanisms occurring during electron transport in the semiconductor structure [28–30]. As a direct consequence, an increase of the effective spin polarization degree of the carriers before radiative recombination can be observed in the active medium. The proof-of-concept of such a geometry has already been demonstrated in earlier work using optical pumping [27]. Additionally, VECSEL are pointed out as a technology of choice for beyond state-of-the-art laser light sources, demonstrating wavelength flexibility, high power, high spatial, temporal and polarization coherence, in CW or ultra short pulsed operation, as well as compactness and functionalities. They exhibit a class-A dynamics without relaxations oscilla-

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tions leading to low intensity and frequency noise [31, 32]. With such characteristics they stand out as attractive candidates for microwave-photonics applications [33]. Finally, as there is no preferential guiding for TE or TM modes like in conventional laser diodes, V(E)CSELs provide a relatively good isotropic emission. Nevertheless residual stress [34], lattice strains [35, 36], temperature [37, 38], cavity geometry [39–41] or even lithography processing of VCSELs can break the in-plane symmetry of the device and give rise to linear birefringence in the structure. The influence of dichroism and birefringence on polarization selection in VCSELs has been clearly highlighted by the Spin-Flip Model [42] and its application to basic polarization mode selection for a single mode emission [43]. We recently highlighted experimentally the strong influence of birefringence on the polarization selection of an optically spin-injected 12 (100)-In22% Ga78% As/GaAs95% P5% QWs VECSEL [27]. In spin-injected V(E)CSEL, the polarization of the oscillating mode is governed by the competition between the residual birefringence γ intrinsic to the semiconductor structure and the circular dichroism gain ∆G emerging from the spin imbalance in the active medium. Despite spin-injection using 100% right (σ + ) or left (σ − ) circularly-polarized pumping [13], we witnessed a locking of the laser on linearly-polarized modes due to the inherent residual birefringence. For our (100) InGaAs/GaAsP QWs VECSEL, the birefringence sets the linear ¯ (TE) with a preferential selection for the [110] ¯ polarization axis along [110] (TM) and [110] direction at threshold. In order to push forward our understanding of the competition between the birefringence γ and the circular dichroism gain ∆G generated in optically spin-injected VECSEL, it is necessary to accurately quantify the birefringence in the structure. In this paper, we report the birefringence measurements of the 12 (100)-In22% Ga78% As/GaAs95% P5% QWs 1/2-VCSEL used in our previous spin-injection experiment [27]. Even though the experiment is conducted in the framework of our research on spin-injection in VECSELs, here we do not focus on the optimization of the spin-injection through pure circularly-polarized pumping. The goal is to precisely quantify the effective birefringence of the semiconductor chip driving the polarization selection in the laser. The measurements are performed with a pump polarization given by the default polarization of the edge-emitting laser diode i.e. slightly elliptical. Accordingly, the spin polarization of the optically-injected carriers can be neglected. In a semiconductor structure, the birefringence emerges from the difference of refractive indexes ∆n = ne − no between the ordinary (no ) and extraordinary (ne ) axis. In this paper, we define the birefringence γ as the dephasing for a round-trip in the laser cavity associated with this difference of refractive indexes ∆n:

γ=

4π · (ne − no ) · l λ

(1)

where λ is the laser wavelength and l is the physical thickness of the birefringent element. In V(E)CSELs, the birefringence triggers a lift of degeneracy between the TE and TM modes resulting in a frequency splitting ∆ν of the two polarization modes. We demonstrate (see section 2) that the birefringence γ relates to this frequency shift ∆ν as follow:

2Lopt γ = · ∆ν 2π c

(2)

where Lopt is the average optical length of the laser cavity. Thus, measuring the frequency shift ∆ν between the cross-polarized TE and TM modes enables to quantify the birefringence γ of the V(E)CSELs. Several measurements of ∆ν have already been reported in the literature for electrically pumped monolithic VCSELs. Different experimental setups were used: #229241 - $15.00 USD (C) 2015 OSA


planar Fabry-Perot Interferometers (FPI) [44, 45], Polarization Beat Technique (PBT) [45], Polarization Noise Fitting (PNF) [46], Reflectance Difference Spectroscopy (RDS) [47, 48], Photo-Current Difference Spectroscopy (PCDS) [49] and Polarized Electro-Luminescence (PEL) [50]. The technique implemented in reference [46] is based on the measurement of the VCSEL’s polarization noise. The phase anisotropy parameters are then extracted by fitting noise spectra. In this paper, we report what is to our knowledge the first birefringence measurement of a VECSEL using the polarization beat technique [45]. This method is based on the analysis of the polarization-resolved intensity noise after projection of the TE and TM modes on the same optical axis using a polarizer. Compared to the more straightforward FPI technique, this setup offers the higher spectral resolution required to perform the ∆ν measurements in VECSELs. As an example, Hendriks et al. performed birefringence measurements of 3-GaAs-QWs VCSELs in the optical domain using a noise-eater to improve the stability of the laser pump combined with a planar FPI [45]. The FPI exhibited a Free Spectral Range (FSR) of 29.3 GHz, a finesse F ≈ 100 and accordingly a maximal resolution R = 293 MHz R = FSR F . The spectral resolution of such FPI is sufficient to measure a frequency shift between the TE and TM modes of few GHz in monolithic VCSELs with micro-metric cavities length. However in the case of VECSELs with long cavities (cm) the frequency shift is expected to be as low as few MHz. Consequently the spectral resolution of such FPI is not sufficient. To overcome this limitation we transferred the optical frequency shift between the two TE and TM modes into the electrical domain by measuring the beatnote between the oscillating TE mode and the Amplified Spontaneous Emission (ASE) lying in the cross-polarized TM mode. In comparison to the PBT experiment reported in [45] on a 21-GaAs-QWs VCSEL, the measurement technique has been slightly modified in order to improve the signal to noise ratio (SNR). Firstly, the 1/2-VCSEL is implemented in an external cavity with class-A dynamics, ensuring shot-noise operation over a wide frequency bandwidth. Secondly, the frequency shift is measured around the laser FSR in order to get rid of Coherent populations Oscillations effects (CPO) [51] which might modify the measured frequency shift. 2.

Theoretical analysis

In this section, we aim at demonstrating the relationship between the frequency shift separating the TE and TM modes and the birefringence γ of the 1/2-VCSEL. We consider the general case of a VECSEL emitting on the TE mode linearly-polarized along the extraordinary-axis while the spontaneous emission of TM mode linearly-polarized along the ordinary-axis is amplified by the cavity but still below threshold [Fig. 2(a)]. In the model, we assume that the birefringence of the active medium (12 strained QWs distributed over 13λ /2) dominates in the structure and we neglect the influence of the DBR’s birefringence. The average optical length of the laser cavity is Lopt = L + nl, ¯ L being the cavity length without the active medium and l the thickness o of the active medium (L = 0 for a monolithic VCSEL). n¯ = ne +n is the average optical index of 2 the birefringent active medium. ne and no are the refractive indexes seen along the extraordinary and ordinary axis respectively. λ defines the laser wavelength and c the celerity of light. We choose to identify the frequencies in the optical domain as ν and the frequencies in the electrical domain as f . Accordingly, the optical frequencies associated with the polarization TE and TM modes at the order p and q respectively are given by:

 p c   νT E = p · 2 (L + n · l) e c q   νT M = q · 2 (L + no · l) #229241 - $15.00 USD (C) 2015 OSA

(3)


(a) Optical spectrum

(b) Optical spectrum

(c)

(After projection on the same optical axis)

(Raw emission)

Oscillating mode TE

(f1 = νTEp+1 – νTEp)

order p

f1 = νTEp – νTEp-1

order p

νTEp

order p-1 TE p-1 νTE

order p+1 TE p+1 TM

TM

νTMp

νTMp-1

Δν

Δν FSR

RF spectrum (Electrical domain)

νTE

TM

νTMp+1

Optical Frequency (ν)

order p-1

order p+1

TE

νTEp

νTEp-1

TE TM

νTMp-1

Δν

TM

νTMp

Δν FSR

f2 = νTEp – νTMp-1

νTEp+1

f3 = νTMp+1 - νTEp

TE TM

νTMp+1

Optical Frequency (ν)

0

Δf

Electrical Frequency (f)

Fig. 2. Optical and electrical mode spectra: (a) Optical spectrum emitted by the laser. For a given mode, the frequency shift between two adjacent orders is equal to the Free Spectral Range (FSR) of the cavity. (b) Corresponding optical spectrum after projection on the same polarization axis using a polarizer. (c) Associated electrical spetrum after quadratic detection by a photodiode of the projected optical spectrum at 45◦ .

However, as the birefringence is expected to be relatively small, the order p and q are equals. Hence, the system of Eqs. (3) becomes:

 c p   νT E = p · 2Le c   νTpM = p · 2Lo

(4)

where Le = L + ne · l and Lo = L + no · l are the optical lengths seen by the modes polarized along the extraordinary (TE) and the ordinary (TM) axis respectively. After projection of the two ordinary and extraordinary optical spectra on the same polarization axis [Fig. 2(b)], we focus on the associated RF spectrum [Fig. 2(c)]. In the electrical domain, the corresponding spectrum displays beatnote frequencies between the different optical modes. On Fig. 2(c): (i) the central peak (light blue) corresponds to the beatnote frequency f1 between the lasing TE mode at the order p (optical frequency νTpE ) and the ASE of the TE mode at the order p-1 (optical frequency νTp−1 E ). It is important to note that the beatnote frequency f 1 also arises from the beating between the lasing TE mode at the order p and the ASE of the TE mode at the order p+1 (optical frequency νTp+1 E ). (ii) On the other hand, the satellite peak f 2 (purple) corresponds to the beatnote frequency between the lasing TE mode at the order p (optical frequency νTpE ) and the ASE of the TM mode at the order p-1 (optical frequency νTp−1 M ). Similarly, the satellite peak f3 (purple) corresponds to the beatnote frequency between the lasing TE mode at the order p (optical frequency νTpE ) and the ASE of the TM mode at the order p+1 (optical frequency νTp+1 M ). Obviously, the beatnote between the lasing TE mode and the nonlasing TM modes at the order p is also present in the low frequency part of the spectrum. However, we do not rely on this peak for our measurements because it suffers from pump to laser noise transfer as well as from CPO effects that cannot be neglected for beatnotes below 1 GHz [51]. The above different frequencies read:

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c f1 = νTpE − νTp−1 E = 2Le pc 1 1 c = f2 = νTpE − νTp−1 · − + M 2 L L 2L e o o      pc 1 1 c p p+1   f 3 = νT M − νT E = + · − 2 Lo Le 2Le        

(5)

Using Eq. (5), we further calculate the frequency shifts f1 − f2 and f3 − f1 between the central peak ( f1 ) and the left ( f2 ) and right ( f3 ) satellite peaks respectively [Fig. 2(c)]:

 1 1 c    f1 − f2 = 2 (1 − p) · L − L e o  1 1 c   f3 − f1 = (1 + p) · − 2 Lo Le

(6)

The difference of refractive indexes ∆n = ne − no can then be extracted from Eq. (6):

∆f =

( f1 − f2 ) + ( f3 − f1 ) pc l lνo = · · ∆n = · ∆n 2 2Lo Le Le

(7)

where ∆ f is the frequency shift between the central ( f1 ) and satellite ( f2 , f3 ) beatnotes. By definition, the dephasing γ associated with ∆n for a round-trip in the laser cavity can be expressed as:

γ=

4π · l · ∆n λ

(8)

Finally, we can express the birefringence γ as a function of ∆ f using the expressions given by Eq. (7) and Eq. (8):

2Lopt γ = ·∆f 2π c

(9)

This relation is established for a round-trip in the cavity. In the particular case of VECSELs with long external cavities: l