Optics Communications

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1 Optics Communications 284 (2) 45 4 Contents lists available at ScienceDirect Optics Communications journal homepage: dynamics in vertical-cavity surface-emitting semiconductor lasers with polarization-selected optical feedback Hiroshi Aoyama a, Shinnya Tomida a, Rui Shogenji b, Junji Ohtsubo b, a Graduate School of Engineering, Shizuoka University, 3-5- Johoku, Naka-ku, Hamamatsu, Japan b Faculty of Engineering, Shizuoka University, 3-5- Johoku, Naka-ku, Hamamatsu, Japan article info abstract Article history: Received 24 August 2 Received in revised form 28 October 2 Accepted 28 October 2 Keywords: Vertical-cavity surface-emitting lasers Polarization Optical feedback Dynamic state maps We study experimentally and numerically the dynamic states of chaotic oscillations in vertical-cavity surface-emitting semiconductor lasers (VCSELs) with polarization-selected optical feedback. We identify the regimes of fully-developed chaotic states, low-frequency fluctuations (s), and coexistent states of s and stable oscillation for the variations of the bias injection current and the optical feedback ratio. In particular, coexistent states of s and stable oscillations are observed at higher optical feedback ratio and lower bias injection current. We draw maps of dynamic states in the space of the bias injection current and the optical feedback ratio. The qualitative agreement between the theory and the experiment is found. 2 Elsevier B.V. All rights reserved.. Introduction Vertical-cavity surface-emitting semiconductor lasers (VCSELs) have many advantages over conventional edge-emitting semiconductor lasers []. For examples, the laser has symmetrical beam profile, single longitudinal mode emission, very low threshold current, and waferscalable integration for laser arrays. Due to anisotropic structures of the laser materials that break a circular transverse symmetry, the output from a VCSEL shows a linearly-polarized oscillation along one of the two orthogonal polarization components (x- and y-polarizations) at a fixed bias injection current. However, the polarization direction of the laser oscillation is changed from the original direction (we here define the y-polarization as the original mode) to the counter one (x-polarization) for the increase of the bias injection current. Such polarization switching often accompanies time-dependent complex dynamics, where the laser exhibits simultaneous unstable oscillations of two polarization modes, polarization hopping, or emission of elliptically polarized light. Polarization instabilities in VCSELs are detrimental for polarizationsensitive laser applications. However, the study of the dynamics is still underway and several efforts have been made to understand the origins and mechanisms of polarization dependent characteristics in VCSELs [ 4]. Though VCSEL usually has a very high facet internal reflectivity of light over 99%, it is still very sensitive to self-optical feedback from external optical components. In addition to similar feedback-induced Corresponding author. Tel./fax: address: tajohts@ipc.shizuoka.ac.jp (J. Ohtsubo). dynamics as observed in edge-emitting semiconductor lasers, VCSEL shows extra instabilities, for example, polarization instabilities depending on the bias injection current, feedback strength, and feedback cavity length. Several experimental and theoretical studies for the dynamics in VCSELs with optical feedback have been reported up to the present [5 6]. Also the dynamics of polarization-selected optical feedback in VCSELs have been studied [7 9]. Unstable oscillation of VCSELs induced by optical feedback is not only the effect, but also stabilization of VCSELs can be attained under certain feedback conditions. Indeed, polarization switching is much suppressed by strong polarization-selected optical feedback for some cases [7,8]. Low-frequency fluctuation () oscillations are typical phenomena in optical feedback instabilities in semiconductor lasers. On the other hand, fast chaotic oscillations, whose main frequency component is almost the same order as the laser relaxation oscillation, are also observable at a higher bias injection current. Another state is a coexistence of unstable and stable oscillations for the time development. However, there exist few reports for coexistent states in VCSELs subjected to optical feedback [3]. While, coexistent states of unstable s and stable oscillations were commonly observed in edge-emitting narrow-stripe semiconductor lasers and broad-area semiconductor lasers subjected to optical feedback [2 22]. The systematic study is still lacked for the dynamics of polarization-selected optical feedback in VCSELs including the occurrence of coexistent oscillations. In this paper, we experimentally investigate the dynamics in VCSELs with isotropic polarization-selected optical feedback. Fast chaotic oscillations, s, and coexistent states are identified depending on feedback strength, feedback cavity length, and bias injection current. We also draw state maps for the dynamics, namely, chaotic oscillations, s, 3-48/$ see front matter 2 Elsevier B.V. All rights reserved. doi:.6/j.optcom.2..99

2 46 H. Aoyama et al. / Optics Communications 284 (2) 45 4 and coexistent states, in the phase space of the bias injection current and the optical feedback strength. In particular, we experimentally identify the areas of coexistent states of and stable oscillations in the phase space, which are also a function of the external optical feedback length. We also conduct numerical simulations for the dynamics by employing a spin-flip model, which is widely used for analyzing VCSEL dynamics and can well represent the dynamic behaviors for both solitary and optical feedback conditions. We obtain the good coincidences between the theory and the experiment. Output Power [mw] Experimental setup The experimental setup is shown in Fig.. A spatially single-mode VCSEL (SONY H5-3-3) that oscillated at a wavelength of 78 nm and a maximum power of 2. mw was used. The bias injection current of the laser was controlled by a stabilized current source driver and the laser temperature was stabilized at 25. C by an automatic temperature control unit. The light-injection current (L-I) characteristic is shown in Fig. 2. The laser at first oscillated at the main polarization mode () above the threshold current of 3. ma, but it switched to the orthogonal polarization mode () at the bias injection current of 5.2 ma. After the switching, the laser stably oscillated at the orthogonal polarization mode. Thus the laser showed a typical polarization switching. Over the measured range of the bias injection current, the laser remained at a single spatial mode, i.e., the lowest spatial Gaussian mode. The laser output was collimated by a lens (CL) and went through a beam splitter (BS). One of the beams was reflected back to the VCSEL together with a polarizer (P), which selected the feedback polarization, and a neutral density filter (NDF), which controlled the feedback fraction. The external cavity length was a variable parameter, which was varied from 3 to 9 cm in the experiment. The other beam was fed into a polarization beam splitter (PBS), and the two polarization components were detected by detectors (D and D2: New Focus, 554-5; bandwidth: 2 GHz) and were analyzed by a digital oscilloscope (OSC: Agilent DSO884; analogue bandwidth: 8 GHz, sampling rate: 4 GSa/s). Two 3 db optical isolators (ISO and ISO2) were used to prevent the reflection from the optical components and the detector surfaces. 3. Experimental results Fig. 3 shows examples of L-I characteristics in the presence of polarization-selected optical feedback. The external mirror was positioned at 9 cm from the laser facet. Fig. 3 and shows the results of y-polarization feedback for the feedback fractions of.5 and 2.% in intensity, while Fig. 3 and shows those x-polarization Fig.. Experimental setup. CL: collimating lens, BS: beam splitter, NDF: neutral density filter, P: polarizer, Ms: mirrors, PBS: polarization beam splitter, ISOs: optical isolators, Ds: detectors, and OSC: digital oscilloscope Fig. 2. Polarization resolved L-I characteristic of solitary laser. feedback for the feedback fractions of.5 and 2.%, respectively. The feedback strength was observed in the external optical loop, so that it was not the exact feedback fraction of light into the laser cavity as will be discussed later in section 5. It is noted that the thresholds are reduced less than that of the solitary oscillation due to the optical feedback. With the increase of feedback fraction in Fig. 3 and, the current at which polarization switching occurs increases (the initial current is 5. ma) and it finally disappears within the observed injection current range at higher optical feedback. Similar results have been reported in the previous papers [7]. The L-I plots are for the mean light intensities so that time variations, which actually exist, are averaged out in these characteristics. In contrast to y-polarization optical feedback, the switching current for x-polarization optical feedback decreases with the increase of the feedback fraction as shown in Fig. 3 and. In Fig. 3, the y-polarization mode, which is the initial main oscillation mode without optical feedback, is completely suppressed over the observed current range and behaves like a non-lasing mode as the time-averaged intensity due to rather stronger x-polarization optical feedback. Fig. 4 shows time-resolved chaotic series in the presence of polarization-selected optical feedback at the bias injection current of 3. ma and the optical feedback length of 4 cm. At this bias injection current, the y-polarization mode is the main oscillation mode. Fig. 4 shows the results for y-polarization optical feedback. When the optical feedback is small enough at.% in Fig. 4, the laser output of the y-polarization mode shows a fast chaotic variation. The counterpart output (x-polarization mode) also shows a chaotic oscillation with anti-phase manner to the y-polarization mode. With the increase of the optical feedback at 3.% in Fig. 4, the output of the y-polarization mode shows typical s and the orthogonal mode exhibits anti-phase oscillations to the y-polarization mode. At the higher feedback ratio of 6.% in Fig. 4, the laser output power shows a different oscillation from ordinary chaotic states or s. Both the polarization modes exhibit oscillations at first, however they suddenly cease and show constant outputs. In this experiment, one state switches to the other after a certain duration and verse visa for the time development and each state lasted for several milliseconds. This phenomenon of the mixture of unstable and stable oscillations is called a coexistent state of chaotic oscillations. Such oscillations are frequently observed in other types of semiconductor lasers [2 22]. Fig. 4 shows the results for x-polarization optical feedback at the bias injection current of 3. ma. Though the original mode of the laser oscillation is the y-polarization mode, the x-polarization mode is strongly excited and the y-polarization mode is suppressed due to x-polarization optical feedback. To compare the oscillations for the y-polarization optical feedback, the same optical feedback ratios as those in Fig. 4 were used. Similar trends of the dynamics with the case of y-polarization optical feedback were observed in Fig. 4, although the roles of the main- and sub-oscillation modes were reversed. For the x-polarization feedback, we also observed

3 H. Aoyama et al. / Optics Communications 284 (2) Output Power [mw] Fig. 3. Experimental L-I curves in the presence of polarization-selected optical feedback. Intensity feedback ratios of.5% and 2.% for y-polarization optical feedback. Intensity feedback ratios of.5% and 2.% for x-polarization optical feedback. coexistent states of unstable and stable oscillations in the case of strong optical feedback. From the observed laser oscillations, we plotted maps of oscillation states for the feedback ratio and the bias injection current. Fig. 5 shows the maps for y-polarization optical feedback at different external cavity lengths of 3, 5, and 9 cm. In the figures, black areas correspond to non-lasing states. The laser shows fast chaotic oscillations as marked all over the region of optical feedback. While states labeled as s encounter for the increase of the feedback ratio even at rather higher bias injection current. Coexistent state labeled by is observed for lower bias injection current and higher optical feedback ratio in the external cavity length at 3 cm. However, coexistent state is never observed for longer external cavity lengths in Fig. 5 and. Fig. 5 shows the results for x-polarization optical feedback. Also similar trends of the state maps as those in Fig. 5 are obtained for the variations of the external cavity lengths at 3, 5, and 9 cm, respectively. For the case of x-polarization feedback, coexistent state is also observed for the external cavity length at 5 cm, although the area is very small. It is noted that the area of coexistent state at the external cavity length of 3 cm is larger than that of y-polarization feedback. 4. Theoretical model As a theoretical model to investigate the dynamics of polarizationselected optical feedback, we employed a spin-flip model [,23,24], by which we can well reproduce the dynamic behaviors of VCSELs, especially sharp polarization switching for the increase or decrease of the bias injection current. For the model of polarization-selected optical feedback, the two orthogonal polarization states of the 5 5 Fig. 4. Experimental time series of polarization-selected optical feedback. Intensity feedback ratios of.%, 3.%, and 6.% for y-polarization optical feedback. Intensity feedback ratios of.%, 3.%, and 6.% for x-polarization optical feedback.

4 48 H. Aoyama et al. / Optics Communications 284 (2) Feedback Ratio [%] Fig. 5. States maps of chaotic oscillations for feedback ratio and injection current. External cavity lengths of 3 cm, 5 cm, and 9 cm for y-polarization optical feedback. External cavity lengths of 3 cm, 5 cm, and 9 cm for x-polarization optical feedback. is chaotic state, s is low-frequency fluctuation oscillations, and is coexistent state of s and stable oscillations. complex field, E x and E y, the total carrier density, N, and the difference of the carrier spin states, n, are written by the following rate equations; de x ðþ t dt h i = κð iαþ fnt ðþ ge x ðþ in t ðþe t y ðþ t γ a iγ p E x ðþ+ t η x E x ðt τþ expðiω x τþ de y ðþ t h i = κð iαþ fnt ðþ ge dt y ðþ+ t inðþe t x ðþ t ð2þ + γ a iγ p E y ðþ+ t η y E y ðt τþ exp iω y τ dnðþ t dt n o = γ N fnt ðþ μg γ N Nt ðþ je x ðþj t + je y ðþj t n o ð3þ iγ N nt ðþ E x ðþe t yðþ E t xðþe t y ðþ t dnðþ t n o = γ dt s nt ðþ γ N nt ðþ je x ðþj t 2 + je y ðþj t 2 n o ð4þ iγ N Nt ðþ E x ðþe t yðþ E t xðþe t y ðþ t where κ is the field decay rate, γ N is the decay rate of total carrier density, γ s is the spin-flip relaxation rate, and α is the linewidth enhancement factor (α-parameter). γ a and γ p are the dichroism and the birefringence of the active layer material, respectively. τ is the round trip time of light in the external cavity, and ω x and ω y are the angular frequency of the laser oscillations for x- and y-polarization modes. η x,y are the feedback ratios and are given by η x;y = pffiffiffiffiffi ð R 2 Þ R pffiffiffiffiffi 3 τ in R 2 ðþ ð5þ where R 2 and R 3 are the intensity reflectivities of the front facet of the laser cavity and the external mirror, and τ in is the round trip time of light within the laser cavity. In the following numerical simulations, either y- or x-polarization feedback is considered, so that η x = for η y, otherwise η y = for η x. In actual numerical simulations, we include the effect of spontaneous emission rate in the rate equations. In the numerical simulations, we used the following parameter values; field decay rate of κ=3 ns, decay rate of total intensity carrier density of γ N =. ns, spin-flip relaxation rate of γ s =5 ns, linewidth enhancement factor of α=3., dichroism of γ a =. ns, birefringence of γ p =45 ns,laserfacetreflectivity of R 2 =.995, and internal round trip time of τ in =.5 ps. The external mirror reflectivity R 3 and the normalized injection current μ=j/j th (where J and the J th are the injection current and the threshold current) are variable parameters. 5. Numerical results Fig. 6 shows the calculated L-I characteristic at solitary oscillation. The injection current at which the polarization switching occurs is μ=.32. This value is rather lower than the experimental switching current of μ exp =.64, however a sharp polarization switching is well reproduced by the numerical simulation. Fig. 7 shows the results of the L-I characteristics in the presence of polarization-selected optical feedback at the external cavity length of 9 cm. Fig. 7 and shows the results of y-polarization optical feedback. It is not easy to simulate an L-I characteristic which is exactly compatible with that of the experiment due to the discrepancies of the parameters between the actual device and the theoretical model. However, we tried to compare the theory and the experiment based on the behaviors of the time series and the dynamic state maps as shown in Fig. 5. For the external optical feedback of.5% in Fig. 7, we could not well reproduce a sharp polarization switch as appeared in the experiment in Fig. 3. However the point

5 H. Aoyama et al. / Optics Communications 284 (2) µ (Injection Current) Fig. 6. Numerical result of polarization resolved L-I characteristic of solitary laser. where the polarization alternation from y- to x-polarization mode occurs shifts toward higher bias injection current, which is consistent with the experimental result. On the other hand, the y-polarization mode is always the main oscillation mode throughout the bias injection current range and only small portion of the x-polarization mode is excited for higher bias injection current in the external optical feedback at.5% in Fig. 7, which is also consistent with the experimental result. Fig. 7 and shows the time-averaged L-I characteristics in x-polarization optical feedback. In Fig. 7, we also cannot observe a sharp polarization switch in the L-I characteristic, however the tendency of the suppression of the y-polarization mode is the same as that in Fig. 3. For the increase of the feedback ratio at.5% in Fig. 7, the time-averaged y-polarization mode is almost suppressed and the x-polarization mode becomes the main oscillation mode. Fig. 8 shows the calculated time series of the laser output power for polarization-selected optical feedback at the bias injection current of. J th and the external cavity length of 4 cm. Fig. 8 shows the results for y-polarization optical feedback, while Fig. 8 shows those for x-polarization optical feedback. The both regimes of y- and x-polarization optical feedback show similar chaotic evolutions as those observed in the experiment in Fig. 4. For a small optical feedback at.5% in Fig. 8 and, the output powers show fast chaotic anti-phase oscillations between the orthogonal polarization modes. For the increase of the optical feedback in Fig. 8 and, anti-phase LLF oscillations are observed between the orthogonal polarization modes. With further increase of the optical feedback at.%, coexistent states are observed both for the regimes of y- and x-polarization optical feedback. These scenarios are quite consistent with the experimental results and can be compared with the time series in Fig. 4. Fig. 9 shows the state maps of laser oscillations for the feedback ratio and the normalized injection current μ in polarization-selected optical feedback. In the plots, black areas again denote non-lasing states. Each dynamic state is labeled as, s, or, which is the same notation as that used in Fig. 5. Fig. 9 shows the results for y-polarization optical feedback at the external cavity lengths of 3, 5, and 9 cm, while Fig. 9 shows those for x-polarization optical feedback. Similar to the experimental maps, the laser shows chaotic states, s, and coexistent states for the increase of optical feedback. However, coexistent states are limited to the range of lower bias injection current. In the numerical simulations, coexistent states are always observable irrespective to the external mirror position, while coexistent states only exist for rather shorter external cavity length in the experiment. It is noted that the area of coexistent states in Fig. 9 shrinks with the increase of the external cavity length, which is compatible with the results of the experiment. As noted in section 3, there are discrepancies of the scales for the feedback fractions between the theoretical calculation and the experimental results (compare Fig. 9 with Fig. 5). One of the reasons comes from the diffraction loss of light on the VCSEL surface due to the collimating lens. Namely, the numerical aperture of the collimating lens was.3 and the measured disk size (light emitting area) of the VCSEL was about 3 μm, so that the actual feedback strength to the laser cavity is roughly estimated as three times less than that observed in the external feedback loop due to the diffraction loss. The other expected losses are the scattering and unwanted losses of light through the optical components, although they are estimated to be smaller than the diffraction loss. Also it is not easy to compare completely the dynamic behaviors between the theory and the experiment, since the laser device parameters used in the numerical simulations were not optimized for those in the experiments. Taking into account these losses, we could obtain a qualitative agreement between the theory and the experiment µ (Injection Current) µ (Injection Current) Fig. 7. Numerical L-I curves in the presence of polarization-selected optical feedback. Intensity feedback ratios of.5% and.5% for y-polarization optical feedback. Intensity feedback ratios of.5% and.5% for x-polarization optical feedback.

6 4 H. Aoyama et al. / Optics Communications 284 (2) Fig. 8. Numerical time series of polarization-selected optical feedback. Intensity feedback ratios of.5%,.5%, and.% for y-polarization optical feedback. Intensity feedback ratios of.5%,.5%, and.% for x-polarization optical feedback. 6. Conclusion We have investigated experimentally and theoretically the dynamics of VCSELs subjected to polarization-selected optical feedback. We studied state maps for the optical feedback ratio and the bias injection current. The dynamic behaviors were categorized into chaotic states, s, and coexistent states depending on the bias injection current and feedback ratio. In particular, we observed coexistent states of oscillations and steady-state output powers at higher optical feedback ratio and smaller optical feedback length in the vicinity of the threshold current. In the coexistent states, one of the two states lasted for the order of ms and it switched to the Injection Current µ Feedback Ratio [%]. 2. Fig. 9. Numerical states maps of chaotic oscillations for feedback ratio and injection current. External cavity lengths of 3 cm, 5 cm, and 9 cm for y-polarization optical feedback. External cavity lengths of 3 cm, 5 cm, and 9 cm for x-polarization optical feedback. is chaotic state, s is low-frequency fluctuation oscillations, and is coexistent state of s and stable oscillations..

7 H. Aoyama et al. / Optics Communications 284 (2) other after the duration. We could numerically reproduce the dynamic evolutions from chaotic states to coexistent states via s with the increase of the optical feedback ratio and we could obtain qualitative agreements between the theoretical and experimental results. In this paper, we only treated the dynamics of isotropic polarization-selected optical feedback in VCSELs. Another scheme of optical feedback is polarization-rotated optical feedback. For example, the y-polarization component of a VCSEL is rotated by 9 and the beam is fed back into the x-polarization component. The study of the dynamics in such a scheme is also an interesting issue as a future investigation. References [] J. Ohtsubo, Seminonductor Lasers: Stability, Instability and, 2nd edition, Springer-Verlag, Berlin, 27. [2] Z.G. Pan, S.J. Jiang, M. Dagenais, R.A. Morgan, K. Kojima, M.T. Asom, R.E. Leibenguth, G.D. Guth, M.W. Focht, Appl. Phys. Lett. 63 (993) [3] B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, G. Verschaffelt, H. Thienpont, I. Verennicoff, J. Opt. Soc. Am. B 6 (999) 26. [4] J. Paul, C. Masoller, Y. Hong, P.S. Spencer, K.A. Shore, Opt. Lett. 3 (26) 748. [5] P.S. Spencer, C.R. Mirasso, K.A. Shore, IEEE Photon. Technol. Lett. (998) 9. [6] A. Valle, L. Pesquera, K.A. Shore, IEEE Photon. Technol. Lett. (998) 639. [7] C. Masoller, N.B. Abraham, Phys. Rev. A 59 (999) 32. [8] M. Sciamanna, C. Masoller, N.B. Abraham, F. Rogister, P. Mégret, M. Blondel, J. Opt. Soc. Am. B 2 (23) 37. [9] T. Ackemann, M. Sondermann, A. Naumenko, N.A. Loiko, Appl. Phys. B 77 (23) 739. [] M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N.B. Abraham, Michel Blondel, Phys. Rev. A 59 (23) 585. [] N. Fujiwara, Y. Takiguchi, J. Ohtsubo, Opt. Lett. 28 (23) 896. [2] Y. Hong, R. Ju, P.S. Spencer, K.A. Shore, IEEE J. Quantum Electron. 4 (25) 69. [3] Y. Hong, K.A. Shore, IEEE J. Quantum Electron. 4 (25) 54. [4] A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, K. Panajotov, Phys. Rev. A 73 (26) 38. [5] H. Lin, Z.J. Lapin, B. Malla, A. Valle, Phys. Rev. A 77 (28) [6] A. Valle, H. Lin, Z.J. Lapin, B. Malla, Phys. Rev. A 78 (28) [7] Y. Hong, P.S. Spencer, K.A. Shore, Opt. Lett. 29 (24) 25. [8] C. Masoller, M.S. Torre, IEEE J. Quantum Electron. 4 (25) 483. [9] Y. Hong, P.S. Spencer, K.A. Shore, J. Lightwave Technol. 24 (26) 32. [2] T. Heil, I. Fischer, Elsäßer, Phys. Rev. A 58 (998) [2] T. Heil, I. Fischer, Elsäßer, Phys. Rev. A 6 (999) 634. [22] Y. Fujita, J. Ohtsubo, Appl. Phys. Lett. 87 (25) 32. [23] M. San Miguel, Q. Feng, J.V. Moloney, Phys. Rev. A 52 (995) 729. [24] J. Martín-Regalado, J.F. Prati, M. San Miguel, N.B. Abraham, IEEE J. Quantum Electron. 33 (997) 765.