Stability of a monolithic integrated filteredfeedback

Transcription

1 Stability of a monolithic integrated filteredfeedback laer Jing Zhao, 1,* Daan Lentra, 1 Rui Santo, 1 Michael J.Wale, 2 Meint K. Smit, 1 and Xaveer J.M. Leijten 1 1 COBRA Intitute, Photonic Integration Group, Eindhoven Univerity of Technology, P.O. Box 513, 56MB Eindhoven, the Netherland 2 Oclaro Inc., Cawell, Towceter, Northamptonhire, NN12 8EQ, UK * j.zhao@tue.nl Abtract: We experimentally and theoretically invetigate the tability of a ingle-mode integrated filtered-feedback laer a a function of the electrically controlled feedback phae. We interpret the meaurement in term of feedback-induced dynamic, compare them with the reult from a tability analyi model for conventional feedback, and find good qualitative agreement. 212 Optical Society of America OCIS code: (14.346) Laer; (23.312) Integrated optic device. Reference and link 1. C. H. Henry, Phae noie in emiconductor laer, J. Lightwave Technol. 4(3), (1986). 2. S. Bauer, O. Brox, J. Kreil, B. Sartoriu, M. Radziuna, J. Sieber, H. J. Wünche, and F. Henneberger, Nonlinear dynamic of emiconductor laer with active optical feedback, Phy. Rev. E Stat. Nonlin. Soft Matter Phy. 69(1), 1626 (24). 3. J. Zhao, P. J. William, M. K. Smit, and X. J. M. Leijten, Monolithic integrated filtered-feedback multiwavelength laer, in Proc. Optical Fiber Communication Conf. (OFC 212), Lo Angele, USA, Mar. 4 8, 212, Paper OW1G E. Kleijn, M. K. Smit, M. J. Wale, and X. J. M. Leijten, New two-port multimode interference reflector, in Proc. 16th Eur. Conf. Int. Opt. (ECIO 12), Sitge-Barcelona, Spain, Apr.18 2, (212). 5. M. Youefi and D. Lentra, Dynamical behavior of a emiconductor laer with filtered external optical feedback, IEEE J. Quantum Electron. 35(6), (1999). 6. G. H. M. Van Tartwijk, Semiconductor laer with optical injection and feedback, Thei Amterdam, 76 8&88 9 (1994); ee alo J. Quantum Semicla. Opt. 7, (1995). 7. G. A. Acket, D. Lentra, B. H. Verbeek, and A. J. Den Boef, The influence of feedback intenity on longitudinal mode propertie and optical noie in index-guided emiconductor laer, IEEE J. Quantum Electron. 2(1), (1984). 8. J. Mork, B. Tromborg, and J. Mark, Chao in emiconductor laer with optical feedback: Theory and Experiment, IEEE J. Quantum Electron. 28(1), (1992). 9. S. H. Strogatz, Nonlinear dynamic and chao: with application to phyic, biology, chemitry, and engineering, (Pereu Book, Addion-Weley Publihing, 1994). 1. D. Lentra, B. H. Verbeek, and A. J. Den Boef, Coherence collape in ingle-mode emiconductor laer due to optical feedback, IEEE J. Quantum Electron. 21(6), (1985). 11. G. Liu, X. Jin, and S. L. Chuang, Meaurement of inewidth enhancement factor of emiconductor laer uing an injection-locking technique, IEEE Photon. Technol. Lett. 13(5), (21). 12. I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, Locking bandwidth and relaxation ocillation of an injection-locked emiconductor laer, IEEE J. Quantum Electron. 24(2), (1988). 1. Introduction Single-wavelength laer with narrow linewidth are required in many photonic application field, e.g. in optical communication and ening. One way to realize uch laer i by utilizing feedback from an external mirror. Although the introduction of delayed optical feedback can be diadvantageou a it may caue intabilitie to the laer like the undamping of relaxation ocillation and coherence collape, under uitable condition it can improve particular feature of the laer, uch a enhanced ide mode uppreion and linewidth narrowing [1]. # $15. USD Received 1 Oct 212; accepted 7 Nov 212; publihed 29 Nov December 212 / Vol. 2, No. 26 / OPTICS EXPRESS B27

2 Many emiconductor external-cavity laer with different feedback configuration have been reported, where mot of them have external cavitie outide the chip and the external cavitie are much longer than the olitary cavity. Unlike the free-pace or fiber-coupled feedback laer ytem, the external cavity of an integrated feedback laer i on-chip and with mall footprint. Compared to an off-chip cavity, the external cavity i at leat two order of magnitude horter, implying better tability, better reproducibility from batch to batch and operation on fater time cale. Here we preent the reult of a theoretical and experimental invetigation of the tability of a monolithically integrated filtered-feedback laer with electrically controlled feedback phae, which i part of a multi-wavelength laer device. A relevant earlier tudy involving a multi-ection laer with phae control i publihed in [2], but it applie to a coupled-cavity laer in the trong coupling limit, wherea our laer operate in the weak-feedback regime, where external cavity mode are non-exitent. In our device, each laer channel operate in ingle wavelength, which ha been achieved by the preence of an arrayed waveguide grating (AWG) filter within the external feedback ection. The experimental tability tudy i obtained by the analyi of the optical and electrical pectra, while the theoretical tudy i baed on a rate equation approach for a ingle-mode laer with conventional external feedback and lead to reult that are in good agreement with experimental finding. 2. Device decription The laer we invetigate here i one channel of an integrated filtered-feedback 4-channel multi-wavelength laer (MWL) with channel pacing of 2 GHz and operating in the C- band, a reported by ome of u earlier [3]. The operation principle of thi MWL can be undertood from it chematic repreentation in Fig. 1(a). The device conit of an array of four Fabry-Pérot (FP) laer, each of which i formed by a emiconductor optical amplifier (SOA) and two on-chip broadband multi-mode interference reflector (MIR) [4] a FPmirror. The MIR provide reflection and tranmiion to and from the laer cavity. The phyical length of each FP-cavity i 82 mm. One ide of each FP-laer i connected to one common arrayed-waveguide grating (AWG) filter through a phae hifter, all on a ingle chip (Fig. 1(b)). Each FP-laer generate a broad pectrum of longitudinal mode, of which the pacing i determined by the FP-cavity length. The AWG multiplexe the light of the FP-laer channel and connect to another on-chip broadband reflector. Thi reflector will reflect the light and ubequently the AWG will demultiplex and route the reflected ignal back to each original FP laer. Only the FP-mode with wavelength within the correponding AWG pa band will have ufficiently low feedback-reduced lo to uppre all other longitudinal mode through gain competition. Hence, each laer will be operating in a ingle mode and the wavelength pacing between the laer i determined by the pacing of the AWG pa band, 2 GHz in thi cae. Thu, the AWG together with the external reflector effectively form an external feedback ection for each FP laer, a hown in Fig. 2. The phae hifting ection (PHS, ee Fig. 1(a)) allow to individually control the feedback phae for each FP-cavity. Each FP-laer ha 49.5 GHz mode pacing, and the two-port MIR forming the cavity have power reflectivity and tranmittivity of R = T = ~.32. The feedback ection i formed by a common 1-port MIR with ~8% reflectivity [4], a ingle AWG channel and a eparate phae hifter for each channel. In the following example we will how recorded pectra for a laer channel that ha an external cavity of ~3. mm phyical length. The AWG i etimated to have 5 db lo per pa. The forward-biaed phae hifter i.35 mm long with negligible lo and phae-hift efficiency of 15 degree per ma per pa, which wa meaured from a tet tructure with a Mach-Zehnder configuration. Including the waveguide and AWG loe back and forth, the effective trength of the feedback i etimated to be 2% of the light tranmitted to the external cavity. # $15. USD Received 1 Oct 212; accepted 7 Nov 212; publihed 29 Nov December 212 / Vol. 2, No. 26 / OPTICS EXPRESS B271

3 SOA SOA SOA SOA λ 4 λ 3 λ 2 λ 1 PHS PHS PHS PHS SOA4 SOA3 SOA2 SOA1 Reflector AWG (a) (b) Fig. 1. (a) Schematic of the device and (b) Microcopy photograph of the realized device. The chip dimenion are approximately mm. Fig. 2. Schematic of one channel: a FP laer and the external cavity with phae hifter inide; On the bottom, ketche of pectra feature are hown: FP mode (left) and the AWG paband (right). 3. Theory and model The laer under tudy are ubject to filtered feedback [5]. The filtering i achieved by the preence of the AWG. The main purpoe of the AWG i to provide lightly reduced lo for the longitudinal mode that fall within a certain channel, o a to force that laer to operate in one particular mode. A the effective width (3-dB paband) of the AWG pa band filter i ~5 GHz and the laer operate in a ingle mode, while the feedback- induced frequency change i below ~2 GHz, the feedback can be modelled a conventional feedback [6], which implifie the treatment and lead to good qualitative agreement with obervation. iφ( t) + iωt We will expre the optical field inide the laer cavity a Pte () + cc., where the power P and the phaeφ depend lowly on time on the cale of the rapid ocillation implied by the optical frequency ω of the olitary laer. The power i in dimenionle unit, uch that P i the number of photon in the cavity. The variable characterizing the gain i the lowly time-dependent number of electron-hole pair N () t, taken with repect to it threhold value for the olitary laer (i.e. without feedback). In term of the three variable P, φ and N, the equation decribing the time evolution of the laer in the preence of feedback are P = ξnp + 2 γ P( t) P( t τ )co[ φ( t) φ( t τ) + ωτ]; (1) 1 Pt ( τ ) φ = αξn γ in[ φ ( t ) φ ( t τ ) + ωτ ], (2) 2 Pt ( ) N = ( 1 + ξ P) N Γ( P P). T (3) 1 whereξ i the linearized gain coefficient at threhold; γ i the feedback rate, defined a [6] # $15. USD Received 1 Oct 212; accepted 7 Nov 212; publihed 29 Nov December 212 / Vol. 2, No. 26 / OPTICS EXPRESS B272

4 2 rext (1 r ) γ = (4) τ r with r ext the (amplitude) reflectivity of the external mirror, r the (amplitude) reflectivity of the laer mirror and τ in the internal roundtrip time of the laer cavity. The parameter τ i the feedback delay time and α the linewidth-enhancement factor; T 1 i the effective carrier lifetime for pontaneou recombination at threhold, Γ the cavity decay rate (invere photon lifetime) and P the olitary laer power, given by [6] in J J P thr = Γ where J thr i the olitary threhold current (in unit of electron per econd). Thi complete the model for the dynamical decription of the laer with feedback ection. In the next ection we will tudy the teady-tate olution to the rate Eq. (1)-(3), followed in ec.3.2 by a tability analyi for the correponding tationary tate. 3.1 Stationary tate Single-frequency laer operation correpond to olution of Eq. (1), (2) and (3) atifying (5) P = P ; N = N ; φ =Δ ω t (6) where P, N and Δω are time independent. Thi yield Δ ω = γ + α α + ωτ +Δ ω τ (7) 2 1 in(arc tan ), 2γ = co( +Δ ωτ ), (8) ξ N ωτ P N P Γ = 1 T 1. (9) ξ N + Γ Firt, the frequency hift Δω i numerically olved from Eq. (7). It wa hown by Ref [7]. 2 that, o long the feedback trength atifie C γτ 1+ α < 1, only one ingle olution to Eq. (7) exit. Subtituting thi olution in Eq. (8) yield a value for N, where after the value for P can be evaluated with Eq. (9). Thu we obtain for each etting of the laer, determined by the value of the feedback phae delay ωτ and the olitary laer power P, a et of value for Δ ω, N and P. It i important to note that the applied phae φ p in the phae hifting element will be accounted for in ωτ a well (ee below, at the end of Sec.3.2). 3.2 Stability Now the iue at take i that the tationary tate defined by Eq. (7), (8) and (9) i not alway table. It i known that the tranition from table to untable operation i aociated with a ocalled Hopf bifurcation, which indicate the birth of an undamped relaxation ocillation (RO) [6,8]. If thi happen, there are, among other, the following poible cenario: # $15. USD Received 1 Oct 212; accepted 7 Nov 212; publihed 29 Nov December 212 / Vol. 2, No. 26 / OPTICS EXPRESS B273

5 1) A elf-utained harmonic RO ha appeared, notable a ocillation in P, N and φ, at a frequency approximately given by with typical value ranging from 1 to 1 GHz. 1 νr = ξ( J Jthr ) (1) 2π 2) The ocillation period may double (frequency halve), often referred to a perioddoubling bifurcation [9]. 3) A the amplitude of the RO increae, higher harmonic appear. 4) The ocillation turn chaotic; in cae the chao i fully developed thi tate of operation i alo referred to a coherence collape [1]. The tability of the tate characterized by Eq. (7)-(9) i invetigated by conidering mall deviation, i.e. putting φ =Δ ω t + δφ; N = N + δn ; P = P + δp. (11) After ubtituting Eq. (11) in Eq. (1)-(3) and Eq. (7)-(9) we obtain, in lowet order, three coupled firt-order differential delay equation for δφ, δ N and δ P, which are analyzed for t olution with time dependence e for complex-valued. Thi lead to a ytem determinant with zeroe in the complex -plane. If at leat one zero ha a poitive real part, the correponding olution Eq. (7)-(9) i untable. Thi ha been invetigated uing the principle of the argument. In thi manner, we have obtained a tability diagram for a laer with delayed feedback indicating whether the laer i table or untable a function of the applied feedback phae φ p (between and 2π ) and the applied pump trength p, where the latter i defined a p ( J Jthr )/ Jthr. The tability diagram i diplayed in Fig. 5(b) of Sec.5.2. Here, the total effective feedback phae ha been taken a ωτ = φp + ω i pi thrτ, where ω i i the (empirical) injectioncurrent-induced frequency hift per ma injection current and I thr i the threhold injection 3 current (in ma), i.e. I thr = 1 qjthr, with q the unit charge. We clearly oberve tilted band of tability and intability, repectively, which connect at 2π. The negative lope of the band i due to the negative current-induced frequency hift of the olitary laer (ee the text pertaining to Fig. 5 in Sec.4). 4. Characterization of the device The meaurement etup i depicted in Fig. 3. The device we invetigated i one channel of the integrated filtered-feedback multi-wavelength laer with external cavity length ~3. mm. The laer chip i mounted on a copper chuck and it temperature i tabilized at 18 C during the meaurement. At thi temperature the laer ha a threhold current of 16 ma. The electrical current applied to the SOA and to the phae hifter, repectively, are provided through two probe needle. A lened fiber mounted on a nano-poitioning tage i ued to collect the light. An optical iolator i ued to avoid the unwanted back reflection into the laer chip. The light # $15. USD Received 1 Oct 212; accepted 7 Nov 212; publihed 29 Nov December 212 / Vol. 2, No. 26 / OPTICS EXPRESS B274

6 Ipump Iphae PD DC BLOCK LASER CHIP TEC ISO 5% 5% ESA Fig. 3. The meaurement etup. I pump i the laer injection current, and I phae i the current on the phae hifter to tune the feedback phae; TEC denote the temperature controller; ISO i an optical iolator. After the 5/5 coupler, one of the two branche of light i fed to a 5 GHz photodiode, amplified by a low noie amplifier (LNA) and meaured with an electrical pectrum analyzer, while the other branch connect to an optical pectrum analyzer. i analyzed uing a 5 GHz bandwidth photodetector with an 8 GHz 3 db gain low noie amplifier connected to a 5 GHz electrical pectrum analyzer [Agilent E4448A]. A fraction of the light i ent to an optical pectrum analyzer [APEX AP241B] with a high reolution of.16 pm. 4.1 Spectral laing regime Firt, the phae hifter i unbiaed, and the SOA injection current i varied until the laer how a table ingle wavelength laing mode. Then keeping the injection current fixed to that value, the feedback phae hift i lowly wept from to 21 by tep of 15. The optical ignal and the noie intenity ignal are recorded only when there i a clear change in the ignal appearance, and preented in Fig. 4. Strong dynamic have been oberved for certain feedback phae condition, and the ize of thi region varie with the injection current level applied to the SOA. The reult preented in Fig. 4 are obtained by applying a fixed current of 72 ma to the SOA. When there i no extra phae hift applied to the feedback, the laer i very table emitting ingle wavelength with narrow linewidth, where the latter could not be reolved by the.16 pm reolution of the OSA (<2 MHz). The electrical pectrum (Fig. 4(a)) preent a flat and relatively low repone. The relaxation ocillation (RO) frequency i damped below the noie level of the pectrum analyzer. With the feedback phae tuned to 9 (Fig. 4(b)), the laer i not table anymore. The RO become undamped and it i identified a a narrow peak in the electrical pectrum at 6.8 GHz, while in the optical pectrum two erie of ide peak appear at ditance equal to multiple of the RO-frequency on both ide of the central peak. When the phae i increaed (Fig. 4(c)), the laer enter a period-doubling regime, identified by more ide peak in the optical pectrum and a new peak at half the RO frequency in the electrical pectrum. In the next three cae, Fig. 4(c)-4(e), the RO ha developed into a more complicated and ultimately irregular ocillation indicating period doubling and higherharmonic effect, but with the dominant frequency near the RO frequency. Gradually, after entering the intability region, the noie floor increae ignificantly, a een in the noie intenity pectra and optical pectra. The lat cae preented in Fig. 4(e) (ϕ = 21 ) how coherence collaped operation [1] dominated by relaxation ocillation. The different laing regime with different feedback phae are very reproducible. To get a clearer picture of the overall tability of our filtered-feedback laer, the ame phae tuning procedure i repeated for all injection current above threhold, with a tep of 2 ma. The ituation a in Fig. 4(a), ingle wavelength laing with no relaxation ocillation dynamic, i conidered a table. We have identified uch table region and made a tability map plotted in Fig. 5(a). The map diplay the laer tability a a function of the feedback phae (horizontal) and injection current (vertical), where white indicate tability and black indicate intability, which include all other untable regime. With injection current increae, the laer demontrate different table region. The location of thee region change with changing feedback phae. Unfortunately, the full 2π phae hift could not be achieved, OSA # $15. USD Received 1 Oct 212; accepted 7 Nov 212; publihed 29 Nov December 212 / Vol. 2, No. 26 / OPTICS EXPRESS B275

7 becaue the phae hifter tart to aturate at current beyond ~7 ma and i fully aturated at 1 ma (Fig. 5(a)), thu limiting the maximum feedback tuning to 21. Fig. 4. Intenity noie (dahed line) and optical pectral (olid line) from the ESA and OSA, repectively, for different feedback phae tuning, 9, 15, 18, Stability analyi A wa mentioned in Sec.3.2, we have applied a numerical tability analyi to the laer with feedback by invetigating the dynamical ytem determinant. Uing the value α = 2.6 for the linewidth enhancement factor, a obtained from injection locking meaurement (ee Appendix A), and the external cavity length and lo etimated a above, we find for the cae of injection current of 72 ma (pump trength p~3) that over a phae range interval of about 1 the ingle frequency operation i table, wherea it i untable for other value of the applied feedback phae. Apparently, Fig. 4(a) i within thi tability interval. # $15. USD Received 1 Oct 212; accepted 7 Nov 212; publihed 29 Nov December 212 / Vol. 2, No. 26 / OPTICS EXPRESS B276

8 Fig. 5. (a) Meaured map of laer tability veru phae hifter current with different injection current. The dark region i the untable region and the bright region i the table region. (b) Theoretical tability diagram for a ingle-mode laer v. pump trength p (vertical) and feedback phae (horizontal), with p defined a p = ( J J thr )/ J thr. Color white denote table 9 1 operation; black denote untable. Parameter are: feedback rate 5 1 ; feedback delay time and α = 2.6 ; the injection-current-induced frequency hift of the olitary laer i.6 GHz/mA. The mot left column give the relaxation ocillation frequency in GHz. Figure 5(b) i the tability map generated from the theoretical model. The tability ituation i recorded a a function of the feedback phae (-2π; horizontal axi) and pump trength (injection current from threhold up to 8 ma, p = 4). The parameter value ued for thi diagram are given in the caption. It i to be noted that zero phae on the horizontal cale in Fig. 5(b) i arbitrary; it doe not necearily coincide with zero current in Fig. 5(a). Comparing thi with the meaured map Fig. 5(a), the tructure of table and untable band with negative lope how good qualitative agreement between experiment and theory, although theory predict wider untable band. The lope i due to the injection current induced phae hift inide the FP laer cavity. 5. Dicuion and concluion An integrated laer with a filtered-feedback configuration ha been realized. The external cavity i integrated on the chip and the phae of the feedback can be controlled via an integrated phae hifter. We have meaured the laer feedback dynamic a a function of the feedback phae and injection current. By changing the feedback phae, the laer can be et to operate in a table ingle-frequency tate a well a in variou untable tate. Comparion of the meaurement with the reult from a tability model, confirm that the theory i applicable to a laer with hort and integrated feedback. We are able to imulate the tability of the device with repect to pump current, feedback phae and delay time. Thi will allow further optimized deign for integrated filtered-feedback laer that will how le or no feedback phae enitivity, thu improving the laer tability and implicity of the circuit. Appendix: linewidth-enhancement factor The linewidth-enhancement factor (α) i one of the key parameter for emiconductor laer. Thi factor i alo ued in the model dicued in ection 3, where it i taken a 2.6. Thi appendix will decribe how the value 2.6 for α i meaured. The determination of the α i baed on meauring the injection-locking range of the laer [11]. The FP-laer in thi meaurement i a tet laer with identical deign of the olitary laer in the filtered-feedback multi-wavelength laer, and i fabricated under the ame technology. # $15. USD Received 1 Oct 212; accepted 7 Nov 212; publihed 29 Nov December 212 / Vol. 2, No. 26 / OPTICS EXPRESS B277

9 The meaurement etup i hown in Fig. 6. An optical pectrum analyzer (OSA, APEX) i ued to meaure the optical pectra of the tet laer and the mater laer. The tunable mater laer (Agilent 861B) and the MIR baed FP laer were both temperature tabilized during the meaurement. The tunable laer wa et to a certain output power, and wa attenuated by a variable optical attenuator. After the attenuator, the light wa connected to a polarizing beam plitter (PBS) through a polarization controller (PC). The PC tune the TE output from the PBS to the maximum, and the TE light i injected into the FP laer via a polarizationmaintaining (PM) fiber. On the other ide of the chip, a lened fiber i aligned to the output facet of the FP laer to couple out the output light, and the light i ent to an APEX optical pectrum analyzer (OSA) for pectral analyi of the emiion. TUNABLE LASER PC ATTENUATOR PM FIBER POLARIZING BEAM SPLITER DUT OPTICAL SPECTRUM ANALYZER Fig. 6. Injection locking meaurement etup. DUT i the device under tet. See the text for other detail. 2 Unlocked Region Detuning (GHz) Unlocked Region Locked Region f max f min Square root of injection power [mw 1/2 ] Fig. 7. Frequency locking range dependence on injected power. FP laer i under injection current of 35 ma at 18 C. The locking range of thi FP laer at 35mA pump current for a longitudinal mode around 1545 nm i meaured. The locked region i determined by both frequency detuning and the external injection light power at a fixed laer pump current. At each injecting power, the wavelength i wept from below and above the frequency of thi mode, and the frequencie when the mode loe locking are recorded and plotted in Fig. 7 veru the quare root of the injection power. The boundarie of the locking region are fitted by the two line. Outide thi area i the unlocked i unlocked region, where the injection level i too low or the detuning i too high to reach injection-locking condition. According to [11,12], the linewidth 2 enhancement factor can be obtained a α = ( Δf max / Δf min ) 1. The ratio of the two lope of the boundarie of the locking region i independent of the optical power. The linewidth enhancement factor of the active material can be etimated to be 2.6. # $15. USD Received 1 Oct 212; accepted 7 Nov 212; publihed 29 Nov December 212 / Vol. 2, No. 26 / OPTICS EXPRESS B278