The optical isolators used to protect semiconductor lasers against optical feedback cannot be integrated. Therefore we propose to fabricate a laser that has a strongly reduced sensitivity to feedback. Simulations show that such a device can be realized by employing a ring laser in which the clockwise and counterclockwise modes are not coupled. To achieve unidirectional lasing, this work proposes to use an intra cavity weak optical isolator based on two phase modulators that are driven 90 degrees out of phase. Simulations show up to 3% of intensity feedback can be tolerated without any distinguishable effect on the laser light

Bente, E.A.J.M.

Lenstra, D.

Schaijk, van, T.T.M.

English

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 Design of feedback insensitive InP ring laserCitation for published version (APA):Schaijk, van, T. T. M., Bente, E. A. J. M., & Lenstra, D. (2015). Design of feedback insensitive InP ring laser. InP. Kockaert, P. Emplit, S-P. Gorza, & S. Massar (Eds.), Proceedings of the 20th Annual Symposium of the IEEEPhotonics Benelux Chapter, 26-27 November 2015, Brussels, Belgium (pp. 117-120). OPERA-photonics,Brussels School of Engineering.Document status and date:Published: 01/01/2015Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. 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Nov. 2023Design of feedback insensitive InP ring laserT.T.M. van Schaijk, E.A.J.M. Bente and D. LenstraThe optical isolators used to protect semiconductor lasers against optical feedback cannotbe integrated. Therefore we propose to fabricate a laser that has a strongly reducedsensitivity to feedback. Simulations show that such a device can be realized by employing aring laser in which the clockwise and counter-clockwise modes are not coupled. To achieveunidirectional lasing, this work proposes to use an intra cavity weak optical isolator basedon two phase modulators that are driven 90 degrees out of phase. Simulations show up to3% of intensity feedback can be tolerated without any distinguishable effect on the laserlight.IntroductionFor decades laser performance has suffered from the effects of external optical feed-back (EOF). This is light that is reflected back into the laser by one or more reflectorsoutside of the cavity[1]. In traditional fiber coupled lasers, the effects of EOF can be greatlyreduced by placing it in series with an optical isolator. An isolator that can be integratedon a chip is demonstrated in [2], but its performance does not meet the requirement ofmore than 30 dB of isolation.This paper proposes to utilize the isolator presented in [2] in a different way. Insteadof using it to directly suppress EOF, it is used to provide a gain difference betweenthe clockwise (CW) and counterclockwise (CCW) modes of a ring laser. This allowsunidirectionally lasing without introducing any optical coupling between the CW andCCW modes (except for the coupling introduced by the EOF). Thus the EOF cannotcoherently interact with the lasing mode in this laser, although effects through variations inthe carrier density may still be present. Analysis shows that this can be accomplished withmuch weaker, intra-cavity, optical isolation than would be required to directly suppressfeedback. In this paper we will present an analytical analysis of this type of laser thatis subsequently compared to an advanced numerical simulation. On the basis of theseanalyses, we predict that an isolation of 7 dB is sufficient to withstand EOF of up to 3 %.Design of the laserThe key to achieving feedback insensitivity that is described in this paper is to separatethe EOF from the lasing mode. As mentioned above, this can be most easily done byemploying a ring laser architecture. If such a laser is lasing in the CW mode, then the EOFwill return to the CCW mode. The CCW mode can then influence the lasing mode in twoways: Firstly it can affect the carrier density in the active material of the laser, and therebyindirectly affect the lasing mode. This effect can be reduced by minimizing the amount oflight in the CCW mode. Secondly, the CCW mode can directly influence the lasing modeThis research is supported by the Dutch Technology Foundation STW, which is part of the NetherlandsOrganisation for Scientific Research (NWO), and which is partly funded by the Ministry of EconomicAffairs.Proceedings Symposium IEEE Photonics Society Benelux, 2015, Brussels, Belgium117-2 f 0 2 f00.10.20.3Frequency (GHz)RelativeintensityFigure 1: Output for reverse direction atmodulation frequency f .SOAFilterUPMMMI⇒Figure 2: Schematic of unidirectional laserwithout optical coupling.if there is any optical coupling between the two. This coupling will be minimized usingthe presented design such that only parasitic coupling will remain. It is to this reducedcoupling that the reduced feedback sensitivity is attributed.Most methods of enforcing unidirectional operation introduce some form of optical cou-pling between the CW and CCW modes, but this is no option in this laser as they all leadto enhanced feedback sensitivity. This coupling is not introduced by the optical isolatordemonstrated in [2].One can think of this optical isolator as consisting of two parts: a unidirectional phasemodulator (UPM) and a wavelength selective filter. The UPM ideally does not influencelight propagating in the forward direction in any way, while it converts light propagating inthe reverse direction to other wavelengths as shown in figure 1. When the filter is designedto allow the original wavelength to pass, while at the same time blocking the convertedwavelengths, the combination acts as a narrowband isolator.For the design of the UPM, various trade-offs were made. First of all increasing theRF operating frequency of the UPM decreases the length of the UPM, increases thefilter length and increases the required electrical frequencies. For our laser an operatingfrequency of f = 5GHz was selected. This results in a total length of the UPM ofapproximately 8 mm. Four asymmetric Mach-Zehnder interferometers (AMZIs) placed inseries were used as an intra-cavity filter, with a total unbalance of approximately 13 mm.Higher unbalances were considered undesirable because of losses. Also, the electro-optic phase modulators (EOPMs) are expected to operate with sufficient efficiency at thisfrequency.Finally, care has to be taken that the laser will operate in a single longitudinal mode.The four-stage filter ensures this is the case. When adding a semiconductor opticalamplifier (SOA) for gain and a multi-mode interferometer (MMI) as an output-coupler, theschematic representation of figure 2 is obtained.Analytical modelIn order to understand the behavior of the laser with the proposed design better, it wasmodeled by using a set of rate equations. We use the slowly varying envelope approxima-tion for the cavity-averaged values for the various variables. We assume only one CW andone CCW mode are relevant and all other modes can be neglected, which is valid whenthe other modes are suppressed by the filter. Furthermore the gain is linearized around thethreshold carrier density and the EOF is modeled as a time-delayed injection from the CWDesign of feedback insensitive InP ring laser118into the CCW mode. The coupling is only in one direction because only light from theCW mode will reach the external reflector.The analytical model then reads as follows:Ėcw =12ξ (1+ iα)NEcw (1a)Ėccw =12ξ (1+ iα)NEccw−∆Γ2Eccw +γ2exp( jω0τ)Ecw(t− τ) (1b)Ṅ = J− NT− (Γ+ξ N)|Ecw +Eccw|2 (1c)Here ξ is the differential gain, α is the line width enhancement factor, N is the numberof carriers minus the number at threshold, Ecw is the electric field strength in the CWdirection, Eccw is the electric field strength in the CCW direction, ∆Γ is the gain differenceintroduced by the combination of the UPM and the filter, γ is a measure for the amountof EOF, ω0 is the natural angular frequency of the laser at threshold, τ is the time delaybefore EOF returns to the cavity, J is the carrier injection rate relative to threshold, T isthe carrier life time and Γ accounts for the optical loss.We can define an optical power and phase as Ea =√Pa exp(iφa) for a equal to CW andCCW. Equations 1 can then be expanded into equations for the optical power and phase byseparating their real and imaginary parts. Assuming the laser will reach a steady state, arelation between the phase of the CW mode at time t− τ and the phase of the CCW modeat time t can then be derived and from this result we can then determine thatPccwPcw≈ γ2∆Γ2(2)This equation allows to determine the gain difference needed to obtain Pccw/Pcw for agiven feedback rate γ .∆Γ can be expressed in the single pass isolation TUPM = Treverse/Tforward to facilitate designof the laser. Since the round-trip gain for the lasing CW mode is unity, the roundtrip gainfor the CCW mode equals TUPM. The loss difference per unit of time will therefore be∆Γ =√1−TUPM/τR, where τR is the cavity round trip time. When assuming an outputcoupler that couples out half of the light, and assuming that the light from the feedbackpasses through the UPM before entering the SOA, the feedback rate is γ =√RTUPM/(2τR)where R is the power reflectivity of an external reflection makingPccwPcw≈ RTUPM4(1−TUPM)(3)This predicts a suppression of the CCW mode of 30 dB relative to the CW mode forTUPM = 20% which can be proven to influence the power in the lasing mode by less than30 dB. This is assumed to sufficiently reduce the effect of the EOF.It can be shown that the power in the side frequencies of figure 1 can be expressed asPn = Jn(2A)2 where Pn is the power at the side frequency, Jn is the bessel function ofthe first kind, nth order and A is the modulation amplitude of the modulating electricalsignal expressed in radians of phase shift. Maximally 91 % of the optical power will bein the first two side peaks and non-linearities will likely reduce this number by less than10 %[2], which totals to slightly more than the desired 80 % suppression. It will thereforebe sufficient to only suppress the first and second side frequencies.Proceedings Symposium IEEE Photonics Society Benelux, 2015, Brussels, Belgium119Numerical ModelNumerical device simulations have been performed using a commercial time domaintraveling wave circuit simulator (PICWave). In this simulator, similar to the analyticalmodel, it is assumed that only one transverse mode is supported by the waveguide. Thesimulated structures are discretized along the longitudinal direction and in the time domain.During a simulation, the simulator steps through time with the desired accuracy whilecomputing the changes to the various quantities (electric field, carrier concentration etc.)at every time step. In the simulations that were run for this project, the circuit of figure 2was implemented using an ideal power splitter as an output coupler, an SOA that showedrealistic characteristics, a UPM consisting of two phase modulators and a filter consisting offour serially placed asymmetric Mach-Zehnder interferometers (AMZIs). The AMZIs hadfree spectral ranges of 10 GHz, 20 GHz, 200 GHz and 2 THz respectively. Together withthe gain profile, this provided more than 40 dB of side-mode suppression in the simulation.Next, compliance with the analytical model was studied. To this end, the laser outputwas connected to a time delay element that introduced τ ≈ 3.3ns of delay and a reflectorwith power reflectivity R. A number of simulations has been run for values of R rangingfrom 0 to 1. For each of the simulations, the laser was allowed to stabilize after which theratio between the CW and CCW modes, central wavelength, line width and RIN numberwere determined. It was found that the ratio between the CCW mode and CW mode wasapproximately 25 dB at R = 1% (30 dB was predicted by the analytical model), and alinear fit of this ratio with respect to R resulted in a relative error of less than 1.5×10−3 ,which agrees well with the predictions from the analytical model. The deviations can beexplained by differences in the modeling of the UPM and filter. Furthermore, the centralwavelength, line width and RIN number were found to be unaffected up to the simulationaccuracy for R up to 1 (linewidth and central wavelength accurate up to 4 MHz, RIN upto 4 %). The average output power was constant for R < 3%, after which it declined byabout 1 % for R = 1.ConclusionWe have presented a proposal for a laser that we expect to be highly insensitive to EOF.This is attributed mainly to the decoupling of the lasing mode from the mode to which theEOF returns. The final robustness of the laser for up to 3 % of EOF is obtained by keepingthe mode that collects the EOF sufficiently far below threshold to reduce variations in thecarrier density. We will proceed with the fabrication of a photonic integrated circuit tocompare these predictions against measurements.References[1] R. Tkach and A. Chraplyvy. Regimes of feedback effects in 1.5-µm distributed feedback lasers. Journalof Lightwave Technology, 4(11):1655–1661, 1986.[2] Christopher R. Doerr, Nicolas Dupuis, and Liming Zhang. Optical isolator using two tandem phasemodulators. Optics Letters, 36(21):4293, November 2011.Design of feedback insensitive InP ring laser120