RECENTLY, studies have begun that are designed to meet

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1 838 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 9, SEPTEMBER 2007 Design of a Fiber Bragg Grating External Cavity Diode Laser to Realize Mode-Hop Isolation Toshiya Sato Abstract Recently, a unique approach has been reported in which optical signal degradation is suppressed by realizing modehop isolation. This paper analyzes the mode-hop isolation condition in fiber Bragg grating type external-cavity diode lasers (FBG- ECDL). As a result, it has become possible to determine whether mode-hop isolation could be achieved. Moreover, it was verified experimentally that the mode-hop isolation of FBG-ECDLs was actually achieved with this method. The analytical method described in this paper is very useful for designing the uncooled ECDLs whose mode-hop must be isolated. Index Terms Gratings, laser stability, nonlinearities, optical fiber communication, semiconductor lasers. I. INTRODUCTION RECENTLY, studies have begun that are designed to meet the demand for simple, compact and economical wavelength-division-multiplexing (WDM) light sources for direct modulation that do not require temperature control [1], [2]. In addition, studies are also underway with the aim of narrowing the wavelength channel spacing, namely stabilizing the lasing wavelength, in such uncooled WDM light sources [3], [4]. One promising WDM light source is the uncooled external-cavity diode laser (UC-ECDL), which employs a unique approach using a nonlinear optical gain (NOG) effect [5], [6]. When ECDLs are used under uncooled conditions, mode-hop cannot be entirely suppressed. Then the ECDL might fall into lasting mode-hop, and it has been reported that the bit error rate of the optical signal output from an ECDL increases greatly [3], [7]. However, it has been clarified theoretically and confirmed experimentally that this bit error rate degradation can be suppressed and disregarded when the lasting mode-hop is suppressed and the mode-hop is isolated [8]. In this paper, I describe a theoretical and quantitative analysis of the requirements of mode-hop isolation by using NOG effect. Section II describes the parameters that decide the requirements of the mode-hop isolation (MHI), and how the MHI condition is determined. Section III analyzes the dependence of first order optical gain (FOG) on wavelength and carrier density, and provides an analytical expression of the practical FOG of an external cavity type diode laser. Here, the FOG is needed to estimate the NOG and thus provide the mode-hop isolation condition. In addition, the carrier density and the photon density in the active region of the gain medium are discussed based on the ECDL rate equations. Moreover, the NOG estimation procedure is described. Manuscript received December 5, 2006; revised February 23, The author is with the Photonics Laboratories, Nippon Telegraph and Telephone Corporation, Kanagawa , Japan ( toshiy@aecl.ntt.co.jp). Digital Object Identifier /JQE Section IV analyzes the loss spectrum of a fiber Bragg grating (FBG), which is the external cavity mirror in the laser cavity, and discusses the variation in the intra-cavity loss originating in the FBG under direct modulation. Section V presents model calculations for the MHI condition and describes an experimental verification showing that the mode-hop of the FBG-EDCL, which was designed to satisfy the MHI condition, is isolated. II. REQUIREMENT OF MODE-HOP ISOLATION In conventional single-mode ECDLs, the reflection bandwidth of the external resonator mirror (ERM) is designed to be very narrow in relation to the longitudinal mode spacing (LMS), as seen in Fig. 1-I, so that the side modes are suppressed simply by the loss difference, which originates in the ERM, between the lasing mode and the side mode. This is based on the premise that conventional ECDLs are temperature controlled to maintain an optimal temperature so that the lasing mode is located at the bottom of the ERM loss profile. Let us assume that the conventional ECDLs are operated without temperature control. The reflection wavelength peak of the ERM and the longitudinal lasing mode wavelength shift corresponding to the temperature change. Then both the lasing mode and the adjoining dominant side mode are located on the steep loss slopes of the ERM loss profile, because the LMS is wide in relation to the reflection bandwidth of the ERM. In addition, the losses in the two dominant modes become comparable around certain specific temperatures that are called mode hopping temperatures as seen in Fig. 1-II. When the ECDL is modulated directly, the movement of the longitudinal mode wavelengths is synchronized with the direct modulation. As a result, a large loss reversal is repeated between the two dominant modes, and the lasing mode hops repeatedly in synchrony with the direct modulation. Moreover, the loss at the lasing mode fluctuates greatly and the optical power also fluctuates, leading to degradation in the optical signals from the ECDL. This optical signal degradation is well known as mode-hopping noise [9]. Here, the following condition, which is not accorded special attention, is usually satisfied in conventional ECDLs where is the difference between the nonlinear gain effect on the adjoining dominant side mode and that on the lasing mode (1) (2) /$ IEEE

2 SATO: DESIGN OF A FIBER BRAGG GRATING EXTERNAL CAVITY DIODE LASER TO REALIZE MODE-HOP ISOLATION 839 Fig. 1. Schematic diagram of I: single-mode operation and II: repetitive mode-hop mechanism of a conventional ECDL. and is the loss reversal between the lasing mode and the adjoining dominant side mode when the wavelength positions of these modes are balanced centering on the peak wavelength of the ECM s reflection profile as seen in Fig. 2. Expression (1) is one of the necessary conditions for the repetitive mode hops that synchronize with the direct modulation. Therefore, the following mode hop isolation condition can be derived as the opposite condition of expression (1) (3) When it is assumed that the nonlinear gain effect is fixed, can be tuned so that it is sufficiently small. In addition, the mode hop isolation condition (expression (3)) can be satisfied by designing the reflection bandwidth (RBW) so that it is wide compared with the longitudinal mode spacing (LMS), (it is usually narrow compared with the LMS), or by designing the LMS so that it is narrow compared with the RBW, (it is usually wide compared with the RBW). In this case, as long as the amplitude of the repeated loss reversal synchronized with the direct modulation between the two adjoining dominant modes is suppressed to a small value compared with, the lasing mode does not hop (Fig. 3-I). Furthermore, mode-hop occurs only once when the loss reversal becomes larger than at some critical temperature. (Fig. 3-II-1), and then the lasing becomes very stable because the loss reversal is canceled out (Fig. 3-II-2). Namely, in this case, the mode-hop is isolated. Moreover, the low level of the optical signal is controlled in order to suppress the optical signal degradation at isolated mode-hop (IMH) by minimizing the difference between the optical output powers before and after the IMH, within a range where the NGS can work so efficiently that the side mode can be adequately suppressed [8]. III. NONLINEAR GAIN EFFECT A. Effective First-Order Optical Gain in External-Cavity Diode Laser In order to estimate the NOG effect, we must estimate both the carrier density and the optical power (photon density) in the active region of the semiconductor gain medium by using the Fig. 2. Schematic diagram of a loss reversal. rate equations of the laser. Then we must understand the relationship between the FOG and the carrier density both quantitatively and simply. It is widely known that the FOG can be obtained simply as a function of the carrier density by using a linear approximation [11]. And the linear approximation is based on an assumption, in which lasing wavelength is almost always tuned to the maximum gain wavelength. However, we cannot use a linear approximation with the ECDL, because the lasing wavelength is almost always fixed at the reflection peak wavelength (RPW) of the external-cavity mirror (ECM). In this section, we obtain a new approximation of the relationship between the FOG and the carrier density for the ECDL. The FOG of the semiconductor laser media can be estimated by using a first order microscopic polarization which is determined based on perturbation theory, and becomes as follows: (6) (4) (5) (7)

3 840 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 9, SEPTEMBER 2007 Fig. 3. Schematic diagram of mode-hop isolation I: lasing mode preservation state and II: mode-hop isolation mechanism of an ECDL. Fig. 4. FOG dependence on both wavelength and carrier density. CURVE-I: Gain coefficient curve at maximum gain wavelength,. CURVE-II: Gain coefficient curve at 1550 nm. Fig. 5. FOG dependence on carrier density. CURVE-I: Gain coefficient curve at maximum gain wavelength. CURVE-II: Gain coefficient curve at 1550 nm. where,,, and are the optical amplitude of the lasing mode, the 3-D standing wave function, the effective index for the optical field, and the electric dipole matrix element, respectively. and indicate the zeroth-order population of the electron in the conduction and valence band, and agree with the Fermi Dirac distribution of a conduction band in quasiequilibrium under a lasing condition and that of a valence band. Fig. 4 shows a numerical calculation result for the FOG of InGaAsP InP bulk type semiconductor laser media. The effective mass of an electron in the conduction band and the effective mass of a hole in the valence band, estimated for In Ga As P ev [11] were used in this calculation. Simultaneously, we assumed that, the intra-band relaxation time, and the neutral condition of the charge is satisfied. Then, carrier density can be estimated by where,, and are the density-of-states, the Fermi Dirac distribution in the conduction band, and the bandgap energy at the band edges. CURVE-I in Fig. 4 is a trace of the gain peak for each carrier density, and CURVE-II is a trace of the gain at a wavelength of 1550 nm. Here, it is assumed that the RPW of ECM is 1550 nm. Fig. 5 shows CURVE-I and CURVE-II on a 2-D graph giving the relationship between the FOG and the carrier density. When (8) Fig. 6. Approximation of FOG at 1550 nm by using analytical expression (8). CURVE-II: numerical calculation. CURVE-III: approximation by using (8). CURVE-IV: approximation error. we deal with a Fabry Perot type diode laser, the FOG characteristic of CURVE-I is important, and the following linear approximation is useful [10] (9) (10) On the other hand, when we deal with an ECDL, the FOG characteristic of CURVE-II is very important, because the RPW of the ECM does not depend on the carrier density and the lasing wavelength is almost always fixed at a stable RPW. Then it is

4 SATO: DESIGN OF A FIBER BRAGG GRATING EXTERNAL CAVITY DIODE LASER TO REALIZE MODE-HOP ISOLATION 841 clear that a linear approximation cannot be used, but we can use the following new useful approximation (11) CURVE-III in Fig. 6 shows an approximation obtained by using (11) (CURVE-III), and the fitting parameters are as follows: Here, the CURVE-IV (red line) in Fig. 6 shows the approximation error. We confirmed that fitting by using (11) can give a good approximation in the carrier density region between m and m. B. Carrier Density, Photon Density and Nonlinear Gain Effect Under Lasing Conditions With an ECDL, the photon density and the carrier density in the active region of the semiconductor laser medium are subject to the following laser rate equations: Here, we can obtain the threshold gain that the SOA must provide in the cavity by solving (12) as follows: (16) With laser oscillation, the optical gain is fixed at the threshold gain and then the carrier density is also fixed at the threshold density. Therefore, the carrier density and the quasi-fermi level under lasing conditions can be estimated by calculating them at the threshold gain based on (10), (11), and (16). In addition, the photon density under lasing conditions can be estimated by solving (13) as follows: (17) By using the parameters mentioned above, we can estimate the symmetric third-order microscopic polarization (18) (12) (13) where,,, and are the confinement factor, SOA length, cavity length, and photon lifetime in the cavity, respectively.,, and are the current injected into the SOA, the quantum efficiency, and the volume of the SOA s active region. Here, it is important to take account of the localization of both the carrier and the optical gain at the SOA section in the cavity. The photon lifetime in the cavity also reflects the external cavity structure and can be expressed as follows: (14) where,, and are the loss of the SOA, the fiber loss, and the coupling loss between the SOA and fiber, respectively. Moreover, is the effective total loss of the cavity mirrors (both the HR end of the SOA and the external cavity mirror), and can be expressed by using both the reflection ratio of the mirrors and as follows: (15) In addition, is a compensation factor that takes the gap between the lasing wavelength and the reflection peak wavelength of the FBG into consideration. and symmetric third-order gain [6], [10] IV. MAXIMUM VALUE OF LOSS REVERSAL BETWEEN ADJACENT LONGITUDINAL MODES UNDER DIRECT MODULATION (19) (20) (21) (22) (23) When the index of a FBG used as an external cavity mirror can be expressed as (24), shown at the bottom of the page, the reflection-wavelength characteristics induced by the Bragg if otherwise (24)

5 842 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 9, SEPTEMBER 2007 Fig. 7. Calculated reflection ratio based on the coupled-mode theory. I: FWHM = 0:2 nm. II: FWHM = 0:4 nm. grating can be estimated by numerically solving the following differential equation based on coupled-mode theory [12], [13]: (25) (26) (27) where,,, and are the reflection ratio, the local average refractive index, the peak-to-peak index variation, the phase, and the Bragg frequency, respectively. And the normalized axial dimension is expressed by the nominal Bragg wave number and propagation axis as With an FBG type external-cavity diode laser (FBG-ECDL), only the reflection characteristic in the region extremely close to the reflection peak dominates the lasing mode. Therefore, an FBG with a particularly complex structure is not needed for the FBG-ECDL. So the simplest FBG, namely one whose structural parameters are, respectively, constant and (28) are used for the ECDL. Here, (24) and (26) become simple as follows: if otherwise (29) (30) and the reflection ratio can be estimated by solving the (30) for under the boundary condition (31) As mentioned above, the reflection wavelength characteristics of an FBG-type cavity mirror can be estimated numerically when the structural parameters are determined. However, in order to analyze the MHI conditions, it is preferable that the FBG s reflection characteristic be given by such dominant characteristic parameters as the reflection peak wavelength, peak reflection ratio, and reflection bandwidth, in the form of an analytical expression. Furthermore, it is even better if the MRLD can be given in the form of an analytical expression. Fig. 7 shows the numerically estimated reflection wavelength characteristics of a uniform FBG. In this calculation, the structural parameters are tuned so that the reflection peak wavelength, full-width half-maximum (FWHM), and peak reflection ratios become 1550 nm, 0.2 nm for I, 0.4 nm for II, and from 5% to 95% in 5% steps, respectively. We can see in these calculation results that as the peak reflection ratio becomes larger, the top region of the reflection profile becomes flatter when the FWHM of the reflection ratio is fixed. As a result, it is difficult to obtain an analytical expression that can provide precise approximation over the whole peak reflection ratio region and over the whole wavelength region. However, we can obtain a precise

6 SATO: DESIGN OF A FIBER BRAGG GRATING EXTERNAL CAVITY DIODE LASER TO REALIZE MODE-HOP ISOLATION 843 Fig. 8. Calculated reflection ratio (red lines): based on the coupled-mode theory and (blue lines): by using approximation expression (32). analytical expression as following Gaussian function when we consider only the important region of the peak reflection ratio (equal or less than 30%) and the important wavelength region (half of the FWHM around the peak wavelength) for the FBG that is used for UC-ECDL (32) where,,, and CF are the peak reflection ratio, Bragg wavelength, FWHM, and a compensation coefficient, respectively. Fig. 8 I IV show the reflection wavelength characteristics estimated by using the analytical expression (32) and those estimated numerically based on the coupled-mode theory. The combinations of peak reflection ratio and FWHM in these calculations are (5%, 0.2 nm) for I, (5%, 0.4 nm) for II, (95%, 0.2 nm) for III, and (95%, 0.4 nm) for IV, respectively. As seen in these figures, there are large calculation errors when using the analytical expression in the high peak reflection ratio region or in the wavelength region far from the peak wavelength. Fig. 9 shows the calculation errors for each case, where the peak reflection ratios are tuned from 5% to 95% in 5% steps. In these calculations, the FWHMs are 0.2 nm for I-1, I-2 and 0.4 nm for II-1, II-2. These calculations confirmed that the calculation errors are less than 0.11 db, and the calculation results obtained by using the analytical expression (32) are good approximations when the peak reflection ratio is limited to below 30%, and when we accept that the significant wavelength region is limited to half of the FWHM around the peak wavelength. Here, the can be derived based on the analytical expression (32) as follows: (33) where and are the wavelength variation width of the lasing mode under direct modulation and the longitudinal mode spacing, respectively. V. CALCULATED AND EXPERIMENTAL RESULTS It is expected that such structural parameters as the reflection bandwidth of the ERM and the longitudinal mode spacing (LMS) will prove very important as regards realizing mode-hop isolation in an ECDL. Therefore, we analyed the dependence of the MHI condition on these parameters based on the conclusions drawn in Sections III and IV. Curves I and II in Fig. 10 show the calculated with of 0.2 and 0.4 nm, and curves III and IV show the calculated with injection currents of 1.3 and 1.5. The following values are used in these calculations,, MHz,, where the value was estimated experimentally. In addition, lines V and VI show the 7-GHz position of the LMS, and the LMS position of a conventional FBG type ECDL nm [14]. Here, it is assumed that the LMS should be increased above 7 GHz to suppress the interference between the adjoining longitudinal modes under 2.5 Gb/s direct modulation. These calculations suggest that the mode-hop cannot be isolated in a conventional ECDL because the MHI condition (3)cannot be satisfied. It is also expected that the mode-hop can be isolated if the structural parameters of the FBG-ECDL are tuned so that they satisfy the MHI condition. In fact, optical signal degradation caused by repetitive mode-hop has been reported in a conventional FBG type ECDL [3], [7]. Moreover, it has been confirmed that the FBG type ECDL, which is designed for uncooled use ( nm, nm), achieves mode-hop isolation [4]. The FBG used for the UC-ECDL is a commercially available uniform grating. And the FWHM of the reflection spectrum and the reflection ratio at the

7 844 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 9, SEPTEMBER 2007 Fig. 9. Approximation error calculated by using approximation expression (32). I-1 and I-2: FWHM = 0:2 nm, II-1, and II-2: FWHM = 0:4 nm. Fig. 10. Mode-hop isolation condition. I and II: calculated. III and IV: calculated. V: 7-GHz position of LMS. VI: LMS of conventional FBG- ECDL. Fig. 11. Optical reflection spectrum of an external cavity mirror (FBG). Fig. 12. Observed isolated mode-hop. I: whole optical signal output from UC-ECDL. II: beat signal with output optical signal lasing in mode-1, which predominates before mode-hop. III: beat signal with output optical signal lasing in mode-2, which predominates after mode-hop. peak are about 0.4 nm (see Fig. 11) and 0.2, respectively. Fig. 12 shows the output signals from the UC-ECDL, and Fig. 12-I, Fig. 12-II and Fig. 12-III show the entire optical signal that was directly detected, the beat signal with output optical signal

8 SATO: DESIGN OF A FIBER BRAGG GRATING EXTERNAL CAVITY DIODE LASER TO REALIZE MODE-HOP ISOLATION 845 to satisfy the MHI condition. The analytical method described in this paper is very useful for designing a UC-ECDL whose mode-hop needs isolating. ACKNOWLEDGMENT The author would like to thank H. Oohashi, K. Kato, Y. Akatsu, and H. Itou for their continuous encouragement. REFERENCES Fig. 13. Optical spectra before and after the isolated mode-hop. lasing in mode-1, and the beat signal with output optical signal lasing in mode-2, respectively. These figures reveal the moment at which the lasing mode hopped from mode-1 to mode-2. These measurements of the optical signal output from the UC-ECDL proved that the mode-hop was isolated. Fig. 13 shows the optical spectra before and after the mode-hop was isolated, and it was confirmed that a good side-mode suppression ratio (SMSR) characteristic was preserved except when an isolated mode-hop occurred. VI. CONCLUSION This paper described the principle and presented a quantitative analysis of mode-hop isolation based on the NOG effect. Mode-hop isolation is needed to suppress the optical signal deterioration induced by repetitive mode-hop in an uncooled directly modulated ECDL. We investigated the dependence of the FOG on carrier density in an ECDL whose lasing wavelength is extremely stable, and provided a new approximate expression for the FOG instead of the conventional linear approximation. The symmetric third order gain effect in an ECDL can be estimated by using both the analytical results for the ECDL s laser rate equations and the new approximate expression for the FOG. Moreover, we derived an analytical expression for the MRLD as a result of our analysis of the reflection wavelength characteristics of the FBG that constitutes the external cavity mirror. By using the above-mentioned results, it became possible to predict whether the MHI condition can be satisfied or not based on such parameters as the longitudinal mode spacing, the reflection bandwidth of the FBG, and the optical power in the active region of the semiconductor laser gain medium. It was confirmed by quantitative analysis that the conventional ECDL, which fall into repetitive mode-hop under uncooled conditions, does not satisfy the MHI condition. In addition, we confirmed experimentally that we could isolate the mode-hop of an ECDL made [1] R. J. C. Campbell et al., Wavelength stable uncooled fiber grating semiconductor laser for use in an all optical WDM access network, Electron. Lett., vol. 32, pp , [2] L. A. Buckman et al., Demonstration of small-form-factor WWDM transceiver module for 10 Gb/s local area networks, IEEE Photon. Technol. Lett., vol. 14, no. 5, pp , May [3] T. S. 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Technol., vol. 21, no. 9, pp , Sep Toshiya Sato is with the Photonics Laboratories, Nippon Telegraph and Telephone corporation, Atsugi, Japan, and has been engaged in research on semiconductor lasers for optical communication systems in Dr. Sato is a member of the Institute of Electronics, Information, and Communication Engineers.