We report on the spectral analysis of the first 1490 nm external cavity laser with an intra-cavity erbium-doped fiber. Self-mode beating and heterodyne beating methods are employed to measure the side mode suppression ratios and to study the effect of the rare-earth doped fiber on the spectrum of the external-cavity laser. Experimental and simulated results show a substantial decrease in the number of the external-cavity modes and a side-mode suppression ratio of >15 dB.
©2006 Optical Society of America
Fiber Bragg grating semiconductor external-cavity lasers (ECL) have a number of applications, such as in wavelength division multiplexing (WDM), optical metrology, spectroscopy, and millimeter-wave generation [1–4]. Compared to a distributed-feedback (DFB) laser, an ECL has a spectrum with higher temperature stability and lower chirp [5–6]. The side-mode suppression ratio (SMSR) of an ECL may be as high as 56 dB and a linewidth less than 25 kHz when the cavity length is ~1 cm . Due to these advantageous characteristics, two ECLs may be used in radio over fiber (ROF) applications to generate a microwave carrier . The stability and the linewidth of the generated radio frequency (RF) signal are defined by the optical stability and the linewidth of the light sources. For an ultimately stable ROF transmission, a laser with a linewidth of the order of kHz would be highly useful. Minimal linewidth of a single-mode ECL is restricted by the length of the external cavity (EC) and the bandwidth of the external fiber Bragg grating (FBG) through the usual linewidth enhancement factors.
Recently, a doped fiber external cavity semiconductor laser (DFECL) has been shown to have a great potential for ROF as well as DWDM applications due to the narrow linewidth [8,9]. The external cavity of a DFECL contains a piece of a rare earth doped fiber (DF) and is at least several times longer (>10 cm) than in a conventional single-mode ECL and operates in a coherence enhanced regime [9,12]. This narrows both the mode spacing between the adjacent resonant longitudinal modes and their linewidths. As the bandwidth of an external FBG is ~150 times larger than the longitudinal-mode spacing, the SMSR is very poor when the output is controlled only by an external FBG. A dynamic grating formed in the intra-cavity DF of a DFECL may suppress the side modes and narrow the output spectrum of the long laser. Stable single-frequency output at 1535 nm has been shown in a DFECL with an erbium doped fiber (EDF) . A temperature- and current-stable operation of a DFECL at 980 nm with ytterbium-doped fiber in the external cavity has also been reported . The linewidths of these lasers were measured with optical methods and the SMSR was not specified. For ROF applications, however, a single-mode laser with a high (>20 dB) SMSR is preferable.
In this paper we analyze a new DFECL with an erbium-doped fiber operating at 1490 nm. The SMSR of a long-cavity DFECL is measured using RF methods: self-mode beating and heterodyne-mode beating. We compare experimental results with dynamic simulations of the laser.
2. Dynamic grating in a DFECL
In a typical cavity of an ECL, composed of a semiconductor laser, a piece of a single-mode fiber, and a narrow-bandwidth FBG, the reflected modes resonate between the FBG and the rear facet of the semiconductor laser with an anti-reflection coating on the front facet. Since the resonant modes inside the external cavity are selected by the FBG, the number of the resonant modes N equals the ratio of a FBG bandwidth and external-cavity mode spacing, and, therefore, is related to the ratio of the length of the external cavity to the length of the fiber Bragg grating. For example, the laser needs the FBG length to almost equal the length of the external cavity in order to operate in a single-mode regime. When several longitudinal modes oscillate in the spectrum of an ECL, the spectral linewidth at -3 dB is related to the mode spacing Δ λMS and the linewidth of a single EC mode Δλmod and may be derived as:
On the other hand, the maximum linewidth of a single EC mode is defined by the mode spacing and the finesse of the cavity, which is related to the reflectivity of the FBG :
Equations (1)–(2) show that a single-mode laser with an ultimately-narrow linewidth needs narrow mode-spacing and a narrow-bandwidth grating. A FBG with a bandwidth of 5 pm at 1490 nm is possible only when the length of the grating is ~31 cm. These gratings are too long to be written with the conventional fiber Bragg grating writing techniques and cumbersome to use. However, using a piece of a DF and its absorption properties in a DFECL, it is possible to induce a dynamic grating with a bandwidth of a few picometers.
In a DFECL (Fig. 1) a dynamic grating is formed in a piece of the DF inside the external cavity due to absorption-bleaching properties of the DF. A high-power optical wave oscillates inside the external cavity of a DFECL and forms a standing wave . The rare-earth DF has a very strong absorption, which may be bleached within the whole absorption band by pumping with a narrow-linewidth source . The standing wave and the power-dependent absorption bleaching result in spatial hole-burning and a spatially periodic modulation of the absorption in the DF. This absorption modulation also produces a periodic modulation of the DF refractive index though the Kramers-Kronig equations. The period of the modulation of the absorption and refractive index is equal to half the oscillating wavelength. Both absorption and refractive index modulation in the DF form a dynamic grating, which defines the ultimate spectral narrowing in these lasers .
Although the absorption grating plays a major role in side-mode suppression of many longitudinal modes, the refractive index grating (i.e. its coupling factor and the length of the EDF, L) define the fine shape of the reflectivity spectrum of the dynamic grating [11,12]. The wavelength of the maximum of the reflectivity spectrum of the refractive index dynamic grating corresponds to the maximum of the oscillating spectrum inside the cavity.
The DF dynamic grating is uniform and may be longer than 10 cm. Its bandwidth is much narrower than the bandwidth of an external FBG, and suppresses the side modes which might exist in the cavity without the DF. Furthermore, with a longer DF the reflectivity of the dynamic grating is higher, which may increase the finesse of the Fabry-Perot cavity, and thus narrow the linewidth of a single longitudinal mode (Eq. (2)). Interplay between the reflectivity spectra of the fixed external and the dynamic gratings define the SMSR and the number of the oscillating longitudinal modes of a DFECL.
3. Set-up of the DFECLs
Two DFECLs operating at 1490 nm were built to study the effect of the DF on the performance of the laser with the external cavity. DFECL-1 had a Fabry-Perot (FP) semiconductor diode laser (with AR front coating and without an isolator), a piece of 28.5 cm EDF, described above, and a FBG (0.2 nm bandwidth and 7 dB of maximum reflectivity). The external cavity of DFECL-1 was ~95 cm long. DFECL-2 had FP semiconductor laser with a piece of 28 cm EDF, and a FBG (0.2 nm bandwidth and 6.5 dB of the reflectivity maximum). The length of the external cavity of DFECL-2 was ~67 cm. Both FP lasers had very broad 1450–1500 nm lasing bandwidths. The peaks of the reflectivity spectrum of the both FBGs were at ~1490 nm.
Figure 2 shows the absorption characteristics of a CorActive erbium DF, used in the DFECLs, which were measured with the method described in Ref.  for the 1530 nm bandwidth. The DF was pumped by a narrow-linewidth source and the spectra at different pump powers were recorded. The maximum absorption at 1490 nm was ~16 dB/m [Fig. 2(a)] when the pump power was <-20 dBm. The maximum bleaching of absorption was 30 dB/m, measured at the peak of the absorption spectrum at 1528 nm [Fig. 2(b)]. Figure 2 shows that the absorption may be bleached by ~15 dB/m at 1490 nm when the pump power is ~6.7 dBm. From the Kramers-Kronig relations, the induced refractive index change at 1490 nm is Δn~1.68×10-6. Assuming that the refractive index of the DF is n ~1.45, we derive the coupling factor of a dynamic grating in this DF: κ ~1.55 m-1.
4. Time-domain simulations
To simulate the DFECL we used a time-domain transmission-line laser model, which has been developed recently for the similar laser oscillating at 980 nm . The algorithm for simulations of a DFECL along with the equations used in the time-domain model has been recently presented in Ref. . In this approach the laser is described as a four-section device. The lengths of the sections (diode, fiber, DF, FBG) in the cavity, the reflectivity, and the bandwidth of the FBG have been assigned to match the parameters of the DFECL-2. The modeling parameters of the diode, lasing at 1490 nm, were adjusted using the measurements of the light-current and spectral characteristics. For time-domain simulation of the absorption changes and the evolution of the dynamic grating in the DF section an experimental dependence of absorption on the input power, shown in Fig. 2, has been used. An ECL with the external-cavity length of 67 cm and a DFECL-2, lasing at 1490 nm, has been simulated.
The spectrum of the ECL had ~100 longitudinal modes suppressed by less than 22 dB from the maximum of the spectrum. This coherence collapse regime does not change with time and the laser spectrum is still multimode after the simulation for several microseconds.
In a DFECL with the doped fiber in the cavity, most of the side-modes are suppressed after approximately 500 nsec of simulation time. Several modes oscillate and the bandwidth of the spectrum (number of modes multiplied by the sum of the mode spacing and the linewidth of a single mode) correspond to the bandwidth of the dynamic grating. In our simulations at the diode drive current of 200 mA the laser had only 5 oscillating modes with the SMSR of less than 22 dB (Fig. 3, solid curve). The laser was able to achieve a single-mode regime when a higher current (210…300 mA) was applied to the diode (red dashed curve in Fig. 3). From our simulations we have concluded that the suppression of the side modes within the bandwidth of the dynamic grating depends on the power inside the cavity, which is defined by the diode drive current.
It should be noted that the laser studied in the present work differs from the laser simulated in Ref. : it has longer dynamic grating and much longer (67 cm vs. 24 cm) external cavity of the DFECL. However, the effect of the dynamic grating is the same: the absorption grating suppresses most of the side modes and then the dynamic refractive index grating selects several and even one mode, depending on the drive current of the diode laser. Our simulations have shown that a single-mode regime in such a long laser is theoretically possible above a certain drive current. When several modes oscillate in the spectrum, the number of modes at any time is defined by the bandwidth of the dynamic grating in the DF.
We have estimated the number of the longitudinal modes that may theoretically oscillate in the DFECLs and the corresponding ECLs without the DF. The bandwidth of the dynamic grating was divided by the sum of the mode spacing and the linewidth of a longitudinal mode (see Eq. (1)). The mode spacing of the DFECL-1 is ~103 MHz, which provides for the oscillation of ~194 modes in the ECL without the DF. However, a dynamic grating with a narrow bandwidth of Δλ~5.42 pm (RDF~17.3%) in the cavity of the DFECL-1, reduces the number of modes to 6. The mode spacing of the DFECL-2 is ~150 MHz. The dynamic grating in the DFECL-2 has the bandwidth Δλ~5.52 pm (RDF~16.8%). Hence, due to the presence of the DF, the number of oscillating modes in a DFECL-2 may be reduced from 175 to 5.
5. Measurement of the linewidth of the DFECL
Since the linewidth of a DFECL is assumed to be less than 1 MHz, it is very difficult to measure by optical instruments, such as a FP optical spectrum analyzer (OSA), a lightwave spectrum analyzer or a wavemeter. To measure the spectrum with high resolution one may use RF methods. These techniques employ the principle of beating of two incoherent fields to generate low frequency RF signals. The generated RF signal may be obtained from the output of a photodetector and measured by a RF spectrum analyzer (SA).
If the side modes are not fully suppressed in the output of a long external-cavity laser, the longitudinal modes may beat with each other to generate the RF beat-note signals, which are a superposition of the mode beat-notes. Assuming that all external-cavity modes have equal linewidths with an equal mode spacing, the measured RF-signal linewidth is double the linewidth of a single EC mode.
The spectrum of the DFECL measured by the RF SA with a photodetector is shown in Fig. 4. The linewidth of the mode beat-note of the DFECL-1 at 1490 nm is approximately 12.5 kHz at the 20 dB points below the peak. Assuming that the spectrum has a Lorentzian profile, the full width half maximum (FWHM) of an EC mode is ~675 Hz. FWHM for the DFECL-2 (67 cm cavity length) was measured to be ~2 kHz.
Our results are in broad agreement with those reported in Ref.  for the DFECL lasing at 1535 nm, where the linewidth of a DFECL was measured by a delayed self-heterodyne beating method. In that experiment the linewidth of less than 1 kHz at 1535 nm was obtained for a 3-meter-long DFECL, and the linewidth of 8 kHz was measured when the cavity length was 0.43 m .
6. Measurements of SMSR of the DFECL using RF methods
In order to find the SMSR of the DFECL-2 we have measured and compared the longitudinal-mode beat-note of two lasers: the DFECL-2 and a laser without a DF, the ECL-2. The design of both lasers used similar FP laser diodes and an external FBG, and their external cavity lengths were nominally the same. Both lasers operated at similar temperatures and diode driving currents.
The longitudinal mode beat-notes of the ECL are shown in black in Fig. 5. The peak amplitude is higher than -10 dBm. The RF beat-signal has a comb-like spectrum, which indicates that the side-mode suppression of the ECL is poor.
The mode beat-note of the DFECL, shown in red in Fig. 5, is much weaker than that of the ECL and the first beat-note of the DFECL in Fig. 5 has the amplitude of approximately -40 dBm. Only the first three beat-notes have amplitudes higher than -60 dBm and the amplitudes of the higher-order beat-notes is <-70 dBm. As compared with the ECL, the DFECL has fewer beat-notes in the RF spectrum and therefore fewer longitudinal modes oscillate in the optical spectrum. Although the lengths of the ECL and the DFECL are almost similar in the experiment, the field intensity inside these two types of the lasers may be different and therefore the absolute side-mode suppression due to the doped fiber in the cavity may not be derived from this experiment. This measurement, however, provides an estimate of the maximum number of the oscillating longitudinal modes in the spectrum, which is calculated using the number of the RF notes with the amplitude higher than the background noise (~-70 dBm).
The SMSR and the amplitudes of the optical longitudinal modes may be estimated analytically from Fig. 5 if a multimode optical field is described as , where Ei , ωi , and ϕi (t) are the intensity, frequency, and the random phase of the ith optical longitudinal mode. In further analysis we assume that the optical spectrum is symmetrical (E-i=Ei ) with only 9 modes E -4, E -3 …E 4 with the amplitude high enough to participate in RF signal generation, and the modes E -2, E -1…E 2 are much stronger than the others.
The RF beat-notes are generated at the mode spacing frequency and at its higher harmonics. The intensities of the first , the second , and the third beat-notes are defined as the overlap of the first-order adjacent modes, second-order adjacent modes, and the third-order adjacent modes of the optical spectrum, respectively. The first beat-note may be derived as:
where R is the optical-electrical conversion rate, which includes photodetector’s sensitivity and all transmission and coupling losses. Substituting the value of the first beat-note in Fig. 5 for the DFECL and using the above assumptions on the symmetry of the spectrum, we get the following equation:
Assuming that E 0>E 1>E 2>E 3, we derive:
The second beat-note may be written as:
Therefore, the second-order longitudinal mode depends on E 0 and E 1 as following:
Deriving similar equations for the third- and the fourth-order beat-notes, we get the following equations:
Using Eqs. (4), (6)–(8) we calculated the amplitudes of the optical modes at various values of the dominant longitudinal mode E 0=10nW…1 mW. The derived RF beat-notes (see Eqs. (3), (5)) at different values of the conversion rate R=0.2…1 were then compared with experiment. The analysis has shown that the suppression of the first-order longitudinal side-modes in the optical spectrum is at least 16 dB and the results do not depend on the value of R. The optical modes, which satisfy the conditions for the RF beat-notes in Fig. 5 and have the highest amplitudes, were estimated to be: E 0=-25.22 dBm, E 1=-42.81 dBm, E 2=-47.77 dBm, E 3=-81.58 dBm, E 4=-76.53 dBm. The measured spectrum has weaker amplitude than in the simulations due to the optical losses resulting from the measurement set-up, therefore only the mode suppression may be compared.
As the optical modes E 3 and E 4 are suppressed by >50 dB at any value of R and E 0, it is clear that the optical spectrum of the laser has maximum of 5 longitudinal modes. Thus Fig. 5 shows that the side mode suppression in a DFECL is more efficient than in an ECL and that the DFECL may have a maximum of 5 longitudinal modes in the optical spectrum.
The SMSR has also been measured by heterodyne beating of two DFECLs. The output of the DFECL-1 and the DFECL-2 were coupled using a fibre coupler and measured simultaneously with a FP OSA and an RF SA (through a photodetector with 15 GHz bandwidth). The peak wavelengths of the DFECLs were adjusted to ~1489.8 nm and ~1489.9 nm and therefore the beat signal was measured at ~10 GHz by a RF SA.
Figure 6(a) shows the heterodyne beat-notes of two DFECLs. The notes lie mostly in the range of 9±0.5 GHz within the envelope of a Gaussian function. The linewidth measured with heterodyne beating is broader than that measured with a self-homodyne method due to the superposition of the beat-notes in heterodyne method and phase noise effects. Fig. 6(b) shows the detailed view of the beat spectrum. As the DFECL’s output has several longitudinal modes, the heterodyne beat-notes are the superposition of beating of all frequencies, including heterodyne and self-mode beating. The dominant beat-note has a maximum amplitude of -3 dBm and is the heterodyne beat-note of the dominant longitudinal modes of two DFECLs. The adjacent notes are the superposition of beating of the dominant modes with the side modes. However, these beat-notes are ~15 dB to 20 dB weaker than the peak note, which indicates that the side modes of each DFECL are suppressed by more than 15 dB.
The weaker signals are caused by beating of high-order side modes with the dominant modes and the side modes with the other side modes. As the two lasers are not exactly the same, the estimate of the number of modes in the optical spectrum with this method may have an error of one mode. Since only 10 beat signals are suppressed by less than 50 dB, one may conclude that each of the DFECLs has maximum of 5 oscillating longitudinal modes suppressed by less than 50 dB. For ROF applications the SMSR of 30 dB is sufficient for high-quality signal transmission. In Fig. 6(b) only 3 beat signals have amplitudes higher than -33 dBm, which gives an estimate of a maximum of 2 modes oscillating in the optical spectrum with the suppression of less than 30 dB.
On the other hand, we may estimate the SMSR from the heterodyne experiment assuming that the spectra of two lasers are identical (Eai =Ebi ) and symmetrical (E -ai=Eai =Ei ). Considering only 9 modes in the oscillating spectra E -4…E 4., we derived equations similar to the Eqs. (3)–(8) for the optical modes and used the beat-notes amplitudes, obtained in the RF heterodyne measurement. Our calculations have shown that under these conditions the SMSR of as low as 20 dB could have been observed in the DFECL optical spectra.
Since the homodyne and heterodyne measurements were set up differently, the coupling loss, inline attenuation and detector responsivity may be different in these experiments. Therefore in this particular case we treated the results (i.e. the derived optical amplitudes) of two experiments separately. However, in further investigations an effort may be made to match the derived optical amplitudes both in a homodyne and heterodyne beat experiments.
Combining the results of the self-mode beating and the heterodyne beating experiments, we may conclude that a DFECL has a SMSR of at least 16 dB. Therefore the FWHM linewidth of the DFECL is the FWHM of a single EC mode. Our experiments agree with the time-domain model: there are only a few longitudinal modes inside the cavity of the DFECL instead of more than 100 modes in the similar ECL with high SMSR and at some currents only one longitudinal mode oscillates. Our recent simulations have shown that further optimization of the DFECL in order to get higher SMSR may be achieved by careful selection of its parameters, drive current and, most importantly, filling the whole external cavity with the doped fiber . A practical implementation of such a laser needs advanced splicing and coupling techniques.
We have shown that the rare-earth doped fiber inside the fiber grating ECL narrows the linewidth and suppresses the side external-cavity modes for the first time at a wavelength of 1490 nm. Two new long-cavity DFECLs at 1490 nm were built and SMSR of >15 dB has been measured. Using the self-mode beating and heterodyne beating techniques we have shown that our DFECL may have up to 5 longitudinal modes in the output instead of more than 100 modes in a similar ECL. These results match our theoretical analysis and time-domain simulations. Our results indicate that the RF mixing technique is indeed very useful for characterising narrow frequency lasers and aid in the fabrication of other such novel potentially single frequency sources.
The authors acknowledge the Canadian Institute for Photonics Innovation (CIPI), the Canada Research Chairs program by the Natural Science & Engineering Research Council of Canada (NSERC), and the NSERC’s Discovery Grants program for their support of the research. The authors are grateful to Philippe de Sandro of CorActive for the provision of the doped fiber.
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