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This paper reports on a technique to improve the coherence length of a high-speed wavelength swept laser. The wavelength swept laser comprises a pigtailed semiconductor optical amplifier and a wavelength-scanning filter in a fiber extended cavity configuration. The laser operates in the 1310 nm wavelength region. The tunable filter consists of a diffraction grating and polygon mirror scanner. Littrow arrangement of external cavity in a specific geometry realizes the quasi-phase continuous tuning over wavelength range emphasizing coherent amplification of cavity modes resulting in spectral narrowing of the instantaneous linewidth to about 0.06nm. Improvement by a factor of two is confirmed in comparison with coherence length without using this technique. Peak power is 12 mW and wavelength swept range is 55 nm, from 1271 nm to 1326 nm. Measured coherence lengths of over 30 mm and 17 mm were achieved at scanning rates of 2.5 kHz and 20 kHz, respectively. Correlation of laser cavity parameters with spectral linewidth is also discussed by introducing the rate equations for multi-mode laser operation. Shorter cavity length is considered effective to further improve the coherence length in terms of shorter roundtrip time as well as higher mode suppression ratio because of higher carrier concentration on cavity modes around the filter center.
©2008 Optical Society of America
1. Introduction
Fast wavelength-swept lasers are increasing being used as light sources for applications that require dynamic or real time measurements with high sensitivity and wide dynamic range. Examples include interferometric measurements such as swept-source optical coherence tomography (SS-OCT) [1–7] and surface profiling, as well as spectroscopic measurements including fiber sensor systems [8], and gas sensing [9–11]. In the case of SS-OCT and surface profiling, coherence length, or instantaneous linewidth of swept source is a key parameters that determines the measurement depth range in cross-sectioned images. In the fiber sensor systems or gas sensing systems, instantaneous linewidth determines the measurement resolution of the system. To maximize the data acquisition rate of such measurement systems it is desirable to increase the scan rate of the swept laser. In general as lasers move to higher sweep speeds there is an increase in instantaneous linewidth, and decrease in coherence length resulting in reduced measurement depth. Typical coherence length previously reported for SS-OCT was limited to 5 to 6 mm [12,13] corresponding to spectral linewidth of about 0.13 nm at swept rates ranging from several kHz to a few tens of kHz. A 5 to 6 mm coherence length corresponds to the single side measurement depth of 2.5 to 3 mm in OCT, which has been sufficient for many clinical OCT applications where the depth of interest is limited to the superficial layer and fundamental absorption and scattering in the tissue limits light penetration. However, increase of coherence length is now desired because of following three reasons; 1) demand of increase of the swept rate while maintaining fair amount of depth range [14], 2) demand of increase of mechanical clearance to the sample surface especially in the case of endoscopic applications so that it can give certain tolerance to the position of the catheter [15,16], and 3) the need of larger scale 3D profiling in industrial applications. Previous work has reported on fiber-extended cavity tunable lasers [17–24]. In these lasers a tunable filter sweeps over the gain bandwidth of a semiconductor optical amplifier (SOA) and accumulated gain on the cavity longitudinal modes within the envelope of the filter will result in lasing output from the fiber cavity. In most cases, cavity longitudinal modes are virtually stationary during the sweep as shown in Fig. 1. If the tunable filter is stationary or slowly tuned, there is strong cavity mode selection within the filter window resulting in narrow spectral envelope of laser output. On the other hand, if the tunable filter is swept at over a few kHz rates, cavity mode selection is reduced resulting in an increase output linewidth. The increase in mode competition is due to the mismatch between the modes preferentially amplified in the SOA and the center of the scanning filter over each roundtrip. This is mainly because the most of swept sources are designed to have a fixed cavity length where cavity modes are relatively stationary with respect to the high-speed swept tunable filter. In order to overcome the increase in output linewidth at higher scan rates, several ideas have been introduced such as the phase matching technique using accousto-optic filter, that matches the wavelength shift over a round trip to the phase shift generated by the filter itself [25]. Another technique is Fourier domain mode locking (FDML), whereby the tunable filter scan frequency is matched to the optical round trip time resulting in a higher Q factor of the cavity in frequency domain [26]. These two approaches, however, require both to operate at a preset resonant condition, i.e. at fixed swept rate, and the latter case needs long fiber length to accommodate several tens of kHz swept rate or slower. Other than using these techniques, adding the ambiguity or complex conjugate removal by adding external phase shifter in the OCT system is known as an alternative way [27–29], but it is not preferable when the system design is cost-sensitive.
In this paper, on the contrary to the above approaches in frequency domain, we demonstrate a rather simple but effective configuration to achieve narrow instantaneous linewidth in time domain. We here call this approach Quasi-Phase Continuous Tuning (QPCT) technique, which is analogous to the classical pivot tuning mechanism in external cavity single longitudinal mode laser [30] which we modified and adapted to the fiber-extended cavity.
2. Concept of Quasi-Phase continuous tuning (QPCT)
Figure 2 shows the concept of a QPCT laser in comparison with the single mode external cavity laser with perfectly phase-continuous tuning. In a conventional single mode-hop free tuning as shown in Fig. 2(a), in a simplified case of Littrow arrangement, if the grating is rotated around the so called pivot, the cavity mode and the filter center is completely synchronized over large tuning range without having a mode-hop [30]. This is a novel tuning method because only one rotary motion is required for continuous tuning, and it has been widely applied to the tunable laser instruments. However, the tuning speed or slope is limited to a few seconds per sweep over 100 nm at 1.3 or 1.55 micron wavelength range. This is because the pivot of the rotation is largely off from the optical axis or the point of diffraction, the faster modulation of large momentum is impossible to achieve with today’s mechanical actuation technologies. In the case of multi-mode envelope tuning as previously explained, wavelength is tuned continuously over a group of longitudinal modes, gradually shifting to next adjacent modes ensuring continuity of tuning. Figure 2(b) shows the schematic of wavelength swept laser based on QPCT with an SOA and a tunable filter that comprises a diffraction grating and deflection mirror in a Littrow arrangement. Deflection of the collimated beam from the fiber output of the SOA by the scanner mirror changes the incident angle to the diffraction grating thus changes the wavelength of diffracted light couple back to the cavity. At the same time during wavelength sweep, the deflection of the beam modulates the phase by the change of diffraction point on the diffraction grating, which corresponds to the cavity length change. If we set an appropriate geometry so that the gradient of wavelength change and phase are nearly equal, the wavelength and the phase can be synchronously modulated to a certain degree. Figure 3(b) shows the evolution of phase in step by step. Even though the filter’s peak wavelength is not perfectly matched to each one of longitudinal mode over entire wavelength range, a majority of longitudinal modes remains in a filter window over the small increment of time allowing a few round trip of light during a scan. As a result, it is expected to enhance the coherent build-up of the laser modes and increase the Q factor of the cavity during the sweep, which was confirmed in the experiment described in section 4.
Fig. 2. (a). Configuration for phase continuous tuning. 2(b) Concept of quasi-phase continuous tuning for mode-hop free tuning.
3. Conditions for QPCT
As previously mentioned, the relation of gradient of wavelength and the phase change simply determines the condition for quasi-phase continuous tuning. Here, total cavity length L is a function of grating incident angle θ, which is expressed in the sum of the optical length from the deflection point to the grating, H/cosθ and the length to the other end of cavity, L 1, thus L=L 1+H/cosθ
Wavelength of the filter, λg and the wavelength of the cavity longitudinal mode, λL at the center of wavelength range are expressed in:
L o, θ c, a are the length and the diffraction angle at the center of wavelength range, and grating pitch, respectively. Then the gradients of these equations are expressed in (3), (4)
and are set to equal, then following relation of geometry is derived.
This is a basic condition for QPCT design, where θ c=asin(λ c/2a).
Figure 4 shows the ratio of H/L 1 with various diffraction grating constants (Λ(=1/a)[g/mm]) and with respect to the center wavelength of the tuning range. This graph indicates that depending on the selection of the grating constants Λ, appropriate ratio of lengths around the point of deflection, H/L1 has a large variation with respect to the desired wavelength range, and also shows that the lower the wavelength range is such as 1050 nm range, the higher the grating constant should be chosen in order to fulfill the condition. Figure 5(a) shows an example of wavelength and phase trace when the above condition is fulfilled. Figure 5(b) shows the cavity mode order n that coincides with filter’s peak wavelength over tuning range. In terms of value R as in reference [17], which is defined as the relative frequency change of the cavity modes with respect to the free spectral range during a single roundtrip, R is substantially small. This mode of operation is completely opposite approach of modeless operation as described in Ref. [17].
We can quantify the degree of phase synchronization in terms of temporal phase lag between longitudinal modes and the filter’s peak wavelength over entire wavelength range as the difference of gradients;
Figure 6 shows the factor of phase lag, P over wavelength range with grating constant of 1312 g/mm.
As shown in Fig. 6, the calculated phase lag over small increment of wavelength change is at worst 40 % at the edges of tuning range, in the other words, 60 % are synchronous resulting in a high cavity resonance leading to narrow linewidth of the source. For an example, for an optical cavity length of 3 m corresponding to a cavity round trip time of 10nsec, and the filter tuning 100 nm at 20 kHz, the tuning slope is 2 nm/µsec. As described in previous work [19], when using an SOA with ASE power of a few milliwatts and over 20 dB gain and a tunable filter with 2–3 dB insertion loss, it takes about three round trips to build up to the saturated optical output. During three round trips, i.e. 30 nsec, filter wavelength shifts by 0.06 nm, which is nearly a half of filter window. In the other words, if the filter window shifts about a single increment of window in the amount of filter bandwidth; 0.12nm, there will be no contribution of any preceding cavity modes from the previous window of the filter to a next increment of window. On the other hand, in the case of QPCT, there is always over 70 % of phase or cavity modes carried over from previous round or window of oscillation as it travels the cavity contributing to the build up of the gain, resulting in narrower linewidth. It is equivalent to the slowing the tuning speed of the tunable filter with respect to the cavity modes.
Cavity length is another important factor in order to improve the resonance of the cavity. The shorter the cavity length is, the higher the gain builds up on lasing cavity modes during the high-speed sweep, by allowing many roundtrips within the filter’s moving window. However the shortest cavity length is limited by the continuity of sweep. If it is too short, unstable mode competition or bistability within a small number of cavity modes within the window results in unstable or noisy temporal optical power profile. In order to have a continuous and stable sweep of wavelength, a few tens of centimeters to a few meter long cavity lengths is considered appropriate. In this experiment, since the use of single mode fiber instead of free space makes it much easier to configure the laser cavity in terms of the alignment and handling, a pigtailed SOA is used as a gain element which is connected to the tunable filter via a collimator lens and terminated with a partial reflection mirror on the other side of fiber pigtail to form an extended cavity structure as shown in Fig. 7. The shortest fiber length that we can prepare for the pigtail part was 0.6m from end to end corresponding to optical length L1 of 0.85 m. To have the length of H in practical range of a couple of tens of centimeters for loss-less free-space coupling by the collimator, we selected a diffraction grating constant of 1312 g/mm according to the Eq. (5) that gives sufficient synchronization over the tunable range considering the practical length that can be achieved by fiber splicing. From the Fig. 4 or Eq. (5), the condition for the quasi-phase continuous tuning is found to be when H=100 mm. Total cavity length at center wavelength at 1310 nm is calculated to 2.5 m per round trip optical path that corresponds to the photon lifetime in the cavity of 8.3 nsec. In this case, the number of longitudinal modes is about 150 within the window of 0.1 nm bandwidth of the filter.
Additionally, Doppler shift may arise as a concern when the cavity length modulation is as large as 100 mm in this case. When swept rate is at 20 kHz, the rate of cavity modulation vf is 100 mm/50 µsec=2,000 m/sec, and the Doppler shift calculated by Δf Doppler=f/(c+v f) is about 1.5 GHz in optical frequency or 9pm in wavelength. This is negligible magnitude because the spectral linewidth of interest in this study is in the order of 0.05 to 0.1 nm. However, either when further lienwidth narrowing is necessary to the order equal to the Doppler shift, or when increasing the swept rate resulting in larger Doppler shift, the Doppler shift becomes non-negligible order to the linewidth, and this needs to be accounted for the design. One way to countermeasure this problem is either scaling down the cavity length or choosing the condition of H≪L1.
4. Experimental setup
Figure 7 shows the schematic of the QPCT laser that was used to verify the proof-of-concept. The laser comprises an SOA (COVEGA BOA1137) and a polygon scanner based grating filter in a Littrow arrangement. Polygon mirror has an inscribed diameter of 60 mm with 30 facets, and its rotation speed is set at 40,000 rpm for 20 kHz swept rate and 5,000 rpm for 2.5 kHz rate. The rotational direction of the polygon scanner is chosen to have positive saw-tooth scanning starting from shorter to longer wavelength since the reverse sweep induces a self-frequency shift due to four-wave mixing by carrier density modulation in the SOA [31,32] lowering laser output power and also widening the spectral linewidth as a results. Collimated beam with a beam diameter (2w at 1/e2) of 800 µm is expanded to 2 mm in lateral direction before the polygon mirror by three prism expanders. Polygon facet width of 6.3 mm is wide enough so that there is no clipping of the beam within effective FSR of the tunable filter. Polarization controllers at the two arms of fiber pigtail are used to match polarization states of the light traveling back and forwards with respect to the diffraction grating and SOA so that the collimate beam is aligned in S-polarization in free-space with respect to the grating, and input and output beam going into the SOA is aligned in TE mode. Modulation constant of the 1312 g/mm is chosen to tune over 100 nm wavelength range around 1320 nm. FSR of tunable filter is 180 nm. The bandwidth of tunable filter is calculated to 0.13 nm. Tunable range is limited by the physical size of the diffraction grating that should cover the effective deflection angle of the beam at the distance H. The prism expander between polygon scanner and the diffraction grating is arranged in a way such that the linearity of sweep slope becomes higher, eliminating the need of so called k-triggering and wavelength rescaling process [7].
Fig. 7. Diagram of polygon scanner -based swept laser source PE: Partial reflector, Col: Collimator lens, PC: Polarization controller, S: SOA, PR: Prism, G: Diffraction grating, POL: Polygon scanner.
5. Results
Instantaneous linewidth of the source with QPCT was measured at various conditions. The bandwidth (FWHM) of the grating filter of 0.126 nm and 0.05 nm was chosen for validation of spectral narrowing effect by QPCT at two different speeds, 2.5k Hz and 20kHz. Filter bandwidth is adjusted by the number of prism expanders inserted in the free-space, thus changing the magnification of the beam. Figure 8 shows the oscilloscope trace of the three consecutive scans. Scan range measured by optical spectral analyzer was 55 nm, from 1271 nm to 1326 nm. Peak and average power are 12 mW and 8m W, respectively. Relative intensity noise (RIN) of the source was measured less than -110dB/Hz over all frequency range as shown in Fig. 9. The cavity modes spacing of 120–130 MHz, or 0.68–0.74 pm in wavelength, accounted for the peak at 120–130 MHz that is inverse of the cavity length, and the splitting of which is due to the modulation of cavity length.
In order to measure the instantaneous linewidth, the swept output is fed into a simple Mach-Zehnder interferometer as shown in Fig. 10, and a high-speed receiver with 2.5 GHz bandwidth is used to detect the fringe signal. When the amplitude of fringe drops in half compared to that at zero delay, the amount of delay equals to the coherence length by definition. Relation of instantaneous linewidth and coherence length is given by Eq. (7). If the dual side of the range around zero delay is included, the range doubles as long as mirror imaging can be cancelled [27–29].
Figure 11 shows the signal power spectrum at several depth positions, with and without QPCT. The one without QPCT has a ratio of H/L1 about less than 0.05(H=60 mm, L1=1.15 m, while the source with QPCT has a ratio of 0.25(H=210 mm, L1=0.85 m). Here we kept the same cavity length for both cases, about 2.5 m round trip, at the center wavelength. As shown in Fig. 11(a), signal power drops 6 dB at the depth of about 2 to 2.5 mm if it is without this technique. The corresponding linewidth nearly equals to the filter bandwidth of 0.13 nm. While, it is extended to over 5 mm if this quasi-phase continuous condition is satisfied, and which corresponds to 0.075 nm of spectral linewidth. If we slow down the swept rate, we get further extension of single side depth up to around 8 mm at 2.5 kHz as shown in Fig. 12. Axial resolution at 2 mm depth as shown in Fig. 11(b) is found about 24 µm, which corresponds to about FWHM of 55 nm of swept range. The obtained swept range was such narrower than FSR of tunable filter 180 nm (duty ratio of about 30 %) mainly because the length of grating we used is not long enough to cover whole deflection angle of the beam. We believe that by using longer grating in size or shortening the total cavity length can improve the swept range over the gain bandwidth of SOA. Figure 13 shows the comparison of spectral linewidth with and without QPCT over different swept rates. Coherence length improvement or linewidth narrowing effect was in the factor of about X1.8 to X2 from the case without using QPCT over 1–20 kHz swept rate.
Fig. 11. (a). OCT signal at different depth positions with and without QPCT (b) Close-up of spectrum (20 kHz swept rate)
Fig. 12. OCT signal at different depth positions with and without QPCT condition (2.5 kHz swept rate)
Replacing the grating to the one with higher modulation constant of 1500 g/mm resulted in a further increase of the coherence length. The calculated filter width in the same configuration except the grating was 0.051 nm. Figure 14 shows the measured OCT signal spectrum at different positions at two swept rates, 2.5, 20 kHz. Coherence length was 30 mm, and 17 mm, corresponding to 0.025 nm, 0.043 nm of linewidth respectively at center wavelength of 1289 nm. It was a factor of X1.2 to X2.0 improvement or narrowing with respect to the filter bandwidth depending on the swept rate. Improvement factor becomes lower than the previous case. This is because the phase lag becomes larger when using modulation constant of 1500 g/mm than the one with 1312 g/mm and also because the phase shift per round trip becomes non-negligible order with respect to the order of linewidth. Table 1.summarizes the results with different parameters.
Table 1. List of summary results
6. Discussion: Estimate of spectral width in multimode lasing in a Gaussian envelope
When QPCT is close to the ideal case, i.e. perfect phase matching condition, instantaneous linewidth is expected to be as narrow as the stationary linewidth. So estimating the stationary linewidth will provide the quantitative factor of how much narrowing effect can benefit to instantaneous linewidth during the scan in QPCT. When the lasing is stationary in wavelength, the spectrum can be simply measured by optical spectral analyzer (OSA) unless the linewidth is smaller than resolution of OSA.
Theoretical estimation of spectral width in this type of multimode Gaussian envelope lasing can be derived from the analysis of mode suppression ratio that is calculated by expanding rate equations in multimode oscillation [33],
where variables of N and N phm, I are total carrier density, photon density on mth cavity mode, and injection current, respectively, and constants of ν g, V, Γ, τ, n g, g m, β sp, R spm are group velocity, volume of active region in the gain medium, confinement factor, cavity life time, group refractive index, spontaneous emission factor, spontaneous electron recombination rate, respectively. In the steady state (i.e. dN/dt=0, dN ph/dt=0), Eqs. (8), (9) yield the followings; (10), (11) for photon density and injection current.
Here, I th, α i, α mm, η i are threshold injection current, internal optical loss of gain medium, the sum of mirror loss and filter loss at mth mode, internal efficiency, respectively. Optical power at a cavity mode order (m) can be expressed as in Eq. (12).
Here, F 1m, α m, is the ratio of power coupled out, and mirror loss that is virtually equal for all modes in this case because of narrow filter window. Mode suppression ratio (MSR) is simply given as the ratio of output power of primary mode (m) to that of the distant nth mode (n).
If modal gain and threshold gain at each mode are given, MSR can be calculated from Eq. (13). Figure 17 shows the optical power per mode with a small gain or loss difference. In the case of multimode laser oscillation with narrow Gaussian envelope as depicted in Fig. 17(b), modal gain and carrier densities are localized in degenerate states so that the group of modes experiences simply a cavity loss variation enforced by the tunable filter at different mode positions. Figure 18 shows the MSR against carrier density per mode. Since carriers are spread to a number of modes within the window, MSR is expected to be substantially lower than that in the case of single mode lasing. Alternatively, total power can be expressed as in Eq. (14), and actual suppression ratio can be simply the ratio of the total output power P total(α mm(λc)) to the output power with insertion loss equivalent to the filter transmission loss at nth mode position, P total (α mn(λc+δλ)).
where I th, I thn are total threshold current on all modes and threshold current when having the filter loss coinciding on nth mode position, respectively. The output power at each mode position is emulated by changing the cavity loss, for an example by adding the attenuation inside the external cavity. 1.5 dB and 3 dB neutral density attenuation plate are inserted in the optical path. Figure 19 shows the output power against injection current to the SOA with 0, 3, 6 dB cavity loss increase. The ratio of output power at two different losses with respect to the 0 dB loss corresponds to MSR stretched from filter’s profile as shown in Fig. 18(a), which is about 7 dB and 11 dB in this example. This gives an approximate profile of the lasing spectrum as shown in Fig. 20. Calculated linewidth from the Gaussian fitted profile using the MSR is 0.075 nm, and the stationary linewidth measured with OSA was 0.052 nm which is close to the instantaneous linewidth at 2.5 kHz swept rate; 0.048 nm. Insufficient data sampling of profile and the error of inserted attenuation value as well as mismatch between actual filter profile and the ideal Gaussian envelope account for discrepancy between the calculated and the measured linewidth. However, it gives an approximate estimate of linewidth especially when the spectral linewidth is smaller than the measurable resolution of OSA, which is a convenient way to assess the linewidth limit when using QPCT technique.
In addition, Eq. (14) indicates the relation of the modal density contributing to the laser. If cavity mode density within the laser spectrum window is lower, distributed carrier density per mode becomes higher leading to higher modal gain; g(N), thus resulting in higher MSR as can be seen in Fig. 18. It suggests that the cavity length should be shorter to give lower cavity density for narrowing the linewidth. Shorter limit for cavity length is restricted by the requirement of continuity of tuning, not inducing bistability of lasing or significant mode hopping. Increase of injection current will also increase the MSR up to the saturated regime, while MSR starts to decrease in the saturated regime when the gain is compressed by excessive depletion of carrier.
7. Conclusion
In this study, we proposed and demonstrated a high-speed wavelength swept laser with a technique to improve coherence length drastically by novel quasi-phase continuous tuning (QPCT). QPCT configured in the extended cavity tunable laser in Littrow configuration enhances the instantaneous linewidth while maintaining the continuous wavelength sweep at high swept rate. Using this technique, instantaneous linewidth of 0.048 nm and 0.075 nm was realized at sweep speed of 2.5 kHz, 20k Hz, respectively, which corresponds to the coherence length of 16 mm, 10 mm at 1310 nm wavelength range. Linewidth narrowing factor that is defined as the ratio of instantaneous linewidth with QPCT to that without QPCT is about X1.8 to X2.0 depending on the swept rate. We confirmed this approach is non-resonant with respect to the swept rate unlike frequency-shifted wavelength swept source or FDML laser proposed in the previous works. Further optimization with using a shorter cavity design and smaller grating modulation constant will improve the enhancement factor. The QPCT technique will contribute not only to the large-depth imaging in OCT applications but also to the high-resolution spectroscopy or dynamic fiber sensing applications as these are gaining attentions in the near future.
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