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Virtual Journal for Biomedical Optics

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  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 2 — Feb. 10, 2009
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Spectral narrowing effect by quasi-phase continuous tuning in high-speed wavelength-swept light source

Changho Chong, Takuya Suzuki, Atsushi Morosawa, and Tooru Sakai  »View Author Affiliations


Optics Express, Vol. 16, Issue 25, pp. 21105-21118 (2008)
http://dx.doi.org/10.1364/OE.16.021105


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Abstract

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

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

30. W. R. Trutna Jr. and L. F. Stokes, “Continuously Tuned External Cavity Semiconductor Laser,” J. Lightwave Technol. 11, 1279–1286 (1993). [CrossRef]

] which we modified and adapted to the fiber-extended cavity.

Fig. 1. Diagram of multi-mode lasing with Gaussian filter envelope

2. Concept of Quasi-Phase continuous tuning (QPCT)

Fig. 2. (a). Configuration for phase continuous tuning. 2(b) Concept of quasi-phase continuous tuning for mode-hop free tuning.
Fig. 3.(a). Phase diagram of Lasing in Fig. 2(a)
3.(b). Phase diagram of Lasing in Fig. 2(b)

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:

λg=2asinθ
(1)
λL=L(θ)LoλL(θc)
(2)

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)

λ'g=dλgdθ=2acosθc
(3)
dλLdθ=λcHtanθc(Locosθc+H)
(4)

and are set to equal, then following relation of geometry is derived.

H=cosθctan2θc1·L1
(5)

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

17. L. A. Kranendonk, R. J. Bartula, and S. T. Sanders, “Modeless operation of a wavelength-agile laser by high-speed cavity length changes,” Opt. Express 13, 1498–1507 (2005). [CrossRef] [PubMed]

], 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

17. L. A. Kranendonk, R. J. Bartula, and S. T. Sanders, “Modeless operation of a wavelength-agile laser by high-speed cavity length changes,” Opt. Express 13, 1498–1507 (2005). [CrossRef] [PubMed]

].

Fig. 4. QPCT conditions with different wavelength ranges
Fig. 5.(a). Phase variation over diffraction angle range
Fig. 5.(b). Cavity mode order over wavelength

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;

P=dλgdλLdθ
(6)

Figure 6 shows the factor of phase lag, P over wavelength range with grating constant of 1312 g/mm.

Fig. 6. Out-of-Phase ratio P over wavelength range

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

31. G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147–159 (1988). [CrossRef]

,32

32. K. Inoue, T. Mukai, and T. Saitou, “Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier,” Appl. Phys. Lett. 51, 1051–1053 (1987). [CrossRef]

] 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

7. Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K. P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13, 10652–10664 (2005). [CrossRef] [PubMed]

].

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

27. S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, “Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting,” Opt. Express 12, 4822–4828 (2004). [CrossRef] [PubMed]

29

29. A. M. Davis, M. A. Choma, and J. A. Izatt, “Heterodyne swept-source optical coherence tomography for complete complex conjugate ambiguity removal,” J. Biomed. Opt. 10, 064005 (2005) [CrossRef]

].

Lc=2ln2πcδν
(7)
Fig. 8. Temporal optical output power
Fig. 9. Relative Intensity Noise
Fig. 10. Balanced Mach-Zehnder interferometer

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)
Fig. 13. Spectral linewidth vs. Scan rate

Fig. 14. OCT signal at different depth positions with and without QPCT condition

Table 1. List of summary results

table-icon
View This Table

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

33. L. A. Coldren and S. W. Corzine “Diode Lasers and Photonic Integrated Circuits,” (Wiley Series in Microwave and Optical Engineering, NY, 1995).

],

dNdt=ηiIqVVτmvggmNphm
(8)
dNphmdt=ΓvggmNphm+ΓβspRspmNphmτph
(9)

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.

Nphm=ΓβspRspm1τphΓvgmgm=ΓβspRspmvgmαi+αmmΓgm
(10)
I=Ith+qVηimvggmNphm
(11)

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).

Pm=F1mvgmαmNphmhνVp=αmΓRspmhνVpαi+αmmΓgm
(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).

MSR=PnPm=gthngn(N)gthmgm(N)
(13)

Ptotal=ηiαmαi+αmmhνq(IIth)=αmαi+αmmhνVmvggmNphm
(14)
MSR=Ptotal(+Δα)Ptotal=(αi+αmm)(IIthn)(αi+αmn)(IIth)
(15)

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.

Fig. 17. Light vs. carrier density for n-th cavity mode
Fig. 18. Mode suppression ratio
Fig. 19. Output power vs. Injection current
Fig. 20. Spectrum comparison

7. Conclusion

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S. H. Yun, D. J. Richardson, D. O. Culverhouse, and B. Y. Kim, “Wavelength-Swept Fiber Laser with Frequency Shifted Feedback and Resonantly Swept Intra-Cavity Acoustooptic Tunable Filter, “IEEE J. Sel. Top. Quantum Electron. 3, 1087–1076 (1997). [CrossRef]

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R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14, 3225–3237 (2006). [CrossRef] [PubMed]

27.

S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, “Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting,” Opt. Express 12, 4822–4828 (2004). [CrossRef] [PubMed]

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29.

A. M. Davis, M. A. Choma, and J. A. Izatt, “Heterodyne swept-source optical coherence tomography for complete complex conjugate ambiguity removal,” J. Biomed. Opt. 10, 064005 (2005) [CrossRef]

30.

W. R. Trutna Jr. and L. F. Stokes, “Continuously Tuned External Cavity Semiconductor Laser,” J. Lightwave Technol. 11, 1279–1286 (1993). [CrossRef]

31.

G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147–159 (1988). [CrossRef]

32.

K. Inoue, T. Mukai, and T. Saitou, “Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier,” Appl. Phys. Lett. 51, 1051–1053 (1987). [CrossRef]

33.

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OCIS Codes
(110.4500) Imaging systems : Optical coherence tomography
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(140.3600) Lasers and laser optics : Lasers, tunable

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: September 18, 2008
Revised Manuscript: November 29, 2008
Manuscript Accepted: November 30, 2008
Published: December 5, 2008

Virtual Issues
Vol. 4, Iss. 2 Virtual Journal for Biomedical Optics

Citation
Changho Chong, Takuya Suzuki, Atsushi Morosawa, and Tooru Sakai, "Spectral narrowing effect by quasi-phase continuous tuning in high-speed wavelength-swept light source," Opt. Express 16, 21105-21118 (2008)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-16-25-21105


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References

  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991). [CrossRef] [PubMed]
  2. S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, "Optical coherence tomography using a frequency-tunable optical source," Opt. Lett. 22, 340-342 (1997). [CrossRef] [PubMed]
  3. A. F. Fercher, C. K. Hitzenberger, G. Kamp, Sy. Y. El-Zaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995). [CrossRef]
  4. B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, "Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr/sup 4+/:forsterite laser," Opt. Lett. 22, 1704-1706 (1997). [CrossRef]
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