Fundamental and practical performance limits of continuously tunable optical sources using extra-cavity mixing process are examined. While the parametric process cannot overcome the fundamental tunable limit set by the uncertainty principle, it offers a new path in overcoming the practical performance limits associated with conventional tunable lasers. Specifically, cavity reconfiguration speed is recognized as a limiting process in all tunable lasers that cannot be circumvented by any conventional approach. Recognizing this barrier, we introduce and experimentally demonstrate a decoupling concept that relies on extra-cavity mixing to increase the tuning speed and range of any tunable laser source.
© 2010 OSA
Continuously tunable oscillator devices have been introduced both in RF and optical domains and rely on diverse technologies [1–3]. A need for very fast, continuously tunable sources over wide spectral range has been recognized in sensing and process control applications . As an illustration of the technical challenge, consider cycle-resolved, MHz-scale resolution combustion process analysis for a modern jet engine that operates at or above 100,000 rpm, generating spectral signatures over hundreds of nanometers across the optical (infrared) range. While capturing the entire spectral content might be demanding, even a partial, 100nm-wide acquisition requires a MHz-linewidth source capable of ~106nm/s tuning (sweep) rate. Similar challenge is posed by the use of tunable sources for biomedical imaging purposes. A video-rate optical coherence tomography (OCT) with sub-micron resolution would dictate ~109nm/s sweep rate over spectral range measured in hundreds of nanometers , which is currently out of reach of conventional tunable laser physics.
A combination of fundamental and practical barriers sets strict limits on laser tuning performance. An ideal tunable source should possess unlimited tuning speed, be capable of sweeping over arbitrarily wide band while attaining narrow linewidth. Unfortunately, the existence of such source is prohibited by the Heisenberg principle, as its operation would imply that the strict spectral localization, inferred by narrow linewidth, is possible in spite of arbitrarily fast tuning speed and range. In a limit, an infinite sweep rate would imply that the source frequency can be anywhere within the tuning range while the near-zero linewidth would guarantee exact spectral localization .
Long before reaching the uncertainty limit, fundamental laser physics would have barred one from constructing fast and coherent tunable source. All known tunable technologies rely on cavity reconfiguration [1–3] to achieve wavelength tuning, in which the length or pass-band center frequency of the laser cavity is varied to enforce the new resonant frequency. Even though the cavity can be reconfigured swiftly, either via mechanical, optical or electrical means, the linewidth is invariably sacrificed since the coherence of the laser wave depends on the photon cavity lifetime . Indeed, in order to tune to the new wavelength, one has to wait longer than the photon cavity lifetime. Worse, the photon lifetime is inversely proportional to the source linewidth: a narrower linewidth implies longer cavity reconfiguration time, implying that highly resonant cavities are not amenable to swift reconfiguration. The later fact represents the true limit of the tunable technology that cannot be circumvented, even in principle, by any cavity engineering techniques. Consequently, the tunable source can be engineered for either tuning speed or narrow linewidth, but not for both simultaneously.
Recognizing this limitation, it is clear that any new principle must rely on decoupling of wavelength tuning from cavity reconfiguration mechanism. This paper introduces the concept of extra-cavity parametric process to achieve qualitatively higher tuning performance. The approach allows for both tuning speed and range of any tunable source to be scaled arbitrarily while preserving the coherence, thus breaking the barrier set by the cavity tuning physics.
This report introduces the cavitless source tuning (CAST) principle first and subsequently describes experimental demonstration and practical implications.
2. CAST Principle
In its simplest form, CAST principle rests on an early observation by Inoue  that the frequency displacement of mixing tones lead to twice the frequency shift of the mixing product. This principle is easily visualized in case of a one-pump parametric mixer, illustrated in Fig. 1 . In static regime, pump photons at frequency ωp co-propagating with seed photons at ωs results in generation of idler photons at ωi due to four photon mixing (FPM). The idler and signal photons are created via annihilation of two pump photons, with idler frequency strictly defined by the conservation of energy as ωi = 2ωp - ωs. In silica, since the photon energy from near-infrared lasers are orders of magnitude below the material band-gap, the response time of electron-mediated FPM process is nearly instantaneous (~10 fs), and much faster than any time scale associated with conventional wavelength tuning. If the pump frequency is shifted by Δωp, the idler frequency will shifted instantly by 2Δωp. Consequently the frequency sweep rate (dω/dt) and range (Δω) are simultaneously doubled. More importantly, since the energy of the generated idler photons is strictly bound to the conservation of energy stated above, the uncertainty in idler photon energy will only be scaled by the same factor. Quantitatively, we may express the enhancement in a laser sweep in terms of a figure-of-merit (FOM), defined by the total sweep range (ΔωT), time lapse for a sweep (Δτ) and the maximum frequency uncertainty (δω) of the laser sweep as:
Therefore the CAST scheme, even in its simplest form, provides a 50% enhancement in FOM. The sweep up-scaling factor, and thus FOM, can be further enhanced by relying on higher-order or cascaded generation, as shown in Fig. 2 . Higher order generation can be achieved by launching higher power pump and seed into the mixer: the idler will eventually be powerful enough to act as a secondary pump source and mix with spectrally-adjacent wave (primary pump in this case). Since the idler contains twice the sweep range and rate of the pump, the resultant mixing product (ωi2) will acquire an up-scaling factor of 3:
If this process is allowed to cascade further by managing the pump-idler powers so that the higher-order idlers are also powerful enough to mix efficiently, the nth-order idler will now attain a sweep range and rate at (n + 1) times of the original (pump) tunable laser. Although multiple components are generated simultaneously, these components are spectrally distinct and therefore can be incorporated as a unified laser sweep with, for instance, multiple receivers to sense the signature carried by each component. Taking the whole sweep generated by higher-order mixing into account, the sweep range is enhanced by a factor of (n + 1)(n + 2)/2, whereas the maximum frequency uncertainty is scaled by a factor of (n + 1). Therefore the FOM is up-scaled by a factor of (n + 2)/2. As a result, the performance of a tunable laser can be up-scaled arbitrarily, provided the available power and mixer performance are sufficient for higher-order mixing to occur.
In the second scheme, illustrated in Fig. 2b, instead of requiring that the single mixer performance is sufficient to generate multiple idler waves, separate mixer stages are introduced to create only first-order idlers. In practical terms, this approach would require lower launch power and less stringent mixer engineering. The idler, which acquires twice the sweep range and rate in the first parametric stage, subsequently mixes with spectrally fixed seed in the next stage, thus generating a secondary idler possessing twice the sweep range of the primary idler, or equivalently, quadruple of the original pump. The laser sweep can therefore be enhance arbitrarily by cascading more parametric stages and results in 2n times sweep up-scaling by the idler generated in the nth stage. Following similar analysis, the FOM is scaled by (2n + 1 – 1)/2n in the cascaded mixing scheme, inferring a FOM up-scaling limit of 2 for high stage count. Even though the FOM cannot be enhanced arbitrarily as in the higher-order mixing scheme, the cascaded mixing scheme provides technically less demanding pathway to up-scale sweep range and rate, which are of higher importance in certain applications . Indeed, practically least demanding realization for cascaded CAST is to enclose the mixer into a re-circulating loop and allows new idlers to be generated during each pass. Unfortunately, not only that maximal FOM would not be reached, but the intracavity noise accumulation would pose significant construction limits.
Finally, by considering two-pump mixing processes , illustrated in Fig. 3 , further increase in source tuning speed and range is easily achieved: the original sweep can be quadrupled or quintupled in a single stage using primary idlers only. Naturally, higher-order and cascaded generation is still applicable with dual-pump mixer stage.
3.1 Higher-order mixing scheme
The experimental setup for demonstrating laser-sweep up-scaling by higher-order mixing is illustrated in Fig. 4 . A wavelength-swept laser, which generated repetitive sweep across 6 nm centered at 1558 nm at a rate of 10000 nm/s, served as the pump source. The tunable source was amplified to 1.5W by an erbium-doped fiber amplifier (EDFA1) and filtered by a 4-nm wavelength-division multiplexing coupler (WDMC) to reject nonlinear portion of the laser sweep range, located at the extrema of the sweep band. The WDMC also served as a low-loss combiner between the pump and a 500-mW, fixed wavelength seed wave at 1537.5 nm. The combined pump and seed were then launched into a spool of 200-m highly-nonlinear fiber (HNLF) serving as the parametric mixing medium. To facilitate wide-band higher-order mixing, a dispersion-flattened HNLF with dispersion below 1 ps/nm/km across the 1500-1650nm band was used, as shown in the inset of Fig. 4. The nonlinear coefficient of the HNLF was 8 W−1km−1. At seed power level of 500 mW, stimulated Brillouin scattering (SBS) was observed and mitigated by phase-dithering the seed wave with a RF noise source, resulting in a broadened linewidth to 450 MHz. In contrast, the pump did not experience SBS effect, which can be accounted by the linewidth broadening due to the wavelength sweep within the characteristic lifetime of phonons in fiber . In practical terms, SBS suppression can be achieved by differential tension synthesis , circumventing any phase dithering of either the pump or the seed. Maximum idler generation efficiency was attained by aligning the states of polarizations (SOPs) of the pump and the seed waves. The parametric mixing process was monitored spectrally by an optical spectrum analyzer (OSA) at the output end of the HNLF, and temporally with the procedures to be described in later text.
Figure 5(a) shows the spectra at the input and output of the HNLF. The widened spectral width of idlers clearly depicts an enhancement in sweep range, scaling proportionally with the idler order. Efficient generation of idlers up to third order was observed with power ripple of 12 dB across a total bandwidth of 77 nm, spanned by the pump and three generated idlers. The power ripple was a result of non-negligible second-order polarization mode dispersion (PMD) in the fiber span of 200 m, which can in principle be reduced by shortening the fiber at the expense of elevated pump power requirement. Alternatively, a near-isotropic HNLF class can be used while maintaining the overall efficiency of the mixer.
The sweep rate of individual components (pump and idlers) was inspected by filtering out a 4-nm slice of the spectral component of interest (either pump or a particular idler), and subsequent filtering by periodic spectral element (interleaver) with free-spectral range (FSR) of 50 GHz. At the output of the interleaver, the sweep was visualized as the laser sweep across the periodic transmission profile, resulting in waveforms shown in Fig. 5(b). In simple terms, the spectrally periodic interleaver response was mapped to periodic temporal response, with period strictly defined by the laser tuning speed. Reduction of the temporal period was observed from the pump to the third-order idler, thus proving the assumption that the sweep rate is enhanced by strict arithmetic order as predicted.
In order to investigate the instantaneous linewidth of the mixing products, a modified heterodyning scheme was constructed. The output light after 4-nm filtering was combined with a tunable external cavity laser (ECL) with a linewidth of 100 kHz and wavelength coinciding the center wavelength of the component being investigated. Coherent mixing between the static laser and the sweeping component resulted in a chirp waveform generated at a photo-detector with 18 GHz bandwidth. The waveform was recorded by a real-time oscilloscope with 16 GHz bandwidth, and the phase noise of the sweeping component was then retrieved by using the algorithm described in the Appendix. Figure 6 shows the retrieved temporal phase noise profiles and lineshapes for the pump and the idlers. Increased phase noise amplitude observed in the first-order idler is inherited from the phase-dithered seed wave. The phase noise amplitudes of the higher-order idlers increase proportionally to the order of idlers as a result of temporal phase transfer . Consequently the higher-order idlers acquired broader linewidths as shown in Fig. 6(b). Such linewidth broadening can be eliminated when phase-dithering can be avoided, for example, by using synthetically strained fiber with higher SBS threshold . Using a pulsed seed source with pulse width below ns-regime also eradicates the necessity of phase-modulation, although the generated idlers will also acquire the same pulse modulation.
3.2 Cascaded mixing scheme
In the second set of experiments, the need for higher-order mixing which mandated the use of high power pump and seed waves, was eliminated by using cascaded parametric stages described in section 2. The setup, shown in Fig. 7 , comprised two parametric mixing stages. Stage 1 shared a similar topology as the previous setup, except the seed power was lowered to 140 mW, thus eliminating the need for SBS suppression by phase dithering. The pump power was reduced to 1W to avoid efficient generation of higher-order idlers and the need for complex filtering scheme at the output. The first stage idler generated at 1579.1 nm was filtered by a fixed, 19-nm wide band-pass filter (BPF) centered at 1576.5 nm. The idler was subsequently re-amplified by EDFA3 to 1 W and combined with the second seed light at 1554.1 nm with a power level of 43 mW. Since part of the pump sweep band was removed by band-pass filtering in the first stage, temporal gaps were created within the waveforms corresponding to the pump and the idler. Consequently, 1600nm distributed feedback (DFB) laser was used in the experiment to clamp the transients in EDFA3. Average power at 1600 nm was maintained to be at least 10 dB lower than that of the idler by offsetting the polarization of the DFB laser from the transmission axis of the polarization beam splitter (PBS). The outputs from both stages were monitored spectrally and temporally using the methodologies described in the previous scheme.
The spectra shown in Fig. 8(a) demonstrate a qualitatively different operation regime than that of a higher-order, single-stage mixer. In contrast to the high-order mixer scheme that required a high-power seed, the cascaded approach relied on low-power seeds: the first-order idler efficiency was maintained with simultaneous suppression of higher-order products. A spectral tilt experienced by the first-order, first-stage idler (idler 1) was deliberately introduced by controlling the pump power to shape the idler generation efficiency spectrally . The spectral tilt subsequently cancelled the gain tilt introduced by EDFA3, resulting in a spectrally-flat pump source for the second stage. The combination of the pump spectral equalization and the reduction of higher-order PMD effects stemming from smaller mixer bandwidth resulted in a power ripple of only 1.2 dB on the second stage idler. A staged increase in sweep bandwidth from 5 nm to 20 nm and the corresponding compression of the temporal fringe period from 40 μs (original pump) to 10 μs (output, idler 2) confirmed a four-fold enhancement in both sweep range and rate, as shown in Fig. 8(b).
Finally, the instantaneous linewidth of the pump and each idler were characterized and shown in Fig. 9 . The lineshape spectra shown in Fig. 9(a) were obtained with a measurement interval of 1.3 μs and averaged over five measurements. The spectral shapes resembled typical Lorentzian lineshapes. The full-width at half-maximum (FWHM) linewidths were revealed by fitting the spectra with Lorentzian functions, as shown in Fig. 9(b). The linewidth of the idler in each stage was approximately twice of their respective pumps. In the quantum (Schawlow-Townes) limit, which assumes a white frequency noise spectrum, linear scaling of frequency noise will result in quadratic linewidth enhancement . In practical laser oscillators, however, variety of mechanisms lead to a low-pass enhancement of frequency noise spectrum and results in linear scaling of laser linewidth , as observed in the experimental work shown here. A detailed description on frequency noise and linewidth scaling in FPM processes will be discussed in future report.
We demonstrated extra-cavity approaches for enhancing tunable laser performance. Parametric process provides physical means to decouple wavelength tuning from cavity reconfiguration mechanism. While confined by conservation of energy and momentum of the interacting photons, cavitless source tuning mechanism is independent of cavity lifetime and is inherently limited only by the nonlinear response time of the mixer. In analogy to the mechanical gear box, CAST mechanism can be seen as an equivalent of true optical frequency scaler, as it allows the tuning range and the tuning (sweep) range to be multiplied, independent of the input laser source properties.
While the generalization of CAST mechanism includes its implementation within the closed (recirculating) loop or within the frequency (wavelength) comb, its principle will remain the same: FPM process will be used as frequency (wavelength) lever to expand spectral (temporal) performance of a tunable device.
Finally, the reported work opens a greater challenge: how close one can approach the tunable Heisenberg limit using the CAST principle or its generalization. While it appears necessary that mixers matching this challenge should be lumped, rather than distributed devices used in this work, it remains to be seen if requisite efficiencies and performance can be reached by any similar platform.
Appendix: Instantaneous linewidth measurement
When the output of a laser-under-test (LUT) is combined with a coherent field at the same average frequency as of the LUT from a reference (Ref) laser with linewidth considerably narrower than the LUT, the heterodyne signal, obtained by detecting the power of the resultant field, can be expressed as follows:
If the power of both laser is constant over time, the heterodyne signal p(t) then carries only the relative phase noise (ϕ LUT – ϕ Ref) information. Since the phase noise of the reference laser is assumed to be much smaller than the LUT, the phase of the reference field ϕ Ref thus becomes quasi-static and convey negligible influence on p(t). Base on these two assumptions, the complex electric field A LUT = A R + jA I of the LUT can then be retrieved by applying Hilbert transform H[.] on the DC-rejected heterodyne signal pAC(t) as follow:
If the LUT is subject to a (linear) frequency sweep, the heterodyne signal will then contain a fast (linear) chirp component. This chirp component is a result of a rapidly (quadratic) increasing phase and is independent to the intrinsic phase noise of the LUT. An example is shown in Fig. A1(a), which was obtained with the same wavelength-swept laser described in the previous sections. In order to retrieve the phase noise covered by this non-static component, the frequency sweep of the LUT ought to be retrieved and cancelled. Using the same treatment described in Eq. (A2), the phase of the LUT was reconstructed, revealing the quadratic phase and thus linear frequency sweep with respect to time as shown in Fig. A1(b).
Noticing the polynomial (nearly quadratic) nature of the phase evolution, the contribution of the frequency sweep can be subtracted from the retrieved phase by a polynomial fit. In practice, a polynomial fit of up to third order may be required to account for the nonlinearity in the frequency sweep, however, higher-order fit should be avoided as the excess degree of freedom in root placement can lead to undesired removal of low-frequency phase noise. The underlying phase noise retrieved after polynomial fit is depicted in Fig. A2(a). Although the heterodyne signal was recorded for 60 μs, only a 1.3-μs slice of the trace was retained for phase noise measurement in order to eliminate the effect of non-uniform frequency response of the photo-detector and the oscilloscope which produced the amplitude ripple as shown in Fig. A1(a). The lineshape of the LUT can then be reconstructed with the availability of phase noise, as shown in Fig. A2(b). A Lorentzian lineshape function fit to the reconstructed lineshape provides a better measure of linewidth (178.6 kHz) as shown in Fig. 9(b).
In order to confirm the accuracy of the instantaneous linewidth retrieval algorithm described here, the measurement result obtained with this algorithm was compared against a measurement made by a commercial high-resolution OSA (Agilent 83453B). The comparison was done by measuring the lineshape of the stationary seed wave used in stage 2 of the cascaded mixing scheme, whereas the described algorithm was deployed to retrieve the lineshape of the generated idler. Since the resolution of the OSA was limited to 1 MHz, a distributed-feedback (DFB) laser diode with linewidth of 30 MHz replaced the seed laser (ECL) used in the previous setup which had a sub-MHz linewidth. The use of the broad linewidth seed laser also reduced the influence of pump source linewidth in the comparison. Fig. A3 shows the retrieved power spectrum of the idler overlaid with the spectrum of the stationary seed laser measured by the OSA. Excellent agreement between the retrieved instantaneous lineshape spectrum and the static measurement performed with the commercial OSA confirms the credibility of the described algorithm.
This work was supported in part by funding from Defense Advanced Research Projects Administration (DARPA) under contract N00014-08-1-1180. The authors also acknowledge Sumitomo Electric for providing the highly nonlinear fiber used in the experiments.
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