Ultra low noise Fourier domain mode locked laser for high quality megahertz optical coherence tomography

We investigate the origin of high frequency noise in Fourier domain mode locked (FDML) lasers and present an extremely well dispersion compensated setup which virtually eliminates intensity noise and dramatically improves coherence properties. We show optical coherence tomography (OCT) imaging at 3.2 MHz A-scan rate and demonstrate the positive impact of the described improvements on the image quality. Especially in highly scattering samples, at specular reflections and for strong signals at large depth, the noise in optical coherence tomography images is significantly reduced. We also describe a simple model that suggests a passive physical stabilizing mechanism that leads to an automatic compensation of remaining cavity dispersion in FDML lasers.


Introduction
FDML lasers are narrow band, high-speed optical frequency swept sources [1] that have proven their value in many different applications such as optical coherence tomography (OCT) [2][3][4][5][6][7][8], stimulated Raman spectroscopy [9], picosecond pulse generation [10], and sensing [11][12][13][14][15][16][17][18]. Their main application is still high speed OCT, where they have enabled recent developments such as ultra-widefield retinal 20], high definition live 3D-OCT [21] and "Heartbeat OCT" [22,23], all applications where multi-MHz A-scan rates are mandatory. The most important parameters of OCT sources, besides sweep rate, central wavelength, spectral shape and bandwidth, are noise and achievable roll-off performance. Many effects influence the performance of FDML lasers [24][25][26][27][28][29] and there are numerous indications that chromatic dispersion in the laser cavity is one of the most important [27,[30][31][32]. Kraetschmer and Sanders showed first, that a typical FDML laser intensity trace can exhibit nearly a hundred percent intensity modulation when measured with sufficiently high detection bandwidth of ~ 4 GHz or more [33]. Depending on the FDML operation parameters, Slepneva et al. identified the observed fluctuations as Turing instabilities or fully chaotic behavior [27]. Interestingly, when the FDML laser output intensity is measured with moderate photo receiver bandwidth of up to ~1 GHz, the output appears very smooth, indicating that the instabilities contain mainly very high frequencies, but still they cause a degradation of OCT images, even if the system only measures up to several hundred MHz electronic bandwidth. However, Kraetschmer and Sanders pointed out that an ultra-stable mode locked behavior centered around a very narrow range at the laser's zero dispersion wavelength exists when the cavity is very well dispersion compensated [33]. This range can be identified by the CW tuning steps described in [27]. In this very small (3.5 nm in their laser) spectral region that Sanders termed "sweet spot", the intensity variation within one sweep is vastly reduced. Up to at least several milliwatt, shot noise is dominant in the laser output, i.e., no excess noise can be measured. Sanders also reported instantaneous linewidths of ~100 MHz corresponding to meters of coherence length. Thus, this sweet spot operation would be extremely interesting for biomedical imaging, spectroscopy and sensing. Since this sweet spot was observed around the zero-dispe extend this ra compensation operation. So our implemen throughout a drastically im Figure 1 sho wavelength sw the optical ro grating (CFBG laser fiber cav The main com CFBG and de (SOA, spool) temperature c and an estim since it is not is performed.  act on the mos og to digital co the lowest noi Previous FDM to achieve the in the slightly educed by inte n the remainin will be further frequency is o ace (Fig. 5(a)) he cavity avelength ant effect ng cavity sity noise ond to the d to 5 Hz ) z s r st modern onverters, ise case is ML lasers e "0 Hz" y detuned entionally ng cavity analyzed optimized ) exhibits very low noise (considering the high electronic bandwidth). The noise spectrum (Fig. 5(b) and c) is flat and at a very low level over most of its range such that even the interleaving spurs caused by the oscilloscope electronics are now visible as spikes in the amplitude spectrum (Fig. 5(c), label ). The increase towards low frequencies (Fig. 5(b), label ) is mainly caused by the intensity envelope itself.

Setup
Detuning the FFP frequency by 1 Hz (Fig. 5(d),e,f -black curves) raises the intensity noise in the time traces to modulation depths up to 100% (Fig. 5. d). Accordingly, the corresponding noise floor in the spectrum is also increased, but interestingly only up to ~30−40 GHz (Fig. 5(e) and f). This decrease between 30 and 40 GHz (Fig. 5(f), ) is not caused by the electronic bandwidth of the detection, which is 50 GHz. The noise suppression is most likely caused by the FFP filter in the FDML laser, which effectively causes low pass filtering of any amplitude and phase fluctuations of the laser light. The FFP filter has an optical bandwidth of 0.165 nm which corresponds at a wavelength of 1300 nm to an optical frequency bandwidth of 29 GHz.
Detuning of 5 Hz causes an almost full 100% intensity fluctuation (Fig. 5g) over the full sweep duration and the level of the noise spectrum is substantially raised (Fig. 5(i)). Additionally, a noise peak around 8 GHz can be observed which may be caused by relaxation oscillations linked to the carrier dynamics in the semiconductor gain medium of the FDML laser ( Fig. 5(i), ). The noise decrease between 30 and 40 GHz can be observed again (Fig. 5(i), ♦). Most interestingly the intensity noise towards low frequencies is actually lower than in the case of 1 Hz detuning (Fig. 5(e) and 5(h)). To better visualize this effect, the average of 1000 FFTs over a range of 0 to 6 GHz is shown in Fig. 6. Between 0 and 2 GHz the 5 Hz detuned FDML laser has lower noise than the laser at 1 Hz detuning, for higher frequencies the noise of the 5 Hz detuned laser is higher. However, both detuned cases have much higher noise than the 0 Hz case.

Characterization of noise 2: counting holes
In the previous section we investigated the situation for a detuning of several Hz where we observe noise in form of intensity fluctuations throughout the whole sweep. For smaller values of detuning (⪅ 100 mHz) most of the intensity trace is "noise free" and we just observe some remaining isolated holes in the sweep as shown in Fig. 2 and Visualization 1. Since most of these holes have a duration of only 50 picoseconds or less they do not contribute substantially to the integrated noise over the 300 ns sweep and thus cannot be identified as increased noise in the noise spectrum. In order to still be able to characterize such low values of intensity noise, we switched to a different technique: we investigate the intensity trace and count the number of such holes as a measure for the remaining noise.
To quantify how the occurrence of holes qualitatively scales with the detuning of the FDML frequency, an algorithm applied a threshold below the mean intensity level and counted these intensity modulations that crossed this threshold as holes. Figure 7( Figure 9 com amounts of c plotted as the Figure 9(a Operating at allowing eigh the dominant intensity leve RTT and inve adjusted so th The sweet sp found as perm As anothe dispersion are remaining RT visibly reduc strongly from the cavity. In the optimum very uniform

Compari
These mea some parts of on the noise dispersion ver driving freque Considerin implies that a intensity noise ior FDML lase w laser with tw ion. In Fig. 9 the also increased group delay of such a filter might further reduce the occurrence of such holes by passive phase stabilization as will be explained in the next paragraph.

FFP group delay and dispersion compensation
As mentioned, we credit a major role for the compensation of the dispersion in the laser cavity to the Fabry-Pérot filter. Like any bandpass filter, the FFP induces a group delay on the incoming signal. The amount of group delay depends on the frequency offset relative to the maximum transmission frequency. In the following, we will show how this frequency dependent group delay could act as a passive dispersion compensation mechanism. The dispersion relation of the FFP is that of an ordinary bandpass filter and can be treated analytically. Using the convention i t e ω − for a plane wave and frequency offset f, the group delay is defined as g d d  Figure 12 shows the group delay for light that arrives at the FFP with a frequency difference relative to the transmission window for a filter with a spectral width of λ 0.165 δ = nm centered at 0 λ = 1292 nm. Light with a frequency that exactly matches the maximum transmission of the filter experiences a group delay of 10 ps when passing the filter. Light with an offset relative to the transmission maximum experiences less group delay. For example, for a frequency offset of ± 15 GHz, the group delay induced by the filter reduces to only about 5 ps.
For a filter window moving in time, this suggests that any wavelength circulating the laser cavity may experience a varying GD in the FFP due to very small delays in the cavity. being the maximum of the FFP filter group delay shown in Fig. 12, any active wavelength can pick a position in the filter window such that the total RTT exactly matches 1 / FFP f . Of course, these temporal offsets must be sufficiently low so the FFP loss (reflected intensity) remains irrelevant. As the light will arrive at the FFP with a constant frequency offset after every roundtrip, as long as ( ) cavity RTT λ doesn't change, we will call this position stationary.
As shown in Fig. 13a, there are two positions for every wavelength in the filter window at which any given wavelength will exactly meet the FDML condition but as will be explained in the following, only one of them is stable. When the inverse filter frequency of the FFP exactly matches the round trip time of the light (including the group delay given by the filter) for every wavelength in the sweep, the FDML laser can be run in a stationary mode with phase matching at the input facet of the FFP, again, as long as there are no changes in ( ) cavity RTT λ . However, these changes will naturally occur continuously, for example due to temperature drifts in the cavity.
We now look at one arbitrary wavelength within this sweep that runs stationary in the negative wing (left half in Fig. 13a) of the filter transmission band. We assume that its cavity RTT increases by a time τ due to a temperature drift in the cavity as sketched in Fig.   13b. When the light arrives delayed at the filter, the center transmission frequency has increased and the light hits the filter with an increased negative frequency offset (for the red to blue sweep). For example, a filter tuning over 100 nm at an A-scan rate of 3.2 MHz will have shifted its center transmission wavelength by ~ 1.1 GHz within 20 ps. Due to the increased negative filter offset, the light passes the FFP faster. This way the FFP group delay can compensate for a part of the delay τ in the cavity. In consecutive sweeps the wavelength under inspection will continue to experience the delay τ in the cavity and will wander to the left of the filter transmission window until the reduction in group delay of the filter equals τ .
From then on it will run in a stationary mode as the RTT equals the filter drive period again. This is sketched in Fig. 13b with the red dots being positions in consecutive sweeps following the black arrow.
When the cavity RTT of this specific wavelength decreases by -τ , the group delay of the filter will increase and, again, after some roundtrips compensate for τ − . This way, we think that the filter can compensate remaining dispersion in the cavity as well as wavelength dependent dynamic changes in the cavity length and therefore allows a stable operation with no or very few holes.
However, when the specific wavelength hits the filter transmission band with a positive frequency offset, any change of the frequency accelerates the wandering of this wavelength to the other border of the transmission window i.e. to the stable regime. The same argument works for the forward sweep, however, then the stable and unstable regimes depicted in Fig.  13  Disclosures TP: Optores GmbH (P,R), MP: Optores GmbH (E), WD: Optores GmbH (I,P,R), RH: Optores GmbH (I,P,R), Optovue Inc. (P,R), Zeiss Meditec (P,R), Abott (P,R).