Principle and functionality of FDML lasers

to build up newly from ASE which is the speed limiting factor in conventional wave-length-swept lasers. In the field of SS-OCT, FDML lasers allow for the fastest high-quality SS-OCT imaging existing at the moment. Record voxel rates of 4.5 GVoxels/s at ultra-high sweep rates of 20.4 MHZ (four spot approach) [8] have been demonstrated. A detailed description of the FDML principle and technology is given in chapter 2.2.2 and chapter 2.2.3.

2.2.1.5 Alternative approaches

Apart from the mentioned approaches, there also have been other completely different techniques to implement fast wavelength-swept light sources, which did not prevail in SS-OCT imaging. One example is a semiconductor wavelength-swept laser which is based on dispersion mode-locking. The laser is operated in active mode locked opera-tion generating short pulses. Due to a high dispersion that is introduced in the cavity, harmonic mode locking condition is only fulfilled within a certain wavelength window.

Therefore, the tuning of the intensity modulation frequency (changing SOA current modulation frequency) results in sweeping of the output wavelength. In this way, sweep rates of 200 kHz and sweep ranges >100 nm were demonstrated [206, 207]. Problems can arise due the lack of a direct filtering mechanism complicating the achievement of a narrowband output. Another example of a fast wavelength-swept light source is the combination of a spectrally broadband, pulsed source with a dispersive fiber, which results in temporal stretching of the short pulses. With this passive technique, using a sub-nanosecond super-continuum pulsed source, very high sweep rates of 5 MHz and a sweep range >100 nm were easily achieved [176]. However, high-quality OCT imaging was not possible due to a very low sensitivity of only 40 dB. Drawbacks of this ap-proach are the need for a broadband source with low intensity noise and a very large amount of dispersion requiring several 10 km of dispersive fiber.

length, can be overcome. This principle was first demonstrated in 1975, using a cw dye laser and a very fast tuned electro-optical filter [191] (sweep range was restricted to

~15 nm). In 2006, this concept was first realized with an external-cavity semiconductor laser [6], allowing for sweep ranges exceeding 100 nm. The main components of this typically all fiber based laser setup (see Figure 2.8) are a fiber based output coupler, the broadband gain medium (usually fiber based semiconductor optical amplifier (SOA)), the tunable bandpass filter (usually a fiber Fabry-Pérot tunable filter) and a typically several 100 to a few 1000 meters long optical fiber delay line (usually standard single mode fiber), which has to be inserted in order to enable the synchronous bandpass filter drive. This laser has been referred to as Fourier domain mode locked laser (FDML) [6].

The reason is that FDML lasers are complementary to standard mode locked laser, comparing the time domain picture in standard mode locked lasers and the frequency domain or Fourier domain picture in FDML lasers. In FDML lasers, the frequency is modulated synchronously to the round-trip time of light rather than the amplitude.

Whereas, FDML lasers generate a sequence of frequency sweeps with a narrow instan-taneous spectrum providing ideally the same output power (continuous wave operation), standard mode locked lasers generate broadband, very short pulses. The frequency sweeps of FDML lasers can also be seen as long, highly chirped pulses. Under ideal operation, the sequential frequency sweeps, or long highly chirped pulses, exhibit the same phase evolution and are mutually coherent, as it is the case with the short pulses in standard mode-locking. In standard mode locked lasers, the phases of the longitudinal laser modes are locked with a constant phase, whereas in an ideal FDML laser the

lon-Figure 2.8: Setup of a typical all fiber based Fourier domain mode locked (FDML) laser. Besides the output coupler, the three main elements are the gain medium, which is most commonly a sem-iconductor optical amplifier (SOA), the tunable bandpass filter, usually a fiber based Fabry-Pérot tunable filter (FFP-TF) and the fiber delay, typically standard single mode fiber (SMF), which has to be inserted in the resonator to enable a filter drive synchronously to the round-trip time of light in the cavity. (PC: Polarization controller, ISO: Optical isolator, FC: Fused fiber coupler)

SOA

output FFP-TF FC

SMF gain medium

fiber delay tunable

bandpass filter

gitudinal laser modes must be locked exhibiting different phases. The spectral, band filtering in an ideal FDML laser can be compared to an infinite number of narrow-band amplitude modulators that are driven slightly out of phase [6]. Note that FDML lasing operation must not be confused with frequency modulation lasers (FM lasers) [208] or frequency modulation mode locking (FM mode-locking) [209]. In FM lasers, a phase modulator is introduced in the cavity, inducing a phase perturbation at a frequency which approximately equals the inverse round-trip time of light in the resonator. This produces an almost constant intensity trace but a temporal change in output wavelength (sweep with very small sweep range). If the phase perturbation fre-quency is set nearly synchronous to the round-trip time, this is the transition to FM mode locking, which is used for short pulse generation.

In FDML lasers, the wavelength of the spectral filter is tuned repetitively and continu-ously (usually sinusoidal drive) with a filter drive frequency over the filter sweep range with alternating sweep directions (bidirectional filter drive, forward and backward sweep). If is the total length of the cavity, is the refractive index of the optical fiber, is the speed of light in vacuum and is a positive integer , the resonance condition for the filter drive can therefore be expressed by the following equation:

2.33

Obviously, FDML operation can only be achieved for discrete filter drive frequencies.

Due to the bidirectional filter drive, FDML operation at the fundamental frequency means that at any time one pair of forward and backward sweeps is optically stored in the cavity, whereas operation at higher harmonics ( implies that this is true for multiple pairs . In order to achieve a sufficient filter tuning range, it can be advantageous to drive the optical bandpass filter with a frequency close to or matching its electro-mechanical resonance [10]. Depending on the filter, typical achievable filter drive frequencies range from several tens to several hundreds of kHz. According to equation 2.33 , typical resonator lengths are therefore in the range of several 100 m to a few  kilometers, explaining the requirement for an optical fiber delay.

Note that the sweep rate or A-scan rate (in OCT) usually exceeds the filter drive frequency if, for example, forward and backward scans are used sim-ultaneously or if the optical buffering technique is applied (see chapter 2.2.3.3).

One important point that has not been considered yet is chromatic dispersion in the FDML cavity, which results in the fact that the FDML criterion (equation 2.33) can on-ly be fulfilled for one distinct wavelength (or several, if dispersion is not constant over wavelength), but is not valid over the entire filter sweep range . In order to estimate the consequences of this effect, it is helpful to compare two different values [178]. On the one hand, there is the round-trip time mismatch between minimal and maximal wavelengths occurring within the optical bandwidth

(where the FDML laser is lasing), which can be expressed as assuming a constant dispersion . On the other hand, there is the gating time

of the bandpass filter (spectral width , which is the approximate time period within the filter can transmit a certain wavelength or the time where the center frequency is swept over . If , only a few round-trips of photons in the cavity are possible until lasing has to build up newly from ASE. If the ratio is increased, this results in a higher number of effective cavity roundtrips. Therefore, is an important prerequisite for optimum FDML operation. Interestingly, under the given assumptions, is indirect proportional to the dispersion, the filter sweep range, the band-width and the number of harmonics , proportional to the spectral filter width but independent of the resonator length L. Light of a certain wavelength, not fulfilling equation 2.33, passes the optical filter a distinct number of times but each time at a different position within the filter shape approaching gradually the edge of the filter curve. If the loss of the filter exceeds the effective gain in the laser, lasing at this wavelength is suppressed and has to build up newly from ASE. Based on these assumptions, the effective number of roundtrips of light of a certain wavelength can be estimated [14]. Note that there are various other effects influencing FDML oper-ation [15, 210], which are not included in this simple estimation, though they have to be considered for a comprehensive understanding of FDML laser dynamics. Examples are saturation effects, linewidth enhancement and recovery dynamics in the SOA, self phase modulation (SPM) or polarization mode dispersion (PMD) in the delay fiber, or addi-tional effects occurring due to optical filtering. Nevertheless, a minimization of chro-matic dispersion in the fiber is an important step to increase the number of effective round-trips and filtering events which, in addition to an appropriate choice of the filter width , can considerably improve coherence and minimize the average instanta-neous linewidth of the laser over the whole sweep, as demonstrated experimentally [14].

Compared to conventional wavelength-swept lasers, the introduction of FDML lasers enabled, on the one hand, a dramatic increase in available sweep rate and, on the other hand, a considerable reduction of the instantaneous linewidth (increase of instantaneous coherence length) due to multiple filtering [6]. Additionally, FDML lasers also provide an improved phase stability [211], which can be advantageous in, for example, Dop-pler-OCT. The most successful application of FDML lasers up to date is ultra-high speed SS-OCT. An FDML laser has been used for the fastest high-quality SS-OCT im-aging existing at the moment. Record voxel rates of 4.5 GVoxels/s at ultra-high sweep rates of 20.4 MHz (four spot approach) [8] have been demonstrated at 1300 nm. Ultra-fast ultrawide-field retinal SS-OCT imaging was enabled at 3.35 MHz sweep rate (sin-gle spot) [7]. However, besides OCT, FDML lasers have the potential to be used in a variety of other applications. Examples are phase sensitive profilometry [211], high-speed spectroscopy [212], optical coherence microscopy (OCM) [213] or fast fiber Bragg grating (FBG) sensing [214-216].

As already mentioned, ideal FDML operation induces longitudinal laser modes which are locked and exhibit a certain well-defined phase relation, making adjacent sweeps mutually coherent. Although there is no doubt that FDML lasers provide improved

per-formance and a stable lasing operation, it is not completely clarified up to now in how far effects occurring in realistic FDML operation (as mentioned in this chapter), influ-ence FDML dynamics. It is not entirely clear if or how these effects interact supporting or impeding a stationary lasing operation. Furthermore, it is not clear in how far the longitudinal laser modes exhibit a definite phase relation or to which extend the modes are locked. Within the framework of this thesis, a completely new approach of short pulse generation has been investigated, which is based on temporal compression of the wavelength-swept output of an FDML laser. Since the achievable minimum pulse width depends on the coherence properties of the laser and on the quality of mode-locking, this approach offered the possibility to gain an insight into these properties and identify parameters which influence the coherence performance. In chapter 4, the results of this approach are presented.