Long-to-short wavelength swept source

Most swept external cavity diode lasers tune in the short-to-long wavelength direction (red tuning). Lower relative intensity noise (RIN) and higher output power are typically possible in this direction. We show here that long-to-short tuning (blue tuning) is possible for a short, linear cavity laser that has both low noise and high power. This mode of operation is made possible by nonlinear frequency broadening in the semiconductor optical amplifier (SOA) followed by clipping of the red portion of the spectrum by the micro-electro-mechanical systems (MEMS) tunable Fabry-Perot filter. Blue shifting during gain recovery is an important broadening mechanism. There is an approximate 50% advantage in coherence length for the same filter bandwidth for blue over red tuning, which allows deeper imaging in optical coherence tomography (OCT) applications. Calculations contrasting the blue tuning mechanism with red tuning are presented. The accuracy of the blue-tuning model is confirmed by coherence and coherence revival measurements and simulations. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Swept lasers are important in optical coherence tomography (OCT) applications because of the signal-to-noise advantage of Fourier domain over time-domain OCT methods [1][2][3][4]. Fourier domain methods are further divided into spectral domain (using broad-band light sources and spectrometers) and swept source methods. Spectral domain methods are favored at 850 nm because of the availability of silicon line cameras to collect the spectra in parallel. At longer wavelength ranges, such as 1060 nm and 1310 nm, swept sources are favored because detector arrays are not cost effective. This is the main source of demand for rapidly swept lasers.
Most swept external cavity diode lasers tune in the short-to-long wavelength direction (red tuning). Lower relative intensity noise (RIN) and higher output power are typically possible in this direction. This includes spinning polygon fiber ring lasers [5,6] and short, linear cavity lasers [7][8][9][10][11][12][13][14]. A short cavity laser that has more symmetric up/down behavior [15] is not included in the following analysis because its grating tuning mechanism introduces cavity length change [16], which is not modeled here. We document here calculations showing long-to-short tuning (blue tuning) for a short, linear cavity laser that has both low RIN and high power. This mode of operation is made possible by nonlinear frequency broadening in the semiconductor optical amplifier (SOA) followed by clipping of the red portion of the spectrum by the microelectro-mechanical systems (MEMS) tunable Fabry-Perot filter. Blue shifting of the wavelength during gain recovery is an important broadening mechanism. Blue tuning is not just of academic interest; there is an approximate 50% advantage in coherence length for the same MEMS filter bandwidth for blue over red tuning. Calculations contrasting the blue tuning mechanism with red tuning can explain this difference and provide a tool to optimize the laser design for blue tuning operation.
In the case red-tuned of short cavity lasers, the diagram in Fig. 1 shows the tuning mechanism. A pulse, circulating at the round-trip time of the cavity, depletes the gain. Depletion is the reduction of gain brought about by stimulated emission pulling energy out of the optical amplifier by recombination of electrons and holes. In this picture we model the SOA as a lumped gain Fig. 1. Rapidly red tuning a short cavity laser causes it to mode lock. The pulses deplete the gain and cause the index to rise. This red shifts the light field, causing the laser to "hop" to a longer wavelength on each trip around the cavity. element, rather than as a traveling wave amplifier. Concomitant with the gain depletion is a rise in the semiconductor optical amplifier's (SOA) refractive index. The power gain and index are linked through the linewidth enhancement factor, α [17], as: The SOA becomes optically longer as the pulse travels through, red shifting the light field. The laser does not tune continuously, but rather hops discretely to the next wavelength on each new pulse. The frequency hop for a SOA of length L is given by: This process works only for red tuning because of the natural red shift brought about by depletion of the gain medium. In most cases, a short cavity laser will pulse chaotically when blue tuned [8,9]. In our development of these short-cavity lasers, we found on occasion that some red-tuning lasers could cleanly tune in the blue direction as well. An effort to understand this resulted in a theoretical model [9] that describes both the blue and red tuning processes by taking into account the position of the SOA in the linear cavity. This allowed reliable blue-tuning lasers to be designed and constructed. The blue-tuning mechanism involved is the main subject of this paper. This is of practical interest because, as we will show, a blue tuning laser has greater coherence length than a red tuning one with similar design parameters including the same tunable filter bandwidth. Fig. 2. Diagram of the blue-tuning laser cavity, which is similar to that of the red tuning laser.

Laser cavity
The blue tuning laser, shown in Fig. 2, has essentially the same cavity as the red tuning short cavity laser [7][8][9][10]. A reflective MEMS Fabry-Perot filter allows creation of a very short cavity [11]. This filter has a reflection peak on resonance, whereas a planar Fabry-Perot described in many textbooks has a reflection minimum. This is because the filter is tilted with respect to the beam and works on a higher transverse mode of the half-symmetric filter cavity formed by one curved mirror and one flat mirror [11]. Although the laser cavity is very short physically, enabling it to fit inside a 14-pin butterfly package, its 39 mm optical length cavity is made possible by adding silicon "spacers" with a refractive index of 3.56. Other relevant laser parameters are listed in Table 1. These are the parameters fed to the numerical model described in [9] to simulate the blue-and red-tuning lasers.

Blue tuning laser data
Experimental sweep data for a blue-tuning short cavity swept laser is shown in Fig. 3. Two sweeps of the laser are shown, starting at the rising edge of the trigger signal and continuing through the red regions of the clock frequency and trigger signal waveforms. The blue optical power waveform shows pulsation in a 4 GHz electronic bandwidth and the red waveform is the time-averaged power. The wide bandwidth power signal is processed into a spectrogram in Fig. 3(d). Several features stand out in the spectrogram. Most prominent is the pulse repetition frequency at around 3000 MHz. That is not a fixed frequency across the sweep. The group delay in the MEMS Fabry-Perot tunable filter accounts for most of the U shape. The MEMS Fabry-Perot filter bandwidth changes from about 13 GHz at the edges of the spectrum to about 4 GHz in the middle. Amplification of the weak leading edge of a pulse advances the pulse to shorten the effective round-trip time. Finally, high dispersion in the SOA and silicon spacers change the effective Fig. 3. Laser sweep analysis. The clock interferometer frequency (a) is for a clock set for a 6.0mm Nyquist depth. The blue power trace (c) shows pulsation in a 4 GHz RF bandwidth and the red trace is the average power (c). This device tunes from 1220 to 1360 nm. The spectrogram (d) of the blue power trace (c), shows the pulsation frequency and the beat between adjacent pulses. The "U-shape" in the pulse repetition rate (d) is primarily due to variation in the MEMS filter linewidth across the tuning range. cavity length by 0.75 mm across the laser's tuning range. The relevant sweep parameters are listed in Table 2. The laser round-trip frequency is reasonably well described by the red dashed curve in Fig. 3(d) using the computational model from [9].
Another feature seen in the spectrogram is interference between a pulse and the previous pulse delayed by another trip through the cavity. That is outlined by the solid red curve in Fig.  3(d). Other lighter features with shapes similar to the solid red interference curve are from stray reflections inside the laser cavity at lengths less than the round-trip length. These reflections, if strong enough, may be seen as fixed patterns in an OCT A-line if the balanced detection suppression of common mode signals is not effective enough. The pulsation acts like a sampling switch, producing sidebands around the sampling rate that are the sum and difference of the interference curve. Despite the almost 100% modulation of the light field, most of these features are irrelevant to OCT operation since the detection band extends only to a few 100's of MHz, and all of the inconvenient signals are filtered away.

Laser simulation
The mathematical model of swept laser operation described in [9] can be used for both red-and blue-tuning simulations using the parameters from Table 1. A diagram of how the model works is shown in Fig. 4. This is a ring model of a linear cavity where the forward and backward gains are linked. The cavity losses and time delays are defined as input parameters. For the simulations shown in Fig. 5, the spatial reference for the curves is in the SOA and the power and instantaneous frequency curves are color coded the same as the dots in Fig. 4. A red-tuning swept laser is simulated in Fig. 5(a). It is a hypothetical design, closely matched to the blue-tuning design, to contrast the modes of operation and impact in terms of coherence length. Each double-humped pulse hops in frequency in discrete steps at an average rate of -5.2 GHz/ns and is chirped with most of the energy inside the tunable filter's passband, which is delineated by a diagonal green band in the "GHz" plot. Depletion and recovery of the gain happens in synchronism with the pulses, as seen in the "Single-pass field gain" plot. It is this mode of operation that we wish to compare with the blue-tuning laser.
The blue-tuning laser is not perfectly mode locked, but is largely so, as seen in Fig. 5(b). There is a slight asymmetry between even and odd pulses and some higher-frequency structure to the pulses. Overall, the laser tunes at +5.2 GHz/ns. A significant part of the pulse energy appears on the long wavelength side of the filter passband. This energy is discarded by the tunable filter, promoting blue tuning. The blue tuning mechanism is roughly a three-step process  Table 1). The wide light-green band in the instantaneous frequency plots marked "GHz" are the full-width half-maximum MEMS filter passbands. The green horizontal lines indicate the extent the light field "hops" in one round trip of the cavity. as diagrammed in Fig. 6: (1) A strong pulse depletes the gain medium red shifting it as in the mechanism of Fig. 1. (2) The MEMS tunable filter discards red components of the field. (3) A weak returning pulse is blue shifted during gain recovery. Gain depletion causes a red shift, but gain recovery shifts the light field to the blue. There is a constant spectral broadening of the light field with the filter throwing away red components. Overall there is tuning to the blue. This complex choreography of pulses is not possible in a ring cavity since it is the double pass of the pulse through the SOA at a specific time interval that makes this behavior possible. Although it is not immediately obvious from the red-and blue-tuning simulations, the blue-tuning mechanism is somewhat gentler, leading to pulses with less chirp and a longer coherence length.

Coherence
The coherence length simulations of Fig. 7 show that the blue-tuning laser has a 50% longer coherence length over a red-tuning laser of similar design (comparison in Table 1). In production of thousands of swept lasers and dozens of separate designs we have validated this type of simulation and use them to initiate new swept laser designs.
Apart from the coherence length itself, a major question about a short cavity swept source is the location and strength of the coherence revival peaks [9,[18][19][20]. Since the laser has one pulse Fig. 7. Coherence length calculations using the procedure and laser model of Ref. [9] for blue-and red-tuning lasers of designs from Table 1. The simulated blue-and red-tuning coherence lengths are 23 and 15 mm respectively, approximately a 50% advantage for blue over red.  Fig. 9 has been corrected by the ratio of the red-to blue-inked peaks.
per round trip, the coherence revival peaks are spaced in depth by the nominal optical cavity length. However, the cavity has a large amount of dispersion from the SOA and long silicon optical spacers. This broadens the coherence revival point spread functions from the transform limit to a width determined by the change in optical cavity length over the tuning range. The fundamental point spread and the first two coherence revival peaks are presented in Fig. 8. The fundamental point spread is near transform limited with no dispersion compensation. The first and second order coherence revival peaks are shown in Figs. 8(c) and 8(e) and the corresponding Fig. 9. Theoretical and experimental coherence length and coherence revival data. The model is dispersionless, so the blue curve had to be adjusted to the green using dispersion data from Fig. 8. The calculation and experiment use a 20 mm depth antialiasing filter. The cavity length is 39 mm. The coherence length is 23 mm. Fig. 10. Experimental interference spectrogram showing main signal and artifacts from coherence revival [9,18,19]. signal chirps in Figs. 8(d) and 8(f). Because of dispersion, each wavelength has a different optical cavity length. These are plotted out as an instantaneous depth on the "Display Depth" axes of Fig. 8. The first coherence revival is formed by the interference of a pulse with one that has circulated through the laser cavity an additional time. The additional trip adds one cavity round trip of dispersion to the pulse. The second order coherence revival peak experiences two cavity round trips of dispersion. Therefore, the instantaneous depth measures the dispersion in the cavity.
An important aspect of Figs. 8(c) and 8(e) is the amplitude difference between the measured coherence revival point spreads shown in red, and the calculated dispersionless point spreads shown in blue. This is important information for interpreting the coherence measurement of Fig.  9.
The coherence length is measured to be 23 mm at -6 dB in Fig. 9. The measurement is continued to deep depth to include the first, second, and third coherence revivals. At each depth, the maximum signal between 0 and 6 mm of the OCT A-line display depth is plotted. The data is compared with a theoretical calculation following the method outlined in [9]. This method assumes a dispersionless cavity, so the calculation needs to be corrected for dispersion. The raw calculation shown in Fig. 9 is incorrect for the coherence revival peaks, so those parts of the calculation are scaled by the amplitude differences of the measured and dispersionless peaks found in Figs. 8(c) and 8(e). The fit is particularly sensitive to the value of the linewidth enhancement factor, α. The figure for α listed in Table 1 was arrived at through this fitting process.
The interference spectrogram introduced in [9] tracks all of the RF signals vs. depth. In this case, instead of plotting RF frequency vs. interferometer length, the signal is resampled into a display depth. The interference spectrogram maps out what may become spurious signals in certain situations. This is especially important with complex OCT optical probe designs with many reflecting surfaces contributing weak stray reflections. The white line in Fig. 10 marked "Signal" is the main signal used for OCT image reconstruction. Everything else is a possible cause of an image artifact. A short cavity swept laser has many admirable characteristics, but the coherence revival properties can be problematic in some system designs. The interference spectrogram is an important tool for designing around these issues.
Some work [18,20] has, rather than considering the coherence revival as a nuisance, used it for imaging with increased depth coverage. The lasers in those studies were of a design with a fiber extended cavity and were 2X harmonically mode locked, meaning that there are two pulses in the cavity at the same time. The lasers discussed in this paper are optically shorter and operate with a single pulse in the cavity. A bigger difference is the silicon cavity extenders which contribute a large amount of dispersion between the beats of successive pulses. This makes the interference beats over the sweep highly chirped as shown in Figs. 8(d) and 8(f), complicating such coherence revival imaging methods. Our experience with standard OCT signal processing (not master/slave [20]) is that we were able to substantially narrow the point-spreads but not get to the transform-limit with simple low-order dispersion compensation methods.

Summary
Many swept laser types, including mode-locked short cavity designs and longer chaotically pulsed designs such as spinning polygon lasers, favor a short-to-long wavelength sweep (red) direction. Sweeping in the other direction tends to produce lower power and unstable operation. Here we show that short linear cavity lasers can be swept in the long-to-short (blue) direction as well. The nonlinear tuning mechanism is a bit more complicated, but can be modeled by the same theory that covers red tuning [9], and the measured performance of the blue-tuning laser matches the theoretical predictions. Simulations show that blue-tuning lasers have an approximately 50% coherence length advantage over red-tuning versions made from the same components. Through understanding of the blue-tuning process, a commercially available higher coherence laser was made possible by careful placement of optical components and reprogramming for the opposite sweep.