Abstract

Optical sampling systems traditionally require either one mode-locked laser with an external delay line or two mode-locked lasers with a controllable repetition rate difference. In this paper we present a novel polarization-multiplexed laser architecture combining the benefits of both approaches. The laser emits two mode-locked pulse trains sharing only one gain section without any external delay line. The colliding pulses in the laser have orthogonal polarization as well as opposite propagation directions to reduce coupling effects. With this, the two pulse trains can be freely phase controlled to conduct pump-probe measurements. To further analyze the timing stability of the system, we conducted a two-photon-absorption experiment, leading to a timing accuracy of 30 fs. Based on the novel laser architecture, we call this new approach single-laser polarization-controlled optical sampling, or SLAPCOPS.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Pump-probe measurements enable time-resolved characterization of physical systems on a time scale not accessible for conventional electronic measurement equipment [1–3]. Essential for this type of measurement is the generation of two optical pulses with an adjustable temporal separation, which are then used to excite and sample the reaction of a sample under investigation. Usually, in a standard setup the output of one fs-laser source is split up into a pump arm and probe arm. The delay is established by changing the optical length difference of the arms [4–5]. Disadvantages of this approach are the limited delay range and measurement speeds. Besides this common approach, it is also feasible to use two fs-laser sources with a detuned repetition rate (asynchronous optical sampling - ASOPS [6]). Here, the delay between consecutive pulse pairs is inherently established. Particularly for fiber-based laser systems one major drawback of this approach is the fixed delay window, which is predetermined by the repetition rate of the fs-laser. Consequently, using a fs-fiber laser with a repetition rate of 250 MHz leads to a delay window of 4 ns, which in most cases exceeds the necessary delay window of the experiment. E.g. in terahertz time-domain spectroscopy (THz-TDS) measurements [7] the delay-window of interest approximately comprises only 100 ps. With a 4 ns delay window this results in a measurement efficiency of only 2.5 %. Addressing this issue, another approach is to make the fs-lasers freely detunable in terms of their repetition rate difference (electronically controlled optical sampling - ECOPS [8]). Now, the delay window can be adapted to the measurement task, leading to an increased measurement efficiency [9]. Nevertheless, one major drawback of the dual-laser approach are the price constraints to todays measurement systems. Another very important aspect which has to be mentioned is the timing stability of the pulse trains. Today, sophisticated phase control and detection electronics pave the way to observe and detect the phase behavior of the system. Hence, providing the necessary accuracy to acquire ultra-fast phenomena in the picosecond range [10]. To combine the performance benefits of a dual-laser system with the cost of a single-laser approach is highly desirable for today’s measurement systems. Here, the usage of multiplexing techniques can provide solutions, due to the efficient share of components and resources in a given setup. It has been shown that a single laser cavity is able to emit two self-mode-locked pulse trains [11–13]. Especially, in the field of dual-comb spectroscopy [14–16] the implementation of multiplexed laser sources shows promising results to reduce the complexity of current approaches. In [17] two pulse trains with orthogonal polarizations are simultaneously emitted from a single non-polarization maintaining cavity. Nevertheless, in all these publications the focus is set on the delivery of two pulse trains with a fixed repetition rate difference and a well defined carrier envelope offset frequency (fceo) to conduct spectroscopic measurements. Being able to equalize and finely detune the repetition rate difference (ΔfRep) to apply the concept of ECOPS is an important possibility to increase the systems performance. Interference effects like cross-phase modulation between the pulse trains in a multiplexed system can lead to unwanted behavior, which prohibits the actual usage. In [18–19] it has been reported that the pulse trains tend to synchronize in repetition rate while approaching ΔfRep= 0 Hz. This tendency to couple has to be avoided. In this paper we give a deeper insight into the physical mechanisms of the start-up and timing stability of an all-polarization maintaining, polarization-multiplexed fiber laser system which uses only one gain section and one pump diode to emit two freely adjustable self-mode-locked pulse trains. In contrast to the laser setup shown in [10], the currently used resonator comprises no free-space sections leading to an improved stability and robustness against environmental changes. Additionally, the mode-lock operation of the resonator is now initiated in a well-defined and reproducible procedure by employing a fiber coupled, polarization-maintaining, voltage-controlled optical attenuator. To verify the short-term timing stability we conducted a cross-correlation measurement of the two pulse trains based on a two-photon-absorption (TPA) experiment. We believe that with the shown results this approach provides a new way of increasing the efficiency of current pump-probe measurement systems. Based on the novel laser architecture, we call this new approach single-laser polarization-controlled optical sampling, or SLAPCOPS.

2. SLAPCOPS System

The complete SLAPCOPS system is shown in Fig. 1. It includes the SLAPCOPS resonator, which is able to emit two pulse trains with adjustable repetition rates, an optical amplifier, which amplifies and nonlinearly compresses the output pulses of the laser [20] and the phase control unit, which establishes a user defined temporal separation (tdelay) of the pulse trains and provides the actual delay information in form of the in-phase (Icomp) and quadrature (Qcomp) signal of the pulse trains. Key component is the novel SLAPCOPS resonator, which consists of two ring resonators (ring 1 and ring 2) sharing one polarization-multiplexed gain section which is unidirectionally pumped by one pump diode (see Fig. 2). Each ring contains one semiconductor saturable absorber mirror (SESAM), a 3-port circulator (CIR), a 90/10 fiber output coupler (OC) to extract the pulse trains and a loss element. The SESAM has a modulation depth of 13 %, a recovery time of 2 ps, a saturation fluence of 90 µJ/cm2, and non-saturable losses of 8 %. Besides the introduction of the fiber coupled SESAM the circulator acts additionally as an optical isolator and determines the propagation direction of the pulses in the corresponding ring. The voltage controlled loss elements ensure stable and robust self-mode-locked operation of both rings. For the necessary fast control of the repetition rate, a short piece of optical fiber is glued onto a piezo stack with a maximum displacement of 9 µm. Slow drifts are addressed with a motorized stretcher unit. All passive fibers used have a group velocity dispersion (GVD) value of −22 ps2/km and a specified beat length of 3-5 mm. The gain medium is a 0.4 m PM erbium-doped fiber with GVD of 20 ps2/km at 1550 nm and a core-absorption coefficient of 80 dB/m at 1530 nm. The gain section is operated polarization multiplexed, by using two polarization beam combiners (PBC). Thus, the colliding pulses in the gain section have orthogonal polarization as well as opposite propagation direction to reduce cross-phase modulation effects between the pulses. Additionally, this design efficiently suppresses crosstalk between the rings caused by non proper polarization maintenance in the polarization-multiplexed part [21]. A 976 nm continuous-wave laser diode (pump) unidirectionally pumps the gain medium through a wavelength-division multiplexer (WDM). The optical length of each ring is approximately 3.5 m leading to a calculated round-trip cavity dispersion of −0.06 ps2.

 figure: Fig. 1

Fig. 1 Schematic diagram of the complete SLAPCOPS system, comprising the SLAPCOPS resonator, an optical amplifier stage and the phase control unit. Also shown is the experimental setup for the investigation of the timing stability of the system (dashed box).

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 figure: Fig. 2

Fig. 2 Schematic setup of the all polarization maintaining SLAPCOPS resonator using only one pump diode and one laser-active section. The colliding pulses in the gain section have orthogonal polarization as well as opposite propagation directions to avoid passive synchronization effects while approaching ΔfRep= 0 Hz. The voltage-controlled loss elements ensure the self-mode-locked operation of both rings.

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The optical amplifier stage consists of two distinct optical amplifiers, providing a maximum gain of 13 dB at a pump power of 800 mW for each pulse train. Each amplifier contains 1.1 m of PM erbium-doped fiber with a core diameter of 3µm and a core-absorption coefficient of 80 dB/m at 1530 nm enclosed by one WDM and a 90/10 OC to extract 10 % of the amplified signals.

This portion of the output signal is guided to the phase control unit where it is measured with two fiber coupled InGaAs photo diodes (DET08CFC) with a −3 dB bandwidth of 5 GHz. In a first stage the 102th harmonic of the repetition rate is down-mixed to approximately 10 MHz via two double-balanced mixers and an RF signal generator. The down-mixed signals are then used to retrieve the phase relation between the pulse trains. This is accomplished with an all-digital, synthetic IQ demodulation scheme, implemented on an FPGA board followed by micro-controller (µC) based arctangent calculation. The phase signal is further send to a control loop, which actuates the piezo inside the laser resonator with a user defined phase set point (tdelay).

3. Mode locked state

To self-mode-lock both rings a pump power of 140 mW is applied to the active section of the resonator. Due to an intrinsic loss mismatch between both rings only ring 2 is able to self-mode-lock. In this state the pump power provide enough energy to ring 2 to mode-lock in a higher harmonic, which ends up in two pulses per round trip time [22] (see upper graph in Fig. 3). To initiate the mode-lock operation of ring 1 the loss of ring 2 has to be increased. By applying a voltage to the corresponding loss element, the transmittance of the element gradually decreases. At a certain point the system enters a regime, where the energy is rapidly fluctuating between both rings. In this state both rings exhibit alternating Q-Switch instabilities, and no ring is able to permanently mode-lock. By increasing the loss further the system enters a regime where both rings self-mode lock with one pulse per round trip time (see lower graph in Fig. 3). In this state the repetition rates are approx. 56.7 MHz and the average output powers are 550 µW for ring 1 and 530 µW for ring 2. A complete transition dynamic of the system acquired with a digital oscilloscope can be seen in Fig. 4.

 figure: Fig. 3

Fig. 3 Mode-lock state before (upper graph) and after (lower graph) the adjustment of the loss element acquired with a 16 GHz digital oscilloscope (DSA-X-91604A). The black curve is flipped in sign for clarity. Before the adjustment ring 2 is mode-locked in a higher harmonic state, providing two pulses per round trip. After equalizing the ring related losses both rings provide one pulse per round trip.

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 figure: Fig. 4

Fig. 4 Transition dynamics of the SLAPCOPS resonator while adjusting the transmittance of the loss element. The black curve shows the output signal of ring 1. The red curve shows the output signal of ring 2 and is flipped in sign for clarity. In the first phase only ring 2 is able to mode-lock. While reducing the transmittance of the loss element, the oscillator is entering a chaotic regime. In this unstable state no ring is able to permanently mode-lock and the energy is rapidly fluctuating between both rings. By further decreasing the transmittance the oscillator enters a stable state, in which both rings are mode-locked simultaneously.

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The radio frequency (rf) spectrum of the individual pulse trains at a center frequency of 12 GHz, measured with a 30 GHz In GaAs PIN photodetector and an RF spectrum analyzer (Anritsu MS2830A) is depicted in Fig. 5. During this measurement the system was controlled to a fixed ΔfRep of 2 Hz. The resolution bandwidth (RBW) and video bandwidth (VBW) were set to 30 Hz. The sweep time (SWT) was 12 s. The measured signal-to-background ratio of the 214th harmonic is larger than 60 dB for both pulse trains without any linear cross talk observable. The green curve shows the results by measuring both pulse trains simultaneously with the same photodiode. The broad pedestal is attributed to nonlinearities of the photodetection process and can be understood as a two-tone mixing process [23]. Due to the detection nonlinearity of the photodiode new frequency components are generated, which manifest as a broad pedestal. The pedestal consists of spectral components with a separation corresponding to ΔfRep.

 figure: Fig. 5

Fig. 5 RF spectra of the 214th harmonic. The red and black curves show the spectrum for the individual pulse trains measured successively with the same photo diode. The green curve results from the superposition of both pulse trains at the photo diode. The broad pedestal arises from the nonlinearity of the detection process. As depicted in the inset the pedestal consists of distinct spectral components with a seperation corresponding to ΔfRep.

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The optical spectra of the emitted pulses (measured with an optical spectrum analyzer OSA AQ6370D) are shown in Fig. 6. It can be seen that both pulse trains exhibit almost the same center wavelength with no interference effects observable. Clearly obvious are the Kelly sidebands indicating the operation of both rings in the solitary regime. The 3 dB bandwidth is 5.8 nm and 6.2 nm for ring 1 and ring 2, respectively. The corresponding center wavelengths are 1558.9 nm and 1558.3 nm. Assuming a transform limited sech2-shaped pulse form this leads to a calculated pulse duration of approximately 400 fs for both rings.

 figure: Fig. 6

Fig. 6 Optical spectra measured at the output of the SLAPCOPS resonator, showing almost the same center wavelength and 3 dB bandwidth. Black indicates the spectrum from ring 1 and red from ring 2, respectively. Kelly sidebands indicate that both rings are working in the solitary regime.

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4. Stability analysis

To verify the timing resolution and stability of the system we conducted a cross-correlation measurement based on a two-photon-absorption (TPA) experiment [24]. In this experiment the incident pulses directly generate a nonlinear TPA photocurrent in the semiconductor of a photodiode. Consequently, the detection of this photocurrent as a function of the delay between the interacting pulses yields the cross-correlation function. The necessary sweep mechanism is established by changing ΔfRep in a sinusoidal manner [9]. The evaluation of the measurement data is based on the scope method [25]. Here, the timing jitter is characterized by the collection of multiple waveforms and the evaluation of the temporal position of the leading and trailing edge at the half maximum point of the TPA signal.

The experimental setup is depicted in the inset of Fig. 1. The amplified pulse trains of the SLAPCOPS resonator are coupled into a single optical fiber via a PM-50/50 fused fiber coupler and guided to a biased silicion detector (DET10A/M). The sech2-fitted pulse widths in this configuration are 160 fs for ring 1 and 140 fs for ring 2. The pulse energy is 220 pJ for each pulse (see Fig. 7). The output current of the photodiode is further amplified with a low-noise transimpedance amplifier (TIA) with a −3 dB gain bandwidth of 50 kHz and a transimpedance gain of 107. The I and Q signals provided by the phase control unit and the TPA signal are simultaneously acquired and processed with a 16 bit, 1 MHz data acquisition card (DAQ). The time axis of the measurement is retrieved by an arctangent operation of the I and Q components. The scan window was set to 2 ps with a scan frequency of 20 Hz.

 figure: Fig. 7

Fig. 7 The sech2-fitted intensity autocorrelation signals of the optical pulses for the TPA experiment. Black indicates the amplified signal from ring 1 and red from ring 2 respectively.

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The collection of 1000 TPA timetraces can be seen in Fig. 8. The color of the heat map indicates the amount of counts at a specific location. The offset corrected TPA signal shows a full width at half maximum (TFWHM) of approximately 200 fs. The evaluation of the timing of the leading and trailing edge leads in both cases to a gaussian shaped timing distribution with a standard deviation (σlead, σtrail) of approximately 30 fs. In contrast to the intensity autocorrelation function of the individual pulses the cross-correlation waveform exhibits an asymmetric shape. This can be explained by pulse distortions occurring during the amplification and nonlinear compression [26].

 figure: Fig. 8

Fig. 8 Heat map of 1000 TPA waveforms (upper graph) and corresponding timing distribution (lower graph). The area of evaluation is highlighted with the white box. The timing jitter showing a standard deviation of approx. 30 fs for the leading and trailing edge of the TPA signal.

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5. Conclusion

In conclusion, we presented a single-laser, all-polarization maintaining pump-probe measurement setup without external delay line. The system is based on a novel fiber laser design, consisting of two ring resonators sharing one polarization-multiplexed gain section and one pump diode. The colliding pulses in the resonator have orthogonal polarization as well as opposite propagation directions. Thus, allowing to freely adjust the phase relation between the emitted pulse trains by controlling the optical length difference of the ring resonators. The timing accuracy of the mode-locked pulse trains is investigated by a two-photon-absorption experiment. The evaluation based on the scope method leads to a gaussian shaped timing distribution with a standard deviation of 30 fs. We have shown that SLAPCOPS shares the same advantages of an ECOPS system, while using only one laser-active medium and one pump diode in the resonator. Further improvement of the system’s performance can be expected by reducing the overall cavity dispersion of the ring resonator. These steps will be covered in future work. We believe that this laser design will find potential applications in a variety of pump-probe measurements.

Acknowledgments

This work is done in collaboration with HÜBNER GmbH & Co. KG, Division Hübner Photonics, Kassel, Germany.

References

1. J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015). [CrossRef]  

2. C. Y. Dong, P. T. So, T. French, and E. Gratton, “Fluorescence lifetime imaging by asynchronous pump-probe microscopy,” Biophysical Journal 69(6), 2234-2242 (1995). [CrossRef]   [PubMed]  

3. M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited review article: pump-probe microscopy,” Review of Scientific Instruments 87(3), 031101 (2016). [CrossRef]   [PubMed]  

4. D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25(7), 7547-7558 (2017). [CrossRef]   [PubMed]  

5. B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016). [CrossRef]  

6. P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Optics 26(19), 4303-4309 (1987). [CrossRef]  

7. D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” JOSA B 7(10), 2006-2015 (1990). [CrossRef]  

8. S. Kray, F. Spöler, T. Hellerer, and H. Kurz, “Electronically controlled coherent linear optical sampling for optical coherence tomography,” Opt. Express 18(10), 9976-9990 (2010). [CrossRef]   [PubMed]  

9. Y. Kim and D. S. Yee, “High-speed terahertz time-domain spectroscopy based on electronically controlled optical sampling,” Opt. Lett. 35(22), 3715-3717 (2010). [CrossRef]   [PubMed]  

10. M. Kolano, B. Gräf, S. Weber, D. Molter, and G. von Freymann, “Single-laser polarization-controlled optical sampling system for THz-TDS,” Opt. Lett. 43(6), 1351-1354 (2018). [CrossRef]   [PubMed]  

11. C. Ouyang, P. Shum, K. Wu, J. H. Wong, H. Q. Lam, and S. Aditya, “Bidirectional passively mode-locked soliton fiber laser with a four-port circulator,” Opt. Lett. 36(11), 2089-2091 (2011). [CrossRef]   [PubMed]  

12. Q. F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Counter-propagating solitons in microresonators,” Nat. Photonics 11(9), 560-564 (2017). [CrossRef]  

13. K. Kieu and M. Mansuripur, “All-fiber bidirectional passively mode-locked ring laser,” Opt. Lett. 33(1), 64-66 (2008). [CrossRef]  

14. B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010). [CrossRef]  

15. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414-426 (2016). [CrossRef]  

16. S. M. Link, D. J. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164-1168 (2017). [CrossRef]   [PubMed]  

17. Z. Gong, X. Zhao, G. Hu, J. Liu, and Z. Zheng, “Polarization multiplexed, dual-frequency ultrashort pulse generation by a birefringent mode-locked fiber laser,” In Lasers and Electro-Optics (2014).

18. M. Rusu, R. Herda, and O. G. Okhotnikov, “Passively synchronized erbium (1550-nm) and ytterbium (1040-nm) mode-locked fiber lasers sharing a cavity,” Opt. Lett. 29(19), 2246-2248 (2004). [CrossRef]   [PubMed]  

19. C. Furst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Quantum Electron. 2(3), 473-479 (1996). [CrossRef]  

20. J. W. Nicholson, A. D. Yablon, P. S. Westbrook, K. S. Feder, and M. F. Yan, “High power, single mode, all-fiber source of femtosecond pulses at 1550 nm and its use in supercontinuum generation,” Opt. Express 12(13), 3025-3034 (2004). [CrossRef]   [PubMed]  

21. M. Kolano, B. Gräf, D. Molter, F. Ellrich, and G. von Freymann, “All-Polarization-Maintaining, Polarization- Multiplexed, Gain-Coupled, Mode-Locked Fiber Laser,” In Laser Applications Conference (pp. JTu2A-29). Optical Society of America (2017).

22. B. G. Bale, K. Kieu, J. N. Kutz, and F. Wise, “Transition dynamics for multi-pulsing in mode-locked lasers,” Opt. Express 17(25), 23137-23146 (2009). [CrossRef]  

23. A. Ramaswamy, N. Nunoya, K. J. Williams, J. Klamkin, M. Piels, L. A. Johansson, A. Hastings, L.A. Coldren, and J. E. Bowers, “Measurement of intermodulation distortion in high-linearity photodiodes,” Opt. Express , 18(3), 2317-2324 (2010). [CrossRef]   [PubMed]  

24. Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, “Multiple- and single-shot autocorrelator based on two-photon conductivity in semiconductors,” Opt. Lett ., 17(9), 658-660 (1992). [CrossRef]   [PubMed]  

25. R. Holzlöhner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and Theoretical Characterization of a 40-Gb/s Long-Haul Single-Channel Transmission System,” J. Lightw. Techn. 20(7), 1124 (2002). [CrossRef]  

26. T. Hochrein, R. Wilk, M. Mei, R. Holzwarth, N. Krumbholz, and M. Koch, “Optical sampling by laser cavity tuning,” Opt. Express 18(2), 1613-1617(2010). [CrossRef]   [PubMed]  

References

  • View by:

  1. J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
    [Crossref]
  2. C. Y. Dong, P. T. So, T. French, and E. Gratton, “Fluorescence lifetime imaging by asynchronous pump-probe microscopy,” Biophysical Journal 69(6), 2234-2242 (1995).
    [Crossref] [PubMed]
  3. M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited review article: pump-probe microscopy,” Review of Scientific Instruments 87(3), 031101 (2016).
    [Crossref] [PubMed]
  4. D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25(7), 7547-7558 (2017).
    [Crossref] [PubMed]
  5. B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016).
    [Crossref]
  6. P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Optics 26(19), 4303-4309 (1987).
    [Crossref]
  7. D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” JOSA B 7(10), 2006-2015 (1990).
    [Crossref]
  8. S. Kray, F. Spöler, T. Hellerer, and H. Kurz, “Electronically controlled coherent linear optical sampling for optical coherence tomography,” Opt. Express 18(10), 9976-9990 (2010).
    [Crossref] [PubMed]
  9. Y. Kim and D. S. Yee, “High-speed terahertz time-domain spectroscopy based on electronically controlled optical sampling,” Opt. Lett. 35(22), 3715-3717 (2010).
    [Crossref] [PubMed]
  10. M. Kolano, B. Gräf, S. Weber, D. Molter, and G. von Freymann, “Single-laser polarization-controlled optical sampling system for THz-TDS,” Opt. Lett. 43(6), 1351-1354 (2018).
    [Crossref] [PubMed]
  11. C. Ouyang, P. Shum, K. Wu, J. H. Wong, H. Q. Lam, and S. Aditya, “Bidirectional passively mode-locked soliton fiber laser with a four-port circulator,” Opt. Lett. 36(11), 2089-2091 (2011).
    [Crossref] [PubMed]
  12. Q. F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Counter-propagating solitons in microresonators,” Nat. Photonics 11(9), 560-564 (2017).
    [Crossref]
  13. K. Kieu and M. Mansuripur, “All-fiber bidirectional passively mode-locked ring laser,” Opt. Lett. 33(1), 64-66 (2008).
    [Crossref]
  14. B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
    [Crossref]
  15. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414-426 (2016).
    [Crossref]
  16. S. M. Link, D. J. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164-1168 (2017).
    [Crossref] [PubMed]
  17. Z. Gong, X. Zhao, G. Hu, J. Liu, and Z. Zheng, “Polarization multiplexed, dual-frequency ultrashort pulse generation by a birefringent mode-locked fiber laser,” In Lasers and Electro-Optics (2014).
  18. M. Rusu, R. Herda, and O. G. Okhotnikov, “Passively synchronized erbium (1550-nm) and ytterbium (1040-nm) mode-locked fiber lasers sharing a cavity,” Opt. Lett. 29(19), 2246-2248 (2004).
    [Crossref] [PubMed]
  19. C. Furst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Quantum Electron. 2(3), 473-479 (1996).
    [Crossref]
  20. J. W. Nicholson, A. D. Yablon, P. S. Westbrook, K. S. Feder, and M. F. Yan, “High power, single mode, all-fiber source of femtosecond pulses at 1550 nm and its use in supercontinuum generation,” Opt. Express 12(13), 3025-3034 (2004).
    [Crossref] [PubMed]
  21. M. Kolano, B. Gräf, D. Molter, F. Ellrich, and G. von Freymann, “All-Polarization-Maintaining, Polarization- Multiplexed, Gain-Coupled, Mode-Locked Fiber Laser,” In Laser Applications Conference (pp. JTu2A-29). Optical Society of America (2017).
  22. B. G. Bale, K. Kieu, J. N. Kutz, and F. Wise, “Transition dynamics for multi-pulsing in mode-locked lasers,” Opt. Express 17(25), 23137-23146 (2009).
    [Crossref]
  23. A. Ramaswamy, N. Nunoya, K. J. Williams, J. Klamkin, M. Piels, L. A. Johansson, A. Hastings, L.A. Coldren, and J. E. Bowers, “Measurement of intermodulation distortion in high-linearity photodiodes,” Opt. Express,  18(3), 2317-2324 (2010).
    [Crossref] [PubMed]
  24. Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, “Multiple- and single-shot autocorrelator based on two-photon conductivity in semiconductors,” Opt. Lett.,  17(9), 658-660 (1992).
    [Crossref] [PubMed]
  25. R. Holzlöhner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and Theoretical Characterization of a 40-Gb/s Long-Haul Single-Channel Transmission System,” J. Lightw. Techn. 20(7), 1124 (2002).
    [Crossref]
  26. T. Hochrein, R. Wilk, M. Mei, R. Holzwarth, N. Krumbholz, and M. Koch, “Optical sampling by laser cavity tuning,” Opt. Express 18(2), 1613-1617(2010).
    [Crossref] [PubMed]

2018 (1)

2017 (3)

Q. F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Counter-propagating solitons in microresonators,” Nat. Photonics 11(9), 560-564 (2017).
[Crossref]

S. M. Link, D. J. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164-1168 (2017).
[Crossref] [PubMed]

D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25(7), 7547-7558 (2017).
[Crossref] [PubMed]

2016 (3)

B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016).
[Crossref]

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited review article: pump-probe microscopy,” Review of Scientific Instruments 87(3), 031101 (2016).
[Crossref] [PubMed]

I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414-426 (2016).
[Crossref]

2015 (1)

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

2011 (1)

2010 (5)

2009 (1)

2008 (1)

2004 (2)

2002 (1)

R. Holzlöhner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and Theoretical Characterization of a 40-Gb/s Long-Haul Single-Channel Transmission System,” J. Lightw. Techn. 20(7), 1124 (2002).
[Crossref]

1996 (1)

C. Furst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Quantum Electron. 2(3), 473-479 (1996).
[Crossref]

1995 (1)

C. Y. Dong, P. T. So, T. French, and E. Gratton, “Fluorescence lifetime imaging by asynchronous pump-probe microscopy,” Biophysical Journal 69(6), 2234-2242 (1995).
[Crossref] [PubMed]

1992 (1)

Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, “Multiple- and single-shot autocorrelator based on two-photon conductivity in semiconductors,” Opt. Lett.,  17(9), 658-660 (1992).
[Crossref] [PubMed]

1990 (1)

D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” JOSA B 7(10), 2006-2015 (1990).
[Crossref]

1987 (1)

P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Optics 26(19), 4303-4309 (1987).
[Crossref]

Aditya, S.

Apkarian, V.

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

Baierl, S.

B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016).
[Crossref]

Bale, B. G.

Bernhardt, B.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Bowers, J. E.

Brocious, J.

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

Carter, G. M.

R. Holzlöhner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and Theoretical Characterization of a 40-Gb/s Long-Haul Single-Channel Transmission System,” J. Lightw. Techn. 20(7), 1124 (2002).
[Crossref]

Coddington, I.

Coldren, L.A.

Dong, C. Y.

C. Y. Dong, P. T. So, T. French, and E. Gratton, “Fluorescence lifetime imaging by asynchronous pump-probe microscopy,” Biophysical Journal 69(6), 2234-2242 (1995).
[Crossref] [PubMed]

Eisele, M.

B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016).
[Crossref]

Ellrich, F.

D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25(7), 7547-7558 (2017).
[Crossref] [PubMed]

M. Kolano, B. Gräf, D. Molter, F. Ellrich, and G. von Freymann, “All-Polarization-Maintaining, Polarization- Multiplexed, Gain-Coupled, Mode-Locked Fiber Laser,” In Laser Applications Conference (pp. JTu2A-29). Optical Society of America (2017).

Elzinga, P. A.

P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Optics 26(19), 4303-4309 (1987).
[Crossref]

Ereifej, H. N.

R. Holzlöhner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and Theoretical Characterization of a 40-Gb/s Long-Haul Single-Channel Transmission System,” J. Lightw. Techn. 20(7), 1124 (2002).
[Crossref]

Fattinger, C.

D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” JOSA B 7(10), 2006-2015 (1990).
[Crossref]

Feder, K. S.

Fischer, M. C.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited review article: pump-probe microscopy,” Review of Scientific Instruments 87(3), 031101 (2016).
[Crossref] [PubMed]

Fishman, D. A.

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

French, T.

C. Y. Dong, P. T. So, T. French, and E. Gratton, “Fluorescence lifetime imaging by asynchronous pump-probe microscopy,” Biophysical Journal 69(6), 2234-2242 (1995).
[Crossref] [PubMed]

Furst, C.

C. Furst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Quantum Electron. 2(3), 473-479 (1996).
[Crossref]

Gong, Z.

Z. Gong, X. Zhao, G. Hu, J. Liu, and Z. Zheng, “Polarization multiplexed, dual-frequency ultrashort pulse generation by a birefringent mode-locked fiber laser,” In Lasers and Electro-Optics (2014).

Gräf, B.

M. Kolano, B. Gräf, S. Weber, D. Molter, and G. von Freymann, “Single-laser polarization-controlled optical sampling system for THz-TDS,” Opt. Lett. 43(6), 1351-1354 (2018).
[Crossref] [PubMed]

M. Kolano, B. Gräf, D. Molter, F. Ellrich, and G. von Freymann, “All-Polarization-Maintaining, Polarization- Multiplexed, Gain-Coupled, Mode-Locked Fiber Laser,” In Laser Applications Conference (pp. JTu2A-29). Optical Society of America (2017).

Gratton, E.

C. Y. Dong, P. T. So, T. French, and E. Gratton, “Fluorescence lifetime imaging by asynchronous pump-probe microscopy,” Biophysical Journal 69(6), 2234-2242 (1995).
[Crossref] [PubMed]

Grigoryan, V. S.

R. Holzlöhner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and Theoretical Characterization of a 40-Gb/s Long-Haul Single-Channel Transmission System,” J. Lightw. Techn. 20(7), 1124 (2002).
[Crossref]

Grischkowsky, D.

D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” JOSA B 7(10), 2006-2015 (1990).
[Crossref]

Guelachvili, G.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Hänsch, T. W.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Hastings, A.

Hellerer, T.

Herda, R.

Hochrein, T.

Holzlöhner, R.

R. Holzlöhner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and Theoretical Characterization of a 40-Gb/s Long-Haul Single-Channel Transmission System,” J. Lightw. Techn. 20(7), 1124 (2002).
[Crossref]

Holzwarth, R.

T. Hochrein, R. Wilk, M. Mei, R. Holzwarth, N. Krumbholz, and M. Koch, “Optical sampling by laser cavity tuning,” Opt. Express 18(2), 1613-1617(2010).
[Crossref] [PubMed]

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Hu, G.

Z. Gong, X. Zhao, G. Hu, J. Liu, and Z. Zheng, “Polarization multiplexed, dual-frequency ultrashort pulse generation by a birefringent mode-locked fiber laser,” In Lasers and Electro-Optics (2014).

Huang, F.

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

Huber, R.

B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016).
[Crossref]

Imamura, S.

Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, “Multiple- and single-shot autocorrelator based on two-photon conductivity in semiconductors,” Opt. Lett.,  17(9), 658-660 (1992).
[Crossref] [PubMed]

Jacquet, P.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Jacquey, M.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Jahng, J.

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

Jiang, Y.

P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Optics 26(19), 4303-4309 (1987).
[Crossref]

Johansson, L. A.

Jonuscheit, J.

Kaplan, D.

B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016).
[Crossref]

Keiding, S.

D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” JOSA B 7(10), 2006-2015 (1990).
[Crossref]

Keller, U.

S. M. Link, D. J. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164-1168 (2017).
[Crossref] [PubMed]

Kieu, K.

Kim, Y.

King, G. B.

P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Optics 26(19), 4303-4309 (1987).
[Crossref]

Klamkin, J.

Kneisler, R. J.

P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Optics 26(19), 4303-4309 (1987).
[Crossref]

Kobayashi, T.

Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, “Multiple- and single-shot autocorrelator based on two-photon conductivity in semiconductors,” Opt. Lett.,  17(9), 658-660 (1992).
[Crossref] [PubMed]

Kobayashi, Y.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Koch, M.

Kolano, M.

M. Kolano, B. Gräf, S. Weber, D. Molter, and G. von Freymann, “Single-laser polarization-controlled optical sampling system for THz-TDS,” Opt. Lett. 43(6), 1351-1354 (2018).
[Crossref] [PubMed]

M. Kolano, B. Gräf, D. Molter, F. Ellrich, and G. von Freymann, “All-Polarization-Maintaining, Polarization- Multiplexed, Gain-Coupled, Mode-Locked Fiber Laser,” In Laser Applications Conference (pp. JTu2A-29). Optical Society of America (2017).

Kray, S.

Krumbholz, N.

Kurz, H.

Kutz, J. N.

Lam, H. Q.

Lange, C.

B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016).
[Crossref]

Laubereau, A.

C. Furst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Quantum Electron. 2(3), 473-479 (1996).
[Crossref]

Laurendeau, N. M.

P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Optics 26(19), 4303-4309 (1987).
[Crossref]

Leitenstorfer, A.

C. Furst, A. Leitenstorfer, and A. Laubereau, “Mechanism for self-synchronization of femtosecond pulses in a two-color Ti:sapphire laser,” IEEE J. Quantum Electron. 2(3), 473-479 (1996).
[Crossref]

Link, S. M.

S. M. Link, D. J. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164-1168 (2017).
[Crossref] [PubMed]

Liu, J.

Z. Gong, X. Zhao, G. Hu, J. Liu, and Z. Zheng, “Polarization multiplexed, dual-frequency ultrashort pulse generation by a birefringent mode-locked fiber laser,” In Lasers and Electro-Optics (2014).

Lytle, F. E.

P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Optics 26(19), 4303-4309 (1987).
[Crossref]

Maas, D. J.

S. M. Link, D. J. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164-1168 (2017).
[Crossref] [PubMed]

Mansuripur, M.

Mei, M.

Menyuk, C. R.

R. Holzlöhner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and Theoretical Characterization of a 40-Gb/s Long-Haul Single-Channel Transmission System,” J. Lightw. Techn. 20(7), 1124 (2002).
[Crossref]

Möller, M.

B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016).
[Crossref]

Molter, D.

Newbury, N.

Nicholson, J. W.

Nowak, D.

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

Nunoya, N.

Okhotnikov, O. G.

Ouyang, C.

Ozawa, A.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Picqué, N.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Piels, M.

Potma, E.O.

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

Ramaswamy, A.

Robles, F. E.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited review article: pump-probe microscopy,” Review of Scientific Instruments 87(3), 031101 (2016).
[Crossref] [PubMed]

Rusu, M.

Shum, P.

So, P. T.

C. Y. Dong, P. T. So, T. French, and E. Gratton, “Fluorescence lifetime imaging by asynchronous pump-probe microscopy,” Biophysical Journal 69(6), 2234-2242 (1995).
[Crossref] [PubMed]

Spöler, F.

Swann, W.

Takagi, Y.

Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, “Multiple- and single-shot autocorrelator based on two-photon conductivity in semiconductors,” Opt. Lett.,  17(9), 658-660 (1992).
[Crossref] [PubMed]

Trierweiler, M.

Udem, T.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55 (2010).
[Crossref]

Urbanek, B.

B. Urbanek, M. Möller, M. Eisele, S. Baierl, D. Kaplan, C. Lange, and R. Huber, “Femtosecond terahertz time-domain spectroscopy at 36 kHz scan rate using an acousto-optic delay,” Appl. Phys. Lett. 108(12), 121101 (2016).
[Crossref]

Vahala, K.

Q. F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Counter-propagating solitons in microresonators,” Nat. Photonics 11(9), 560-564 (2017).
[Crossref]

Van Exter, M.

D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” JOSA B 7(10), 2006-2015 (1990).
[Crossref]

von Freymann, G.

Waldburger, D.

S. M. Link, D. J. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164-1168 (2017).
[Crossref] [PubMed]

Warren, W. S.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited review article: pump-probe microscopy,” Review of Scientific Instruments 87(3), 031101 (2016).
[Crossref] [PubMed]

Weber, S.

Westbrook, P. S.

Wickramasinghe, H.

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

Wilk, R.

Williams, K. J.

Wilson, J. W.

M. C. Fischer, J. W. Wilson, F. E. Robles, and W. S. Warren, “Invited review article: pump-probe microscopy,” Review of Scientific Instruments 87(3), 031101 (2016).
[Crossref] [PubMed]

Wise, F.

Wong, J. H.

Wu, K.

Yablon, A. D.

Yampolsky, S.

J. Jahng, J. Brocious, D. A. Fishman, S. Yampolsky, D. Nowak, F. Huang, V. Apkarian, H. Wickramasinghe, and E.O. Potma, “Ultrafast pump-probe force microscopy with nanoscale resolution,” Appl. Phys. Lett. 106(8), 083113 (2015).
[Crossref]

Yan, M. F.

Yang, K. Y.

Q. F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Counter-propagating solitons in microresonators,” Nat. Photonics 11(9), 560-564 (2017).
[Crossref]

Yang, Q. F.

Q. F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Counter-propagating solitons in microresonators,” Nat. Photonics 11(9), 560-564 (2017).
[Crossref]

Yee, D. S.

Yi, X.

Q. F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Counter-propagating solitons in microresonators,” Nat. Photonics 11(9), 560-564 (2017).
[Crossref]

Yoshihara, K.

Y. Takagi, T. Kobayashi, K. Yoshihara, and S. Imamura, “Multiple- and single-shot autocorrelator based on two-photon conductivity in semiconductors,” Opt. Lett.,  17(9), 658-660 (1992).
[Crossref] [PubMed]

Zhao, X.

Z. Gong, X. Zhao, G. Hu, J. Liu, and Z. Zheng, “Polarization multiplexed, dual-frequency ultrashort pulse generation by a birefringent mode-locked fiber laser,” In Lasers and Electro-Optics (2014).

Zheng, Z.

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Figures (8)

Fig. 1
Fig. 1 Schematic diagram of the complete SLAPCOPS system, comprising the SLAPCOPS resonator, an optical amplifier stage and the phase control unit. Also shown is the experimental setup for the investigation of the timing stability of the system (dashed box).
Fig. 2
Fig. 2 Schematic setup of the all polarization maintaining SLAPCOPS resonator using only one pump diode and one laser-active section. The colliding pulses in the gain section have orthogonal polarization as well as opposite propagation directions to avoid passive synchronization effects while approaching ΔfRep= 0 Hz. The voltage-controlled loss elements ensure the self-mode-locked operation of both rings.
Fig. 3
Fig. 3 Mode-lock state before (upper graph) and after (lower graph) the adjustment of the loss element acquired with a 16 GHz digital oscilloscope (DSA-X-91604A). The black curve is flipped in sign for clarity. Before the adjustment ring 2 is mode-locked in a higher harmonic state, providing two pulses per round trip. After equalizing the ring related losses both rings provide one pulse per round trip.
Fig. 4
Fig. 4 Transition dynamics of the SLAPCOPS resonator while adjusting the transmittance of the loss element. The black curve shows the output signal of ring 1. The red curve shows the output signal of ring 2 and is flipped in sign for clarity. In the first phase only ring 2 is able to mode-lock. While reducing the transmittance of the loss element, the oscillator is entering a chaotic regime. In this unstable state no ring is able to permanently mode-lock and the energy is rapidly fluctuating between both rings. By further decreasing the transmittance the oscillator enters a stable state, in which both rings are mode-locked simultaneously.
Fig. 5
Fig. 5 RF spectra of the 214th harmonic. The red and black curves show the spectrum for the individual pulse trains measured successively with the same photo diode. The green curve results from the superposition of both pulse trains at the photo diode. The broad pedestal arises from the nonlinearity of the detection process. As depicted in the inset the pedestal consists of distinct spectral components with a seperation corresponding to ΔfRep.
Fig. 6
Fig. 6 Optical spectra measured at the output of the SLAPCOPS resonator, showing almost the same center wavelength and 3 dB bandwidth. Black indicates the spectrum from ring 1 and red from ring 2, respectively. Kelly sidebands indicate that both rings are working in the solitary regime.
Fig. 7
Fig. 7 The sech2-fitted intensity autocorrelation signals of the optical pulses for the TPA experiment. Black indicates the amplified signal from ring 1 and red from ring 2 respectively.
Fig. 8
Fig. 8 Heat map of 1000 TPA waveforms (upper graph) and corresponding timing distribution (lower graph). The area of evaluation is highlighted with the white box. The timing jitter showing a standard deviation of approx. 30 fs for the leading and trailing edge of the TPA signal.

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