The taccor comb - high power frequency comb with 1 GHz mode spacing
The strictly periodic pulse train emitted by a mode-locked femtosecond laser leads to a perfectly uniform comb in optical frequency space and enables a phase-coherent link between the microwave and optical domains in a stunningly simple manner. This concept has led to the award of the physics nobel prize to Theodor Hänsch and John Hall in 2005 [1].
The Fourier transformation of the electric field emitted by a femtosecond laser yields the relationship
fn=f0+n×fR
for the optical frequencies fn emitted by the laser. These frequencies are spaced by the laser repetition rate fR and carry integer mode numbers n with typically 6 to 7 digits. For example, a typical Ti:Sapphire laser with 1 GHz repetition rate, such as the Laser Quantum taccor (figure 1), has about 20,000 modes under its spectral envelope with mode numbers around 375,000. The existence of the carrier-envelope offset frequency f0 is owed to the fact that the carrier wave (375 THz for an 800 nm Ti:Sapphire laser) travels at the phase velocity while the pulse envelope travels at the group velocity. As these two are usually not equal, the relative position of the carrier under the envelope slips at a rate given by f0 and the modes are offset from the integer harmonic of fR by f0.
Figure 1: Laser Quantum’s taccor
The potency of the femtosecond laser frequency comb (FLFC) originates from the simple fact that the optical frequencies fn are defined by two easily measureable radio-frequencies (f0 and fR). Optical frequency measurements relative to the Cs clock have become simpler in recent times and no longer require the expertise of a National Facility with specialty equipment occupying an entire laboratory [2]. In essence, the FLFC provides a ruler for optical frequencies with the precision of the Cs clock.
Figure 2: Red: Typical taccor output spectrum used for CEO detection and comb applications. Blue: Output spectrum after 1 m photonic crystal fiber.
Figure 3: Heterodyne beat between two ultrastable cw lasers at 532 THz and at 456 THz via a Laser Quantum 1 GHz Ti:Sapphire laser recorded at the U.S. National Institute of Standards and Technology.
In the early years of the FLFC, following the first demonstrations in 1999, applications were mostly for measurements, comparisons of optical frequencies or to function as clockworks in optical atomic clocks in Optical Frequency Standard Laboratories such as PTB in Germany, NPL in the UK or NIST in the USA [3-6]. Later FLFCs found more widespread applications, such as direct frequency comb spectroscopy [7], arbitrary waveform generation [8], dual-comb FTIR spectroscopy [9] or CARS microscopy [10] and the calibration of astronomical spectrographs [11].
Almost all FLFC applications benefit from a repetition rate around 1 GHz for several reasons. The much larger mode-spacing, compared with other solid-state lasers or fiber lasers with fR between 70 and 250 MHz, allows easier identification of the mode number, as required for all frequency measurements. At the same time, radio-frequency (RF) filtering of the relevant beat signals is less demanding when the forest of modes is less dense to begin with. A less dense comb also leads to more power available in each mode, i.e. a 1 GHz laser has 10 times more power per mode than a 100 MHz laser at a given average power (typically between 100 mW and 1 W for commonly used lasers). A further advantage, again by a factor of 10 at 1 GHz, is related to the commonly used nonlinear photonic crystal fibers (PCF) used for super-continuum generation in typical FLFC setups (see figure 2 for a typical super-continuum at 1 GHz mode spacing). It has been shown that above a threshold of a few 100 pJ of pulse energy, the coherence of the frequency comb is heavily reduced or even lost entirely at the output of the fiber due to nonlinear noise amplification[12].
Figure 4: Carrier-envelope offset beat obtained from the taccor comb. The signal-to-noise ratio is limited by the RF spectrum analyzer. The close-up in the inset reveals the true signal-to-noise ratio of >40 dB in 100 kHz of bandwidth.
This means there is a limit to the pulse energy that can be launched through the fiber, typically around 300 pJ. In a 1 GHz pulse train, this corresponds to 300 mW of average power versus 30 mW in a 100 MHz train. So in total, the useful power per mode in a coherent super-continuum scales with the square of the repetition rate, giving a 1 GHz system 100-fold advantage over a 100 MHz system. Finally, a higher repetition rate means a lower pulse-to-pulse separation causing the dead-time in dual comb FTIR, CARS or similar applications to be less, therefore more data acquisition time is spent on gathering useful data and less time is spent acquiring ‘zeros’.
Laser Quantum’s 1 GHz femtosecond lasers have found widespread use in frequency metrology in many National Laboratories and other research groups around the world. In an international comparison between four independently constructed systems, each using a Laser Quantum laser, these lasers have been shown to support optical frequency measurements at the 10-19 accuracy level with stability at the 10-17 level in 1 s of averaging time and mode linewidths below 1 Hz [13,14], see figure 3. Hence, for the foreseeable future, these lasers are capable to support even the world’s most accurate and stable optical atomic clocks as optical clockwork and will not be a limiting factor in the most demanding optical frequency measurements [15]. Furthermore, applications in ultralow-noise microwave generation have been shown [16].
Figure 5: Laser Quantum’s comb extension showing dimensions.
To support applications of the taccor as a frequency comb, Laser Quantum has recently developed the comb extension to its successful range of 1 GHz lasers, now making the taccor comb available to the market, see figure 5. It consists of a matched dispersion compensation module, super-continuum generation and a nonlinear f-2f interferometer. The taccor comb provides a long-term stable RF signal at the carrier-envelope offset frequency with more than 40 dB signal-to-noise ratio in 100 kHz bandwidth, as shown in figure 4. Phase detection between the measured fCEO and a given reference signal is performed and converted into a feedback signal using the XPS800-E stabilisation unit by Menlo Systems GmbH. This feedback signal controls the intensity of the finesse pure CEP pump laser built within the taccor, in order to stabilize the comb’s fCEO signal. The finesse pure CEP laser features our patented CEPLoQTM technology and allows direct modulaton of the 532 nm pump light leading to a faster and more stable response than traditional methods, e.g. using an AOM. Thus, a very high feedback bandwidth of up to 250 kHz can be applied to phase-lock the CEO frequency to an external reference (figure 6 & figure 7).
Figure 6: Close-up of the phase-locked fCEO. The data is acquired using a resolution bandwidth of 200 Hz. The servo bandwidth is about 250 kHz as indicated by the symmetrical peaks around the carrier.
Figure 7: Long term deviations from the lock point of a CEO beat stabilised at 310 MHz over 25 h showing exceptional stability (limited by RF reference input).
References:
[1] T.W. Hänsch, “Passion for Precision”, available at www.nobelprize.org (2005).
[2] H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, “First Phase-Coherent Frequency Measurement of Visible Radiation”, Phys. Rev. Lett. 76, 18 (1996).
[3] T. Udem, J. Reichert, R. Holzwarth, T.W. Hänsch, “Absolute Optical Frequency Measurement of the Cesium D1 Line with a Mode-Locked Laser”, Phys. Rev. Lett. 82, 3568 (1999).
[4] S.A. Diddams, “Direct Link between Microwave and Optical Frequencies with a 300 THz Femtosecond Laser Comb”, Phys. Rev. Lett. 84, 5102 (2000).
[5] R. Holzwarth, T. Udem, T.W. Hänsch, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, “Optical Frequency Synthesizer for Precision Spectroscopy”, Phys. Rev. Lett. 85, 2264 (2000).
[6] S.A. Diddams, T. Udem, J.C. Bergquist, E.A. Curtis, R.E. Drullinger, L. Hollberg, W.M. Itano, W.D. Lee, C.W. Oates, K.R. Vogel, D.J. Wineland, “An Optical Clock Based on a Single Trapped 199Hg+ Ion”, Science 293, 825 (2001).
[7] V. Gerginov, C.E. Tanner, S.A. Diddams, A. Bartels, L. Hollberg, “High-resolution spectroscopy with a femtosecond laser frequency comb”, Opt. Lett. 30, 1734 (2005).
[8] J.T. Willits, A.M. Weiner, S.T. Cundiff, “Line-by-line pulse shaping with spectral resolution below 890 MHz”, Opt. Expr. 20, 3110 (2012).
[9] F. Keilmann, C. Gohle, R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer”, Opt. Lett. 29, 1542 (2004).
[10] T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picque, T.W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs”, Nature 502, 355 (2013).
[11] D.A. Braje, M.S. Kirchner, S. Osterman, T. Fortier, and S.A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs”, Eur. Phys. J. D 48, 57 (2008).
[12] L. Hollberg, C.W. Oates, E.A. Curtis, E.N. Ivanov, S.A. Diddams, T. Udem, H.G. Robinson, J.C. Bergquist, R.J. Rafac, W.M. Itano, R.E. Drullinger, and D.J. Wineland, “Optical Frequency Standards and Measurements”, IEEE JQE 37, 1502 (2001).
[13] L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R.S. Windeler, G. Wilpers, C.W. Oates, L. Hollberg, and S.A. Diddams, “Optical Frequency Synthesis and Comparison with Uncertainty at the 10-19 Level”, Science 303, 1843 (2004).
[14] A. Bartels, C.W. Oates, L. Hollberg, and S.A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths”, Opt. Lett. 29, 1081 (2004).
[15] C.W. Chou, D.B. Hume, J.C.J. Koele meij, D.J. Wineland, and T. Rosenband, “Frequency Comparison of Two High-Accuracy Al+ Optical Clocks”, Phys. Rev. Lett. 104, 070802 (2010).
[16] A. Bartels, S.A. Diddams, C.W. Oates, G. Wilpers, J.C. Bergquist, W.H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references”, Opt. Lett. 30, 667 (2005).
The strictly periodic pulse train emitted by a mode-locked femtosecond laser leads to a perfectly uniform comb in optical frequency space and enables a phase-coherent link between the microwave and optical domains in a stunningly simple manner. This concept has led to the award of the physics nobel prize to Theodor Hänsch and John Hall in 2005 [1].
The Fourier transformation of the electric field emitted by a femtosecond laser yields the relationship
fn=f0+n×fR
for the optical frequencies fn emitted by the laser. These frequencies are spaced by the laser repetition rate fR and carry integer mode numbers n with typically 6 to 7 digits. For example, a typical Ti:Sapphire laser with 1 GHz repetition rate, such as the Laser Quantum taccor (figure 1), has about 20,000 modes under its spectral envelope with mode numbers around 375,000. The existence of the carrier-envelope offset frequency f0 is owed to the fact that the carrier wave (375 THz for an 800 nm Ti:Sapphire laser) travels at the phase velocity while the pulse envelope travels at the group velocity. As these two are usually not equal, the relative position of the carrier under the envelope slips at a rate given by f0 and the modes are offset from the integer harmonic of fR by f0.
Figure 1: Laser Quantum’s taccor
The potency of the femtosecond laser frequency comb (FLFC) originates from the simple fact that the optical frequencies fn are defined by two easily measureable radio-frequencies (f0 and fR). Optical frequency measurements relative to the Cs clock have become simpler in recent times and no longer require the expertise of a National Facility with specialty equipment occupying an entire laboratory [2]. In essence, the FLFC provides a ruler for optical frequencies with the precision of the Cs clock.
Figure 2: Red: Typical taccor output spectrum used for CEO detection and comb applications. Blue: Output spectrum after 1 m photonic crystal fiber.
Figure 3: Heterodyne beat between two ultrastable cw lasers at 532 THz and at 456 THz via a Laser Quantum 1 GHz Ti:Sapphire laser recorded at the U.S. National Institute of Standards and Technology.
In the early years of the FLFC, following the first demonstrations in 1999, applications were mostly for measurements, comparisons of optical frequencies or to function as clockworks in optical atomic clocks in Optical Frequency Standard Laboratories such as PTB in Germany, NPL in the UK or NIST in the USA [3-6]. Later FLFCs found more widespread applications, such as direct frequency comb spectroscopy [7], arbitrary waveform generation [8], dual-comb FTIR spectroscopy [9] or CARS microscopy [10] and the calibration of astronomical spectrographs [11].
Almost all FLFC applications benefit from a repetition rate around 1 GHz for several reasons. The much larger mode-spacing, compared with other solid-state lasers or fiber lasers with fR between 70 and 250 MHz, allows easier identification of the mode number, as required for all frequency measurements. At the same time, radio-frequency (RF) filtering of the relevant beat signals is less demanding when the forest of modes is less dense to begin with. A less dense comb also leads to more power available in each mode, i.e. a 1 GHz laser has 10 times more power per mode than a 100 MHz laser at a given average power (typically between 100 mW and 1 W for commonly used lasers). A further advantage, again by a factor of 10 at 1 GHz, is related to the commonly used nonlinear photonic crystal fibers (PCF) used for super-continuum generation in typical FLFC setups (see figure 2 for a typical super-continuum at 1 GHz mode spacing). It has been shown that above a threshold of a few 100 pJ of pulse energy, the coherence of the frequency comb is heavily reduced or even lost entirely at the output of the fiber due to nonlinear noise amplification[12].
Figure 4: Carrier-envelope offset beat obtained from the taccor comb. The signal-to-noise ratio is limited by the RF spectrum analyzer. The close-up in the inset reveals the true signal-to-noise ratio of >40 dB in 100 kHz of bandwidth.
This means there is a limit to the pulse energy that can be launched through the fiber, typically around 300 pJ. In a 1 GHz pulse train, this corresponds to 300 mW of average power versus 30 mW in a 100 MHz train. So in total, the useful power per mode in a coherent super-continuum scales with the square of the repetition rate, giving a 1 GHz system 100-fold advantage over a 100 MHz system. Finally, a higher repetition rate means a lower pulse-to-pulse separation causing the dead-time in dual comb FTIR, CARS or similar applications to be less, therefore more data acquisition time is spent on gathering useful data and less time is spent acquiring ‘zeros’.
Laser Quantum’s 1 GHz femtosecond lasers have found widespread use in frequency metrology in many National Laboratories and other research groups around the world. In an international comparison between four independently constructed systems, each using a Laser Quantum laser, these lasers have been shown to support optical frequency measurements at the 10-19 accuracy level with stability at the 10-17 level in 1 s of averaging time and mode linewidths below 1 Hz [13,14], see figure 3. Hence, for the foreseeable future, these lasers are capable to support even the world’s most accurate and stable optical atomic clocks as optical clockwork and will not be a limiting factor in the most demanding optical frequency measurements [15]. Furthermore, applications in ultralow-noise microwave generation have been shown [16].
Figure 5: Laser Quantum’s comb extension showing dimensions.
To support applications of the taccor as a frequency comb, Laser Quantum has recently developed the comb extension to its successful range of 1 GHz lasers, now making the taccor comb available to the market, see figure 5. It consists of a matched dispersion compensation module, super-continuum generation and a nonlinear f-2f interferometer. The taccor comb provides a long-term stable RF signal at the carrier-envelope offset frequency with more than 40 dB signal-to-noise ratio in 100 kHz bandwidth, as shown in figure 4. Phase detection between the measured fCEO and a given reference signal is performed and converted into a feedback signal using the XPS800-E stabilisation unit by Menlo Systems GmbH. This feedback signal controls the intensity of the finesse pure CEP pump laser built within the taccor, in order to stabilize the comb’s fCEO signal. The finesse pure CEP laser features our patented CEPLoQTM technology and allows direct modulaton of the 532 nm pump light leading to a faster and more stable response than traditional methods, e.g. using an AOM. Thus, a very high feedback bandwidth of up to 250 kHz can be applied to phase-lock the CEO frequency to an external reference (figure 6 & figure 7).
Figure 6: Close-up of the phase-locked fCEO. The data is acquired using a resolution bandwidth of 200 Hz. The servo bandwidth is about 250 kHz as indicated by the symmetrical peaks around the carrier.
Figure 7: Long term deviations from the lock point of a CEO beat stabilised at 310 MHz over 25 h showing exceptional stability (limited by RF reference input).
References:
[1] T.W. Hänsch, “Passion for Precision”, available at www.nobelprize.org (2005).
[2] H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, “First Phase-Coherent Frequency Measurement of Visible Radiation”, Phys. Rev. Lett. 76, 18 (1996).
[3] T. Udem, J. Reichert, R. Holzwarth, T.W. Hänsch, “Absolute Optical Frequency Measurement of the Cesium D1 Line with a Mode-Locked Laser”, Phys. Rev. Lett. 82, 3568 (1999).
[4] S.A. Diddams, “Direct Link between Microwave and Optical Frequencies with a 300 THz Femtosecond Laser Comb”, Phys. Rev. Lett. 84, 5102 (2000).
[5] R. Holzwarth, T. Udem, T.W. Hänsch, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, “Optical Frequency Synthesizer for Precision Spectroscopy”, Phys. Rev. Lett. 85, 2264 (2000).
[6] S.A. Diddams, T. Udem, J.C. Bergquist, E.A. Curtis, R.E. Drullinger, L. Hollberg, W.M. Itano, W.D. Lee, C.W. Oates, K.R. Vogel, D.J. Wineland, “An Optical Clock Based on a Single Trapped 199Hg+ Ion”, Science 293, 825 (2001).
[7] V. Gerginov, C.E. Tanner, S.A. Diddams, A. Bartels, L. Hollberg, “High-resolution spectroscopy with a femtosecond laser frequency comb”, Opt. Lett. 30, 1734 (2005).
[8] J.T. Willits, A.M. Weiner, S.T. Cundiff, “Line-by-line pulse shaping with spectral resolution below 890 MHz”, Opt. Expr. 20, 3110 (2012).
[9] F. Keilmann, C. Gohle, R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer”, Opt. Lett. 29, 1542 (2004).
[10] T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picque, T.W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs”, Nature 502, 355 (2013).
[11] D.A. Braje, M.S. Kirchner, S. Osterman, T. Fortier, and S.A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs”, Eur. Phys. J. D 48, 57 (2008).
[12] L. Hollberg, C.W. Oates, E.A. Curtis, E.N. Ivanov, S.A. Diddams, T. Udem, H.G. Robinson, J.C. Bergquist, R.J. Rafac, W.M. Itano, R.E. Drullinger, and D.J. Wineland, “Optical Frequency Standards and Measurements”, IEEE JQE 37, 1502 (2001).
[13] L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R.S. Windeler, G. Wilpers, C.W. Oates, L. Hollberg, and S.A. Diddams, “Optical Frequency Synthesis and Comparison with Uncertainty at the 10-19 Level”, Science 303, 1843 (2004).
[14] A. Bartels, C.W. Oates, L. Hollberg, and S.A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths”, Opt. Lett. 29, 1081 (2004).
[15] C.W. Chou, D.B. Hume, J.C.J. Koele meij, D.J. Wineland, and T. Rosenband, “Frequency Comparison of Two High-Accuracy Al+ Optical Clocks”, Phys. Rev. Lett. 104, 070802 (2010).
[16] A. Bartels, S.A. Diddams, C.W. Oates, G. Wilpers, J.C. Bergquist, W.H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references”, Opt. Lett. 30, 667 (2005).
