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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 5793–5802
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Endless frequency shifting of optical frequency comb lines

Erik Benkler, Felix Rohde, and Harald R. Telle  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 5793-5802 (2013)
http://dx.doi.org/10.1364/OE.21.005793


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Abstract

The functional principle of a novel technique for frequency shifting lines of an optical frequency comb is demonstrated. The underlying principle is to shift the carrier frequency by changing the carrier phase within the time span between subsequent pulses of a mode-locked laser used as comb generator. This universal frequency shifter does not require intrusion into the comb generator and provides high agility for arbitrary temporal frequency evolutions.

© 2013 OSA

1. Introduction

Optical frequency combs had a seminal impact on optical precision metrology during the past decade [1

1. R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical Frequency Synthesizer for Precision Spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000). [CrossRef] [PubMed]

, 2

2. J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications, (Kluwer Academic Publishers / Springer, 2005), http://jila.colorado.edu/yelabs/pubs/scienceArticles/2005/sArticle_2005_YeCundiff_CombBook.pdf.

]. In this paper, we present a novel approach for shifting the frequencies of an optical frequency comb enabling an unsurpassed degree of agile, arbitrary and highly precise manipulation of its frequency and phase, which will further expand the application fields of frequency combs.

Tuning of the OFS output frequency (phase) is then achieved by either tuning the frequency (phase) offset between the comb line and the cleanup-field [4

4. J. D. Jost, J. L. Hall, and J. Ye, “Continuously tunable, precise, single frequency optical signal generator,” Opt. Express 10(12), 515–520 (2002). [CrossRef] [PubMed]

, 5

5. T. R. Schibli, K. Minoshima, E. L. Hong, H. Inaba, Y. Bitou, A. Onae, and H. Matsumoto, “Phase-locked widely tunable optical single-frequency generator based on a femtosecond comb,” Opt. Lett. 30(17), 2323–2325 (2005). [CrossRef] [PubMed]

], or by tuning the frequency (phase) of the comb line [6

6. V. Ahtee, M. Merimaa, and K. Nyholm, “Single-frequency synthesis at telecommunication wavelengths,” Opt. Express 17(6), 4890–4896 (2009). [CrossRef] [PubMed]

].

Cw optical frequency synthesizers should not be confused with general optical arbitrary waveform generators [7

7. S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766 (2010). [CrossRef]

] (although they can be regarded as cw optical arbitrary waveform generators [8

8. I. Coddigton, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing Fast Arbitrary CW Waveforms With 1500 THz/s Instantaneous Chirps,” IEEE J. Sel. Top. Quantum Electron. 18(1), 228–238 (2012). [CrossRef]

]). Furthermore, mere optical frequency comb generators based on mode locked lasers are often referred to as optical frequency synthesizers [1

1. R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical Frequency Synthesizer for Precision Spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000). [CrossRef] [PubMed]

]. However, comb generators are not cw OFSs, but rather multiline-OFSs with fixed frequency and phase relations between the individual lines. Although such optical frequency comb generators are commercially available since many years, there is no widely tunable cw OFS product on the market. This may be due to the drawbacks or constraints of the tunable cw OFS approaches as known hitherto. An impairment of the techniques based on frequency-offset phase locking a cw “cleanup-laser” to a comb line is an ambiguity at critical frequencies exactly on or exactly midway between neighboring comb lines which requires conditional decisions during frequency tuning. All other tuning approaches reported so far which do not exploit an offset phase-lock are limited either in their frequency tuning range or agility due to insufficient control elements for optical carrier frequencies. Tuning the carrier frequency by piezo-controlled macroscopic resonator length changes [6

6. V. Ahtee, M. Merimaa, and K. Nyholm, “Single-frequency synthesis at telecommunication wavelengths,” Opt. Express 17(6), 4890–4896 (2009). [CrossRef] [PubMed]

], for example, requires components to be mechanically moved which is slow and susceptible to acoustic perturbations.

A new approach to tunable OFSs is enabled by the frequency shifter presented in this paper. It is a carrier frequency shifter which exploits the properties of frequency combs and achieves unprecedented simultaneous tuning range and agility, i.e. control bandwidth.

It is applicable to frequency combs regardless of how they are generated, as long as they correspond to a periodic train of pulses. In particular, it does not require any intrusion into the resonator of the comb generator. Such a resonator external approach is more universal than existing resonator internal approaches and does not impair the comb generation process. Furthermore, it does not require conditional decisions and is thus ideally suited for implementations of agilely and widely tunable OFSs.

2. Principle of the frequency comb shifter

The principle of the frequency comb shifter is first described in a time-domain picture. Frequency shifting is fundamentally based on the relation between instantaneous frequency ν(t) and phase ϕ(t):
ν(t)=ν0+Δν(t)=ν0+12πdϕdt,
(1)
where ν0 is the initial carrier frequency at t=0 and Δν(t) is the frequency shift. This means that a frequency shift can be achieved by changing the carrier phase within a certain time span. This is the basic principle exploited for the frequency shifter presented here.

In the following, an optical frequency comb corresponding to a train of strictly time-periodic short pulses is considered. As shown in Fig. 1
Fig. 1 Basic building blocks of the frequency comb shifter.
, its optical field is sent through an electro-optic modulator (EOM) whose refractive index depends on an applied voltage. By modification of the refractive index, the carrier phase of the light field transmitted through the EOM is changed. The short pulses sample the instantaneous refractive index of the EOM at sampling points of time tm=mΔT, where the time span between the pulses is given by the inverse of the pulse repetition rate: ΔT=1/frep. It is remarkable that it does not matter how the EOM refractive index evolves during the time between the pulses, i.e. while the light is off and hence cannot sense the refractive index. For this reason, the method is not applicable to frequency combs which do not correspond to a pulse train, but e.g. to a cw signal with periodic short phase excursions instead.

The pulses thus experience the EOM-induced phase shifts φm=ϕ(tm) and the change of the carrier phase between subsequent pulses is given by
ΔϕΔT=φmφm1ΔT,
(2)
which can be plugged into a discretized version of Eq. (1) with the result of a frequency shift Δνm at time tm of the m-th pulse:
Δνm=Δν(tm)=φmφm12πΔT.
(3)
Equation (3) shows that wrapping the phase difference between subsequent pulses by 2π corresponds to wrapping the frequency by the repetition rate frep. Furthermore, for a given temporal evolution of frequency shifts, the phase shifts applied by the EOM have to evolve according to the discrete integration of Eq. (3):
φm=2πΔTk=1mΔνk.
(4)
For example, a targeted constant frequency shift Δν requires a phase shift at the m-th pulse
φm=2πΔTΔνm,
(5)
which increases proportionally to the pulse index. It is clear that without further actions, the maximum voltage applicable to the EOM would be exceeded after a few pulses. However, since the optical carrier field is periodic with phase shifts of 2π, it is sufficient to apply phase shifts
φm=(2πΔTk=1mΔνk)mod2π
(6)
allowing to keep the EOM voltage within a limited window. This requires 2π-fly-back jumps if the voltage would exceed the limits otherwise, which can be conveniently implemented by fast digital electronics as described later in section 3. In practice, the fly-back jumps of the EOM refractive index cannot be implemented with infinite speed, which can have disturbing effects if these transients are sensed by the light field. However, if the fly-back jumps are allowed to occur only during the time between the pulses, they are not sensed and thus do not pose a problem.

It is instructive to highlight the process alternatively in the frequency domain. In this picture, the frequency comb can be treated as a multitude of equally-spaced cw fields. Each of these cw fields experiences phase shifts according to Eq. (6), where for the moment we neglect the wavelength dependence of these phase shifts for a given voltage applied to the EOM. The cw fields sense the evolution of the EOM refractive index including the transients of the fly-back jumps, which leads to spurious signals for each cw field. The existence of darkness between the pulses is equivalent to the fact that the cw fields interfere destructively during that time. As a consequence also all spurious signals sensed by the cw fields between the pulses identically add up to zero.

Unlike assumed before, the carrier phase shift φ induced by an electric field E in a LiNbO3 crystal of length L via the electro-optic effect in general is wavelength-dependent [9

9. O. Gobert, P. M. Paul, J. F. Hergott, O. Tcherbakoff, F. Lepetit, P. D. Oliveira, F. Viala, and M. Comte, “Carrier-envelope phase control using linear electro-optic effect,” Opt. Express 19(6), 5410–5418 (2011). [CrossRef] [PubMed]

]:
φ(λ,E)=πne3(λ)r33(λ)λLE,
(7)
where λ is the optical wavelength, ne the extraordinary refractive index and r33 the electro- optic coefficient of LiNbO3 [10

10. K. Yonekura, L. Jin, and K. Takizawa, “Measurement of Dispersion of Effective Electro-Optic Coefficients r13E and r33E of Non-Doped Congruent LiNbO3 Crystal,” Jpn. J. Appl. Phys. 47(7), 5503–5508 (2008). [CrossRef]

]. Even if material dispersion, i.e. the wavelength-dependence of ne and r33 is neglected, the voltage-induced phase-shift is proportional to optical frequency, which is in fact the dominating wavelength-dependent effect in LiNbO3 at λ = 1.55 µm.

Since a frequency-proportional phase shift corresponds to a temporal group delay, the pulse envelope experiences a timing jitter according to the instantaneous phase actuating values |φm| of Eq. (6). Assuming a peak amplitude of |φm|π as it is the case with the described technique using 2π-fly-back jumps, this leads to a peak pulse envelope timing deviation of 2.5fs@ν=200THz. Pulse timing jitter rms-values of this order are typical for low-noise mode locked fiber lasers, as integrated over all Fourier frequencies above the kHz range. Hence, the timing jitter accompanying the carrier frequency shift can be tolerated in many cases.

The fact that the voltage-induced phase shifts are not wavelength-independent leads to spurious signals at optical frequencies for which fly-backs do not correspond to 2π. These spurs consist, amongst others, of the remaining unshifted lines of the input frequency comb. However, this does not imply any problem in single-frequency applications because the phase shift at one single and well-known carrier frequency can be easily held at its proper value by adjustment of the EOM driver gain via feed-forward techniques.

If actually necessary, simultaneous broadband operation requires more sophisticated approaches, e.g. introduction of an additional time-proportional phase shift mapped to a frequency-proportional phase shift using longitudinal spectral decomposition of the light pulses [11

11. R. E. Saperstein, N. Alić, D. Panasenko, R. Rokitski, and Y. Fainman, “Time-domain waveform processing by chromatic dispersion for temporal shaping of optical pulses,” J. Opt. Soc. Am. B 22(11), 2427–2436 (2005). [CrossRef]

].

Although several alternative approaches for comb-generator external frequency comb shifters have been published, our method has the potential to achieve high frequency and phase precision, traceability to a reference signal, high agility, wide tuning range, large optical bandwidth and low levels of spurious signals simultaneously.

Furthermore, most conventional frequency shifters do not allow what we call “endless” frequency shifting of comb lines: The pattern of the comb lines can be frequency-shifted endlessly, while the power of an individual line is determined by ist position inside the comb’s envelope. It increases during entering the envelope on one edge and vanishes upon leaving it on the other. One example for conventional frequency shifters are acousto-optical modulators, which are limited both in optical (~10 nm) and control bandwidth (~100 kHz), introduce higher-order chromatic dispersion and, at least in single-pass configuration, angular dispersion of the frequency-shifted beam. Another alternative are integrated suppressed-carrier single-sideband modulators [18

18. M. Izutsu, S. Shikama, and T. Sueta, “Integrated Optical SSB Modulator/Frequency Shifter,” IEEE J. Quantum Electron. 17(11), 2225–2227 (1981). [CrossRef]

], which are limited in tuning range (≤ 100 GHz) as well as in optical bandwidth, and their spur free dynamic range is sensitive to environmental conditions. The limited tuning range, however, could be circumvented using modulation frequencies modulo frep when applied to frequency combs (compare comment to Eq. (3)).

The novel method is related, but not equivalent to traditional serrodyne techniques, and should not be confused with them. In order to achieve tolerable spurious signals, conventional serrodyning schemes require the fly-backs to occur with a very small duty factor [19

19. R. Kohlhaas, T. Vanderbruggen, S. Bernon, A. Bertoldi, A. Landragin, and P. Bouyer, “Robust laser frequency stabilization by serrodyne modulation,” Opt. Lett. 37(6), 1005–1007 (2012). [CrossRef] [PubMed]

], or, when applied to mode locked lasers, to be synchronized to an integer multiple of the repetition rate [20

20. M. A. Duguay and J. W. Hansen, “Optical frequency shifting of a modelocked laser beam,” IEEE J. Quantum Electron. 4(8), 477–481 (1968). [CrossRef]

]. In the latter case only the spectral envelope can be changed, in analogy to a blazed grating. Our method instead can be seen as a generalization of the serrodyne concept, using conditional fly-backs, which only occur when they do not cause spurious signals (e.g. when the light is off between the pulses). Thus it allows spur-free 'serrodyne' frequency shifting of a comb line.

A fundamental limit to the control bandwidth of the novel frequency shifter is the Nyquist-criterion: Since a frequency shift requires more than two subsequent pulses sampling the change of the EOM refractive index to be unambiguous, this limit is given by Δνmax=frep/2N, where N is an oversampling factor. Even with oversampling, this results in more than 10 MHz control bandwidth for frequency combs with line spacings in the 50-500 MHz range. Within this limit, the maximum agility, i.e. change of the frequency shift over time is given by
dνdtΔνmaxT=frep22N.
(8)
For two-fold oversampling to guarantee unambiguity, this corresponds to 1014 - 1017 Hz/s. This limit can in principle be overcome using advanced techniques, e.g. higher wrapping orders, combined with suitable feed-forward, thus ensuring unambiguity of the comb line order. Such a coarse feed-forward signal can be derived, e.g., from a transfer-interferometer.

3. Experimental setup

The 2π phase fly-backs characteristic for the frequency shifting method can be implemented with digital electronics. The central element of these electronics is a numerically controlled oscillator (NCO, the time- and amplitude-discrete part of a direct digital synthesizer, DDS [21

21. M. Thompson, “Low-Latency, High-speed Numerically Controlled Oscillator Using Progression-of-States Technique,” IEEE J. Solid-St. Circulation 27, 113–117 (1992).

, 22

22. L. Cordesses, “Direct Digital Synthesis: A Tool for Periodic Wave Generation (Part 1),” IEEE Signal Process. Mag. 21(4), 50–54 (2004). [CrossRef]

], implemented in an Analog Devices AD9958 evaluation board) clocked by the repetition rate of the frequency comb or a multiple thereof. The tuning word of the NCO determines the increment of its phase accumulator value per clock cycle, i.e. per pulse. The driving voltage at the EOM is generated by A/D conversion from the phase accumulator value where the conversion gain is adjusted such that the accumulator’s most significant bit (MSB) corresponds to a phase shift of π. Consequently, the 2π fly-back jumps mentioned above automatically take place during the overflow events of the phase accumulator. Thus, this scheme can be considered as an optical DDS, since the time-varying value of the digital accumulator is converted to the (optical) carrier’s phase, similar to its rf-counterpart. It is noteworthy that the NCO is frequency agile, i.e. the tuning word can in principal be changed every clock cycle with an immediate effect on the frequency shift. Furthermore, the scheme is robust against changes of the repetition rate, since the NCO clock is synchronized with it.

Without further provisions, the maximum clock rate of the digital electronics may pose the limit for the repetition rate of the pulse train in the general case. Current state of the art digital electronics reach clock rates up to the GHz range. However, using undersampling techniques like changing the EOM phase only every N-th pulse can in principle overcome this limit at the cost of increased spurious signal levels and of tuning speed.

For a first demonstration of the novel frequency comb shifter function, an experiment is set up providing both the original, unshifted frequency comb emitted by a mode-locked Erbium-doped fiber laser, and the frequency shifted comb. During the experiments, the frequency shift follows a target temporal evolution. This is implemented by sending a corresponding sequence of tuning words to the NCO in the EOM control electronics. For analysis, the temporal evolution of the shifted optical comb spectrum is tracked with respect to the unshifted comb using a scanning-cavity based optical spectrum analyzer. This provides a coarse overview at a moderate frequency resolution. In order to simultaneously analyze the temporal evolution as well as unwanted spurious signals with high frequency resolution, the spectrum of the beat note between the field of the shifted and unshifted frequency comb is monitored.

Figure 2
Fig. 2 Experimental setup. See text for details.
shows a schematic sketch omitting a distinction between free space and fiber optical parts of the optical setup. A mode locked Erbium-doped fiber laser providing 100 fs short pulses at a repetition rate of frep = 56.2 MHz and 1560 nm wavelength is used as optical frequency comb generator. By means of a grating-based prefilter, the comb spectrum is narrowed to ~100 GHz FWHM and subsequently amplified using an Erbium-doped fiber amplifier (EDFA). Such prefiltering reduces potentially detrimental dispersion effects of the mirrors [23

23. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 251–256 (2009). [CrossRef]

] employed in the cavity for spectral analysis of the comb spectra.

The light path is split in two paths with orthogonal linear polarizations using polarizing beam splitter PBS1. In path 1, the EOM introduces a time-dependent frequency shift which we want to demonstrate. The acousto-optical modulator (AOM) in path 2 is used for shifting the frequency of the beat-note between the fields in path 1 and 2, see below. The light pulses are recombined with orthogonal linear polarizations at PBS2.

The light then enters the V-shaped, folded scanning cavity consisting of coupling mirror M1 (R = 98%) and the end mirrors M2 and M3. Due to the reflection birefringence of M1 under oblique incidence, the V-shaped cavity resonances show a polarization splitting in dependence on the reflection angle. The orthogonally polarized light from paths 1 and 2 is coupled into the cavity polarized along its two principle axes, such that the polarization splitting does not mix the light from the two paths. The resonator length is scanned with M3 mounted on a piezo actuator which is driven by a triangular voltage. The free spectral range (FSR) of the cavity is adjusted to match to an integer multiple (factor 19) of the comb generator repetition rate, resulting in νFSR1.07GHz. The FWHM line width of the cavity resonances is Δνres8MHz, corresponding to a Finesse of F130 in accordance with the cavity losses. Each cavity resonance can select a single comb line, because the resonance line width is smaller than the comb line separation, Δνresfrep. Since the cavity free spectral range coincides with the 19-fold comb line separation, the cavity is resonant with every 19th comb line simultaneously. The result of linearly ramping the resonator length is that the temporal evolution of the power transmitted through the resonator corresponds to the convolution between the comb spectrum and the cavity resonance.

Both cavity output signals at the principal polarizations are coupled out by the 50:50 beam splitter BS, separated using PBS3 and detected with photodiodes PD1 and PD2. Their output signals are captured by an oscilloscope which is conditionally triggered by the piezo driving voltage and the signal from path 2, i.e. the comb which was not shifted with the EOM. In this way, the spectra of the combs from path 1 and path 2 are mapped to the oscilloscope traces. The amplitude of the piezo driving voltage is adjusted for a stroke larger than 10 frep and the scanning frequency is 80 Hz. The angle of the V-shaped cavity and thus its polarization splitting of resonance frequencies is set to match the AOM driving frequency, i.e. the resonance maxima of both signals coincide for zero frequency shift in path 1.

For the simultaneous high-resolution analysis, the beat note between both signals is characterized with an rf spectrum analyzer. To this end, the pulses from the two paths are temporally overlapped using a delay line not shown in Fig. 1, and the polarization planes of the signals reflected at the cavity are mixed by means of a polarizer Pol oriented at 45°. The resulting beat note is detected with PD3. Considering the output of path 2 as local oscillator (LO), the scheme enables heterodyne detection of the output signal of path 1. Owing to the LO frequency offset as given by the fixed AOM driving frequency of 80 MHz, it allows detection of unwanted spurious signals generated even at frequency shifts equal or close to zero and integer multiples of frep/2.

4. Experimental results

In the first experiment, we apply a target temporal evolution of the control variable, i.e. the desired frequency shift consisting of a sequence of 5 sinusoidal periods with a peak-to-peak amplitude of one comb line distance followed by a linear ramp over 10 comb lines, and subsequently a cubic time dependence with opposite sign as shown by the overlaid green solid line in Fig. 3(a)
Fig. 3 (a) Color-coded PD1 photocurrent showing the measured temporal evolution of the optical frequency comb. The overlaid green solid line shows the target temporal evolution of the frequency shift. (b) Video (Media 1) corresponding to (a), yellow: target frequency evolution, green: PD1, violet: PD2. A high-quality version of the video is available [24].
.

For generation of the plot in Fig. 3(a), oscilloscope traces of the photocurrent of PD1, i.e., of the power transmitted through the scanned cavity, were recorded sequentially using the FastFrames mode of a Tektronix TDS 5104B oscilloscope. Each pixel column in the image corresponds to one oscilloscope trace in the recorded sequence. The photocurrent is color coded (blue corresponding to zero, red to maximum photocurrent). Small fluctuations and slight distortions of the experimental data can be observed, stemming from acoustics and pressure fluctuations in the cavity and from nonlinear scanning errors.

Before the start of the target sequence at t = 0, a representation of the optical frequency comb is visible as parallel horizontal lines separated from each other by one repetition rate. At t = 0, the target temporal evolution starts and is accurately followed by the frequency comb. At t33s, the sequence ends. In principle, much faster changes of the frequency shift are possible. However, for the purpose of visualization in a video (Fig. 3(b)) intended here, faster changes are not useful. Simultaneous with the recording of the oscilloscope data using the FastFrames mode, the oscilloscope screen was recorded with a video camera. The right pane in the video shows the oscilloscope screen, whereas in the left pane the synchronized target temporal frequency shift evolution is shown as a yellow solid line. The red bar and dot indicates the current position. The upper half of the oscilloscope screen shows about 16 comb lines (green: PD1 = shifted comb from path 1, violet: PD2 = comb from path 2), whereas the lower part is a zoom spanning four lines as indicated by the violet dashed lines in the upper half. In spite of the observable fluctuations due to acoustics and air pressure variations in the cavity, the video demonstrates in an intuitive way that the frequency comb follows the target frequency evolution.

The results demonstrated in Fig. 3 prove the correct operation of the novel frequency shifter. However, it does neither provide a high-resolution insight nor can spurious signals be analyzed. We define spurs as optical signal power at frequencies where signal power should be zero in the ideal case. One example is remaining power at the lines of the input frequency comb. In the ideal case all power of the input lines should be shifted to the lines of the shifted comb. In a real system this is not the case, because the required phase fly-back jumps are not exact integer multiples of 2π, e.g. for the reasons discussed in section 2. The time-averaged power of a spurious signal depends on the rate of occurrences of the causing event (e.g. inaccurate 2π fly-back), which in turn depends on the frequency shift. The highest rate of 2π fly-backs occurs at a frequency shift of nfrep/2,n as the jump occurs for every second pulse.

Hence, these and nearby frequency shifts are susceptible to this type of spurs. There exist also other sources of spurs, such as nonlinearities or thermal effects in the EOM driver electronics. The spurs can be observed in the beat spectrum detected with PD3 and an electrical spectrum analyzer (ESA).

Figure 4
Fig. 4 Frame from video of a linear frequency sweep showing optical (right) and beat photocurrent spectrum (left) of the shifted and unshifted combs along with the target frequency shift evolution (lower pane) (Media 2). A high-quality version of the video is available [25].
shows a frame from a video. It comprises a video of the beat spectrum on the ESA (left) along with the synchronized video of the oscilloscope trace (right) and target frequency evolution (lower pane). The target evolution is simply a high-resolution linear frequency sweep over a span of 2 frep. Before recording the video, we optimized both the trigger delay between digital electronics and temporal pulse position, as well as the amplitude of the EOM driving signals, for minimum spurs during a linear frequency sweep between two or more comb lines.

The beat spectrum on the ESA is shown over a span of one comb line separation frep = 56.2 MHz. Aliasing causes the presence of mirror frequencies, which renders the spectrum symmetric about the center frequency at 28.1 MHz. Small deviations from this symmetry result from the fact that the sweep time of the ESA is slightly too slow for the 30 Hz video frame rate. The frequency shifted comb line and its mirror counterpart are marked as (1) and (1'). The two prominent central spurs marked as (2) and (2') in Fig. 4 are the mentioned remaining lines of the unshifted comb from path 1 beaten with the comb shifted by 80 MHz in path 2. Hence, their frequencies are (80 – 56.2 = 23.8) MHz and the mirror frequency at 32.4 MHz. The spurs remain more than 22 dB below the beat notes between shifted comb lines and LO for any frequency shift in the video. Even in this first experimental demonstration, this spur-free dynamic range is comparable to that of dual-parallel-Mach-Zehnder interferometer based SC-SSB (suppressed-carrier single sideband) modulators, however at the benefit of a weaker sensitivity on environmental parameters such as temperature. The observed spurs could in principle be further reduced with more sophisticated driving electronics of the EOM, which avoid, e.g., thermal effects.

5. Conclusions

A novel approach to shift the frequencies of an optical frequency comb has been presented. This resonator-external approach relies on changes applied to the carrier phase within the time between subsequent pulses. Arbitrary time-dependent frequency shift evolutions have been experimentally demonstrated for the first time using this technique. A spur-free dynamic range of more than 22 dB under all circumstances was demonstrated in this first proof of principle.

The described endless frequency shifter for optical frequency combs is a key component for a precisely and agilely tunable optical frequency synthesizer with a broad range of applications, e.g. in precision spectroscopy, dimensional metrology, telecommunication, Terahertz science or quantum optics.

Acknowledgments

The work was funded by the Ministry of Economics and Technology, following a decision of the German Parliament (ZIM project KF2303709).

References and links

1.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical Frequency Synthesizer for Precision Spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000). [CrossRef] [PubMed]

2.

J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications, (Kluwer Academic Publishers / Springer, 2005), http://jila.colorado.edu/yelabs/pubs/scienceArticles/2005/sArticle_2005_YeCundiff_CombBook.pdf.

3.

K. Shimizu, T. Horiguchi, and Y. Koyamada, “Technique for translating light-wave frequency by using an optical ring circuit containing a frequency shifter,” Opt. Lett. 17(18), 1307–1309 (1992). [CrossRef] [PubMed]

4.

J. D. Jost, J. L. Hall, and J. Ye, “Continuously tunable, precise, single frequency optical signal generator,” Opt. Express 10(12), 515–520 (2002). [CrossRef] [PubMed]

5.

T. R. Schibli, K. Minoshima, E. L. Hong, H. Inaba, Y. Bitou, A. Onae, and H. Matsumoto, “Phase-locked widely tunable optical single-frequency generator based on a femtosecond comb,” Opt. Lett. 30(17), 2323–2325 (2005). [CrossRef] [PubMed]

6.

V. Ahtee, M. Merimaa, and K. Nyholm, “Single-frequency synthesis at telecommunication wavelengths,” Opt. Express 17(6), 4890–4896 (2009). [CrossRef] [PubMed]

7.

S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766 (2010). [CrossRef]

8.

I. Coddigton, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing Fast Arbitrary CW Waveforms With 1500 THz/s Instantaneous Chirps,” IEEE J. Sel. Top. Quantum Electron. 18(1), 228–238 (2012). [CrossRef]

9.

O. Gobert, P. M. Paul, J. F. Hergott, O. Tcherbakoff, F. Lepetit, P. D. Oliveira, F. Viala, and M. Comte, “Carrier-envelope phase control using linear electro-optic effect,” Opt. Express 19(6), 5410–5418 (2011). [CrossRef] [PubMed]

10.

K. Yonekura, L. Jin, and K. Takizawa, “Measurement of Dispersion of Effective Electro-Optic Coefficients r13E and r33E of Non-Doped Congruent LiNbO3 Crystal,” Jpn. J. Appl. Phys. 47(7), 5503–5508 (2008). [CrossRef]

11.

R. E. Saperstein, N. Alić, D. Panasenko, R. Rokitski, and Y. Fainman, “Time-domain waveform processing by chromatic dispersion for temporal shaping of optical pulses,” J. Opt. Soc. Am. B 22(11), 2427–2436 (2005). [CrossRef]

12.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74(1), 1–6 (2002). [CrossRef]

13.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78(3-4), 321–324 (2004). [CrossRef]

14.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006). [CrossRef]

15.

H. R. Telle, “Absolute Measurement of Optical Frequencies,” in Frequency Control of Semiconductor Lasers, M. Ohtsu ed. (Wiley, 1996), Chap. 5, pp. 137.

16.

F. L. Walls, “Phase noise issues in femtosecond lasers,” Proc. SPIE 4269, 170–177 (2001). [CrossRef]

17.

F. L. Walls and A. DeMarchi, “RF Spectrum of a Signal After Frequency Multiplication; Measurement and Comparison with a Simple Calculation,” IEEE Trans. Instrum. Meas. 24(3), 210–217 (1975). [CrossRef]

18.

M. Izutsu, S. Shikama, and T. Sueta, “Integrated Optical SSB Modulator/Frequency Shifter,” IEEE J. Quantum Electron. 17(11), 2225–2227 (1981). [CrossRef]

19.

R. Kohlhaas, T. Vanderbruggen, S. Bernon, A. Bertoldi, A. Landragin, and P. Bouyer, “Robust laser frequency stabilization by serrodyne modulation,” Opt. Lett. 37(6), 1005–1007 (2012). [CrossRef] [PubMed]

20.

M. A. Duguay and J. W. Hansen, “Optical frequency shifting of a modelocked laser beam,” IEEE J. Quantum Electron. 4(8), 477–481 (1968). [CrossRef]

21.

M. Thompson, “Low-Latency, High-speed Numerically Controlled Oscillator Using Progression-of-States Technique,” IEEE J. Solid-St. Circulation 27, 113–117 (1992).

22.

L. Cordesses, “Direct Digital Synthesis: A Tool for Periodic Wave Generation (Part 1),” IEEE Signal Process. Mag. 21(4), 50–54 (2004). [CrossRef]

23.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B 96(2-3), 251–256 (2009). [CrossRef]

24.

http://youtu.be/8XOGWFBGroc.

25.

http://youtu.be/JBkFEaoUQHQ

OCIS Codes
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing
(140.3600) Lasers and laser optics : Lasers, tunable

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: December 5, 2012
Revised Manuscript: December 28, 2012
Manuscript Accepted: December 29, 2012
Published: March 1, 2013

Citation
Erik Benkler, Felix Rohde, and Harald R. Telle, "Endless frequency shifting of optical frequency comb lines," Opt. Express 21, 5793-5802 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5793


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References

  1. R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical Frequency Synthesizer for Precision Spectroscopy,” Phys. Rev. Lett.85(11), 2264–2267 (2000). [CrossRef] [PubMed]
  2. J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications, (Kluwer Academic Publishers / Springer, 2005), http://jila.colorado.edu/yelabs/pubs/scienceArticles/2005/sArticle_2005_YeCundiff_CombBook.pdf .
  3. K. Shimizu, T. Horiguchi, and Y. Koyamada, “Technique for translating light-wave frequency by using an optical ring circuit containing a frequency shifter,” Opt. Lett.17(18), 1307–1309 (1992). [CrossRef] [PubMed]
  4. J. D. Jost, J. L. Hall, and J. Ye, “Continuously tunable, precise, single frequency optical signal generator,” Opt. Express10(12), 515–520 (2002). [CrossRef] [PubMed]
  5. T. R. Schibli, K. Minoshima, E. L. Hong, H. Inaba, Y. Bitou, A. Onae, and H. Matsumoto, “Phase-locked widely tunable optical single-frequency generator based on a femtosecond comb,” Opt. Lett.30(17), 2323–2325 (2005). [CrossRef] [PubMed]
  6. V. Ahtee, M. Merimaa, and K. Nyholm, “Single-frequency synthesis at telecommunication wavelengths,” Opt. Express17(6), 4890–4896 (2009). [CrossRef] [PubMed]
  7. S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics4(11), 760–766 (2010). [CrossRef]
  8. I. Coddigton, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing Fast Arbitrary CW Waveforms With 1500 THz/s Instantaneous Chirps,” IEEE J. Sel. Top. Quantum Electron.18(1), 228–238 (2012). [CrossRef]
  9. O. Gobert, P. M. Paul, J. F. Hergott, O. Tcherbakoff, F. Lepetit, P. D. Oliveira, F. Viala, and M. Comte, “Carrier-envelope phase control using linear electro-optic effect,” Opt. Express19(6), 5410–5418 (2011). [CrossRef] [PubMed]
  10. K. Yonekura, L. Jin, and K. Takizawa, “Measurement of Dispersion of Effective Electro-Optic Coefficients r13E and r33E of Non-Doped Congruent LiNbO3 Crystal,” Jpn. J. Appl. Phys.47(7), 5503–5508 (2008). [CrossRef]
  11. R. E. Saperstein, N. Alić, D. Panasenko, R. Rokitski, and Y. Fainman, “Time-domain waveform processing by chromatic dispersion for temporal shaping of optical pulses,” J. Opt. Soc. Am. B22(11), 2427–2436 (2005). [CrossRef]
  12. H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B74(1), 1–6 (2002). [CrossRef]
  13. N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B78(3-4), 321–324 (2004). [CrossRef]
  14. R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B82(2), 265–273 (2006). [CrossRef]
  15. H. R. Telle, “Absolute Measurement of Optical Frequencies,” in Frequency Control of Semiconductor Lasers, M. Ohtsu ed. (Wiley, 1996), Chap. 5, pp. 137.
  16. F. L. Walls, “Phase noise issues in femtosecond lasers,” Proc. SPIE4269, 170–177 (2001). [CrossRef]
  17. F. L. Walls and A. DeMarchi, “RF Spectrum of a Signal After Frequency Multiplication; Measurement and Comparison with a Simple Calculation,” IEEE Trans. Instrum. Meas.24(3), 210–217 (1975). [CrossRef]
  18. M. Izutsu, S. Shikama, and T. Sueta, “Integrated Optical SSB Modulator/Frequency Shifter,” IEEE J. Quantum Electron.17(11), 2225–2227 (1981). [CrossRef]
  19. R. Kohlhaas, T. Vanderbruggen, S. Bernon, A. Bertoldi, A. Landragin, and P. Bouyer, “Robust laser frequency stabilization by serrodyne modulation,” Opt. Lett.37(6), 1005–1007 (2012). [CrossRef] [PubMed]
  20. M. A. Duguay and J. W. Hansen, “Optical frequency shifting of a modelocked laser beam,” IEEE J. Quantum Electron.4(8), 477–481 (1968). [CrossRef]
  21. M. Thompson, “Low-Latency, High-speed Numerically Controlled Oscillator Using Progression-of-States Technique,” IEEE J. Solid-St. Circulation27, 113–117 (1992).
  22. L. Cordesses, “Direct Digital Synthesis: A Tool for Periodic Wave Generation (Part 1),” IEEE Signal Process. Mag.21(4), 50–54 (2004). [CrossRef]
  23. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B96(2-3), 251–256 (2009). [CrossRef]
  24. http://youtu.be/8XOGWFBGroc .
  25. http://youtu.be/JBkFEaoUQHQ

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