1. Introduction

Manipulating the optical spectrum, in particular shifting its carrier frequency, is a commonly used tool in various photonic systems. For instance, frequency shifting has been used in applications including Raman Interferometry [1], lidar [2], and optical frequency transfer over long fiber links [3], to name a few. There are several methods of unidirectionally shifting an optical frequency (e.g. shifting the carrier frequency of a laser) which include acousto-optic modulators (AOMs) [4] and specialized electro-optic (EO) modulators [5]. Typical fiber-coupled AOMs are capable of reasonably low loss (< 3 dB), particularly for < 250 MHz shifting frequencies, and polarization-independent operation. However, their performance tends to degrade at higher shifting frequencies.

EO modulators operating in a single-side-band mode can perform a unidirectional frequency shift and are compatible with inducing high frequency (e.g. >10 GHz) shifts [6]. However, their complexity, for instance sophisticated required DC biasing, and several dBs of insertion loss make them ill-suited for some applications. Some EO frequency shifting methods, like applying a sinusoidal phase shift in a phase modulator [7] or using carrier-suppressed modulation in a Mach-Zehnder interferometer modulator [5], create symmetric spectral tones which thus send <50% of the output signal to any one spectral tone. For situations where a single output tone is desired this manifests itself as a loss, and moreover can generate large and disruptive unwanted spectral tones creating a challenging spectral filtering issue. Additionally, most EO based modulators are polarization sensitive.

A simple method of unidirectionally shifting an optical frequency is to apply a periodic linear phase-ramp of a magnitude equal to an integer number (i) of 2·π radians, sometimes called serrodyne frequency shifting [8]. A linear phase shift of i·2·π applied over a ramp of time T adds a constant change in phase with respect to time thereby leading to a fixed optical frequency shift of i/T. Such a method generally needs a very precise electrical ramp modulation signal, which can be difficult to generate at high rates, although >1 GHz frequency shifts have been observed [9,10]. Most high-speed EO phase modulators are polarization sensitive and have several dB’s of insertion loss. In principle one can cascade two modulators with their axis of modulation oriented at 90 degrees to each other in order to build a polarization-insensitive phase modulator, but this also increases insertion loss.

An interesting technique to phase-modulate a fiber-coupled signal with extremely low insertion loss is to use cross phase modulation (XPM) directly in fiber [11,12]. Such a method can essentially eliminate coupling loss since the signal is confined to fiber throughout the device. As an example, a Mach-Zehnder Interferometer all-fiber XPM switch for 1550 nm signals has recently been demonstrated with 1 dB of insertion loss [12]. The use of a 1070 nm band pump pulse allows wavelength-division-multiplexers (WDMs) with very low insertion loss at the signal wavelength (e.g. 0.1 dB), maintains high pump-power efficiency due to the low level of group velocity mismatch between the pump and signal wavelengths, and controls spontaneously generated Raman noise allowing the switch to operate on the sub-photon level signals typically used in quantum communications [12]. Additionally, a wide variety of lasers and amplifiers are commercially available near 1070 nm. Note that although 1070 nm is slightly multi-moded in standard single mode fiber (e.g. SMF 28e), the optical energy can be predominantly confined in the fundamental mode over long lengths of fiber [13].

In this paper we will describe an all-fiber XPM phase shifter that can be used as a serrodyne frequency shifter (SFS). The XPM-SFS translates an energy change (via fiber propagation loss) experienced by a short pump pulse as it propagates through a nonlinear fiber into a quasi-linear time-varying phase change on the input signal. The effect is enabled by the pump and signal wavelengths temporally walking-off each other in the fiber by a time of t_g·L, where t_g is the temporal walk-off per unit length between the pump and signal wavelengths and L is the total nonlinear fiber length. Setting the pump pulse period T_p = t_g·L, or equivalently the pump pulse repetition rate to be R_p = (t_g·L)⁻¹, makes the pump pulses shift exactly one pulse period with respect to the frame of reference of the signal during propagation through the nonlinear fiber. The pump intensity generally degrades exponentially, and for small net loss levels (e.g. 3 dB), the exponential function can be well approximated by a linear function. XPM imprints this near-linear pump intensity change into a near-linear phase change on the signal with period T_p. Choosing the pump pulse energy so that the difference between the maximum and minimum XPM-induced phase shift is i·2·π radians where i is an integer (in our case i = 1) produces an efficient unidirectional frequency shift of magnitude i·R_p. Note that while the pump is pulsed at R_p, the signal does not require any special synchronization to the pump, including the use of a CW signal. In this sense, the pump frequency can be viewed as analogous to the RF driving frequency of an AOM.

Due to the all-fiber design the XPM-SFS can have exceptionally low insertion loss (e.g. < 1 dB), and the use of a depolarized pump enables polarization-insensitive operation without an adverse impact on the insertion loss. In principle the XPM frequency shifter does not require any electrical driving signal, for instance when pumped by a passively mode-locked laser, so we call it an all-optical serrodyne frequency shifter. However, in our experimental proof-of-concept implementation an electrically-defined optical pump pulse is employed.

In a proof-of-concept experiment, we use a signal in the lowest loss fiber band near 1550 nm, and a pump pulse near 1070 nm. The loss at the pump wavelength is about 3.7 dB over the 4.6 km length of fiber. A high pump loss actually makes the system more pump-power efficient since the XPM induced quasi-phase-ramp is governed by the change in pump energy along the fiber. However, the higher the net amount of pump loss through the nonlinear fiber the less linear the exponential pump loss appears, thereby moving further away from the desired perfectly-linear phase-ramp of traditional serrodyne frequency shifting. With this wavelength choice a reasonable amount of pump loss can be achieved while simultaneously having low signal losses due to the significant different between fiber loss near 1070 nm (∼0.8 dB/km) and 1550 nm (∼0.2 dB/km). The design thus balances multiple needs to achieve a novel type of frequency shifting device with very attractive properties including extremely low signal loss (1.5 dB) for a high-speed fiber-coupled frequency shifter. The experiment generates an output spectrum where >75% of the output energy is shifted by R_p = 135 MHz. The percent of output energy in the desired shifted tone is significantly reduced from the ideal due to insufficient experimental pump power. The pump power deficit is partially compensated by operating at a reduced pump repetition rate, which also causes less power to be shifted to the desired tone. Alternative designs are predicted to achieve shifting frequencies well into the multi-GHz range.

2. System description and analysis

A diagram of a XPM-SFS is shown in Fig. 1. A short pump pulse at pulse-rate R_p is combined with an input signal using a wavelength division multiplexer (WDM). The pump pulse and signal co-propagate through a nonlinear fiber, for instance standard single mode SMF-28e fiber, so as to maintain very low loss at the signal wavelength. During propagation through the nonlinear fiber the pump power is exponentially attenuated as P(z) = P₀·exp(−α_p·z), where P₀ is the pump power input to the fiber, z is distance along the fiber, and α_p is the pump attenuation coefficient. For small losses, for instance when α_p·L < 0.25 corresponding to < 1.25 dB of pump insertion loss, the pump intensity change can be well approximated using a linear first order Taylor expansion as P(z) = P₀·(1− α_p· z).

 

Fig. 1. XPM-SFS diagram. Pump pulses at a repetition rate of R_p shift the signal’s optical frequency by R_p. WDM: wavelength division multiplexer.

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Figure 2(a) depicts the change in pump intensity in relative time with respect to the signal for a 6 dB net pump propagation loss. Since the total walk-off between the pump and signal over the fiber length L is T_p, a relative time of 0 corresponds to the pump pulse at the fiber input and of T_p corresponds to the pump pulse at the fiber output. Figure 2(b) depicts the corresponding temporal phase change imprinted on the signal. Although in this case the net pump loss is fairly large, the phase shift on the signal visually still roughly approximates a linear phase ramp. Setting the difference between the ramp’s maximum induced XPM phase shift ϕ_max and the minimum XPM phase shift ϕ_min to ϕ_max − ϕ_min = i·2·π where i is an integer then approximates a serrodyne frequency shift of magnitude i·R_p, where the sign of the frequency shift depends on the sign of the group velocity mismatch (a pump traveling slower than the signal leads to a positive frequency shift).

 

Fig. 2. (a) Pump intensity as a function of relative time follows an exponential loss curve. Total loss through the fiber is 6 dB. (b) Signal phase as a function of relative time tracks the pump intensity and approximates a linear phase ramp (solid line represents an ideal serrodyne frequency shift).

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For short pump pulses, for instance pulses with a full-width-at-half-maximum < 0.1·${t_g}$·L, the rise-time of the XPM-induced ramp-like temporal phase-shift written onto the signal can be very sharp, as required for high quality serrodyne frequency shifting [8]. Note that a short pump pulse not only produces the desired fast transition in the phase ramp, but also necessitates a wide pump spectrum thereby inhibiting Brillouin scattering and allowing for higher average pump powers to be injected into the nonlinear fiber. Since it is practically easier to generate short optical pulses than fast rise-time electrical signals the frequency range over which serrodyne shifting can be performed is extended beyond that possible with typical electronics.

A useful metric is the required pump power to achieve ϕ_max − ϕ_min = 2·π, which is the minimum pump power required for optimum serrodyne frequency shifting. This becomes important because there is in practice a power limit that can be injected into the nonlinear fiber, for instance the maximum output power of the pumping system. Using the relationship ϕ_min / ϕ_max = exp(−α_p·L) we find ϕ_max = 2·π / [1− exp(−α_p·L)]. For the special case where the pump transmission can be approximated as linear, this translates to ϕ_max = 2·π / α_p·L, which clearly shows that more pump loss directly translates into a smaller maximum required peak phase shift (smaller pump energy). Physically this is due to the residual pump power elevating ϕ_min, therefore also requiring a larger ϕ_max. An estimate for the operating pump power ${P_{op}}$, which is the pump energy per pulse E_p multiplied by the pump repetition rate R_p, can be calculated as:

 

Fig. 3. Pump power (solid line) and pump repetition rate (dashed line) required for optimal frequency shifting as a function of the length of fiber used in the XPM-SFS for a 1550 nm signal. (a) SMF-28e fiber with a 1070 nm pump. (b) True-Wave NZDSF fiber with a pump shifted 6.4 nm from the signal.

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An alternative design changes the fiber to a non-zero dispersion shifted fiber (NZDSF). This design allows fine control of the walk-off parameter by tuning the wavelength separation δλ between the pump and signal wavelengths, where t_g ≈ D· δλ and D is the fiber dispersion in ps/(nm·km). Low walk-off can be achieved by placing both the pump and the signal in the 1550 nm telecommunications C-band, which as per Eq. (1) can be leveraged to increase the frequency shift (R_p) for a fixed pump power.

Additionally, it is possible to change t_g by appropriately tuning the pump wavelength, which is an experimentally simple way to change the nominal frequency shift of (t_g·L)⁻¹ over a large range (the pump pulse repetition rate should also be changed to match the nominal frequency shift). Consider the use of True-Wave non-zero dispersion shifted fiber (NZDSF), with estimated parameters of L = 2.6 km, pump transmission loss of 0.2 dB/km, and D ≈ 6 ps/nm·km (near 1550 nm). If the pump is tuned to be 6.4 nm from the signal, then t_g = 38.4 ps/km leading to an optimal R_p = 10 GHz. Tuning the pump to be 25.6 nm from the signal would change the optimal R_p to 2.5 GHz. In addition to the large attainable tuning range, there is the option of changing the sign of the frequency shift by placing the pump wavelength at either a longer or shorter wavelength than the signal.

We see the NZDSF design is more appropriate for reaching large frequency shifts. Filtering the output pump becomes somewhat more difficult since it is in the same band as the signal, but dense wavelength division multiplexing (DWDM) filters can achieve strong extinction with fairly modest loss, e.g. 0.8 dB, when the pump/signal separation is more than 1.6 nm, and coarse wavelength division multiplexing filters can achieve strong extinction with even lower loss, e.g. 0.5 dB, but require a larger separation between the pump and signal wavelengths. Taking into account the added filter loss and the longer nonlinear fiber make the anticipated insertion loss of this design more like 1.5-2.5 dB. Another issue is that the closely spaced pump and signal wavelengths will generate stronger Raman background noise and may degrade the output signal-to-noise ratio, particularly for input signals of very small power levels. If needed, narrow-band filtering can be used to cut-down on the wide-band Raman noise [12].

We estimate ${C_{XPM}}$ for NZDSF assuming it is inversely related to the fiber effective area [14] and scaling the parameter accordingly. The effective area of SMF-28e is about 1.5 times larger than True-Wave fiber, so neglecting the wavelength dependence of the mode size we estimate ${C_{XPM}}\; $ = 3/W·km. Figure 3(b) shows the relationship between ${P_{op}}$ and R_p versus L for NZDSF with δλ = 6.4 nm. A 5.4 W pump using 3 km of fiber can achieve R_p of 8.7 GHz, supporting the ability of NZDSF to reach large frequency shifts.

While increasing pump transmission loss does lead to better pump power efficiency, higher pump loss also leads to an exponential XPM phase shift that is less well approximated by a linear function. We examine the impact of the pump transmission loss on the shifted spectrum of the signal using a numerical discrete Fourier Transform (FT). The signal vector is 256 points, containing 16 sinusoidal cycles. While for the pump periods we are considering (0.1-10 ns) this signal vector is far from an optical frequency, it is sufficient to produce the desired two-sided spectral profile. The signal vector is modulated with an exponential phase shift of some fixed ratio of ϕ_min / ϕ_max corresponding to the net pump loss (2, 3, or 6 dB). Figure 4(a) shows the spectrum for these three cases when ϕ_max − ϕ_min = 2·π. The fraction of power shifted by R_p is 99.7%, 97.4%, and 89.5% with 2, 3, or 6 dB pump loss, respectively, with the corresponding extinction ratio (ER) between the strongest output tone and the next highest output tone being 28.7, 19.1, and 13 dB, respectively. Thus, the shifting efficiency of the serrodyne scheme is fairly tolerant to the exact level of pump loss, with ER being the limiting performance factor. We note that these simulations assumed a delta-function for the pump and the actual ER will also depend on the pump pulse parameters, especially the temporal pump duration.

 

Fig. 4. Computed output spectra for the optical serrodyne frequency shifter. X-axis is the offset from the original optical carrier frequency in units of R_p. Y-axis is the energy magnitude in dB relative to the highest tone (dBr). (a) 2 dB (open circles), 3 dB (crosses), and 6 dB (diamonds) pump loss. (b) 3 dB pump loss with a pump that walks-off the signal 100% of t_g·L (crosses), or just 90% of t_g·L (open boxes).

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A given system design can implement a tunable frequency shift by relaxing the constraint that the pump repetition rate is exactly (t_g·L)⁻¹. Figure 4(b) plots the computed spectra with a net 3 dB pump insertion loss both when the applied XPM phase shift is exactly (t_g·L)⁻¹ and when it is modified by setting the last 26 points of the phase shifting vector to zero, mimicking a situation where the pump repetition rate has been decreased by about 10%. The amount of output power in the main tone and the ER, somewhat surprisingly, actually marginally increases in the reduced pump repetition rate case to 98% and 24.1 dB, respectively. However, there is still a clear negative impact of the change in pump repetition rate seen in the further out tones, which plateau to about −33 dB relative to the strongest carrier tone (dBr) instead of consistently dropping as they move further from the strongest spectral tone. The fairly modest change in the spectrum supports the claim that the frequency shift of the XPM-SFS system can in many applications be tuned over a ∼10% range.

3. Experiment

As a proof-in-principle experiment the system of Fig. 1 is constructed using a SMF-28e fiber of L = 4.6 km, a 1070 nm pump, and a 1550 nm CW signal of 0 dBm. The pump pulses are carved from a Fabry-Perot semiconductor laser of > 1 nm spectral bandwidth using a Mach-Zehnder interferometer (MZI) based pulse carver (NuCrypt PG-100) to about 150 ps full-width at half maximum (FWHM) as measured by a polarization insensitive 20 GHz detector. The pump is partially depolarized by injecting it into 5 meters of polarization maintaining (PM) fiber at an angle in-between the fast and slow axis of the fiber which has minimal effect on the pump-width but is sufficient for near polarization-independent operation due to the large spectral bandwidth of the pump laser. The pump is amplified in a Ytterbium doped fiber amplifier (YDFA) and combined with the signal using a pump/signal WDM.

Figure 3(a) predicts 1.2 W of pump power (injected into the nonlinear fiber) with a 180 MHz repetition rate would be appropriate for this system. The YDFA used has a +32 dBm maximum saturation power. However, we find that our experimental apparatus is not capable of achieving sufficient pump power to strongly suppress the carrier. Note that the saturation power of the amplifier includes amplified spontaneous emission noise, and based on measurements from an optical spectrum analyzer we expect the effective power at the pump wavelength to be about 2 dB lower than the saturation power. Additionally, there is about 1 dB insertion loss at the pump/signal WDM (at the pump wavelength). Additional nonidealities such as an imperfect extinction ratio of the carved pump pulses further effectively reduce the peak pump power. These factors cause the pump power that is injected into the nonlinear fiber to be several dB’s below the level necessary to obtain strong suppression of the original carrier frequency near a 180 MHz pump repetition rate.

Operating at a somewhat reduced pump repetition rate can improve the pump power efficiency, at the cost of a less-ideal ER. Loosely speaking, reducing the pump repetition rate to R_p = A·(t_g·L)⁻¹ where A<1 can be understood to improve power efficiency in two ways. Firstly, for a fixed output power it increases the pulse energy by a factor of 1/A thereby directly reducing the required average pump power for a given ϕ_max. Secondly, since the pump period is now longer than the walk-off the last portion of the periodic phase shift goes to zero and when A is chosen correctly and the net pump loss is sufficiently large then ϕ_max can roughly be approximated as 2π instead of the prior approximation of 2·π / [1− exp(−α_p·L)]. This second point is merely a guide for intuition, and the actual optimal phase shift should be analyzed using a Fourier transform analysis.

Figure 5 plots how much of the output power appears at the desired shifted tone and the corresponding ER when A=0.75 and the pump loss through the nonlinear fiber is 3.7 dB. The data of Fig. 5 is calculated using the numerical Fourier Transform method previously described. Note that in Fig. 5 the strongest output tone is always the tone shifted by R_p and the next highest tone is always the residual carrier, so ER is just the ratio between these two tones. In this case, the optimal peak phase shift is near 5.3 radians as opposed to the 11 radians needed when A=1. The required pump power is reduced to ∼(5.3/11)·0.75 or 4.4 dB less than the ideal power needed when A=1. This suggests a power level near 26.5 dBm injected into the nonlinear fiber. We note that under this operating condition only 75% of the carrier power can be transferred to the desired tone. Figure 5 also shows that the optimal ER is limited to 9.8 dB, further indicating the performance trade-off being made by operating at the 25% reduced pump repetition rate. Although not plotted in Fig. 5, the ratio of powers between the tones shifted by + R_p and −R_p is, in this case, 13.7 dB, again showing the limitation in spectral quality when under this operating condition. The plots also show that the power transferred, and to a lesser extent the ER, are fairly insensitive to the exact peak phase shift (pump power).

 

Fig. 5. Calculated performance when A=0.75 and 3.7 dB of pump loss as a function of peak phase shift. Grey curve is % of output power in the shifted tone and black curve is the ER.

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The output signal spectrum is monitored with a scanning Fabry-Perot spectrometer (Thorlabs SA210-12B). Figure 6(a) shows the measured spectrum when the pump is off, and when the YDFA output power is set to either 26 dBm or 29 dBm, with the plot normalized to the signal passively propagating through the XPM frequency shifter (with the pump off). The pump repetition rate is 135 MHz. Due to the laser frequency drifting in-between measurements these curves have been time-shifted so that their spectral peaks overlap. The plots clearly show how the spectrum evolves from a single peak at the carrier frequency to progressively more power in the shifted tone as the pump power is increased (note negative time corresponds to a positive frequency shift). The shifted frequency can contain nearly 80% of the original carrier frequency representing a much higher fraction of shifted power than would be possible with symmetric shifting techniques and roughly being consistent with the idealized Fourier transform analysis using A=0.75. While the resolution and dynamic range of this measurement is limited, the residual power at the carrier is measured to be near 15% (about 7 dB ER). We were not able to improve the extinction of the residual carrier power by further optimizing the pump power, which is likely due in part to the resolution limit of the spectrometer and to various system imperfections including the finite pump pulse width. We did verify the residual carrier power and shifted carrier power are not sensitive to the polarization of the incoming signal.

 

Fig. 6. Oscilloscope traces of the scanning Fabry-Perot spectrometer where voltage represents intensity. (a) Traces for a 135 MHz pump repetition rate. Time corresponds to frequency and the x-axis is shifted so the carrier frequency is at 0 ms. The YDFA power is zero (Black), +26 dBm (Blue, double-peak), and +29 dBm (Grey, shifted peak). (b) Traces for a variety of pump repetition rates (see labels). The x-axis has been rescaled to represent frequency (0 MHz is the original carrier) and the y-axes of each rate are offset by 0.05 V for easy visual comparison. The raw data is averaged over 0.6 GHz to reduce noise so as to more clearly show the higher order spectral tones.

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Figure 6(b) shows a series of spectrum when the pump repetition rate is changed (130, 135, 140, 145, and 150 MHz) with a fixed pump power of 29 dBm. Changing the pump repetition rate changes the shifting frequency, and also changes the pump power level needed for optimal performance. All the pump frequencies shown lead to qualitatively similar spectrum with >70% of the output light being shifted to the desired tone thereby indicating a useful operating bandwidth. The 135 MHz case appears optimal, having both the largest shifted peak and a nearly invisible hump of the first order tone on the negative frequency side (with respect to the smooth background level). Moving the pump frequency ±5 MHz begins to expose the first order hump on the negative frequency side, and moving to a 150 MHz frequency causes a noticeable reduction in the ER of the original carrier frequency. No attempt was made to re-optimize the pump power for optimal performance each time the pump frequency is changed. Thus, the spectrum at each frequency is not fully optimized but instead demonstrates the fairly low dependence of the spectral behavior on shifting frequency at a fixed pump power.

4. Conclusion

We describe what to our knowledge is a novel scheme for shifting an optical frequency using a serrodyne-like all-optical cross-phase modulation effect. The scheme is well-suited for very low loss in a fiber-to-fiber implementation and does not require a high-fidelity modulator driving signal such as an electrical ramp. The pump is instead a short pulse, which can be generated using a number of well-known techniques. Our analysis suggests that using widely spaced pump/signal wavelengths (1070/1550 nm) can lead to <1 dB of net insertion loss and 100’s of MHz of achievable nominal frequency shift, while designs that use pump/signal wavelengths in the same band can achieve many GHz of frequency shift with a somewhat higher insertion loss. The systems also allow a considerable amount of frequency-shift tunability, with some associated degradation in performance. When using certain types of fibers, such as NZDSF fiber, tuning the pump wavelength can lead to much wider tuning ranges. These properties bode well for the use of this scheme to replace electro-optic or acousto-optic methods in some applications, especially when low insertion loss and polarization independence are desired.

A proof-of-concept experiment was performed using external modulator carved 1070 nm pump pulses and a 1550 nm signal. We find >70% of the output light is shifted into the desired 1^st order tone for frequency shifts from 130-150 MHz, even though our experimental apparatus was not capable of generating the optimal pump power level. The device is polarization insensitive and has just 1.5 dB of passive insertion loss. While the system has yet to be carefully optimized, the basic principle of XPM-based optical serrodyne frequency shifts via pulsed pump pulses has been demonstrated.