## Abstract

A novel approach to generating an optical frequency comb based on repeated frequency shifting is proposed and experimentally demonstrated. The frequency shifting is implemented via optical carrier suppression and single-sideband modulation using two Mach-Zehnder modulators in conjunction with a bidirectional asymmetric Mach-Zehnder interferometer with wavelength-shifted transmission spectra along the opposite directions. A theoretical analysis is performed, which is confirmed by a proof-of-concept experiment. A stable optical comb covering a spectral range of 0.18 THz is generated.

© 2009 OSA

## 1. Introduction

Optical frequency comb generation (OFCG) is an important technique that can find numerous applications, such as dense-wavelength-division multiplexing, optical signal processing [1], millimeter- and terahertz wave generation [2] and arbitrary waveform generation [3]. A number of techniques have been reported to generate an optical comb. An optical comb can be generated using a sinusoidally driven phase modulator placed in a fiber loop with a loop gain slightly less than unity [4–6]. Once the loop resonance frequency is an integral subharmonic of the modulation frequency and of the input optical frequency [4], a wide optical comb can be obtained [5]. The major difficulty associated with this technique is the poor stability. To ensure a stable operation, a feedback control is required [6]. The incorporation of an optical resonant structure (e.g., a Fabry-Perot cavity) can also improve the resonance stability [7]. The improvement in [6] and [7] was achieved at the cost of a higher complexity and a lower tunability. External modulation, using a dual-electrode Mach-Zehnder modulator (MZM) driven by two sinusoidal signals, has been proposed to generate a flexible, yet stable optical comb [8,9]. The major limitation of this approach is that the RF power has to be as high as several Watts to generate a wide comb, which limits the suitability for practical applications. To eliminate the requirement for a high RF power while maintaining other advantages, optical nonlinear effects in an optical fiber have been used in combination with the external modulation approach to generate a stable and flexibly tunable comb [10,11], but a high power erbium-doped fiber amplifier (EDFA) and a highly nonlinear fiber should be used. An optical comb can also be generated using a single-sideband modulator based on repeated frequency shifting [12]. As an input light wave is circulating in the loop, after each circulation, a new comb line is generated thanks to the frequency shifting. The single-sideband modulator is a specially designed integrated device that consists of three sub-MZMs [13]. Since the operation of the single-sideband (SSB) modulator requires three DC bias controls, an extra care must be made to minimize the bias drifting, to avoid the generation of undesired optical sidebands, which would generate positive feedback in the loop, further deteriorating the stability.

In this paper, a novel approach to generating an optical comb based on repeated frequency shifting is proposed and demonstrated. Instead of using three sub-MZMs, two MZMs and a bidirectional asymmetric Mach-Zehnder interferometer (AMZI) with wavelength-shifted transmission spectra along the opposite directions are used to realize the frequency shifting. A theoretical analysis is presented to give the profile of the generated optical comb, which is verified by a proof-of-concept experiment. A stable optical comb spanning a spectral range of 0.18 THz is generated. Compared with the previous approaches [6–11], the key significance of the technique is that a stable optical comb is generated through repeated frequency shifting without the limitations such as the requirement for precise resonant conditions [6,7], and the need for high RF power amplifiers [8] or very high power EDFAs [10,11]. In addition, the use of two MZMs would make it easier to demonstrate the system without the need of a specially designed three sub-MZM-based SSB modulator.

## 2. Principle

The schematic of the proposed optical comb generator is shown in Fig. 1(a)
. The system consists of a continuous-wave laser source, a 1:1 and a 1:9 optical coupler, three polarization controllers (PCs), a bidirectional AMZI serving as a bidirectional optical comb filter (BOCF), two MZMs and an EDFA. The two MZMs are biased at the optical carrier suppression (OCS) mode and driven by two microwave signals with frequencies *f*
_{e1} and *f*
_{e2} (assume *f*
_{e1} < *f*
_{e2}). Thank to the OCS, the MZM would only generate odd-order sidebands. Since the phase modulation index of the MZM is small, only the first-order sidebands are considered and the higher-order sidebands can be ignored. The free spectral range (FSR) of the BOCF is *f*
_{FSR}, and the two transmission spectra of the AMZI along the two opposite directions are shifted by *f*
_{shift}, as shown in Fig. 1(b). The process of the frequency up-shifting in the optical spectral domain is illustrated in Fig. 1(b). The incident light wave at frequency *f*
_{o} is sent to the first MZM (MZM1) and only two sidebands *f*
_{o} ± *f*
_{e1} are generated thanks to the OCS. After going through the AMZI, the sideband *f*
_{o} – *f*
_{e1} is removed and the sideband *f*
_{o} + *f*
_{e1} is kept if *f*
_{o} is tuned at the rising edge of a transmission window of the AMZI, and *f*
_{e1} < *f*
_{FSR}/2. The sideband *f*
_{o} + *f*
_{e1} is then modulated by the second MZM (MZM2) and the generated two new sidebands *f*
_{o} + *f*
_{e1} ± *f*
_{e2} are then sent to the AMZI along the opposite direction. When the transmission spectrum along the opposite direction is shifted by a proper *f*
_{shift}, we have

The sideband *f*
_{o} + *f*
_{e1} – *f*
_{e2} is removed while the *f*
_{o} + *f*
_{e1} + *f*
_{e2} is kept and then amplified by the EDFA. The 10% output of the EDFA is sent to an optical spectrum analyzer (OSA) via the 1:9 coupler, and the 90% is routed to MZM1 via the 1:1 optical combiner. After the first circulation, the frequency of the incident lightwave *f*
_{o} is up-converted to *f*
_{o} + *f*
_{e1} + *f*
_{e2}. If

*f*

_{o}to a transmission window of the AMZI will be the same as that of

*f*

_{o}+

*f*

_{e1}+

*f*

_{e2}=

*f*

_{o}+

*f*

_{FSR}. Once the sideband

*f*

_{o}+

*f*

_{e1}+

*f*

_{e2}is routed back to MZM1, it will also be up-shifted to

*f*

_{o}+ 2(

*f*

_{e1}+

*f*

_{e2}) after the second circulation and such frequency up-shifting repeats as the circulation continues. If

*f*

_{o}is located at the falling edge of a transmission window and

*f*

_{e1}>

*f*

_{FSR}/2, to realize the frequency up-shifting, Eq. (1) will be replaced by

For frequency down-shifting, if *f*
_{o} is located at the rising or falling edge of a transmission window, Eq. (1) will be replaced by

After each more circulation, a new sideband or comb line will be generated at the output port of the EDFA with a power lower than that of the previous comb line and the frequency of the new comb line will be higher or lower than that of the previous comb line by *f*
_{FSR}. The frequency shifting process will become stable until the EDFA is saturated. The spacing between two adjacent comb lines is equal to the FSR of the transmission spectra of the AMZI. Under a steady-state operation, we assume that the optical comb at the input port of MZM1 has a power distribution of *P*(*n*) which represents the power of the incident light wave, and *n* = 0, 1, 2, …, refers to the *n*
^{th} comb line except for *n* = 0. With frequency shifting, the power distribution of the new comb at the input port of the EDFA is

*η*is the power efficiency of the frequency shifting. The total input power

*P*

_{in}to the EDFA is given by

The gain *G* of the EDFA is a function of the input power *P*
_{in} given by [14],

*G*

_{max}is the unsaturated, small-signal gain,

*P*

_{sat}is an internal saturation power and

*α*is a characteristic parameter of the EDFA. Therefore, after amplified by the EDFA, the power distribution of the optical comb becomes

*GP*′(

*n*+ 1). The amplified comb is then routed back to MZM1 via the two optical couplers with a total coupling coefficient of

*κ*. Since the system is under steady-state, the power distribution of the optical comb must satisfy

Therefore, we have

Due to the gain saturation in the EDFA, the value of *κGη* will be less than 1. Equation (7) is rewritten as

From Eq. (10), the 3-dB comb width *W* is given by

For a given EDFA and the values of *η* and *κ*, *G* can be calculated by solving Eq. (8) and Eq. (11), and so is the *P*(*n*). Figure 2
shows a theoretically calculated comb envelope of the power distribution *P*(*n*) for three different values of *κGη.* From Fig. 2, it is obvious that the power of the comb line is decreasing as *n* is increasing, and the comb envelope becomes flatter and wider as the value of *κGη* is greater.

According to Eq. (11), as the value of *κGη* increases to unity, *P*
_{in} will increase significantly, which would lead to a decrease of the value of *G*. Due to the tradeoff between the gain of the EDFA and *P*
_{in}, increasing the value of *κGη* up to unity is difficult. To further flatten the profile of the generated comb, a chirped fiber Bragg grating (FBG) filter or simply an optical notch filter can be incorporated in the loop, as shown in Fig. 1, to intentionally discontinue the frequency shifting process and limit the number of the comb lines to a finite number, *N*. In such a case, the total input power *P′*
_{in} to the EDFA is given by

It can be seen from Eq. (13) that for a given *N* there is an upper limit to the value of *P*
_{in}. Thus, the value of *κGη* can be increased to unity to generate a flat comb [13]. The number of the comb lines will be decided by the spectrum width of the chirped FBG filter or the spacing between the wavelength of the input light wave and the centre wavelength of the optical notch filter.

A chirped FBG can also be used to modify the profile of the comb, by reshaping the gain curve of the EDFA. In such a case, the gain of the EDFA *G*(*n*) depends on the frequency of the comb line, namely, the value of *n*. *P*(*n*) becomes *P*
_{FBG}(*n*). Equation (10) is rewritten as

*G*(*n*)/*G*(1) is decided by the reflection spectrum of the chirped FBG. The first term in the right-hand side of Eq. (15) is the power distribution of the comb given the value of *κG*(1)*η* without the FBG; the second term is the modification term introduced by the chirped FBG to modify the profile of the generated comb. From Eq. (15), for a desired *P*
_{FBG}(*n*), *G*(*i*) is calculated by

The chirped FBG with the corresponding reflection spectrum can by designed based on *G*(*n*).

Since the proposed optical comb generator is implemented based on frequency shifting, no resonant conditions [4–6] are required. Therefore, the dispersion of the fiber and devices in the generator will not affect the performance of the comb generation, and neither will the loop length variations. The power distribution of the comb is only determined by the values of *κ*, *G* and *η*. In the previous methods, however, the power distribution of the optical comb is also dependent on the dispersion, since the resonant conditions must be met [4]. In addition, the use of frequency shifting would not introduce any positive feedback to the loop, which significantly improves the operation stability. The comb spacing is equal to the sum of *f*
_{e1} and *f*
_{e2}. Once *f*
_{e1} and *f*
_{e2} are set, the comb spacing is determined. Any variation of the FSR of the AMZI and *f*
_{shift} due to the instability of the AMZI would degrade the SSB modulation and to reduce the frequency shifting efficiency *η*. In addition, the variations of these parameters will also cause the generation of undesired sidebands which may not be perfectly removed by the AMZI.

## 3. Experimental results and discussion

A proof-of-concept experiment is performed based on the setup shown in Fig. 1(a). The two MZMs are two polarization dependent LiNbO_{3} electro-optical modulators. Three PCs are used to adjust the polarization of the input light waves to minimize the polarization dependent loss. The AMZI is implemented using a polarization-maintaining fiber (PMF) in conjunction with two optical circulators (OCs) and two polarization analyzers (PAs), as shown in Fig. 3(a)
. Since the light waves with orthogonal polarizations are traveling in the same fiber, the AMZI has a better stability compared to an AMZI with a structure having two physically separated arms. The two PAs are actually the two MZMs since the waveguides inside the MZMs support only the TE mode. The transmission spectra of the AMZI along the two opposite directions are measured and shown in Fig. 3(b). The FSR is approximately 26.8 GHz and the isolation depth is more than 30 dB. The frequency shift *f*
_{shift} is adjusted to make it be equal to one quarter of *f*
_{FSR}, which is 6.7 GHz, and *f*
_{o} is located at the falling edge of one transmission window. According to Eqs. (2) and (3), we have *f*
_{e1} = 20.1 GHz, *f*
_{e2} = 6.7 GHz.

By either gradually increasing the gain of the EDFA or decreasing the input power *P*(0), the value of *κGη* can be increased. The optical spectrum at the output of the 10% port of the 1: 9 optical coupler is observed by the OSA. Figure 4
shows the recorded optical spectra of the generated optical frequency comb. The comb line spacing is 26.8 GHz, which is equal to the FSR of the AMZI. From Fig. 4, it can be clearly seen that as the gain of the EDFA is increased, more and more comb lines are generated and the comb envelope becomes flatter. Due to the large insertion loss in the loop and SSB modulation loss, the power efficiency of the frequency shifting is very low, an optical comb with comb lines up to seven spanning a spectral range over approximately 0.18 THz is generated. But the results have clearly demonstrated the capability of the proposed approach in optical comb generation. It is believed that more comb lines with a much flatter envelope would be obtained with a much greater *κGη*. The comb line spacing can be tuned by changing the FSR of the AMZI and *f*
_{e1} and *f*
_{e2。}

In Fig. 4, some small peaks between dominant comb lines are observed. The generation of these small peaks can be caused by the following reasons: 1) the sum of *f*
_{e1} and *f*
_{e2} is not exactly equal to *f*
_{FSR}; 2) the wavelength shift of the AMZI spectra does not exactly satisfy Eq. (3); and 3) the two MZMs are not biased perfectly at the OCS.

The stability of the comb generator mainly depends on the stability of the AMZI and the OCS of the two MZMs. The long-term stability of the system could be affected by the bias drift of the MZMs and the transmission spectra shift of the AMZI. To improve the stability and to simplify the system, the two LiNbO_{3} electro-optical modulators can be replaced by two polarization modulators (PolMs) [15]. It was demonstrated that a PolM with a polarization analyser (PA) can operate eqiuvelently as a MZM, but free from bias drift [16].

## 4. Conclusion

A novel approach to generating an optical frequency comb based on repeated frequency shifting has been proposed and experimentally demonstrated. The frequency shifting was implemented via OCS and SSB generation using two MZMs in conjunction with a bidirectional AMZI with wavelength-shifted transmission spectra along the opposite directions. The proposed technique enables the generation of a flexible and stable optical comb with a simple and compact configuration. A theoretical analysis was presented, which was verified by a proof-of-concept experiment. An optical comb covering a spectral range of 0.18 THz was obtained. With a higher frequency shifting efficiency, an optical comb with a wider width and a flatter envelope can be generated. A chirped FBG filter or an optical notch FBG filter can also be incorporated in the loop to flatten or modify the profile of the optical comb.

## Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through its strategic project grants program.

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