Picosecond-pulse wavelength conversion based on ... - OSA Publishing

Picosecond-pulse wavelength conversion based on cascaded second-harmonic generation– difference frequency generation in a periodically poled lithium niobate waveguide Yong Wang, Jorge Fonseca-Campos, Chang-Qing Xu, Shiquan Yang, Evgueni A. Ponomarev, and Xiaoyi Bao

The wavelength conversion of picosecond optical pulses based on the cascaded second-harmonic generation– difference-frequency generation process in a MgO-doped periodically poled lithium niobate waveguide is studied both experimentally and theoretically. In the experiments, the picosecond pulses are generated from a 40 GHz mode-locked fiber laser and two tunable filters, with which the lasing wavelength can be tuned from 1530 to 1570 nm, and the pulse width can be tuned from 2 to 7 ps. Newfrequency pulses, i.e., converted pulses, are generated when the picosecond pulse train and a cw wave interact in the waveguide. The conversion characteristics are systematically investigated when the pulsed and cw waves are alternatively taken as the pump at the quasi-phase-matching wavelength of the device. In particular, the conversion dependences on input pulse width, average power, and pump wavelength are examined quantitatively. Based on the temporal and spectral characteristics of wavelength conversion, a comprehensive analysis on conversion efficiency is presented. The simulation results are in good agreement with the measured data. © 2006 Optical Society of America OCIS codes: 190.2620, 190.4360, 160.3730, 320.7110.

1. Introduction

All-optical wavelength conversion is a key technology in future optical wavelength-division multiplexing (WDM) networks.1,2 Among the various proposed wavelength-conversion techniques, the one based on quasi-phase-matched (QPM) periodically poled LiNbO3 (PPLN) waveguides is a competitive candidate, and it has attracted much attention recently due to excellent conversion properties such as broad bandwidth, high efficiency, and low noise.3– 6 The simplest implementation of the wavelength conversion in those QPM PPLN waveguides is based on difference-frequency generation (DFG).3,4 A pump

Y. Wang ([email protected]), J. Fonseca-Campos, and C.-Q. Xu are with the Department of Engineering Physics, McMaster University, Hamilton, Ontario, Canada. S. Yang, E. A. Ponomarev, and X. Bao are with the Department of Physics, University of Ottawa, Ottawa, Ontario, Canada. Received 6 October 2005; revised 17 January 2006; accepted 13 February 2006; posted 15 February 2006 (Doc. ID 65173). 0003-6935/06/215391-13$15.00/0 © 2006 Optical Society of America

wave at frequency ␻p interacts with a signal wave at frequency ␻s, and generates a new wave at frequency ␻c 共⫽ ␻p ⫺ ␻s兲, which is also called the converted wave. For those signal and converted waves in the third telecommunication spectral window, the pump wavelength is required to be in the 0.77 ␮m wave band, which can cause certain difficulty in the optical coupling between the traditional single-mode fibers and the PPLN waveguides because of a large wavelength difference. The cascaded second-harmonic generation (SHG)–DFG process can overcome this problem, where the two input waves, i.e., the pump and signal, are in the same 1.5 ␮m wave band.5–7 In this case, the 1.5 ␮m band pump (frequency ␻p) first generates a second-harmonic (SH) wave at frequency ␻SH 共⫽ 2␻p兲; the latter can play the role of the pump source in the successive DFG process and generate the desired converted wave at frequency ␻c 共⫽ 2␻p ⫺ ␻s兲. Conversion efficiency is important in these applications. Like many other optical nonlinear processes, the conversion efficiency of the cascaded SHG–DFG process depends on the powers of the two input waves and the related phase-matching conditions.8 In a QPM 20 July 2006 兾 Vol. 45, No. 21 兾 APPLIED OPTICS

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PPLN waveguide, the ferroelectric domains are inverted periodically, and thus the phases of the two interacting waves are controlled in a coherent length to produce constructive interference between the original and the generated waves in different regions during their propagation.3,4,9 By choosing an appropriate pump wavelength for a given poling period in the QPM structure, the SH, signal, and converted waves can be phase matched in a very large wavelength range in this kind of devices. As a result, the propagating waves can undergo the largest nonlinear interaction in the crystal, enhancing conversion efficiency and offering the possibility of engineering the nonlinearity. These are the major advantages of the QPM technique over other phase-matching techniques.8 For a wavelength conversion involving ultrashort pulses, another critical factor is the group-velocity mismatching (GVM),10 –14 noting that different frequency components propagating in a nonlinear medium may have different group velocities. The effect of GVM can cause the so-called walk-off, which is related to the widths of the interacting pulses. In the presence of GVM, the SHG and DFG efficiencies are reduced, and waveform distortion may happen to the generated pulses. There are some recent experimental and theoretical reports on picosecond-pulse wavelength conversion in PPLN waveguides based on the cascaded SHG–DFG process.6,15–21 Typically, in experiments, Xu et al. used a wavelength-variable cw control signal and a wavelength-fixed pulse train to demonstrate a fixedin–variable-out wavelength conversion,16 and later used a pulsed control signal to realize pulse demultiplexing from 40 to 10 GHz.17 Using the beam propagation method, Ishizuki and co-workers18,19 recently reported a purely numerical analysis on the solutions of the coupled-mode equations for both the cw and pulsed pump without consideration of device losses. Recently, Razzari and co-workers20 utilized the effect of nonlinear phase shift in a PPLN waveguide to realize wavelength conversion and pulse reshaping by employing a cw signal and a pulsed pump in a Mach– Zehnder interferometer. As will be shown in this paper, the practical conversion efficiencies in terms of pulse energy and optical spectrum are more complicated than have been predicted previously.19,20 Moreover, the efficiency dependences on the pump wavelength and power have not been systematically examined in previous works.15–21 Since there are two input waves in the cascaded SHG–DFG process, to avoid confusion in this paper, the one set at the QPM wavelength is always called the pump, and the other is correspondingly called the signal. According to the temporal formats of the input waves (pulsed or cw), in this work we focus on the conversion characteristics in the following two pumping schemes: Y Scheme I: cw pump and pulsed signal, Y Scheme II: pulsed pump and cw signal. In both cases, the converted output, as expected, is in the format of pulses, and the SH wave is consistent 5392

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with the pump wave. Also, one can see another two schemes, i.e., both the pump and signal are cw or pulsed. Since the conversion property of the scheme with both cw waves has been extensively studied and reported in the literature,1,5 it is unnecessary to illustrate it here. Since complicated synchronization techniques are required in the scheme with two pulsed inputs, this scheme is infrequently demonstrated in practical systems. We have found that the wavelength conversion in this scheme exhibits many unique properties and implies a few novel applications, which will be detailed in another paper. In most digital optical communication systems, the transmitted information (the code trains) is usually carried by the amplitude modulation of lightwaves (optical pulse trains). Correspondingly in our cascaded SHG–DFG wavelength conversion system, the pulsed wave is regarded as the information carrier, and the cw wave is taken as the control wave. To transfer the information of optical codes from one wavelength to another, the codes can be applied either to the signal in Scheme I or to the pump in Scheme II, in terms of our previous definition. Unless the reshaping of the output pulses is required, a basic requirement of wavelength conversion in these systems is that the converted output have similar temporal and spectral properties to those of the pulsed input except for the central wavelength of pulses. In particular, the pulse width and the spectral width (the FWHM) of the converted pulses should be the same as or close to those of the input pulses, and the amplitudes of the output pulses should be high enough with acceptable noises. These equally require a certain device transparency to input codes and good conversion efficiency. As one can see, a significant difference between these two schemes is that the wavelength difference between the pulsed input and the converted output in Scheme I is twice that in Scheme II. Furthermore, one may ask the following questions regarding the converted outputs in Schemes I and II. Are there any differences in output pulse shape, optical spectrum, and conversion efficiency? And what are the efficiency dependences on the aforementioned three factors, i.e., the pulse width, input power, and pump wavelength, in this nonlinear process? To find out the quantitative answers, we investigated the wavelength conversion properties experimentally in a periodically poled MgO-doped lithium niobate (PPMGLN) waveguide by using a 40 GHz tunable picosecond-pulse source, whose central wavelength can be tuned from 1530 to 1570 nm, and whose pulse width can be adjusted from 2 to 7 ps. The conversion characteristics and efficiencies in the above two pumping schemes are compared systematically in terms of pulse width, input power, and pump wavelength, which have not been reported in the literature to the best of our knowledge. Furthermore a comprehensive theoretical analysis is provided to explain the physical insights for the related experimental observations, and to indicate more features that cannot be measured in the experiments. The simulated and experimental data are compared with each

Fig. 1. Experimental setup of (a) mode-locked fiber laser and (b) wavelength conversion through a PPMGLN waveguide. ISO, isolator; VOA, variable optical attenuator; TLS, tunable laser source.

other. The results presented in this paper are important to characterize and optimize the wavelength conversion in QPM PPLN waveguides. 2. Experimental Setup and Results

The experimental setup is shown schematically in Fig. 1, including a picosecond-pulse light source, a PPMGLN waveguide, two optical tunable filters, two erbium-doped fiber amplifiers (EDFAs), a circulator, and a fiber Bragg grating (FBG). The 40 GHz ultrashort pulses were generated from the mode-locked fiber ring laser shown in Fig. 1(a),22 which was composed of a 7 m long erbium-doped fiber (EDF), a 250 mW laser diode at 1480 nm, a 40 GHz LiNbO3 electro-optical phase modulator, an optical filter, two isolators, and signal synthesizing and control units. The total cavity length was approximately 19 m, and the fundamental cavity frequency was measured to be 10.755 MHz. The 40 GHz repetition rate was achieved by locking at one of its higher-order harmonics. Filter 1 inserted in the laser cavity is a bandpass filter with a variable central wavelength and a fixed bandwidth 共5 nm兲. Filter 2 has both a variable central wavelength and a variable bandwidth. Therefore by adjusting these two filters, we achieved a lasing wavelength from 1530 to 1570 nm and a pulse duration from 2 to 7 ps with a side-mode suppression ratio of 55 dB at 40 GHz. For the cascaded wavelength conversion, two input waves, i.e., the output pulse train from the modelocked fiber laser and a cw output from a tunable laser (HP 8164A), were combined together through a three-port circulator and a narrowband highreflectivity FBG, whose Bragg wavelength is the same as that of the cw wave. Two EDFAs were used to boost the input powers, and a variable optical attenuator

(VOA) was used to adjust the power of the pulses. The pulsed and cw waves were then coupled into the PPMGLN waveguide. The QPM structure was poled by the corona discharge method, while a waveguide with a length of 4.5 cm was fabricated by the proton exchange technique and supported only the TM modes. The poling period is approximately 18.5 ␮m, and the exact QPM wavelength of the pump was measured to be 1543.0 nm in the cw regime when the wavelength converter was kept at 40 °C.23 In our setup, all optical fibers and optoelectronic elements are polarization maintained, in which all the waves propagate in only one polarization direction. Note that by employing a ring structure, a polarization-independent wavelength conversion in this PPMGLN waveguide can be realized.24 In the time domain, the pulse widths (FWHM) were obtained through autocorrelation traces measured with an autocorrelator (Femtochrome FR-103MN). Due to the sensitivity limitation of the adopted autocorrelator 共10⫺7 W2 兲, only the input pulses could be measured directly in the experiments. In the optical spectrum domain, the optical spectra of the pump, signal, converted, and SH waves were measured with an optical spectrum analyzer (OSA, Agilent 81642A) at a resolution of 0.06 nm. In this work we are concerned only with the influences of the variations of the input pulse train on the converted wave. Therefore in the experiments, the power of the cw wave was kept approximately constant except for its wavelength adjustment when playing different roles in the two pumping schemes. The wavelength conversion in Scheme I (i.e., cw pump plus pulsed signal) was investigated first. For three typical pulse widths 共⌬␶s ⫽ 2.6, 4.0, and 6.4 ps兲, the autocorrelation traces of the input signal pulses and the output optical spectra of the pump, signal, converted, and SH pulses are depicted in Fig. 2, in which the average input powers are kept constant (19.7 and 9.9 dBm, respectively, for the cw pump and pulsed signal measured at the output of the circulator), and their central wavelengths are 1543.0 and 1549.9 nm. To adjust the signal pulse width we set the central wavelengths of filters 1 and 2 at 1549.9 nm and changed the optical bandwidth of filter 2. It is well known that with a decrease in bandwidth, the pulse width tends to be broader. With the same pulse energy, the pulse peak power decreases with an increase of pulse width, as observed in Figs. 2(a), 2(d), and 2(g). It can be seen in Figs. 2(b), 2(e), and 2(h) that the optical spectra of the signal pulses exhibit multiple peaks, and the bandwidth of the spectral envelope decreases and correspondingly the spectral peak rises when the pulse width is increased. Particularly for ⌬␶ ⫽ 2.6, 4.0, and 6.4 ps, the spectral widths are approximately 1.2, 0.7, and 0.6 nm, and their peak values are ⫺12.8, ⫺12.1, and ⫺10.5 dBm, respectively. The optical spectra of the converted pulses have similar widths and structures to those of the signal pulses, and they also become higher with decreasing the signal pulse width. The 20 July 2006 兾 Vol. 45, No. 21 兾 APPLIED OPTICS

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Fig. 2. Autocorrelation traces, output spectra of pump, signal, converted pulses, and secondharmonic wave for different signal pulse widths in Scheme I.

optical spectrum of the cw pump is much narrower than the other two and has no change when ⌬␶ varies. As shown in Figs. 2(c), 2(f), and 2(i), the spectra of the SH waves resemble the corresponding pump spectra, and are independent of the signal pulse width. It is worth noting that the multipeak structure in the signal optical spectrum is attributed to the effect of a pulse train. In fact, the frequency spacing between any neighboring two peaks in the spectrum is equal to the repetition rate of pulses in the time domain, i.e., 40 GHz. The corresponding wavelength spacing is 0.32 nm in the 1.55 ␮m wave band. In contrast to Scheme I, the output spectra in Scheme II (i.e., pulsed pump plus cw signal) are plotted in Fig. 3 with the same pulse widths 共⌬␶p ⫽ 2.6, 4.0, and 6.4 ps) for the pump, in which the left column shows the output spectra in the 1.5 ␮m band, and the right column shows the SH spectra in the 0.77 ␮m band. The pump and signal central wavelengths are still 1543.0 and 1549.9 nm, and their average input powers are 11.7 and 19.7 dBm, respectively. In these three cases, the pump and signal spectra have the same features as those described in Fig. 2 (Scheme I), whereas the spectral width of the converted wave is narrower than that of the pump, and the SH spectra exhibit multipeak structures like the pump. However, in the 0.77 ␮m wave band, the 40 GHz repetition rate of the SH pulses leads to a 0.08 nm wavelength spacing. Due to an insufficient OSA resolution and a narrower SH spectral width, the multipeak phenomena are not as apparent as those in the 5394


pump spectra. Compared with that in Fig. 2, the converted pulse train has a lower spectral amplitude for any pulse width, implying a lower conversion efficiency in Scheme II. Moreover, it is worth noting that in any case of Figs. 2 and 3, there is a small peak located at 773.2 nm beside the SH spectral peak, whose amplitude is nearly the same in the two schemes. This newly generated wave is attributed to

Fig. 3. Output spectra of pump, signal, converted pulses, and secondharmonic wave for different pump pulse widths in Scheme II.

of pump wavelength is required in Scheme I compared with Scheme II. 3. Theoretical Modeling and Numerical Simulation

To describe the pulse propagation and nonlinear interactions among the pump, the SH, signal, and converted waves inside the PPMGLN waveguide with the poling period ⌳ and length L, the derived coupledmode equations, similar to the previous analyses,5,19,20 are given by ⭸Ap ⭸Ap j p ⭸2 Ap p ⫺ j␻p␬pp Ap*ASH ⫽ ⫺␤1 ⫺ ␤2 ⭸z ⭸t 2 ⭸t2 ␣p ⫻ exp共⫺j⌬kp z兲 ⫺ (1) A, 2 p

Fig. 4. Output spectra of pump, signal, and converted pulses for different average pump powers in Scheme II.

the sum-frequency generation (SFG) in conjunction with the pump and signal, and its influence on the desired wavelength conversion can be ignored due to its very weak intensity. The conversion characteristics under different average powers of input pulses were then examined. In the experiments, the power of the cw wave was fixed at 19.7 dBm, and the average power of the pulsed wave was changed through the VOA. To facilitate the comparison, the pulse width was fixed at 4.0 ps, and the pump and signal central wavelengths were fixed at 1543.0 and 1549.9 nm, respectively. In Scheme I (constant cw pump) it was observed that the spectral amplitude of the converted pulses was nearly proportional to that of the pulsed signal, and their spectral widths remain unchanged. In Scheme II, as exemplified in Fig. 4, the decrease of the SH spectral peak is almost twice that of the pump. Furthermore, the tolerance of the pump wavelength ␭p was studied. Figure 5 shows the output spectra of the pump, signal, and converted pulses for three different central wavelengths of pump, where the left and right columns correspond to different pulse widths of 4.0 and 3.0 ps, respectively. The average input pump and signal powers were 13.0 and 19.7 dBm, respectively. The converted spectrum behaves similarly for different pulse widths; an approximate 0.8 nm shift of the pump central wavelength reduces the converted wave by approximately 10 dB. As mentioned earlier, the QPM wavelength for this waveguide device is 1543.0 nm. Therefore a deviation of ␭p from 1543.0 nm can lead to a reduction in the SH amplitude. It was found in Scheme I, with a deviation of ␭p from 1543.0 nm, that the reduction in the amplitude of the converted spectrum is independent of the signal pulses and is faster than that in Scheme II, which is very similar to the previous results observed in the cw regime.23,24 A 0.5 nm shift of the pump central wavelength can greatly eliminate the converted wave. These indicate that a smaller tolerance

⭸ASH j SH ⭸2ASH ⭸ASH SH ⫽ ⫺␤1 ⫺ ␤2 ⭸z ⭸t 2 ⭸t2 ⫺ j␻p␬pp Ap Ap exp共 j⌬kp z兲 ⫺ 2j␻p␬sc As Ac exp共 j⌬kc z兲 ⫺

␣SH ASH, 2

⭸As j s ⭸2As ⭸As ⫺ j␻s␬sc Ac*ASH ⫽ ⫺␤1s ⫺ ␤2 ⭸z ⭸t 2 ⭸t2 ␣s ⫻ exp共⫺j⌬kc z兲 ⫺ As, 2 ⭸Ac j c ⭸2Ac ⭸Ac c ⫺ j␻c␬sc As*ASH ⫽ ⫺␤1 ⫺ ␤2 ⭸z ⭸t 2 ⭸t2 ␣c ⫻ exp共⫺j⌬k c z兲 ⫺ Ac, 2 ⌬kp ⫽ ␤共␻SH兲 ⫺ 2␤共␻p兲 ⫺ ⫽

(2)

(3)

(4)

2␲ ⌳

2␲ 4␲ n ␭ ⫺ ne共␭p兲兴 ⫺ , ␭p 关 e共 SH兲 ⌳

(5)

2␲ ⌳ 2␲ 2␲ 2␲ 2␲ ne共␭SH兲 ⫺ ne共␭s兲 ⫺ ne共␭c兲 ⫺ ⫽ , ␭SH ␭s ␭c ⌳ (6)

⌬kc ⫽ ␤共␻SH兲 ⫺ ␤共␻s兲 ⫺ ␤共␻c兲 ⫺

␬pp ⫽

␬sc ⫽

deff ⫽

冑2␮0兾c deff 冑ne共␭SH兲ne共␭p兲2Aeff

,

冑2␮0兾c deff 冑ne共␭SH兲ne共␭s兲ne共␭s兲Aeff

(7)

,

2 d , ␲ 33

(8)

(9)

where Ap, ASH, As, and Ac, as functions of the time t and position z, represent the complex electric fields of the pump, the SH, signal, and converted waves under 20 July 2006 兾 Vol. 45, No. 21 兾 APPLIED OPTICS

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冉

冊

1 dne ␭3 d2ne d2ne ⫽ . ⫹␻ ␤2 ⫽ 2 c d␻ d␻2 2␲c2 d␭2

Fig. 5. Comparison of output spectra for different pump central wavelengths and pulse widths in Scheme II.

the slowly varying envelope approximation, and ␭p, ␭SH, ␭s, and ␭c are their central wavelengths. ␤1 p and ␤2 p are the first and second derivatives of the propagation constants with respect to the angular frequency ␻, calculated at ␻p for the pump wave; while ␤1SH and ␤2SH 共␤1s, ␤2s, and ␤1c, ␤2c) are defined similarly for the SH (signal and converted) wave and calculated at ␻SH 共␻s and ␻c). Kpp 共Ksc兲 is the SHG (converted wave) coupling coefficient in the waveguide,5 deff is the effective nonlinear coefficient, and Aeff is the effective interaction area. ␣p, ␣SH, ␣s, and ␣c are the attenuation coefficients of waveguide for the pump, the SH, signal, and converted waves, respectively. ⌬kp 共⌬kc兲 refers to the phase mismatching in the SHG–DFG process, and ne is the effective refractive index of waveguide, whose dependence on wavelength ␭ can be approximated by the Sellmeier equation8 ne2共␭兲 ⫽ A ⫹

B ␭ ⫺C 2

⫺ D␭2.

(10)

Here we took A ⫽ 4.5469, B ⫽ 0.094779, C ⫽ 0.04439, and D ⫽ 0.026721 for our device in the simulation. With ⌳ ⫽ 18.5 ␮m, the QPM wavelength of pump leading to an ideal SHG phase matching 共⌬kp ⫽ 0兲 is 1543.0 nm, at which a maximum conversion efficiency of SHG can be expected. When ␻p and ␻s are set, we have ␻SH ⫽ 2␻p, ␻c ⫽ ␻SH ⫺ ␻s,

⌬kc ⬇ 0.

(11)

With ne known, the parameters ␤1 and ␤2 can be calculated for all propagating waves through the following relations: ␤1 ⫽ 5396

冉

冊

1 dne ne ␭ dne ne ⫹ ␻ ⫽ ⫺ , c d␻ c c d␭


(12)

(13)

The above coupled-mode differential equations were solved using the split-step Fourier method.25 In this work, we chose z ⫽ 0 as the input of the waveguide and introduced a new time variable T ⫽ t ⫺ z␤1p measured in the reference frame moving with the input pulse. In addition, we took L ⫽ 45 mm, Aeff ⫽ 45 ␮m2, ␣p ⫽ ␣s ⫽ ␣c ⫽ 0.45 dB兾cm, ␣SH ⫽ 0.90 dB兾cm, and deff ⫽ 16.5 pm兾V in the simulations. Based on the above model and parameters, the propagation and conversion characteristics of all four waves in Schemes I and II were numerically studied. In this section, some typical temporal and spectral characteristics are shown and compared with the measured spectra. More results, such as the conversion efficiencies varying with pulse width, average power and pump wavelength, as well as the quantitative comparison between the two pumping schemes, are given in Section 4. The wavelength conversion in Scheme I is simulated first. The selection of the simulation parameters is based on the previous experimental results shown in Fig. 2. The input signal is a 40 GHz Gaussian pulse train with a 4.0 ps pulse width, a 52 mW peak power, a 40 dB signal-to-noise ratio, a ⫺55 dBm amplified spontaneous emission (ASE) noise background, and a 1549.9 nm wavelength. The cw pump power is 80 mW (19.0 dBm), and its wavelength is 1543.0 nm. Note that a 0.5 dB coupling loss between the fiber and the waveguide and a 0.2 dB connector loss have been included. Figure 6 shows the pulse shapes (left column) and the optical spectra (right column) for all the waves at the device input and output ports, respectively. One can see that except for a 2 dB reduction in amplitude caused by the device loss, the outputs of the cw pump and the signal pulse [Figs. 6(d) and 6(e)] have nearly the same waveforms and optical spectra as those of the inputs [Figs. 6(a) and 6(b)]. The SH wave shown in Fig. 6(c) indicates similar temporal and spectral characteristics to the pump except for a slight notch near T ⫽ 4 ps in the time domain. This is due to an energy transfer to the converted wave, and the 4 ps delay results from the walk-off effect, which will be discussed later. Hence, the SH wave can be considered to be quasi-cw. The converted pulse exhibits a similar pulse shape and optical spectrum to those of the signal pulse except for lower amplitudes. In particular, the pulse peak is still located at T ⫽ 0, and the pulse shape and spectral envelope both remain symmetric with nearly the same widths as those of the signal. As a result, the product of the pulse width and frequency bandwidth of the converted pulses is the same as that of the input signal pulses. Furthermore, the output waveforms of all waves are plotted together on a logarithmic scale in Fig. 7(a) for a detailed comparison. The difference in pulse shape between the signal and converted pulses occurs only on the two edges far from the pulse peak, and hence can be neglected. The

Fig. 7. Detailed comparisons of output pulse shapes and optical spectra individually shown in Fig. 6.

Fig. 6. Simulated pulse shapes and optical spectra of input– output pump, signal, converted, and second-harmonic waves for the 4 ps signal pulse in Scheme I.

overall output spectrum in the 1.5 ␮m band is also shown in Fig. 7(b) for the purpose of comparison with the measured spectrum shown in Fig. 2(e). Good agreement between the simulated and measured results indicates the validity of our theoretical model and the high precision of the simulation. The wavelength conversion in Scheme II is then simulated. Consistent with the previous experimental parameters in Fig. 3, the input pump pulse has a 4.0 ps pulse width, a 71 mW peak power, a 40 dB signal-tonoise ratio, a ⫺50 dBm ASE noise background, and a 1543.0 nm central wavelength. The cw signal power is 80 mW and its wavelength is 1549.9 nm. Similar to the previous results for the pump and signal waves, their output temporal and spectral features resemble those of the inputs. The output SH wave has significantly different temporal and spectral characteristics from those in Scheme I. Though the SH wave is in the form of pulses, it is distinct from the pump pulse. Compared with the output pump pulse, the peak of the output SH pulse is delayed by approximately 12 ps, the peak power is

lower by two orders of magnitude, and the pulse width is enlarged 1.7 times. Accompanied by the broadening of the SH pulse, the SH spectrum is narrowed, and shows similar multipeak structures to those of the pump, as observed in the previous experiments. Since the SH pulse travels more slowly than the pump pulse in the waveguide, the nonlinear interaction occurs on the trailing edge of the pump pulse and the leading edge of the SH pulse when the walk-off takes effect in the SHG process. As a result, the generated SH pulse is asymmetric, having a slow leading edge and a steep trailing edge. The walk-off also takes effect between the converted and the SH pulses in the DFG process. Since the converted pulse moves faster than the SH pulse, according to the same mechanism, the converted pulse is also asymmetric, and has a steep leading edge and a long tail. In particular, its peak appears at T ⫽ 2.4 ps, and its width is broader than that of the pump pulse by 25%. Since the pump and the converted waves are in the same wave band, the walk-off between the pump (converted) and the SH pulses in the SHG (DFG) process can be estimated simply by introducing the so-called walk-off length LwSH 共Lwc兲, denoted by LwSH ⫽

ⱍ␤

1

⌬␶p SH

⫺ ␤1

ⱍ

p

,

Lwc ⫽

ⱍ␤

1

⌬␶SH c

⫺ ␤1SH

ⱍ

, (14)

where ⌬␶p and ⌬␶SH are the pump and SH pulse widths, and ␤1SH ⫺ ␤1p 共␤1c ⫺ ␤1SH兲 represents the group-velocity mismatching. Substituting Eq. (12) into Eq. (14), one can obtain the walk-off lengths for different pulse widths. For example with ␭p ⫽ 1543.0 nm, ␭SH ⫽ 771.5 nm, we have ␤1SH ⫺ ␤1p ⬇ ␤1SH ⫺ ␤1c ⫽ 0.3 ps兾mm; consequently, LwSH is 13 mm for a 4.0 ps pump pulse and Lwc is 23 mm for a 6.8 ps SH pulse. This indicates that the walk-off effect in the SHG process is inevitable in our 45 mm long device unless broader pump pulses with ⌬␶ ⬎ 13 ps are adopted. The generation of the converted pulses is a 20 July 2006 兾 Vol. 45, No. 21 兾 APPLIED OPTICS

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Fig. 9. Detailed comparisons of output pulse shapes and optical spectra individually shown in Fig. 8.

Fig. 8. Simulated pulse shapes and optical spectra of input– output pump, signal, converted, and second-harmonic waves for the 4 ps signal pulse in Scheme II.

cascaded process, and the walk-off effect on the pulse shape and delay is consequently more complicated in Scheme II. By contrast, there is no significant walk-off effect in Scheme I due to the cw pump and quasi-cw SH wave. In Fig. 8(f)(2), the spectral bandwidth of the converted pulse is almost symmetric, but its bandwidth is narrower than that of the pump by 25%. Correspondingly, the product of pulse width and frequency bandwidth is reduced by 10%. For the purpose of comparison, all output waveforms are plotted together with respect to a pump pulse on a logarithmic scale in Fig. 9(a), and the whole output spectrum in the 1.5 ␮m band is shown in Fig. 9(b). One can see clearly that the peaks of the pump, the SH and converted pulses are not synchronous, and the long tails of the SH and converted pulses both enter the successive period of the pulse. These are significant differences between the two pumping schemes. In addition, a comparison between Figs. 9(b) and 3(c) can further verify the accuracy of our simulation. 5398


With the aid of our simulation, the temporal and spectral characteristics of the converted wave in Schemes I and II can be examined precisely, which can help us understand many physical insights for the wavelength conversion in these two schemes. We can see that when a cw pump is set at the QPM wavelength (Scheme I), the SH wave is quasi-cw, and the converted pulse has nearly the same temporal waveform and spectral shape as those of the input pulse, which indicates that the device operated in Scheme I is highly transparent to the format of input optical codes. When the pulsed input is set at the QPM wavelength playing the role of a pump (Scheme II), the walk-off can take effect. Compared with the input pump pulse, the output SH and converted pulses are delayed to some extent, and their shapes become asymmetric. Since the SH pulse travels more slowly than the pump pulse, it has a slow leading edge and a steep trailing edge. On the contrary, the converted pulse has a steep leading edge and a slow trailing edge, and its peak lies between the pump and the SH pulse peaks. Both the SH and the converted waves suffer from a certain narrowing in the optical spectrum. At a very high repetition rate 共⬎40 Gb兾s兲, such temporal distortions may exert a certain influence on the transmission system through the overlapping of two neighboring SH pulses. For example, it could generate a temporal cross talk and hence limit the transmission bit rate. To avoid this, the walk-off of pulses should be minimized by appropriately selecting a device length and input pulse width. Furthermore, in terms of conversion efficiency, the conversion properties of the two schemes are quantitatively compared under different input conditions, which is detailed in Section 4. 4. Analysis of Conversion Efficiency

From Eqs. (1)–(4), one can see that in the cascaded nonlinear interactions, the converted pulses are related to the GVM, power, and phase mismatching. From the previous analysis, we know that for a given PPLN waveguide, these three factors are determined mainly by the input pulse width, pump and signal

powers, and pump wavelength, respectively. Therefore to characterize the performance of a wavelength converter, one has to investigate the dependences of conversion efficiency on pulse width, input power, and pump central wavelength, which we will discuss in Subsections 4.B– 4.D. However, prior to the discussion on efficiency dependences, we need to define the efficiency explicitly. A.

Definition of Efficiency

Conversion efficiency is one of the most important device characteristics in wavelength conversion. To qualify the device performance we adopt the traditional conversion efficiency, which is usually defined as the energy ratio of output to input. One can see that in the cascaded process the converted wave is related to both the pump and signal waves. Therefore we need to consider two energy ratios (i.e., the ratios of the converted pulse energy to that of the pump and to that of the signal), ␩Ec兾p and ␩Ec兾s, which are given by

␩Ec兾p ⫽

冕ⱍ 冕ⱍ 冕ⱍ 冕ⱍ

Ac共t, L兲ⱍ 2dt ⫽ Ap共t, 0兲ⱍ 2dt

Ac共t, L兲ⱍ 2dt

␩E

c兾s

⫽

⫽ As共t, 0兲ⱍ 2dt

冕冕冕冕

Sc共␭, L兲d␭ ,

(15)

Sp共␭, 0兲d␭

Fig. 10. Simulated (solid curves and lines) and measured (symbols) energy efficiencies and spectral-peak efficiencies versus signal pulse width in Scheme I.

sured optical spectra by the OSA. To avoid possible confusion, ␩E and ␩S are called the energy efficiency and spectral-peak efficiency, respectively, in the next discussions. B.

Sc共␭, L兲d␭ ,

(16)

Ss共␭, 0兲d␭

where the integrals in the numerators denote the converted pulse energies measured at the waveguide output port 共z ⫽ L兲; while those in the denominators stand for the input pulse energies 共z ⫽ 0兲. The last term in Eqs. (15) and (16) is introduced for the calculation of efficiency from the measured optical spectra by the OSA. We take the pulse repetition period as the integral duration, so that the defined efficiencies can apply for both the cw and the pulsed waves. In addition to ␩E, we define another efficiency ␩S to indicate the spectral-peak ratio of output to input in the optical spectrum domain. When the ASE background is not negligible, the influence of ASE noise can play a significant role in conversion performance. In optical communication systems, the reduction of signal-to-noise ratio, usually called the noise figure, is an important index of a device or subsystem. For example, from a simple comparison between Figs. 2(e) and 3(c), one can see that the converted pulse in Scheme I has a higher signal-to-noise ratio. Furthermore, from Eqs. (15) and (16), one can see that under the same ␩E, if the spectral width is narrower and its peak is higher, ␩S will be higher, which can take advantage of a lower in-band ASE noise. Unlike ␩E, ␩S can be obtained directly from the mea-

Pulse-Width Dependence

The dependences of the two conversion efficiencies on input signal pulse width ⌬␶s were studied first in Scheme I under the experimental conditions corresponding to Figs. 2 and 6. The simulated results of ␩E and ␩S versus ⌬␶s are given in Fig. 10 together with the measured data (the symbols with error bars), in which the simulated results agree very well with the measured results. Varying with ⌬␶s, the average powers of the pump and signal are both kept constant, and the signal peak power and the spectral bandwidth are almost inversely proportional to ⌬␶s. From the simulation results shown in Figs. 10(a) and 10(b), one can see that with an increase of pulse width, against the pump, ␩E c兾p decreases slightly, whereas ␩S c兾p increases, apparently. In particular, when ⌬␶s is increased from 1 to 10 ps, ␩Ec兾p drops by only 0.4 dB, and ␩Sc兾p increases by 9.0 dB. Against the signal, with the same change in ⌬␶s, ␩Ec兾s drops by 0.4 dB, and ␩Sc兾s drops by 1.0 dB. With an increase of ⌬␶s, such small changes in energy efficiency indicate that under the same pump power (cw), the wavelength conversion in Scheme I is nearly independent of signal pulse width, while the increase in spectral-peak efficiency indicates that a broader input pulse takes advantage of a higher signal-to-ASE-noise ratio in the spectral domain. The conversion efficiencies versus input pump pulse width ⌬␶p were then analyzed in Scheme II. Based on the experimental conditions shown in Figs. 3 and 8, the experimental and simulation results are compared in Fig. 11, in which one can see excellent accordance between the measured and simulated data. From the simulation results shown in Figs. 11(a) and 11(c), we can see that varying with ⌬␶p, the 20 July 2006 兾 Vol. 45, No. 21 兾 APPLIED OPTICS

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Fig. 11. Simulated (solid curves and lines) and measured (symbols) energy efficiencies and spectral-peak efficiencies versus pump pulse width in Scheme II.

energy efficiencies against the pump and signal have similar trends. For the same average pump power, when ⌬␶p is decreased from 10 to 1 ps, the peak power of the input pump pulse is elevated 10 times, whereas ␩Ec兾p and ␩Ec兾s are both increased by only 2.8 dB. This is attributed mainly to the walk-off effect, which can deteriorate the conversion efficiency for narrow input pulses. The spectral-peak efficiency against the pump is different from that against the signal. With an increase of ⌬␶p from 1 to 10 ps, the former drops by 10.1 dB, while the latter has nearly no change. This indicates that the spectral peak of the converted wave is nearly independent of ⌬␶p. With an increase of ⌬␶p, the decrease of ␩Sc兾p is due to the corresponding increase of the spectral peak of pump. It is therefore concluded that in Scheme II, under the same average pump power, narrower input pump pulses take advantage of higher conversion efficiency. From Figs. 10 and 11, we can see distinct characteristics of conversion efficiencies in the two pumping schemes. Here we show a quantitative comparison between them for different input powers. Since the two input waves (cw and pulsed) play different roles in the conversion, to make a reasonable comparison we take the same powers for them, leading to two different cases. One is that the pump and signal have the same average powers, the other is that they have the same peak powers. In other words, varying with the pulse width, the pulse average power or peak power is kept constant, respectively, in these two cases. Of course in these two cases, the cw wave can be regarded as an ideal square pulse with a duty cycle of unity. Therefore in the former case (with the same average power), the pulsed wave has a higher peak power than the cw wave; correspondingly in the latter case, the pulsed wave has a lower average power. We still take 1543.0 and 1549.9 nm for the pump and signal, respectively. In addition, we consider only the conversion efficiencies of the converted pulse with respect to the pulsed input (the information carrier). Figure 12 shows the 5400


Fig. 12. Efficiencies versus input pulse width in two schemes under constant average power and peak power (20 dBm) for input pump and signal. The solid curves refer to different pulse widths but the same average powers. The dashed curves refer to the same peak powers.

simulated energy and spectral-peak efficiencies versus the input pulse width under the same input power 共20 dBm average and peak powers) for the input pump and signal, where the efficiencies are related to the pulsed signal in Schemes I (left column) and to the pulsed pump in Scheme II (right column). First, we consider the energy efficiency (Fig. 12, top row). For any pulse width, the energy efficiency is higher in Scheme II under constant average power (solid curves), but higher in Scheme I under constant peak power (dashed curves). One can understand that under constant average power, a narrower input pulse corresponds to a higher peak power, yielding a higher conversion efficiency; under the same peak power, a broader input pulse leads to a higher efficiency due to an increase of average input power. Then we consider the spectral-peak efficiency (Fig. 12, bottom row). The conclusion is similar to that for energy efficiency, i.e., Scheme II is better than Scheme I under constant average power and is worse under constant peak power. It is also concluded that in Scheme I narrower input pulses are slightly better; in Scheme II, given the same average power, narrower pump pulses are better, whereas given the same peak power, broader pump pulses are better. Meanwhile, we can see that the differences in efficiencies tend to decrease with an increase of pulse width. One can understand further that with the pulse width approaching the pulse repetition period 共25 ps in the 40 GHz case) there will be no difference between the two pumping schemes. C.

Pulse-Power Dependence

Given a constant power for the cw input wave, the dependences of the conversion efficiencies on the average power of the pulsed wave were examined. First in Scheme II the measured and simulated ␩E and ␩S versus the average input pump power are depicted in Fig. 13, in which the simulation parameters are

Fig. 13. Simulated (solid lines) and measured (symbols) energy efficiencies and spectral-peak efficiencies versus average pump power in Scheme II.

Fig. 14. Simulated energy efficiencies and spectral-peak efficiencies versus average signal power in Scheme I.

based on the previous experiments shown in Fig. 4. Once again, one can see excellent agreement between the simulated and measured results. It indicates that in Figs. 13(a) and 13(c) the energy efficiency against the pulsed pump is proportional to average pump power, and consequently the converted pulse energy obeys a square relationship with pump pulse energy. As shown in Figs. 13(b) and 13(d), the spectral-peak efficiencies over the pump and signal have similar trends, noting that the spectral peak of the converted wave increases by 20 dB with a 10 dB increase of average pump power. These factors indicate that the wavelength conversion for the pulsed input in Scheme II has similar efficiency characteristics to those for the cw input3–9 though the converted pulse has certain delay and distortion. Then in Scheme I, given a constant cw pump power 共20 dBm兲, the simulated ␩E and ␩S versus the average input power of the pulsed signal are depicted in Fig. 14. The signal pulse width is 4.0 ps. One can see that given a constant pump power, the output average power of the converted pulses is nearly proportional to the average input signal power like that observed in the experiment, and a slight saturation 共⬍0.1 dB兲 starts to occur when the average input signal power exceeds 13 dBm. Consistent with the simulation, there was no notable saturation observed in the experiment for a signal power of 13 dBm. Given the same cw input power, when the conversion efficiency against the pulsed input is compared between the two pumping schemes, we can conclude from Figs. 13(a) and 14(c) that Scheme I has a better efficiency at a relatively low average pulse power, while at a high power Scheme II can perform better.

the pump wavelength to meet the QPM conditions 共⌬kp ⫽ 0兲, and large wavelength ranges for the DFG process due to ⌬kc ⬇ 0. This can be easily verified by substituting Eq. (10) into Eqs. (5) and (6). Therefore in our device a certain deviation of the pump wavelength ␭p from the QPM wavelength 共1543.0 nm兲 can significantly deteriorate the total conversion efficiency, as demonstrated in the experiments and shown in Fig. 5. The pump-wavelength dependences of the conversion efficiencies were investigated first in Scheme II. The measured and simulated ␩E and ␩S versus ␭p are depicted in Fig. 15 for different pump pulse widths. Several measured spectra of the output pump and SH pulses have been shown in Fig. 5. In the simulation, the average input pump power and cw signal power were 13.0 and 19.7 dBm, respectively. We can see good agreement between the simulation and the experimental results, and the tendencies of ␩E and ␩S

D. Pump-Wavelength Dependence

The deviation of the pump wavelength from the QPM wavelength leads to a mismatch of phase between the pump and SH waves, and consequently to the efficiency deterioration of the SHG. The unique property of uniform-period QPM devices determines that these kinds of devices have relatively small tolerances of

Fig. 15. Simulated energy efficiencies and spectral-peak efficiencies versus pump central wavelength compared with the experimental data (symbols) for different pump pulse widths in Scheme II. 20 July 2006 兾 Vol. 45, No. 21 兾 APPLIED OPTICS

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Fig. 16. Simulated energy efficiencies and spectral-peak efficiencies versus pump central wavelength in Scheme I.

varying with ␭p are very similar. In particular, with an increase of ␭p from 1543.0 nm, both efficiencies decrease for any pulse width, and efficiency differences between different pulse widths basically tend to be larger in the range 1543–1544 nm. Similar behaviors were also observed when decreasing ␭p from 1543.0 nm (hence not plotted here). From the theoretical curves of ␩E over the pump and signal shown in Figs. 15(a) and 15(c), the 3 dB wavelength tuning bandwidth of ␩E, at which the efficiency ␩E drops by 3 dB, is 1.5, 1.0, 0.8, and 0.5 nm for the 2.0, 3.0, 4.0, and 10.0 ps input pump pulses. The same wavelength tuning bandwidth can be obtained from the tuning curve of ␩S. This implies that a narrower pulse width of pump takes advantage of a larger pumpwavelength tolerance. In Scheme I when the cw pump is regarded as a square pulse with a 25 ps width, the pumpwavelength tolerance is expected to be narrower. This has been confirmed in our experiments. Here some quantitative results are shown in Fig. 16 for 4 ps signal pulses and the same powers as those in Fig. 15. In fact, there are no differences in the efficiencies for different signal pulse widths including the cw signal. However, the efficiencies decrease promptly with a deviation of the pump wavelength from 1543.0 nm, and the aforementioned 3 dB wavelength tuning bandwidth is only 0.3 nm. By comparing the conversion efficiencies in the two pumping schemes, we can conclude that the use of ultrashort pulses as the pump in the QPM wavelength conversion can significantly enlarge the tolerance of the pump central-wavelength deviation from the desired QPM wavelength. 5. Conclusions

By using a 40 GHz tunable fiber laser, we have studied the cascaded SHG–DFG based picosecond-pulse wavelength conversion in a MgO-doped PPLN waveguide. The temporal and spectral characteristics are analyzed both experimentally and theoretically in two pumping schemes, i.e., Schemes I and II, correspond5402


ing to the cw and pulsed pump, respectively. The simulation results agree well with the measured data, verifying the validity of our theoretical model. It is found that the converted pulses exhibit different temporal and spectral features in the two schemes. In Scheme I (cw pump), the converted pulse shape and spectral envelope are quite similar to those of the input pulse. In Scheme II (pulsed pump), compared with the symmetric input pulse, the converted pulse becomes asymmetric and has a certain time delay; meanwhile, the pulse width tends to be broader and its spectral bandwidth tends to be narrower. These variations are incurred mainly due to a group-velocity mismatch. Only in Scheme I, the product of pulse width and frequency bandwidth is kept nearly constant. To quantify the conversion performance of the device, we defined the two conversion efficiencies in terms of pulse energy and spectral peak. The dependences of the two conversion efficiencies on pulse width, average power, and central pump wavelength are then obtained. It is shown that in Scheme I the energy efficiency is nearly independent of signal pulse width, and broader pulses take advantage of higher spectral-peak efficiency; in Scheme II narrower input pump pulses lead to higher energy efficiency, and the spectral peak of the converted wave is independent of pump pulse width. For different pulse widths the two efficiencies are higher in Scheme II under the same average power, and higher in Scheme I under the same peak power. Regarding the power dependence, in both schemes the output average power of the converted pulses approximately obeys a square relationship with input pump power, and it is proportional to input signal power before the occurrence of saturation. However, Scheme I has a better efficiency at a relatively low average pulse power; at a high power, Scheme II can perform better. When the pump central wavelength deviates from the desired QPM wavelength of the device, both conversion efficiencies decrease in the two schemes. The use of picosecond pulses as the pump in Scheme II can significantly enlarge the selection tolerance of the pump wavelength. The quantitative results obtained in this work provide some guidelines for the applications of QPM waveguide devices to wavelength conversion. The authors thank the Ontario Photonics Consortium (OPC), the Natural Sciences and Engineering Council of Canada (NSERC), the Canadian Institute for Photonic Innovation (CIPI), the Canada Foundation for Innovation (CFI) under New Opportunities Program, and Fuji Photo Film Co., Ltd., for the crystal poling. J. Fonseca-Campos also thanks the Consejo Nacional de Ciencia y Tecnología (CONACYT) of México for the scholarship and financial support and the Unidad Profesional Interdisciplinaria de Ingeniería y Tecnologías Avanzadas (UPIITA) of the Instituto Politécnico Nacional (IPN) of México. References 1. S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14, 955–966 (1996).

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