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Abstract
Ultra-short optical pulses in the femtosecond and picosecond regime are typically generated using mode-locked lasers. However, in mode-locking, the pulse repetition rate is fundamentally linked to the cavity length of the laser, making it difficult to synchronize these laser pulses to other light sources. Here, we apply a pulse-on-demand approach to picosecond pulse generation with an electro-optic intensity modulator (EOM). The high, 40 GHz bandwidth of the EOM enables low picosecond pulses, however it shifts the problem of pulse generation to the electronic pulses, requiring high bandwidth electronics. In this study, we present an electro-optic operation, leveraging the periodic interference condition of intensity EOMs by operating it with rising edges at twice its Vπ voltage. Utilizing this method, pulse durations as short as 10.9 ps were achieved by employing a 35 ps edge from an arbitrary waveform generator. The pulses were measured directly on a high-speed oscilloscope as well as indirectly through the spectral broadening of the generated optical pulses. We employ this approach to show arbitrary pulse length generation by applying step functions with only one Vπ voltage, thus permitting direct pulse-on-demand generation of pulses with arbitrary pulse length, shape and repetition rate for applications in spectroscopy, sensing and nonlinear imaging.
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1. Introduction
Since the development of the first laser systems in the 1960s [1], there have been many possible applications for this new technology. A wide range of these applications require the operation of pulsed lasers. These include industrial cutting lasers, medical lasers for bleed-free tissue ablation and lasers for biomedical imaging such as multiphoton microscopy (MPM) [2–4]. The latter is a promising technology for intravital imaging, providing deep tissue penetration, high 3D resolution and low photobleaching [5]. MPM is a nonlinear imaging technique, thus it is crucial to make maximum use of the quadratic intensity dependence of the excitation probability by using high intensity laser illumination. Traditionally, femtosecond pulses from a mode-locked laser are employed, providing typically about 125 fs pulses at repetition rates of 80 MHz [6], but their synchronization with other light sources proves challenging due to the inherent coupling of pulse repetition rate and resonator length in mode coupling. In addition, however, femtosecond pulses have a wide spectral bandwidth due to the time-bandwidth limitation, which leads to chromatic dispersion-based pulse distortion when used in optical setups and fibre-optic systems [7,8]. Further, the high peak powers of femtosecond pulses can lead to adverse nonlinear effects due to photodamage and photobleaching in tissue scaling supra-quadratically [5,9]. Conversely, longer pulses can lead to similar MPM signal levels while employing lower peak powers [10–12]. Furthermore, recent studies have been applying picosecond pulses as pulse-on-demand alternatives for synchronized fluorescence lifetime imaging and high-speed microscopy [13–15]. EOM based pulse modulation was shown to be able to produce pulses in the picosecond and even femtosecond regime [16–18]. Here, we utilize a Mach-Zehnder-based intensity electro-optic modulator (EOM), which splits an optical beam into two partial beams and induces a phase modulation in one of the partial beams by means of the electro-optic effect driven by an applied voltage [19]. Being waveguide-based, a small driving voltage of 5 V is sufficient to achieve a full $V_{\pi }$ modulation between constructive and destructive interference. To achieve short picosecond pulses, typically electrical pulse generators are required to provide the short picosecond electrical pulses [20].
2. Experimental setup
Many studies have already shown the generation of ultrashort pulses in the low picosecond range by using Mach-Zehnder based EOMs [21–24]. In this letter, however, we report on another way of generating picosecond pulses using an intensity EOM with a driver signal that provides the double half-wave voltage $V_{\pi }$.
The operating principle harnesses the periodic interference condition of intensity EOMs. An intensity EOM employs a Mach-Zehnder interferometer where one arm contains a crystal providing an electro-optic phase shift upon an applied voltage [19]. Hence, in this arm the refractive index of the material can be changed by applying an electrical voltage, thus changing the speed of light in the crystal. This leads to a phase change of the light wave passing through. Afterwards the two partial beams are reunited. After recombination, the two waves generate an interference condition, which is voltage-dependent due to the induced phase shift. Thus, destructive or constructive interference conditions can be generated. Destructive interference occurs if the phase offset is $\Phi = \Phi _0 + (2n+1)\pi$, where $\Phi _0$ represents the phase of the light source at the entrance of the EOM. If the phase offset is an integer multiple of the original phase ($\Phi = \Phi _0 + 2n\pi$), constructive interference periodically occurs (cf. Fig. 1). First, in experimental operation, a bias voltage is set for destructive interference, i.e. the intensity EOM has maximum optical extinction (typically >30 dB using high-extinction ratio EOMs). For typical pulse modulation, an electrical pulse with $V_{\pi }$ amplitude is applied to the RF voltage port and superimposed with the bias voltage. The resulting optical intensity follows the RF pulse shape, multiplied by a sinusoidal transfer function resultant of the interference condition. Thus, the input laser light is pulsed depending on the electrical pulse shape and pulse rate. However, in this work, we apply an electronic step function at twice the $V_{\pi }$ voltage to toggle rapidly between two consecutive destructive interference conditions, ($V_{Bias}$ and $V_{Bias}+2V_{\pi }$), resulting in a rapid optical pulse output. Thus, the resulting optical pulse has a much shorter pulse width than the electronic rise/fall time. Typically, a square wave signal was used to generate optical pulses on both edges, resulting in an optical pulse repetition rate at twice the electrical signal repetition rate. The basic principle is shown in Fig. 1. We employed a waveguide-based EOM with travelling wave condition which requires a low $V_{\pi }$ of only 3 V. The EOM used for this study provides a bandwidth of up to 40 GHz (Optilab ML-1550-40-PM-V-HER). To generate square wave signals with fast edges, an arbitrary waveform generator (AWG, Tektronix AWG7122B) was used, which provides a rise and fall time of 35 ps (80 %/20 %). The amplitude of the generated electrical signal was amplified to $2V_{\pi }$ using a 47 GHz electronic amplifier. The experimental setup is shown in Fig. 2.
Fig. 1. Priciple of a Mach-Zehnder-based intensity modulator with constructive and destructive interference due to electro-optically induced phase shifts (a). By employing a $V_{\pi }$ or a $2V_{\pi }$ voltage (b), two modes of operation can be realized. In regular $V_{\pi }$ mode, an arbitrary pulse length can be generated. In $2V_{\pi }$-mode, electro-optically leveraged pulses are formed for each edge of the applied electronic waveform.
Fig. 2. Experimental setup with electrical components for generating electrical signals and measurement in the green box. The red box represents the optical path.
The green box contains the components of the electrical setup with the AWG, the amplifier (AMP) and the real-time oscilloscope. In the red box the optical setup including a 1550 nm laser diode, the EOM and a fast 50 GHz photodiode is depicted. Here, the AWG generates rectangular signals at 100 MHz with a duty cycle of 50 %. After amplification, the signals drive the EOM to generate optical pulses with a repetition rate of 200 MHz - one optical pulse per slope. Figure 3(a) shows a square wave signal with a rise and fall time of 35 ps. The amplitude of the AWG output is 800 mV.
Fig. 3. Picosecond pulse generation using the $2V_{\pi }$-method. Graph a) shows the square wave signal generated by the AWG with a slope of 35 ps (80 %/20 %), which was subsequently amplified to approximately 6 V. Fig. b) displays optical pulses generated by the EOM on each edge of the square wave signal. The FWHM of the pulses here is 10.9 ps.
3. Results and discussion
The electronic amplifier boosts the amplitude to 6 V (corresponding to twice the $V_{\pi }$ of the EOM). Figure 3(b) shows the resulting ultrashort pulses with a full width at half maximum (FWHM) of 10.9 ps on rising and falling edges of the square wave signal. The electro-optic leverage is thus a factor of about 3.2 from the 80/20 rise/fall time to the FWHM of the optical pulse. The AWG permits a flexible pulse pattern and pulse repetition rate. Figure 4 depicts an exemplary pulse train with a repetition rate of 2 GHz, resulting of a square waveform at 1 GHz frequency.
Fig. 4. Short pulse train of optical pulses generated by using the $2V_{\pi }$-Method with a electrical signal frequency of 1 GHz, resulting in an optical pulse repetition rate of 2 GHz.
The experiments showed that this new method is suitable for generating ultrashort pulses in the 10 ps range. The optical pulses were measured using a 50 GHz photodiode (XPDV2320R, Finisar) and a real-time, 63 GHz oscilloscope (DSOZ634A, Keysight). Following equation
can be used to approximate the rise time (RT) of a system based on its bandwidth (BW) [25]. Thus, the theoretical resolvable RT of the photodiode should be 7 ps (90 %/10 %). The oscilloscope is capable of resolving 5.55 ps, which is consistent with the manufacturer specification. Taking these values into account, the measured optical pulse length of 10 ps is at the limit of what can be resolved with the measurement equipment. To allow future characterization of even shorter pulses using the $2V_{\pi }$-Method, a spectral characterization of the temporal pulse width was explored. This follows the time-bandwidth product (TBP) modification of ultra-short pulse modulation. The short temporal profile of the pulse broadens the spectral bandwidth of the pulse. Thus, measuring the spectral broadening of the pulses using an optical spectrum analyzer (OSA) can be utilized to determine the temporal pulse width of the modulated pulses denoted by $\Delta t$. In case of Gaussian pulses, the time-bandwidth product assumes a characteristic value of 0.44 [26]. Thus, the change in spectral bandwidth due to short pulse modulation can be utilized to indirectly determine the pulse length. Equation (2) describes the time-bandwidth product. Here, $\Delta t$ is the optical pulse width and $\Delta f$ the frequency-domain bandwidth:Equation (3) sets out the relationship between the wavelength and frequency ranges of an optical spectrum [26]. Here, $\lambda _0$ is the central wavelength, $x$ represents half of the spectral bandwidth (Half Width at Half Maximum (HWHM)) and $c_0$ denotes the speed of light in vacuum.
For this study, pulse spectra were measured in addition to oscilloscope measurements to test wether the pulses are TBP limited. Figure 5 shows the plot of two spectra. The spectrum shown in blue represents the continuous wave (CW) light of a 1550 nm laser diode. In contrast, the orange spectrum represents the recorded pulse spectrum, where a significant deviation can be observed due to the spectral pulse broadening. Due to the limited extinction ratio of the EOM, some remaining CW light contribution is visible in the spectrum. This component can be identified in the centre of the pulse spectrum, where the shape of the curve corresponds exactly to the CW light of the laser diode. To attribute the spectral broadening exclusively to pulse modulation, the CW component was extracted manually by applying a threshold value. Thus we exclude values above this threshold (denoted by dotted line in Fig. 5). The pulse data that no longer contained these values were linearised and fitted with a Gaussian function. The determined FWHM for the pulse-broadened spectral width lead to a time-bandwidth limited pulse width of 13.19 ps (assuming a Gaussian pulse shape). This was compared to a direct measurement on the high-speed oscilloscope, yielding a temporal measurement of 12.49 ps. The comparison shows a deviation of only 5.3 %, thus proving the high fidelity of the spectrum-based pulse-width determination method. Furthermore, this indicates that the presented $2V_{\pi }$ pulse modulation method produces time-bandwidth limited ultrashort pulses. A second pulse with an electronically determined length of 42 ps yielded 34.7 ps in the spectral analysis, which amounts to a deviation of 21 %. The higher deviation probably originates from a non-gaussian pulse shape of the longer pulses. Since this spectral pulse-width determination shall be used for short pulse characterization beyond the electronic bandwidth of the real-time oscilloscope, where pulse shapes can be assumed of Gaussian type, the TBP-determination method is deemed highly suitable. The optical pulses with a pulse length of 10.9 ps achieved in this study were also measured using this method, confirming the oscilloscope measurement with a deviation of 1.71 %.
Fig. 5. Spectra of a 1550 nm laser diode, with CW spectrum in blue and the pulsed spectrum in orange. Owing to the TBP, the pulsed spectrum exhibits a broader range compared to the CW spectrum. Values above the CW cut-off threshold (black dotted line) are excluded from the fit. The upper left image shows the gaussian fit (red) to the linearised pulse spectrum without CW values (blue).
In another embodiment of this method, we studied arbitrary pulse length modulation by combining the $V_{\pi }$ and $2V_{\pi }$ modulation methods in a single time-trace. This can be used to generate different pulse shapes and repetition rates in a single pulse train. For this purpose, an AWG file was programmed that generates a $V_{\pi }$ voltage in the form of a square wave signal with a duration of 1 ns, followed by an electrical $2V_{\pi }$ signal with a duration of approximately 2.5 ns. Figure 6 shows the AWG signal and the resulting optical pulses measured on the real-time oscilloscope. The amplitude of the AWG signal represents the binary values from the generated AWG file (range 0-255), with the respective amplitudes corresponding to the voltages appropriate for EOM operation after subsequent electrical amplification. Although this electrical signal produces the targeted optical pulses, the 1 ns long optical square pulse shows a signal drop in the middle because the electrical signal does not exactly correspond to $V_{\pi }$. Electrical overshoots due to impedance mismatches or parasitic inductances cause the EOM to transmit a small amount of light for a short time as it can be seen at the last ultrashort pulse. The AWG output trace was then modified by reducing the amplitude of the $V_{\pi }$ pulse to provide a more rectangular shaped optical pulse. To show the effect of the amplitude reduction, the boundary values of the pulse were left unchanged, resulting in the two peaks at the borders of the $V_{\pi }$ pulse as shown in Fig. 7(a). The $2V_{\pi }$ signal used to generate the ultrashort pulses was not modified. Figure 7(b) shows the effect of the signal adjustment. Now, the optical rectangular pulse has a uniform shape, with the peaks of the electrical signal leading to the two expected short signal drops at the edges of the pulse, demonstrating the generation of various pulse pattern. The amplitude of the ultrashort pulse has an amplitude of 39.2 mV, whereas the mean amplitude of the CW-like square pulse is about 47 mV, which corresponds to an efficiency of 83.4 % with this $2V_{\pi }$ method. Compared to conventional pulse generation with a 42 ps pulse generator, the efficiency increases up to 100 %, as the optical pulse amplitudes are almost identical.
Fig. 6. Binary AWG signal file for 1 ns long pulse modulation with $V_{\pi }$ followed by a $2V_{\pi }$ signal in a). Graph b) shows the resulting optical pulses with 1 ns followed by two ultrashort pulses of about 10 ps length.
Fig. 7. Adjusted binary AWG signal file for a 1 ns long pulse modulation with $V_{\pi }$ followed by a $2V_{\pi }$ signal in a). Graph b) shows the resulting optical pulses with 1 ns foll-owed by two ultrashort pulses in the range of 10 ps length.
Since this study refers to pure optical pulse generation with a single mode laser diode, the output power depends on the laser source and in this case is too low to be used directly. Due to the high efficiency of this method, it can nevertheless be used to modulate the laser light source in a master oscillator power amplifier (MOPA) setup, where the peak pulse power can be increased to several hundred watts by using one or more optical amplifier stages [18]. The MOPA architecture can then in turn be applied in many different subject areas.
4. Conclusion
The results of this study offer a cost-effective alternative for generating ultrashort pulses compared to the use of electrical pulse generators. Furthermore, the novel operating mode enables the generation of arbitrary shaped optical pulses in a range of a few picoseconds to CW-like behaviour. In addition, the applicability of spectral analysis was successfully demonstrated. Moreover the methods presented in this paper will find application in areas such as multiphoton microscopy with kHz frame rates as well as in fast inertia-free light detection and ranging (LiDAR) imaging [14,27,28]. Currently, the electronic bandwidth of the EOM is not limiting, thus future developments will investigate wether it is possible to obtain single-digit picosecond pulses by employing faster electronic edges.
Funding
Land Schleswig-Holstein (SH-Excellence Chair Program); European Commission (H2020-EU project FAIR CHARM); Leibniz-Gemeinschaft (T94/2021); Deutsche Forschungsgemeinschaft (EXC 2167-218 390884018, project ADAPT (KA 4354/6-1), Precision Medicine in Inflammation).
Acknowledgments
We gratefully acknowledge Robert Huber for access to the high-speed oscilloscope and providing the infrastructure at the Institute for Biomedical Optics in Lübeck. Further we gratefully acknowledge funding from the European H2020-ICT project FAIR CHARM (FAst InfraRed Coherent HARmonic Microscopy, http://www.faircharm.eu), the DFG WEAVE project ADAPT and funding from the Leibniz-Transfer program of the Leibniz Association (project BSLIDE3). S.K. gratefully acknowledges the Juniorprofessorship with financial support by the state of Schleswig-Holstein (Excellence chair program by the universities Kiel and Luebeck) and funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy. Last, we acknowledge financial support by Land Schleswig-Holstein within the funding programme Open Access Publikations fonds.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.
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