Optical Function Generator

Abstract

To provide an optical function generator capable of generating directly from an AM mode-locked laser high output and high quality optical pulses having arbitrary time waveforms without using any waveform shaping technology outside the laser.SOLUTION: A laser resonator includes an optical phase modulator 3, an optical amplifier 2, and an optical filter 4. The optical filter 4 has variable amplitude and phase characteristics. By setting amplitude and phase characteristics in accordance with the shape of the optical pulse to be output, an optical pulse having an arbitrary shape is outputted.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an optical function generator. [Background technology]

[0002] Ultrashort optical pulses have a wide range of applications, including ultrafast optical communications, optical measurement, and optical signal processing. Various pulse light sources, including Q-switched, gain-switched, and mode-locked lasers, have been developed. Among these, mode-locked lasers are widely used as picosecond to femtosecond ultrashort optical pulse sources with repetition rates in the MHz to GHz range. It is known that the shape of the optical pulses output from a mode-locked laser can generally be converted to a Gaussian pulse by inserting an optical filter with Lorentzian transmission characteristics into the laser resonator (see, for example, Non-Patent Documents 1 and 2). Furthermore, by utilizing a nonlinear optical effect known as the soliton effect within the resonator, it is possible to generate a sech pulse, and such a laser is known as a soliton laser (see, for example, Non-Patent Documents 3 and 4). More recently, it has been revealed that parabolic pulses with a parabolic shape can also be generated using non-linear optical effects (see, for example, Non-Patent Documents 5, 6, and 7). Such parabolic pulses are also called similiton pulses because of their self-similar wave propagation characteristics (see, for example, Non-Patent Document 8).

[0003] To generate pulse waveforms other than the Gaussian, Sech, and parabolic waveforms mentioned above, a method of spectral shaping the waveform outside the mode-locked laser is used. Specifically, if the waveform and spectrum of the pulse directly output from the laser are u(t) and U(ω), respectively, and the waveform to be generated is a(t) and its frequency spectrum is A(ω), an optical pulse with a waveform given by a(t) can be obtained by inserting an optical filter outside the laser whose transfer function is given by F(ω) = A(ω) / U(ω).

[0004] One method proposed to realize such an optical filter is to use a diffraction grating to separate an ultrashort optical pulse and then use a spatial optical filter to apply the desired amplitude and phase change to each frequency component. Also, a programmable optical filter using LCoS (Liquid Crystal on Silicon) has been put to practical use as such a waveform-shaping optical circuit (see, for example, Non-Patent Document 9).

[0005] Another known method is to use an optical frequency comb instead of a mode-locked laser. When a CW laser is input into an optical comb generator, multiple longitudinal modes with equal intensity and regular spacing are generated from a single longitudinal mode. By passing the resulting flat optical comb through an optical filter with a transfer function of A(ω), an optical pulse with a spectral shape of A(ω) and a time waveform of a(t) can be obtained. [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] D. Kuizenga and A. Siegman, “FM and AM mode locking of the homogeneous laser - Part I: Theory”, IEEE J. Quantum Electron., November 1970, vol. 6, no. 11, pp. 694-708 [Non-patent document 2] HA Haus, “A theory of forced mode locking”, IEEE J. Quantum Electron., July 1975, vol. QE-11, no. 7, pp. 323-330 [Non-patent document 3] https: / / doi.org / 10.1103 / PhysRevLett.111.2013 , Google Scholar Crossref , CAS 10. LF Mollenauer and RH Stolen, “ The soliton laser ,” Opt. Lett., January 1984, vol. 9, no. 1, pp. 13-1

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[0007] However, the waveform shaping methods described in Non-Patent Documents 1 to 9 reduce the power of the original optical signal by one-third to one-fifth due to the insertion loss of the optical filter itself. Therefore, after shaping, it is necessary to compensate for these optical losses using an optical amplifier. As a result, spontaneous emission noise from the optical amplifier is superimposed on the pulse, significantly degrading the optical signal-to-noise ratio (OSNR). In other words, conventional waveform shaping methods have difficulty generating optical pulses with high output power and high OSNR. In particular, with methods using an optical frequency comb, the power of the original CW light is dispersed into multiple longitudinal modes, resulting in low power per longitudinal mode during the optical comb signal generation stage, resulting in significant degradation of the OSNR. These waveform shaping methods still have significant challenges in practical use.

[0008] The present invention is intended to solve these problems, and aims to provide an optical function generator that can generate high-power, high-quality optical pulses with arbitrary temporal waveforms directly from an AM mode-locked laser without using waveform shaping technology outside the laser. [Means for solving the problem]

[0009] In order to achieve this object, the optical function generator of the present invention has an AM mode-locked laser equipped with an optical intensity modulator, an optical amplifier, and an optical filter within a laser resonator, and the optical filter has variable amplitude and phase characteristics, and by setting the amplitude and phase characteristics according to the shape of the optical pulse to be output, it is possible to generate an optical pulse of any shape.

[0010] In the optical function generator according to the present invention, the optical intensity modulator has a repetition rate of Ω m and the optical filter is provided so that the amplitude and phase characteristics correspond to the modulation degree of the optical intensity modulator and the spectrum A(ω) of the optical pulse to be output, and mA function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m ) may be composed of.

[0011] In the optical function generator according to the present invention, the optical intensity modulator is driven at a repetition rate of Ω m A sinusoidal modulated signal of Ω m In this case, the optical filter may superimpose a harmonic of the spectrum A(ω) and A(ω) of the optical pulse to be outputted at an angular frequency Ω. m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m ), and A(ω) as Ω m Harmonics of NΩ m A function A(ω-NΩ) shifted positively or negatively by m ), A(ω+NΩ m Furthermore, the optical filter may be configured to provide a band limit to the amplitude and phase characteristics in accordance with the spectral width of the optical pulse to be output, thereby obtaining a TL (Transform-limited) pulse.

[0012] In the optical function generator according to the present invention, the optical filter is configured to calculate the amplitude characteristic by a Gaussian function A(ω) and a function A(ω) repeated at an angular frequency Ω m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m ) to generate a Gaussian pulse. The optical filter may be configured to generate a Gaussian pulse by repeating the amplitude characteristic with a Sech function A(ω) and A(ω) at an angular frequency Ω. m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m ) to generate a sech pulse.

[0013] The optical filter also calculates the amplitude characteristic by a Lorentz function A(ω) and repeating A(ω) at an angular frequency Ω m A function A(ω-Ω) shifted positively or negatively bym ), A(ω+Ω m ) to generate a pulse having a shape of a double exponential function. Also, the optical filter may be configured to generate a pulse having a shape of a double exponential function by providing the amplitude characteristic as a square function A(ω) of a sinc function, and a pulse having a shape of a double exponential function by repeating A(ω) at an angular frequency Ω. m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m ) to generate a pulse having a triangular shape.

[0014] In the optical function generator according to the present invention, the optical intensity modulator applies an angular frequency of 3 Ω to the modulating signal. m The optical filter is provided to superimpose a sine wave of a squared sinc function A(ω), and the amplitude characteristic is determined by repeating A(ω) at an angular frequency Ω. m and 3 ohms m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m ), A(ω-3Ω m ), A(ω+3Ω m ) to generate a pulse having a triangular shape.

[0015] In the optical function generator according to the present invention, the optical filter calculates the amplitude characteristic by a function sin ω / ω 3 and cos ω / ω 2 A(ω) is given by the sum of A(ω) and A(ω) is repeated at angular frequency Ω m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m ) to generate a pulse having a parabolic shape. The optical filter may be configured to calculate the amplitude and phase characteristics by applying a Lorentz function A(ω) and a repeating function A(ω) at an angular frequency Ω m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m ) to generate a semi-exponential pulse. [Effects of the Invention]

[0016] The optical function generator according to the present invention can generate a pulse train with an arbitrary temporal waveform and a high OSNR, depending on the amplitude and phase characteristics of the optical filter inserted into the resonator of the mode-locked laser. Therefore, a highly functional and high-quality optical function generator for optical measurement and optical signal processing can be provided with a simple configuration. Furthermore, the present invention can provide an optical function generator that can generate high-power, high-quality optical pulses with an arbitrary temporal waveform directly from an AM mode-locked laser, without using waveform shaping technology outside the laser. [Brief explanation of the drawings]

[0017] [Figure 1] 1 is a block diagram showing the configuration of an optical function generator according to an embodiment of the present invention. [Figure 2] 1 is a block diagram for explaining the operating principle of an optical function generator according to an embodiment of the present invention. [Figure 3] (a) Transfer function of the optical filter, (b) Shape of the filter with a band limit of 200 GHz (±100 GHz), (c) Waveform of a stationary pulse (Gaussian pulse) obtained by computer analysis, and (d) Its spectrum of the optical function generator of the first embodiment of the present invention. [Figure 4] (a) Transfer function of the optical filter, (b) shape of the filter with a band limit of 200 GHz (±100 GHz), (c) waveform of the steady pulse (sech pulse) obtained by computer analysis, and (d) its spectrum of the optical function generator of the second embodiment of the present invention. [Figure 5] (a) Transfer function of the optical filter, (b) shape of the filter with a band limit of 640 GHz (±320 GHz), (c) waveform of a stationary pulse (biexponential pulse) obtained by computer analysis, and (d) its spectrum of the optical function generator according to the third embodiment of the present invention. [Figure 6](a) Transfer function of the optical filter, (b) Shape of the filter with a band limit of 640 GHz (±320 GHz), (c) Waveform of a stationary pulse (triangular pulse) obtained by computer analysis, and (d) Its spectrum of the optical function generator according to the fourth embodiment of the present invention. [Figure 7] (a) Modulation function, (b) transfer function of the optical filter, (c) shape of the filter with a band limit of 640 GHz (±320 GHz), (d) waveform of a stationary pulse (triangular pulse) obtained by computer analysis, and (e) its spectrum of the optical function generator according to the fifth embodiment of the present invention. [Figure 8] (a) Transfer function of the optical filter, (b) Shape of the filter with a band limit of 640 GHz (±320 GHz), (c) Waveform of a stationary pulse (parabolic function pulse) obtained by computer analysis, and (d) Its spectrum of the optical function generator of the sixth embodiment of the present invention. [Figure 9] (a) Real part and (b) imaginary part of the transfer function of the optical filter of the optical function generator of the seventh embodiment of the present invention, (c) real part and (d) imaginary part of the filter with a band limit of 640 GHz (±320 GHz), (e) waveform of a stationary pulse (single-exponential pulse) obtained by computer analysis, and (f) its spectrum. [Figure 10] FIG. 1 is a block diagram showing the configuration of a 1.55 μm wavelength band harmonic AM mode-locked erbium fiber laser used in an experiment of an optical function generator according to an embodiment of the present invention. [Figure 11] 1A shows an optical filter implemented with an LCoS element, and FIG. 1B shows an enlarged waveform of the central portion of the optical function generator according to the first embodiment of the present invention. [Figure 12] (a) Intensity waveform of a Gaussian pulse obtained using the optical filter in Figure 11, (b) waveform converted to amplitude by taking the square root of (a), and (c) optical spectrum. [Figure 13]10A shows an optical filter implemented with an LCoS element, and FIG. 10B shows an enlarged waveform of the central portion of the optical function generator according to the second embodiment of the present invention. [Figure 14] (a) Intensity waveform of the SECH pulse obtained using the optical filter in Figure 13, (b) waveform converted to amplitude by taking the square root of (a), and (c) optical spectrum. [Figure 15] 10A shows an optical filter implemented with an LCoS element, and FIG. 10B shows an enlarged waveform of the central portion of the optical function generator according to the third embodiment of the present invention. [Figure 16] (a) Intensity waveform, (b) waveform converted to amplitude by taking the square root of (a), and (c) optical spectrum of a biexponential pulse obtained using the optical filter of Figure 15. [Figure 17] 10A shows an optical filter implemented with an LCoS element, and FIG. 10B shows an enlarged waveform of the central portion of the optical function generator according to the fourth embodiment of the present invention. [Figure 18] (a) Intensity waveform of a triangular pulse obtained using the optical filter in Figure 17, (b) waveform converted to amplitude by taking the square root of (a), and (c) optical spectrum. [Figure 19] 13A shows the absolute value of an optical filter implemented with an LCoS element, and (b) its phase, in the optical function generator according to the sixth embodiment of the present invention. [Figure 20] (a) Intensity waveform of the parabolic pulse obtained using the optical filter in Figure 19, (b) waveform converted to amplitude by taking the square root of (a), and (c) optical spectrum. [Figure 21] 13 shows (a) the amplitude characteristics and (b) the phase characteristics of an optical filter implemented with an LCoS element in the optical function generator according to the seventh embodiment of the present invention. [Figure 22] (a) Intensity waveform of a single exponential pulse obtained using the optical filter in Figure 21, (b) waveform converted to amplitude by taking the square root of (a), and (c) optical spectrum. DETAILED DESCRIPTION OF THE INVENTION

[0018] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. Mode-locked lasers are generally classified into two types: passively mode-locked lasers and actively (forced) mode-locked lasers. Passively mode-locked lasers can easily generate ultrashort pulses in the femtosecond range by inserting a saturable absorber into the resonator or by generating nonlinear polarization rotation. However, their repetition rates are generally slow, ranging from several tens to several hundred MHz. On the other hand, actively (forced) mode-locked lasers can generate pulses synchronized with an externally supplied modulation signal by inserting an optical modulator into the resonator. In this case, the pulse width is picoseconds to subpicoseconds, and the repetition rate can be increased to several tens of GHz. Actively (forced) mode-locked lasers can be further classified into two types depending on the modulation method: AM (amplitude modulation) mode-locked lasers and FM (frequency modulation) mode-locked lasers. In this invention, an AM mode-locked fiber laser is used.

[0019] 1 to 22 show an optical function generator according to an embodiment of the present invention. An example of the configuration of an optical function generator according to an embodiment of the present invention is shown in Figure 1. An optical fiber 1 constitutes a laser ring resonator, and the resonator comprises an optical amplifier 2 used as a gain medium, an optical intensity modulator 3 used as a mode locker, and an optical filter 4 whose amplitude and phase characteristics can be set arbitrarily. The optical amplifier 2 may be an erbium-doped fiber amplifier (EDFA), a semiconductor optical amplifier (SOA), a solid-state laser element, or the like. The optical intensity modulator 3 may be a Mach-Zehnder modulator using an LN (LiNbO3) crystal, or the like, which receives an external frequency f m (Angular frequency Ω m = 2πf m ), modulation depth M AM Sine wave M AM cos(Ω mAs will be described later, the modulation signal is m The optical filter 4 is a programmable optical filter made of LCoS or the like. Assuming the generation of asymmetric pulse waveforms, as will be described later, it is desirable that the optical filter 4 be able to control not only the amplitude (transmission) characteristics but also the phase characteristics.

[0020] The operating characteristics of this optical function generator (AM mode-locked fiber laser) and the design method of the optical filter 4 will be explained using the block diagram in Figure 2. In Figure 1, the loss of the resonator is L, the gain is G, and the transfer function of the optical filter 4 is F. A (ω). In this case, if the electric field amplitude of the light circulating in the resonator is a(t) and its spectrum is A(ω), then in the steady state, A(ω) satisfies the following equation (1):

[0021]

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[0022] where Φ[a(t)] is the Fourier transform of a(t), and Φ[(1+ M AM cosΩ m t)a(t)] is the signal (1 + M AM cosΩ m t)a(t) spectrum. Φ[(1+ M AM cosΩ m t)a(t)] is expressed by equation (2) using the spectrum A(ω) of a(t).

[0023] Therefore, equation (1) can be written as equation (3). A Solving for (ω), we obtain equation (4). The gain G is chosen to balance the loss L, so we can set GL = 1, and as a result, equation (4) gives F A (ω) is given by equation (5).

[0024]

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[0025] Therefore, when a desired pulse waveform a(t) is to be generated using an AM mode-locked laser, the spectrum A(ω) is used to calculate the transfer function F of the optical filter 4. A (ω) can be designed as shown in equation (5). As will be described later, F A (ω) is generally a complex function, and optical filters have not only amplitude transmission characteristics but also phase characteristics. Specifically, when the waveform is symmetric, such as Gaussian or SECH, F A (ω) has only a real part and does not have a phase characteristic. However, when the waveform is asymmetric, such as a single exponential function described in the seventh embodiment, F A (ω) has not only a real part but also an imaginary part, and the optical filter has a phase characteristic.

[0026] [First embodiment] In the first embodiment of the present invention, a Gaussian pulse can be generated. The waveform a(t) of the Gaussian pulse is given by equation (6). T is a parameter representing the pulse width, and a 2 (t) Full width at half maximum (FWHM) W p and T means W p =2(ln2) 1 / 2 T relationship. From the Fourier transform of equation (6), the spectrum A(ω) of the Gaussian pulse is given by equation (7). The shape of the optical filter 4 for generating this Gaussian pulse is given by equation (8) by substituting equation (7) into equation (5). By inserting this optical filter into the resonator instead of the Lorentz-type optical filter normally used in mode-locked lasers, a Gaussian pulse can be generated.

[0027]

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[0028] The transfer function F of the optical filter 4 used in this embodiment A An example of the shape of (ω) is shown in Figure 3(a). Here, the pulse width T = 6 ps (W p = 10 ps), modulation frequency Ωm = 2π×10 GHz, modulation index M AM = 1. The black dots in the figure represent the frequencies where longitudinal modes (10 GHz intervals) exist in the optical spectrum. A Although the base of (ω) gradually decays, it is possible to set a band limit to the extent that the waveform is not distorted. Figure 3(b) shows the shape of the filter that imposes a band limit of 200 GHz (±100 GHz) in Figure 3(a). Figures 3(c) and (d) show the results of computer analysis of the steady-state solution of the laser using this filter. Figure 3(c) shows the waveform of a steady-state pulse, and Figure 3(d) shows its spectrum and the ideal spectral shape (A(ω) in equation (7)) as black lines. It can be seen that this laser can output a Gaussian pulse.

[0029] [Second embodiment] In the second embodiment of the present invention, a SECH pulse can be generated. The waveform a(t) of the SECH pulse is given by equation (9). 2 (t) Full width at half maximum (FWHM) W p and T means W p =[ln(3+2×2 1 / 2 )]T. From the Fourier transform of equation (9), the spectrum A(ω) of the sech pulse is given by equation (10). The shape of the optical filter 4 for generating this sech pulse is given by equation (11) by substituting equation (10) into equation (5).

[0030]

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[0031] The transfer function F of the optical filter 4 used in this embodiment A An example of the shape of (ω) is shown in Figure 4(a). Here, the pulse width T = 6 ps (W p = 10.6 ps), modulation frequency Ω m = 2π×10 GHz, modulation index M AM = 1. The black dots in the figure represent the frequencies where longitudinal modes (10 GHz intervals) exist in the optical spectrum. ASince (ω) has a flat base, it is necessary to set a band limit. Figure 4(b) shows the shape of the filter that imposes a band limit of 200 GHz (±100 GHz) on the filter in Figure 4(a). Figures 4(c) and (d) show the results of computer analysis of the steady-state solution of the laser using this filter. Figure 4(c) shows the waveform of a steady-state pulse, and Figure 4(d) shows its spectrum and the ideal spectral shape (A(ω) in Equation (10)) as black lines. It can be seen that this laser can output SECH pulses. While optical nonlinearity is essential for outputting SECH pulses in a conventional mode-locked laser, the unique feature of the present invention is that optical nonlinearity is not required.

[0032] [Third embodiment] In the third embodiment of the present invention, a bi-exponential pulse can be generated. The waveform a(t) of the bi-exponential pulse is given by equation (12). 2 (t) Full width at half maximum (FWHM) W p and T means W p = (ln2)T. From the Fourier transform of equation (12), the spectrum A(ω) of the double exponential pulse is given by equation (13). The shape of the optical filter 4 for generating this double exponential pulse is given by equation (14) by substituting equation (13) into equation (5).

[0033]

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[0034] The transfer function F of the optical filter 4 used in this embodiment A An example of the shape of (ω) is shown in Figure 5(a). Here, the pulse width T = 6.25 ps (W p = 4.33 ps), modulation frequency Ω m = 2π×10 GHz, modulation index M AM = 1. The black dots in the figure represent the frequencies where longitudinal modes (10 GHz intervals) exist in the optical spectrum. ASince (ω) has a shape with a flat base, it is necessary to set a band limit. Figure 5(b) shows the shape of the filter that imposes a band limit of 640 GHz (±320 GHz) on Figure 4(a). Figures 5(c) and (d) show the results of computer analysis of the steady-state solution of the laser using this filter. Figure 5(c) shows the waveform of a steady-state pulse, and Figure 5(d) shows its spectrum and the ideal spectral shape (A(ω) in equation (13)) as black lines. It can be seen that this laser can output both exponential pulses.

[0035] [Fourth embodiment] In the fourth embodiment of the present invention, a triangular pulse can be generated. The waveform a(t) of the triangular pulse is given by equation (15). 2 (t) Full width at half maximum (FWHM) W p and T means W p =(2-2 1 / 2 )T. From the Fourier transform of equation (15), the spectrum A(ω) of the triangular pulse is given by equation (16). The shape of the optical filter 4 for generating this triangular pulse is given by equation (17) by substituting equation (16) into equation (5).

[0036]

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[0037] The transfer function F of the optical filter 4 used in this embodiment A An example of the shape of (ω) is shown in Figure 6(a). Here, the pulse width T = 37.5 ps (W p = 22.0 ps), modulation frequency Ω m = 2π×10 GHz, modulation index M AM = 1. The black dots in the figure represent the frequencies where longitudinal modes (10 GHz intervals) exist in the optical spectrum. ASince (ω) does not attenuate and maintains a constant magnitude even as the frequency increases, it is necessary to set a band limit. Figure 6(b) shows the shape of the filter in Figure 6(a) that imposes a band limit of 640 GHz (±320 GHz). Figures 6(c) and (d) show the results of computer analysis of the steady-state solution of the laser using this filter. Figure 6(c) shows the waveform of a steady-state pulse, and Figure 6(d) shows its spectrum and the ideal spectral shape (A(ω) in equation (16)) as black lines. It can be seen that a triangular pulse can be output from this laser.

[0038] [Fifth embodiment] In the fifth embodiment of the present invention, triangular pulses can be generated with higher accuracy than in the fourth embodiment. In this embodiment, a modulation signal for driving the optical intensity modulator 3 is a pulse having an angular frequency Ω m sine wave plus 3Ω m The modulation function is given by equation (18). Here, the coefficient 1 / 9 is the 3Ω m This modulation function is shown in Figure 7(a). The black line shows the normal sine wave cosΩ. m t, it can be seen that the shape of the modulated signal is closer to a triangle. When the modulation function of Equation (18) is used, the transfer function F of the optical filter 4 for generating the triangular pulse is A (ω) is given by equation (19) instead of equation (17).

[0039]

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[0040] This F A The shape of the (ω) is shown in Figure 7(b), and the shape with a band limit of 640 GHz (±320 GHz) is shown in Figure 7(c). The steady-state solution of the laser obtained by computer analysis using this filter is shown in Figures 7(d) and (e). Figure 7(d) shows the waveform of the steady-state pulse, and Figure 7(e) shows its spectrum and the ideal spectral shape (A(ω) in equation (16)) as black lines. 3Ω mIt can be seen that by superimposing the harmonics of the modulated signal, a triangular pulse can be generated with higher accuracy than in Figure 6(c).

[0041] [Sixth embodiment] In the sixth embodiment of the present invention, a parabolic pulse can be generated. The waveform a(t) of the parabolic pulse is given by equation (20). 2 (t) Full width at half maximum (FWHM) W p and T means W p =2(1-1 / 2 1 / 2 )T. From the Fourier transform of equation (20), the spectrum A(ω) of the parabolic pulse is given by equation (21). The shape of the optical filter 4 for generating this parabolic pulse is given by equation (22) by substituting equation (21) into equation (5).

[0042]

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[0043] The transfer function F of the optical filter 4 used in this embodiment A An example of the shape of (ω) is shown in Figure 8(a). Here, the pulse width T = 25.0 ps (W p = 27.1 ps), modulation frequency Ω m = 2π×10 GHz, modulation index M AM = 1. The black dots in the figure represent the frequencies where longitudinal modes (10 GHz intervals) exist in the optical spectrum. A Since (ω) does not attenuate and maintains a constant magnitude even as the frequency increases, it is necessary to set a band limit. Figure 8(b) shows the shape of the filter that imposes a band limit of 640 GHz (±320 GHz) on the frequency in Figure 8(a). Figures 8(c) and (d) show the results of computer analysis of the steady-state solution of the laser using this filter. Figure 8(c) shows the waveform of a steady-state pulse, and Figure 8(d) shows its spectrum and the ideal spectral shape (A(ω) in equation (21)) as black lines. It can be seen that a parabolic pulse can be output from this laser.

[0044] [Seventh embodiment] In the above-described embodiment, a pulse having a time-symmetric waveform is targeted, but in the seventh embodiment of the present invention, a semi-exponential pulse can be generated as an example of a pulse having an asymmetric waveform. The waveform a(t) of the semi-exponential pulse is given by equation (23). a 2 (t) Full width at half maximum (FWHM) W p and T means W p = (ln2)T / 2. From the Fourier transform of equation (23), the spectrum A(ω) of the single-exponential pulse is given by equation (24). Unlike the symmetric pulse (first to sixth embodiments), the spectrum of the asymmetric pulse has not only a real part but also an imaginary part. The shape of the optical filter 4 for generating this single-exponential pulse is given by equation (25) by substituting equation (24) into equation (5). Since A(ω) has an imaginary part, the optical filter also has an imaginary part. Therefore, the optical filter 4 has not only amplitude but also phase characteristics.

[0045]

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[0046] The transfer function F of the optical filter 4 used in this embodiment A An example of the shape of (ω) is shown in Figures 9(a) and 9(b). A (ω) is the real part, and Figure 9(b) is the imaginary part. Here, the pulse width T = 6.25 ps (W p = 2.17 ps), modulation frequency Ω m = 2π×10 GHz, modulation index M AM = 1. The black dots in the figure represent the frequencies where longitudinal modes (10 GHz intervals) exist in the optical spectrum. ASince (ω) does not attenuate and maintains a constant magnitude even as the frequency increases, it is necessary to set a band limit. In Figures 9(a) and (b), the shape of the filter with a band limit of 640 GHz (±320 GHz) is shown in Figure 9(c) (real part) and Figure 9(d) (imaginary part). The steady-state solution of the laser obtained by computer analysis using this filter is shown in Figures 9(e) and (f). Figure 9(e) shows the waveform of a steady-state pulse, and Figure 9(f) shows its spectrum and the ideal spectral shape (A(ω) in Equation (24)) as black lines. It can be seen that this laser can output a single-exponential pulse.

[0047] A specific experimental example will be shown below. In the experiment, as shown in FIG. 10, a harmonic AM mode-locked erbium fiber laser (see Non-Patent Document 10) oscillating at a wavelength of 1.55 μm and having a repetition rate of 10 GHz was used, and an LCoS element was inserted into the resonator (resonator length 15.6 m). The filter function F A (ω) is implemented in the LCoS element using software. The frequency resolution of the LCoS element is 1 GHz. In the following experimental example, the modulation index is M AM = 1.

[0048] The shape of the optical filter used to generate a Gaussian pulse in the first embodiment of the present invention is shown in Fig. 11. Fig. 11(b) is an enlarged view of Fig. 11(a). The solid line indicates the F A The broken line shows the filter shape implemented on the LCoS element, which is an approximation of this with a step function every 10 GHz. The LCoS element used in the experiment originally has a frequency resolution of 1 GHz, but in consideration of fluctuations in the longitudinal mode frequency of the laser, the F A (ω) is approximated as a step, and this is implemented in an LCoS element.

[0049] The waveform and optical spectrum of the Gaussian pulse generated using this filter are shown in Figure 12. Figure 12 (a) shows the intensity waveform a observed with an optical sampling oscilloscope. 2(t) and (b) show the square roots of these values ​​converted to amplitude a(t), and (c) shows the optical spectrum A(ω) observed with an optical spectrum analyzer, displayed in dB (20 log|A(ω)|). The black line shows the experimental results, and the solid line shows the computer analysis results shown in Figure 3(c) and (d). The two lines match well, demonstrating that Gaussian pulses can be generated as designed using the optical filter in Figure 11. Furthermore, the time-bandwidth product is 0.44, demonstrating that TL Gaussian pulses can be obtained directly from the laser.

[0050] The shape of the optical filter used to generate the sech pulse in the second embodiment of the present invention is shown in Figure 13. Figure 13(b) is an enlarged view of Figure 13(a). The solid line indicates the F A The filter (Fig. 4(b)) has a band limit of 200 GHz (ω), and the dashed line shows the filter shape implemented on the LCoS element after approximating this with a step function every 10 GHz.

[0051] The waveform and optical spectrum of the SECH pulse generated using this filter are shown in Figure 14. Figure 14(a) shows the intensity waveform a observed with an optical sampling oscilloscope. 2 (t) and (b) show the square roots of these values ​​converted to amplitude a(t), and (c) shows the optical spectrum A(ω) observed with an optical spectrum analyzer, displayed in dB (20 log|A(ω)|). The black line shows the experimental results, and the solid line shows the computer analysis results shown in Figure 4(c) and (d). The two lines match well, demonstrating that sech pulses can be generated as designed using the optical filter in Figure 13. Furthermore, the time-bandwidth product is 0.32, demonstrating that TL sech pulses can be obtained directly from the laser.

[0052] The shape of the optical filter used to generate the biexponential pulse in the third embodiment of the present invention is shown in Figure 15. Figure 15(b) is an enlarged view of Figure 15(a). The solid line indicates the F AThe filter (Fig. 5(b)) has a band limit of 640 GHz (ω), and the dashed line shows the filter shape implemented on the LCoS element after approximating this with a step function every 10 GHz.

[0053] The waveform and optical spectrum of the biexponential pulse generated using this filter are shown in Figure 16. Figure 16(a) shows the intensity waveform a observed with an optical sampling oscilloscope. 2 (t) and (b) show the square roots of these values ​​converted to amplitude a(t), and (c) shows the optical spectrum A(ω) observed with an optical spectrum analyzer, displayed in dB (20 log|A(ω)|). The black line shows the experimental results, and the solid line shows the computer analysis results shown in Figures 5(c) and (d). The two lines match well, demonstrating that the optical filter in Figure 15 can generate bi-exponential pulses as designed.

[0054] The shape of the optical filter used to generate the triangular pulse in the fourth embodiment of the present invention is shown in Fig. 17. Fig. 17(b) is an enlarged view of Fig. 17(a). The solid line indicates the F A The filter (Fig. 6(b)) has a band limit of 640 GHz (ω), and the dashed line shows the filter shape implemented on the LCoS element by approximating this with a step function every 10 GHz.

[0055] The waveform and optical spectrum of the triangular pulse generated using this filter are shown in Figure 18. Figure 18(a) shows the intensity waveform a observed with an optical sampling oscilloscope. 2 (t) and (b) show the square roots of these values ​​converted to amplitude a(t), and (c) shows the optical spectrum A(ω) observed with an optical spectrum analyzer, displayed in dB (20 log|A(ω)|). The black line shows the experimental results, and the solid line shows the computer analysis results shown in Figures 6(c) and (d). The two lines match well, demonstrating that the optical filter in Figure 17 can generate bi-exponential pulses as designed.

[0056] The shape of the optical filter used to generate the parabolic pulse in the sixth embodiment of the present invention is shown in Fig. 19. (a) in the figure shows the absolute value, and (b) shows the phase. The solid line shows F in equation (22). A The filter (Fig. 8(b)) has a band limit of 640 GHz (ω), and the dashed line shows the filter shape implemented on the LCoS element by approximating this with a step function every 10 GHz.

[0057] The waveform and optical spectrum of the parabolic pulse generated using this filter are shown in Figure 20. Figure 20(a) shows the intensity waveform a observed with an optical sampling oscilloscope. 2 (t) and (b) show the square roots of these values ​​converted to amplitude a(t), and (c) shows the optical spectrum A(ω) observed with an optical spectrum analyzer, displayed in dB (20 log|A(ω)|). The black line shows the experimental results, and the solid line shows the computer analysis results shown in Figures 8(c) and (d). The two lines match well, demonstrating that the optical filter in Figure 19 can generate bi-exponential pulses as designed.

[0058] The shape of the optical filter used to generate a single-exponential pulse in the seventh embodiment of the present invention is shown in Fig. 21. (a) of the figure shows the amplitude characteristics, and (b) of the figure shows the phase characteristics. The solid line in (a) of the figure shows the F A The filter (Fig. 9(c)) has a band limit of 640 GHz (ω), and the dashed line shows the filter shape implemented on the LCoS element by approximating this with a step function every 10 GHz.

[0059] The waveform and optical spectrum of the single-exponential pulse generated using this filter are shown in Figure 22. Figure 22 (a) shows the intensity waveform a observed with an optical sampling oscilloscope. 2 (t) and (b) are the amplitudes a(t) converted by taking the square root, and (c) is the optical spectrum A(ω) observed with an optical spectrum analyzer, displayed in dB (20 log|A(ω)|). The black line is the experimental result, and the solid line is the computer analysis result shown in Figures 9(e) and (f). The two are in good agreement, demonstrating that the optical filter in Figure 21 can generate bi-exponential pulses as designed. [Industrial Applicability]

[0060] As explained in detail above, the present invention makes it possible to easily generate pulses with any time waveform by appropriately designing the amplitude and phase characteristics of an optical filter inserted into a laser resonator. Pulse trains with time waveforms such as exponential, triangular, and parabolic waveforms obtained by the present invention can be used in a wide range of applications, including signal pulses for ultrafast time-division multiplexed optical communications and sampling pulses for ultrafast measurement. [Explanation of symbols]

[0061] 1. Optical fiber 2. Optical amplifier 3 Optical Intensity Modulator 4 Optical Filter 5. Polarization-maintaining erbium fiber 6 Pump LD 7 WDM coupler 8 Intensity Modulator 9 Etalon 10 PZT element 11 Coupler 12 Isolator 13 LCoS element 14 Amplifier 15 Phase Shifter 16 10 GHz clock extraction circuit

Claims

1. an AM mode-locked laser including an optical intensity modulator, an optical amplifier, and an optical filter in a laser resonator; the optical intensity modulator is provided so as to be drivable by a sine wave having a repetitive angular frequency of Ω m ; The optical filter has variable amplitude and phase characteristics, and the amplitude and phase characteristics are given by a transfer function FA(ω) expressed by the following equation (1) using the modulation depth M AM of the optical intensity modulator, the spectrum A(ω) of the optical pulse to be output, and functions A(ω-Ω m) and A(ω+Ω m) ​​obtained by shifting A(ω) by Ω m in both positive and negative directions: [Equation 1] By setting the amplitude and phase characteristics according to the shape of the optical pulse to be output, it is possible to generate an optical pulse having any shape. An optical function generator characterized by:

2. An AM mode-locked laser having an optical intensity modulator, an optical amplifier, and an optical filter in a laser resonator, the optical intensity modulator is provided so as to superimpose a harmonic of Ω m on a driving sinusoidal modulation signal having a repetition angular frequency Ω m ; the optical filter has variable amplitude and phase characteristics, and the amplitude and phase characteristics consist of functions A(ω-Ω m ) and A(ω+Ω m ) obtained by repeatedly shifting the spectra A(ω) and A(ω) of an optical pulse to be output in positive and negative directions by an angular frequency Ω m , and functions A(ω-NΩ m ) and A(ω+NΩ m ) obtained by shifting A(ω) in positive and negative directions by a harmonic NΩ m of Ω m ; By setting the amplitude and phase characteristics according to the shape of the optical pulse to be output, it is possible to generate an optical pulse having any shape. An optical function generator characterized by:

3. An optical function generator as described in claim 1 or 2, characterized in that the optical filter is configured to set a band limit on the amplitude and phase characteristics according to the spectral width of the optical pulse to be output, thereby obtaining a TL (Transform-limited) pulse.

4. The optical filter converts the amplitude characteristic into a Gaussian function A(ω), and repeats A(ω) at an angular frequency Ω m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m 2. An optical function generator according to claim 1, wherein said optical function generator is capable of generating a Gaussian pulse by applying a voltage to said optical function generator.

5. The optical filter calculates the amplitude characteristic by a sech function A(ω) and repeats A(ω) at an angular frequency Ω m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m 2. An optical function generator according to claim 1, wherein the optical function generator is capable of generating a sech pulse by applying a signal to the optical function generator.

6. The optical filter calculates the amplitude characteristic by a Lorentz function A(ω) and repeating A(ω) at an angular frequency Ω m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m 2. An optical function generator according to claim 1, wherein said optical function generator is capable of generating a pulse having a shape of a double exponential function by applying a voltage to said optical function.

7. The optical filter calculates the amplitude characteristic by a squared sinc function A(ω) and repeating A(ω) at an angular frequency Ω m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m 2. An optical function generator according to claim 1, wherein said optical function generator is capable of generating a pulse having a triangular shape by applying a voltage to said optical function generator.

8. The optical intensity modulator uses a modulation signal with an angular frequency of 3 Ω. m A sine wave of The optical filter calculates the amplitude characteristic by a squared sinc function A(ω) and repeating A(ω) at an angular frequency Ω m and 3 ohms m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m ), A(ω-3Ω m ), A(ω+3Ω m ) by which a triangular pulse can be generated.

3. An optical function generator according to claim 2.

9. The optical filter calculates the amplitude characteristic as a function sin ω / ω 3 and cos ω / ω 2 A(ω) is given by the sum of A(ω) and A(ω) is repeated at angular frequency Ω m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m 2. An optical function generator according to claim 1, wherein said optical function generator is capable of generating a pulse having a parabolic shape by applying a pulse having a parabolic shape to said optical function generator.

10. The optical filter calculates the amplitude and phase characteristics as a Lorentz function A(ω), and repeats A(ω) at an angular frequency Ω m A function A(ω-Ω) shifted positively or negatively by m ), A(ω+Ω m 2. An optical function generator according to claim 1, wherein said optical function generator is capable of generating a single exponential pulse by applying a voltage to said optical function generator.

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