Optical coherent light pulses as short as a few femtoseconds (1 femtosecond = 1 fs = 1×10-15sec) have been generated, and it currently becomes a routine work to generate sub 100-fs optical pulses. The recent unification of phase control of ultrawide-bandwidth laser with ultrafast laser technology has enabled the precise generation of optical frequency combs [6-18]. It is now possible to control the carrier-envelope phase of ultrafast pulses. It appears to have all the experimental techniques in hand for complete control over coherent light-matter interaction. These tools include the ability to generate coherent optical pulses with arbitrary shape, precisely control frequency and phase, and synthesize coherent light from multiple sources, etc.
Numerous phenomena that happen on such short time scales are important to study. Some key processes in biology –such as photosynthesis, vision transduction, protein-folding, etc. – contain events that occur on fs time scale. Crucial processes in chemistry – such as molecular vibrations, re-orientations, and collisions in
condensed-phase – also occur on this time scale. Several important events in physics and engineering—such as high-lying excited-state lifetimes, photo-ionization, and photo-excited electron-hole relaxation in optical detectors and optoelectronics – are very fast too. Therefore to probe more deeply into the ultrafast light-matter interaction with a more controllable way is an important step toward an effective design and control of advanced materials and devices.
To achieve the goal, first we have to prepare a light pulse which is shorter than the event that we want to analyze. In general, any optical measurement of a medium or a device is ultimately limited by our ability to measure and control the light into
and out of the medium being studied. Complete-field characterization methods for optical pulse diagnosis can be categorized into two different types: Frequency- resolved optical gating (FROG), sonogram, and spectral phase interferometry for direct electric-field reconstruction (SPIDER), etc. belong to the first category. They can measure but can’t compensate the ultrafast pulses involved. The second class of pulse characterization methods involves a pulse shaper, a nonlinear detection method and global optimization algorithm. This approach is capable of doing both pulse characterization and compensation simultaneously. This capability is extremely useful and can be incorporated into the ultrafast laser system being used.
This thesis presents theoretical and experimental studies on the design, characterization, and adaptive coherent control of ultrafast optical pulses. The application of the methodology on nonlinear optical microscopy is also given. This thesis is organized as follows: Chapter 2 shows our experimental setup of the laser system and femtosecond pulse shaping apparatus. Some critical procedures for aligning the pulse shaper are briefly described. We also demonstrate how to design and synthesize optical pulses by using Gerchberg-Saxton algorithm. Simulated and experimental results are shown for comparison. Concepts about how to improve this method and related discussion are offered.
In Chapter 3, we describe first a newly developed phase-freezing scheme. Some simulated results are presented in order to design a better phase compensation scheme with high immunity to noise. Applications of the method on several types of saturable Bragg reflector (SBR) devices are shown and finally discussion is offered.
In Chapter 4, application of the new phase freezing scheme on nonlinear optical microscopy is presented. We applied our apparatus for complete-field characterization and compensation for phase distortion from laser optics, microscope objective, and sample surfaces. One of the major concerns in this chapter is to find out the relation
between the absorption and spectral sensitivity. The influence of an intermediate level on the coherent-control nonlinear optical microscopy is also discussed. Finally, the conclusion and discussion are made.
Chapter 2 Synthesis of Femtosecond Optical Pulses
In this chapter, we shall introduce our laser system and phase-only pulse shaping apparatus. A Cr4+:Forsterite femtosecond laser is first described in Section 2.1. The phase-only pulse shaping apparatus and some critical procedures for aligning the pulse shaper will be presented in Section 2.2. Some application examples of the setup for synthesis of femtosecond optical pulses with Gerchberg-Saxton algorithm are shown in section 2.3.
2.1 Cr
4+:Forsterite Femtosecond Laser System
The schematic of a Cr4+:Forsterite femtosecond laser system from Avesta Project Ltd. (http://www.avesta.ru), which can generate ultrashort optical pulses in near infrared (λ~ 1250 nm), is shown in Figure 2.1. The laser is self mode-locked by keeping lasing longitudinal cavity modes in phase to produce ultrashort near
transform-limited optical pulses with pulse duration about 50 fs. The Cr4+:Forsterite oscillator gives pulses with a typical full-width-at-half maximum (FWHW) bandwidth of about 45 nm at a repetition rate of 76 MHz and average power 270mW. The
ultrashort pulse duration can yield an enormous peak power density after focusing.
The Cr4+:Forsterite laser is pumped by a 7.8-W Ytterbium-doped fiber laser.
Fig 2.1: Left: Optical schematic of Cr4+:Forsterite laser system. Right: The spectrum of the ultra short optical pulses generated from the Cr4+:Forsterite laser
2.2 All-Reflective Pulse Shaping Apparatus
Our phase-only pulse shaper follows the design of 4-f dispersionless configuration, which consists of a pair of gratings (600 grooves/mm), two spherical reflectors with a focal length of f=10 cm, and a liquid crystal spatial light modulator (SLM, Cambridge Research and Instrumentation Inc. (CRI) Woburn, MA, SLM-128). The SLM consists of 128 2-mm-high phase-modulating elements with 97-µm width, and a 3-µm gap between adjacent pixels.
Fig 2.2: Schematic and real setup of our phase-only pulse shaper
To achieve minimum aberration and a dispersionless condition, properly aligned the apparatus is required. We devise an effective procedure to ensure that such conditions
have been met. The critical alignment steps are depicted in the following:
1. First let the laser beam go through a BBO crystal to generate a visible second-harmonic beam at 628 nm.
2. Adjusting the red input beam to propagate on a horizontal plane which is parallel to the optical table.
3. Checking out all the diffraction beams propagate on the horizontal plane. The broadband optical spectral components should also spread on the plane.
4. Place the first spherical mirror at approximately one focal length away from the first grating. Rotate the first grating to let the second-order diffracted beam to be centered on the spherical mirror.
5. Make sure that the image is on the SLM plane and all spreading optical spectral components still propagate on the horizontal plane.
6. Position the second spherical mirror at a distance of 2f from the first spherical mirror. Adjusting the angle of the second spherical mirror to let all spectral components approximately overlapped on the center of the second grating. Be sure that all beams still propagate on the horizontal plane.
7. Fine tuning the position and the angle of the second grating to let all diffracted spectral components collimate. One can put a mask on the SLM plane and just let two spectral components pass through. This two components will cross on the grating by adjusting the position of G’, and let the diffracted components into the same direction by adjusting the angle of G’.
8. Finely adjusting the distance between the two spherical mirrors to optimize the output spot for as circular as possible. Make sure the distance between these two spherical mirrors to be 2f. The output spot shall look like circular in far field.
9. Repeat step 7 and 8 until a circular spot in the far field is obtained.
10. Place SLM at approximately the image plane of the first spherical mirror where
individual spectral components are focused to their minimum size.
2.3 Synthesis of Femtosecond Optical Pulses with Gerchberg-Saxton Algorithm
In this section, we shall demonstrate synthesis of femtosecond optical pulse with arbitrary pulse profile by using Gerchberg-Saxton algorithm (GSA).
2.3.1 Brief Description of Gerchberg-Saxton Algorithm
Fig 2.3: Schematic of the Gergberg-Saxton algorithm employed for retrieval of the spectral phase of the electric field desired. The red point denotes the starting point of the algorithm and the blue spot indicates the monitoring point for the deviation between the target pulse { I t( )} and the temporal pulse { E t( ) } at this moment.
In literature, GSA had been used for recovering two-dimensional spatial phase information of images when only the amplitude of the optical field is available at near and far-field planes [23, 24, 25]. Fig. 2.3 displays a flow chart of the procedure, where { I( )ω } denotes the available spectral amplitude, { E( )ω } is the amplitude of the field, { I t( )} is the amplitude of the target pulse, { E t( ) } is the temporal field
profile, and {β ω( )} is the spectral phase needed for producing the desired target pulse from an input pulse.
The pulse synthesis procedure starts with transforming a trial electric field to the frequency domain. We replace the resulting { E( )ω } by { I( )ω } (the measured spectrum of the input pulse) while leaving the phase unaltered. Then the field is transformed back to the time domain and replaces { E t( ) } with { I t( )} while leaving the phase unaltered. The procedure is repeated until the deviation between the amplitude of the desired pulse { I t( )} and temporary field { E t( ) } as small as possible. Usually, the whole procedure can be achieved within about 20 iterations to yield the desired spectral phase profile { ( )β ω }. By using the algorithm we determine the spectral phase pattern needed by the SLM (128-pixel 1D LC array) for producing the target pulse { I t( )}.
2.3.2 Simulation of the Optical Synthesis Procedure
To successfully implement the algorithm, first we have to measure the spectrum of the input laser pulse ( I( )ω ). To synthesize the desired pulse we express the target pulse profile ( )I t on a FFT grid, which corresponds to the number of the SLM elements. We start the algorithm at the position marked by red spot in Fig. 2.3. A trial electric field with a spectral amplitude being the square root of the measured spectrum { I( )ω } and an initial spectral phase { ( )β ω } being either constant or random noise distribution is used. We then launch the algorithm until the deviation between the amplitude of the target pulse ( I t( )) and the temporary field (E t( ) ) estimated at the blue spot in Fig. 2.3 is less than an error upper limit. We can also
implement a proper error checking criterion to automate the procedure.
Four examples are presented in Figure 2.4. Examples shown in Figure 2.4(a) and 2.4(b) are aimed to demonstrate how to precisely synthesize periodic pulses from a single input pulse. Note that only spectral phase modulation is used to achieve the goal. The other two examples are used to test whether GS algorithm is capable of finding the spectral phase pattern required for generating a specified waveform.
The first row of the Figure 2.4 shows the available spectral amplitude { I( )ω } in blue-colored curve and the desired spectral phase { ( )β ω } shown by the green curve. The second row presents the temporal intensity profile of the target pulse (red-colored line) and the best output pulse (black line). In the third row, the root-mean-squared (RMS) deviation of the best temporal profile from the target profile is shown as a function of iterations, which indicates that a satisfactory result can be obtained with only 10 to 20 iterations. The initial random phase pattern yields an optimal result faster than that with a constant phase pattern [24]. Although the exact number of iterations depends on the initial phase pattern, the algorithm converges to the same solution in all cases being studied.
a b
c d
Fig 2.4: Simulated results to demonstrate the optical synthesis of femtosecond optical pulses with GSA. The first figure row shows the spectrum of the input pulse (blue-colored line) and the spectral phase profile (green line) needed for generating the target pulse. The second row presents the comparison of the resulting output pulse profile from pulse shaper (black line) and the target pulse (red line). The third row shows the root-mean-squared (RMS) deviation of the best result of temporal pulse profile from the target pulse as a function of iterations. The target pulses used are (a) pulses train separated by 1 ps; (b) pulses train separated by 0.5 ps; (c) 0.55-ps rectangular pulse; and (d) 200-fs pulse separated with an arbitrary pulse by 1-ps.
2.3.3 Experimental Results of Optical Synthesis of Femtosecond Optical Pulses
Experimental verification of the simulated results with GSA was carried out by using second-harmonic generation frequency-resolved optical gating (SHG-FROG) technique. The optical phase retardation patterns obtained from GSA were uploaded to our phase-only pulse shaper with an LC SLM-128 in the Fourier plane. The output pulse from the shaper is brought to a home-made SHG-FROG setup. When the optical phase retardation pattern of Figures 2.4(a) and 2.4(b) were uploaded to SLM128, the resulting FROG traces are presented in in the Figs. 2.5(a) and 2.5(b), respectively.
Some differences between simulated and experimental results may come from the actual spectral resolution of the SLM, the diffraction caused by SLM, and the non transform-limited pulses from laser. The results confirm that we can indeed synthesize femtosecond optical pulses with a specific period. However, if we want to
synthesize optical pulse more accurately, we have to use a feedback signal to inform computer about the current status of the temporal pulse. Relying on this signal, computer could know how to improve the optical phase retardation pattern to approach the desired target pulse [8].
Fig 2.5: The first row shows the measured FROG traces of the output pulses from the pulse shaper with optical phase retardation patterns of Figs. 2.4(a) and 2.4(b). The second row shows the corresponding intensity autocorrelation curves obtained by integrating the FROG traces over the time axis. The third rows show the calculated autocorrelation curves of the electric fields with the optical phase retardation patterns of Figures 2.4(a) and 2.4(b).
Chapter 3 Complete-Field Characterization with Freezing Phase Scheme
In the quest to control and steer the quantum states of complex systems, an attractive scheme is adaptive laser pulses control, as first introduced by Judson and Rabitz [1]. An algorithm is employed to tailor a coherent optical field to prepare specific products on the basis of fitness information. The concept appears to be universal and several progresses have already been reported in literature [1-11].
By using the broadband property of an ultrashort laser pulse, Silberberg et al.
had developed a coherent control scheme to demonstrate selective imaging of molecules with single-pulse coherent anti-Stokes Raman scattering [2]. Similar enhancement with coherent control technique was also observed in two-photon fluorescence process [3, 4]. Along this study, the question remained is whether the optimal laser field contains a set of rational rules that govern the dynamics. Recent study appears to reveal that the answer could be affirmative [5]. Therefore, the purpose of femtosecond coherent control study is not only to control the evolution of a complex system but also to deduce the detailed dynamic mechanism from the optimal laser field used.
Coherent control technology has been demonstrated with femtosecond optical pulses by using a pulse shaper with spatial light modulation devices [6-18]. The simplest approach of pulse shaping with conserved pulse energy is to adjust spectral phase for tailoring the pulse shape [6-11]. We can imagine the spectral phase components involved in a coherent pulse to be a system of interacting particles. If a temperature sensor to reveal how cold it is at zero degree and a thermal pump to control the amount of heat to be added into or taken from the system are available, information about the interacting-particles can be yielded by studying how the system
responses to a thermal excitation.
In this chapter, we implement this concept into a coherent control setup for yielding both functions of adaptive pulse shaping and characterization [4]. A spatial light modulator (SLM) plays the role of thermal pump and a phase-sensitive photon detector provides the thermal-sensing function. We note that to generate the highest second-harmonic signal from a transparent nonlinear optical crystal, all the spectral phase components of a coherent pulse shall be in-phase (hereafter this state is termed as frozen-phase state). We use SLM to manipulate the phases of the spectral components and adaptively reduce the deviation from the frozen-phase state with our new phase compensation scheme.
This chapter is organized as follows: in Section 3.1, we present the theoretical background of the new freezing phase scheme. Our experimental setup is then detailed in Section 3.2. We offer some simulation results in Section 3.3.A in order to develop an efficient phase compensation scheme with highest noise immunity. Finally experimental results of several types of SBR devices are presented and discussion is offered in Section 3.3.B.
3.1 THEORETICAL BACKGROUND
To verify the functionality of the freezing phase scheme, we first express optical field in terms of its spectral components in 128 elements:
( )
where ∆ω is the width of spectral components involved in the coherent pulse, φn and An denote the phase constant and amplitude of each spectral component, and
ω0 is the optical carrier frequency.
In a typical 4-f pulse shaping setup, the pulse spectrum is angularly dispersed by
a grating [19]. The 128-pixels SLM can be used to impose a phase retardation pattern {Θn} on the optical spectrum and transforms the coherent field into a shaped field of
( ) produce the shortest pulse and therefore the highest peak intensity. Equation (3-2) indicates that the peak amplitude of the shaped field E(t) can reach a maximum value when φn = −Θ . n
We first note that two-beam interference can accurately yield the information of phase difference. In brief our algorithm can first divide the elements of SLM into two groups:
By changing one phase and let the other interfere with each other. The
second-harmonic (SH) signal generated from a nonlinear optical crystal with the optical coherent pulse can vary with
4 In other words, SLM can be used to make those two spectral groups in-phase.
To further illustrate the freezing phase procedure, we use four phasors to represent the spectral phase profile of a coherent optical pulse. The optical field can therefore be simplified as i i
i
( . The distorted phase profile of the pulse in the complex field plane is shown in Fig. 3.1(a). To freeze the spectral phases, we first
pick up a spectral component and align the phasor with the summed direction of the rest spectral components by using SLM to introduce a compensation phase.
Specifically, for example, we can combineν1e ,iφ1 ν2eiφ2 and ν3eiφ3 into the reference group and allow ν4eiφ4to vary (see Fig. 3.1(b)). The same procedure is repeated onν3eiφ3,ν2eiφ2 and ν1e (Fig. 3.1(c) →(e)). In Fig. 3.1(f) a final fine tuning is iφ1 performed on ν4eiφ4 again to achieve a frozen phase state.
Fig. 3.1: (a→f) corresponding intensity autocorrelation curves obtained by integrating the FROG traces over the time axis.
3.2 EXPERIMENTAL DETAILS
Figure 3.2 presents the schematic of an adaptive pulse shaping apparatus19 used in this study. The laser system is a Cr4+: forsterite laser pumped by a diode-pumped Yb: fiber laser (IPG Photonics, Ltd.). A typical output of the Cr: forsterite laser was 280 mW of average power at a repetition rate of 76 MHz with a 7.5-W pump. The central wavelength is 1.252 µm, and a typical full-width-at-half maximum (FWHM) bandwidth was approximately 42 nm, corresponding to 50-fs pulse duration. All those experimental setup is mentioned as previous chapter.
The pulse is tailored by a pulse shaper consisting of a pair of gratings (600 g/mm), two concave reflectors with a focal length of f =10 cm, and a liquid crystal SLM (Cambridge Research and Instrumentation Inc. (CRI) Woburn, MA, SLM-128).
The SLM consists of 128 97-µm-wide pixels, with a 3-µm gap between adjacent pixels. After reassembled by the output grating, the shaped pulse is focused onto a sample under test. The phase distortion in the reflected optical pulse can be pre-compensated by the SLM. An optical pulse with constant phase can therefore be yielded before a 3-mm thick type-I β-Ba2BO4 (BBO) second harmonic generation (SHG) crystal. Note that transform-limited pulse with constant phase can produce a maximum second-harmonic (SH) signal from a transparent nonlinear optical crystal.
We therefore combine BBO SHG with a photodiode to offer a functionality of constant phase detection. The photodiode signal is sent to a computer for generating phase compensating pattern with the freezing-phase algorithm.
Fig. 3.2: Schematic of the adaptive coherent control system with an all reflective 4-f
Fig. 3.2: Schematic of the adaptive coherent control system with an all reflective 4-f