READ ME File For 'Dataset in support of the PhD thesis 'High-energy ultrafast Ytterbium-doped fibre laser technologies'

Dataset DOI https://doi.org/10.5258/SOTON/D3896

ReadMe Author: Jikun Yan, University of Southampton [OPTIONAL add ORCID ID]

This dataset supports the publication:
AUTHORS: Jikun Yan
TITLE: Dataset in support of the PhD thesis 'High-energy ultrafast Ytterbium-doped fibre laser technologies
PAPER DOI IF KNOWN


This dataset contains experimental data for the paper:


The figures are as follows:

Figure 3.1 	Energy-level structure and effective four-level model of Yb³⁺ ions in glass hosts. (a) Stark-split manifolds of the 
		ground (_^2)F_(7⁄2)  and excited (_^2)F_(5⁄2)  states. (b) Simplified four-level scheme used for rate-equation modeling: 
		level 0 is the ground state, level 1 the lower laser level, level 2 the upper laser level, and level 3 the pump level.  
		Pump absorption occurs at 0→3, followed by ultrafast nonradiative relaxation into level 2. Stimulated emission 2→1 and  
		signal absorption 1→2 form the laser transition. Because the populations of levels 3 and 1 decay on timescales much  
		shorter than the upper-state lifetime, they can be adiabatically eliminated, reducing the system to an effective 
		two-level model (N_0 and N_2). This effective model provides the basis for the subsequent derivation of the rate 
		equations and the gain expression.

Figure 3.2 	Chromatic dispersion D(λ) of fused silica computed from the three-term Sellmeier model over 800-1600 nm. The Yb band
		lies in the normal-dispersion region.

Figure 3.3 	Schematic of local dispersion (green) and pulse duration (red) evolution in a fundamental soliton fibre laser. The 
		local dispersion remains constant and anomalous along the cavity, enabling a fixed pulse duration through the balance 
		of GVD and SPM.

Figure 3.4 	Numerical illustration of temporal and spectral evolution in a soliton regime. Both envelopes remain invariant 
		over successive round trips, characteristic of a conservative soliton solution.

Figure 3.5 	Schematic of local dispersion (green) and pulse duration (red) evolution in a DMS fibre laser. The local dispersion 
		alternates between anomalous and normal segments, producing periodic breathing in temporal width.

Figure 3.6 	Numerical illustration of pulse evolution in a DMS regime. Temporal and spectral breathing over each dispersion 、
		period reduces peak power for most of the cavity, allowing larger nonlinear phase accumulation before instability.

Figure 3.7 	Schematic of local dispersion (green) and pulse duration (red) evolution in a dissipative soliton fibre laser operating 
		in an ANDi cavity. Gain, spectral filtering, and SPM collectively shape the pulse toward a strongly chirped steady state.

Figure 3.8 	Numerical illustration of pulse evolution in a dissipative soliton regime. The pulse remains broad and strongly 
		chirped in fibre segments, with narrowing occurring at the intracavity filter before re-amplification.

Figure 3.9 	Numerical illustration of pulse evolution in a similariton regime. Temporal and spectral profiles broaden monotonically 
		in the gain segment, approaching the self-similar attractor before being reset by intracavity shaping elements.

Figure 3.10 	Temporal and spectral evolution in a MO, obtained from numerical simulation of propagation between two offset spectral 
		filters. (a) Simulated temporal intensity evolution over one filter-to-filter segment. (b) Full-width at half-maximum 
		(FWHM) pulse duration versus normalized propagation distance, showing monotonic broadening in the gain fibre followed  
		by abrupt narrowing at the filter. (c) Simulated spectral evolution over the same segment, illustrating strong SPM-induced  
		broadening. (d) 10-dB spectral bandwidth versus normalized propagation distance, with sudden reduction at the filter 
		due to the step-like spectral gating.

Figure 3.11 	Principle of DFT measurements[194]. A broadband ultrashort pulse undergoes linear propagation in a highly dispersive 
		fibre, where different spectral components experience distinct group delays. This frequency-to-time mapping enables  
		direct reconstruction of the optical spectrum from the temporally stretched pulse intensity waveform, provided the 
		temporal Fraunhofer approximation is satisfied.

Figure 4.1 	Absorption (blue curve) and emission (red curve) section spectrum of Yb-doped fibre.

Figure 4.2 	Flowchart of the resonant cavity simulation under the steady-state gain approximation. Each active fibre segment is solved 
		using the SSFM with locally updated dispersion, nonlinearity, and gain operators. The population inversion ΔN(z)is computed 
		at each spatial step. The round-trip loop continues until convergence or a predefined iteration count is reached.

Figure 4.3 	Subroutine for computing the local steady-state population inversion and gain spectrum. The inversion ΔN(z)is obtained from 
		the steady-state solution of the rate equations using local pump and signal powers, and subsequently used to calculate the 
		frequency-dependent gain coefficient g(z,ω).

Figure 4.4 	Flowchart of the resonant cavity simulation under the dynamic gain model. The algorithm explicitly separates signal-induced 
		gain depletion and pump-induced recovery of the population inversion. At each spatial step, the gain spectrum is computed 
		from the initial inversion 〖ΔN〗_i (z), while the depleted inversion amount 〖ΔN〗_e (z)  is evaluated during pulse 
		amplification, yielding the post-amplification inversion 〖ΔN〗_(after_amp) (z). Gain recovery during the inter-pulse interval
 		is then used to update 〖ΔN〗_i (z) for the next round trip.

Figure 4.5 	Subroutine for dynamic gain calculation. The gain spectrum is computed from the initial inversion 〖ΔN〗_i (z). 
		Signal-induced gain depletion yields the exhausted inversion 〖ΔN〗_e (z), which is subsequently used to simulate pump-driven 
		recovery before the next round trip.

Figure 4.6 	Comparison of SS and Dy gain models for 10 kHz pulse repetition rate. All results converge after 40 pulse injections in 
		the Dy model. The negligible difference between SS and Dy confirms that the SS model remains valid under full recovery conditions.

Figure 4.7 	Comparison at 1 MHz repetition rate. The Dy model requires 2888 pulse injections to reach SS. The SS model significantly 
		overestimates gain due to neglecting gain depletion. The Dy model reveals reduced pulse energy and spectral narrowing caused 
		by incomplete inversion recovery.

Figure 5.1 	Schematic diagram of the MO used in the experiment. The cavity includes two spectrally offset bandpass filters and two 
		Yb-doped fibre amplifiers to enable mode-locking. A 0.4 m PM PF is inserted between the pre-amplifier and the main amplifier. Both 
		amplifiers are pumped by 975 nm multimode laser diodes (LDs). The oscillator is externally seeded to facilitate self-starting of the 
		mode-locking process. Optical components: L, lens; DM, dichroic mirror; PBS, polarization beam splitter; λ/2, half-wave plate; BPF, 
		bandpass filter.

Figure 5.2 	Input spectrum of the SLD and amplified spectra of the gain fibres. The blue, red, and green curves represent the SLD 
		seed, pre-amplifier output, and main amplifier output, respectively.

Figure 5.3	(a) Measured LD output, residual, and absorbed pump powers for the main amplifier as functions of LD drive current. 
		(b) Estimated absorbed pump powers for the pre-amplifier (P_1) and main amplifier (P_2).

Figure 5.4 	Measured transmission spectra of the 1st filter (red) and the 2nd filter (blue).

Figure 5.5 	(a) Average output power of the MO as a function of absorbed pump power in the main amplifier. (b) Output optical spectrum 
		at maximum pulse energy (381 nJ), centered at 1062 nm with a 10-dB bandwidth of 120 nm.

Figure 5.6	Schematic of the external pulse compressor used for characterizing the output of the MO. A pair of transmission gratings provides 
		dispersion compensation.

Figure 5.7 	(a) Measured ACF (orange) of the compressed pulse and the calculated TL ACF (green). Blue dashed line: Gaussian fit. 
		(b) Measured ACF of the compressed pulse over a 5 ps span, showing no evidence of side pulses.

Figure 5.8 	(a) RF spectrum measured at 20.03 MHz with a 1 Hz resolution bandwidth and 700 Hz span. (b) A wider span RF spectrum showing 
		fundamental repetition rate and harmonics.

Figure 5.9 	Schematic of the external seed source used to initiate mode-locking in the MO. The system comprises four modules: a 
		SESAM-based mode-locked fibre laser, a fibre amplifier, a grating-based pulse compressor, and a nonlinear pulse spectrum 
		broadener. The spectrum broadening stage utilizes ~1.5 m of SMF to induce SPM. Optical components: SESAM, semiconductor saturable 
		absorber mirror; PM-WDM, PM wavelength division multiplexer; CFBG, chirped fibre Bragg grating; ISO, isolator; OC, optical coupler.

Figure 5.10 	Single-pulse characteristics of the SESAM-based mode-locked fibre laser. (a) Output power as a function of pump current; (b) Pulse 
		train measured on an oscilloscope, showing a repetition rate of ~19.64 MHz; (c) Optical spectrum at the operating point for 
		single-pulse operation.

Figure 5.11 	Performance of the seed pulse after amplification and compression. (a) Spectrum of the amplified pulse before compression; 
		(b) Autocorrelation trace of the shortest compressed pulse, with an FWHM of 422 fs; (c) Optical spectrum after nonlinear spectral 
		broadening in single-mode fibre, showing an increased 10-dB bandwidth from 14.3 nm to 24.9 nm.

Figure 5.12 	Comparison between simulation (blue dashed curve) and experiment (red dashed curve). (a) Output spectrum; (b) Autocorrelation of 
		compressed pulse.

Figure 5.13	(a) B-integral values versus gain fibre length in the main amplifier, with fixed output energy of 384 nJ. (b) Corresponding output 
		spectra for different gain fibre lengths, showing a redshift of the central wavelength with increasing fibre length.

Figure 5.14	(a) Simulated B-integral in the main amplifier and (b) pulse energy injected into the main amplifier, plotted as functions of the 
		P_1. Output pulse energy was fixed at 384 nJ.

Figure 5.15 	(a) B integral as a function of the center wavelength of the λ_c1, with output energy fixed at 384 nJ;(b) Output pulse energy as 
		a function of λ_c1, with the B integral fixed at 35 π. In both cases, the pre-amplifier pump power P_1 was fixed at 4.0 W.

Figure 5.16 	(a) Output pulse energy versus B integral for various values of λ_c1, with P_1 = 1.5 W. Data series: blue circles (1030.0 nm), 
		orange asterisks (1032.5 nm), yellow squares (1035.0 nm), purple stars (1040.0 nm). (b) Spectral broadening of the seed pulse in 
		the pre-amplifier for P_1 = 1.5 W (orange) and 4.0 W (blue). The original seed spectrum (purple dashed) is also shown for reference.

Figure 5.17 	(a) Accumulated B-integral in the main amplifier and (b) pulse energy injected into the main amplifier as functions of the L_PF2, 
		under a fixed output energy of 384 nJ.

Figure 5.18 	Influence of the L_PF2 on the pulse characteristics before entering the main amplifier. (a) Temporal pulse profiles and (b) corresponding 
		spectra for different L_PF2 values. (c) Extracted pulse durations and (d) peak powers as functions of L_PF2.

Figure 5.19 	Simulated spectral evolution in the main amplifier for different L_PF2. (a) Spectral evolution for L_PF2 = 0.4 m, showing significant 
		asymmetry. (b) Evolution for L_PF2 = 2.0 m, with reduced asymmetry. (c) Evolution for L_PF2 = 7.0 m, where the spectrum remains highly symmetric.

Figure 5.20 	Simulated output pulse characteristics of the MO with an extended PF length L_PF2 = 10.0 m. (a) Temporal intensity profile. 
		(b) Corresponding optical spectrum.

Figure 5.21 	Output pulse energy as a function of B-integral under different values of GDD: 0 ps² (blue cross), +0.2 ps² (red diamond), -0.2 ps² 
		(yellow circle), +0.4 ps² (purple star), and -0.4 ps² (green square).

Figure 5.22 	Spectral evolution of the pulse in the main amplifier at an output energy of ~850 nJ under (a) GDD = -0.2 ps² and (b) GDD = +0.2 ps². 
		Positive dispersion suppresses spectral narrowing compared to negative dispersion.
Figure 5.23 	(a) Pulse duration evolution and (b) peak power evolution during amplification for GDD values of -0.2 ps² (blue dotted curve) and +0.2 ps² 
		(red dash-dotted curve). Positive dispersion leads to lower peak power throughout the amplifier length.

Figure 5.24 	Measured transmission spectra of the two filter combinations used in the optimization experiments. (a) Combination with a central wavelength 
		separation ∆λ_c of 8.7 nm, where the 1st and 2nd filters are centered at 1035.5 nm and 1044.2 nm, respectively. (b) Combination with ∆λ_c = 15.1 nm, 
		corresponding to central wavelengths of 1032.1 nm and 1047.2 nm for the 1st and 2nd filters, respectively.

Figure 5.25 	(a) Output pulse energy as a function of absorbed pump power under two different filter settings: ∆λ_c = 8.7 nm (blue circles) and ∆λ_c = 15.1 nm 
		(red hexagrams). The maximum output energies achieved were 377 nJ and 426 nJ, respectively. (b) Normalized output spectra corresponding to the 
		maximum output energies under the two filter settings. The -10 dB bandwidths were measured as 116.2 nm for ∆λ_c = 8.7 nm and 126.7 nm for ∆λ_c = 15.1 nm.

Figure 5.26 	ACFs of compressed pulses corresponding to the spectra shown in Figure 5.25 (b). (a) Pulse under ∆λ_c = 8.7 nm condition: experimentally measured 
		pulse duration is 44.8 fs with a TL duration of 26.8 fs. (b) Pulse under ∆λ_c = 15.1 nm condition: compressed to 35.2 fs with a TL duration of 
		24.2 fs. Blue dashed lines represent the calculated TL traces, and red dotted lines are the measured ACFs. All pulse durations are deconvolved 
		assuming Gaussian temporal profiles.

Figure 5.27 	Dependence of E_2rd  on the λ_(seed_c) for two E_seed levels: 25 pJ (blue circles) and 250 pJ (orange squares). The shaded red region indicates 
		the threshold level P_(1_thr).

Figure 5.28	Influence of τ_seed on the E_2rd   under (a) spectral overlap condition, λ_(seed_c)=1040.0 nm, and (b) spectral offset condition, 
		λ_(seed_c)=1035.0 nm. Blue circles: E_seed =25 pJ; red squares: E_seed=250 pJ. The shaded area indicates the P_(1_thr) for 
		the mode-lcoking of the MO.

Figure 5.29	Influence of seed pulse chirp (GDD) on the extracted energy E_2rd   under (a) spectral overlap condition, λ_(seed_c)=1040.0 nm, 
		and (b) spectral offset condition, λ_(seed_c)=1035.0 nm. Blue circles: E_seed =25 pJ; red squares: E_seed=250 pJ. The shaded 
		area indicates the P_(1_thr) for the mode-lcoking of the MO.

Figure 5.30	Schematic of the simplified femtosecond seed laser used to initiate the MO. The oscillator adopts a similar structure to that 
		in Figure 5.9, with a shortened cavity length to provide net intracavity dispersion of approximately -0.1 ps², facilitating 
		dispersion compensation in the downstream PF.

Figure 5.31	Characterization of the simplified femtosecond seed oscillator. (a) Optical spectrum of the oscillator output centered at 
		1041.4 nm with a full width at -10 dB of 12.7 nm. (b) Oscilloscope trace showing a pulse repetition rate of 40.24 MHz.

Figure 6.1 	Structural and optical properties of the in-house fabricated NANF, a type of antiresonant HCF. (a) Optical microscope image of 
		the fibre cross-section showing the nested antiresonant structure. (b) Measured loss spectrum, exhibiting a minimum attenuation
		of 1.3 dB/km near 1040 nm. (c) Simulated dispersion profile showing anomalous dispersion (D = 2.36 ps/(nm·km)) at the laser 
		operating wavelength.

Figure 6.2 	Experimental setup and performance of the MO incorporating a 12.5 m-long NANF for repetition rate reduction.

Figure 6.3 	(a) Transmission spectrum of the 1st filter. (b) Detected pulse train showing stable single-pulse mode-locking at a repetition
		 rate of 11.24 MHz. (c) Output pulse energy as a function of absorbed pump power P_2, showing a nearly linear dependence.

Figure 6.4 	Schematic of the MO incorporating a 240 m-long in-house fabricated NANF to achieve ultra-low repetition rates. The NANF replaces 
		the short PF segment after the first spectral filter, increasing the total cavity length to ~254 m and resulting in a repetition 
		rate of ~1.18 MHz. The the λ_c1=1040 nm, with a 2.5 nm bandwidth,  and the λ_c2 =1047 nm,  with a 2.8 nm bandwidth.

Figure 6.5  	(a) Output power of single-pulse mode-locking at different pump power at the main-amplifier. (b) Output spectrum at 514 nJ pulse energy.

Figure 6.6 	(a) The intensity AC traces of the compressed pulses (green) and TL pulses (orange) with a span of 500 fs. (b) The intensity 
		AC traces of the compressed pulses with a span of 5 ps.

Figure 6.7  	(a) RF spectrum with a NBW of 1 Hz and a span of 500 Hz. (b) RF spectrum with a NBW of 10kHz and a span of 20 MHz.

Figure 6.8 	Numerical simulation results for MOs using PF and NANF, each delivering 300 nJ output pulse energy. (a) Spectrogram of the 
		intra-cavity pulse before entering the main amplifier in the NANF-based MO, showing a negatively chirped (down-chirped) pulse. 
		(b) Spectrogram of the intra-cavity pulse before entering the main amplifier in the PF-based MO, showing a positively 
		chirped (up-chirped) pulse.

Figure 6.9 	Numerical simulation results for MOs using PF and NANF, each delivering 300 nJ output pulse energy. (a) Evolution of the 
		spectral bandwidth along the gain fibre of the main amplifier for both configurations (blue: NANF; orange: PF). 
		(b) Evolution of the pulse peak power along the gain fibre, indicating NPS accumulation (blue: NANF; orange: PF).

Figure 6.10	Numerical simulation results comparison between simulated and experimental output spectra for both Mos, each delivering 300 nJ 
		output pulse energy. Upper panel: NANF-based MO; lower panel: PF-based MO.

Figure 7.1	Schematic diagrams of grating pair compressors. (a) Configuration using transmissive diffraction gratings, which offers 
		higher efficiency. (b) Configuration using reflective diffraction gratings. In both cases, angular dispersion separates 
		spectral components, and path length differences among wavelengths introduce negative GDD and positive TOD for pulse compression.

Figure 7.2 	Schematic diagrams of prism pair compressors. (a) Standard unfolded geometry where the beam propagates through two prisms 
		and experiences material and angular dispersion. (b) Folded configuration that enhances compactness by folding the beam 
		path with mirrors. Prism compressors generate negative GDD and negative TOD by adjusting prism separation and insertion 
		depth, making them suitable for compressing sub-100 fs pulses.

Figure 7.3 	Schematics of CM design and CM-based pulse compressor. (a) Layer structure of a CM, where dielectric layers are chirped 
		in thickness to induce wavelength-dependent reflection delays. (b) CM compressor configuration using a sequence of reflections 
		to accumulate dispersion compensation. CMs offer precise, high-efficiency dispersion control and are widely used for few-cycle pulse compression.

Figure 7.4 	Pulse shaping compressor based on a SLM in a 4f configuration. The input pulse is angularly dispersed by a diffraction 
		grating and focused by a lens onto the SLM placed at the Fourier plane. The SLM modulates the spectral phase and/or 
		amplitude of each frequency component. After symmetric recombination, the output pulse exhibits the desired time-domain 
		waveform. This approach enables arbitrary dispersion compensation and waveform shaping, but is limited by the SLM's 
		spectral resolution and damage threshold.

Figure 7.5 	Schematic layout of the experimental setup for pulse compression using NANF. The setup includes two compression branches 
		(NANF and grating pair), polarization-based beam splitting, power control optics, and diagnostic tools (OSA and autocorrelator). 
		Attenuation optics are inserted before diagnostic tools to prevent damage from high-energy pulses.

Figure 7.6 	GVD curve of the NANF, derived from the chromatic dispersion parameter shown in Figure 5.30 (c). The orange dashed line 
		indicates the zero-dispersion wavelength.

Figure 7.7 	Modified MO structure used in the compression experiment. Compared with the setup in Section 5.2.1, the main amplifier uses 
		a PLMA 30/250 fibre (30 µm core diameter) for higher output energy. The beam coupling optics were also adjusted for better mode-field matching.

Figure 7.8 	Characterization of the MO performance.(a) Oscilloscope trace showing stable mode-locked pulse train at 19.34 MHz.(b) Output 
		power and single-pulse energy as functions of absorbed pump power.(c) 10-dB spectral bandwidth broadening with increasing pump 
		power.(d) Measured autocorrelation of the output pulse at maximum power, yielding a 2 ps pulse width under Gaussian assumption.

Figure 7.9 	Normalized spectra measured at the reflection port of the PBS under different reflected power levels. (a) Original output 
		spectrum of the MO. (b-g) Reflected spectra corresponding to decreasing reflected powers: 6.84 W, 4.56 W, 2.64 W, 1.24 W, 
		and 0.40 W, respectively. As the reflected power decreases, the spectrum exhibits increasing distortion relative to the 
		original MO spectrum, with a progressive shift of the spectral center towards shorter wavelengths and suppression of 
		long-wavelength components. This effect arises from the wavelength-dependent extinction of the beam-splitting optics and 
		highlights the need for careful polarization control to maintain spectral fidelity when comparing the performance of 
		different pulse compression techniques.

Figure 7.10 	Normalized reflection spectra at different HWP angles (0°, 15°, 30°, and 45°) after replacing the conventional HWP and 
		PBS with an achromatic HWP and a broadband PBS. The reflected power is adjusted from maximum to minimum by rotating the 
		HWP. The recorded spectra exhibit excellent spectral fidelity across most settings, with only the 45° case (corresponding 
		to the minimum reflected power) showing noticeable spectral distortion due to the extremely high extinction ratio. This 
		result demonstrates that the upgraded polarization optics significantly reduce wavelength-dependent reflection bias, 
		enabling fair spectral comparison between subsequent compression branches. However, the extinction at minimal reflection 
		power still limits the spectral integrity, suggesting that practical measurement should be performed at a slightly 
		lower-than-maximum reflection power.

Figure 7.11	Comparison of the collected spectra at the output of the NANF using different lengths of MMF. The input spectrum (blue 
		dashed line) is shown for reference in each panel.(a) Spectral collection using a 5 m MMF at low pulse energy, where 
		minimal spectral broadening is observed.(b) Collection with the same 5 m MMF at higher pulse energy after near-full 
		compression, revealing additional spectral features including a prominent Raman shoulder.(c) Spectral collection using 
		a shortened 1 m MMF at high pulse energy, which effectively preserves the original spectral shape. All spectra are 
		normalized in power for comparison.

Figure 7.12 	Characterization of the NANF transmission performance under different input pulse conditions.(a) Measured input and output 
		pulse energies as a function of the input spectral bandwidth. Diamond markers indicate the input pulse energy before the 
		NANF, and circle markers indicate the corresponding output energy after the fibre.(b) Overall transmission efficiency of 
		the NANF as a function of the pulse spectral bandwidth. The slight decrease in efficiency with broader spectra is attributed 
		to chromatic aberration from the coupling lens.

Figure 7.13 	Pulse compression performance using NANF and a grating-based compressor.(a) Measured compressed pulse durations as a 
		function of NANF length (purple dots), fitted using the GVD model (blue dashed line), and compared with the theoretical 
		curve based on TL input pulses (orange dashed line). The shortest experimental duration from the grating-based compressor 
		is also shown (green line).(b) Normalized spectra before and after NANF compression at the optimum condition (10.8 m fibre 
		length, 424 nJ output).(c) Autocorrelation traces of compressed pulses from the NANF and grating-pair compressors, along 
		with the TL trace.

Figure 7.14 	Far-field beam profile of the NANF output, exhibiting a near-Gaussian mode shape. The noise pattern in the beam image is 
		likely caused by interference from the thin-film filter mounted in front of the camera sensor. To mitigate the influence 
		of such noise, horizontal and vertical cross-sections through the beam center were extracted and fitted with Gaussian 
		functions (red line), confirming the symmetric Gaussian profile and effective excitation of the fundamental mode.

Figure 7.15	Calculated TOD curve of the NANF based on its GVD characteristics (see Figure 7.6). In the 1 μm spectral region, the 
		NANF exhibits positive TOD while providing negative GVD.

Figure 8.1 	Schematic of the experimental setup for investigating the build-up dynamics of the MO using DFT. The output of the MO 
		is split into two branches: one is directed to an OSA, optical spectrum analyzer, for average spectral characterization, 
		while the other is processed through a dispersive fibre and detected by high-speed photodetectors to reconstruct 
		spectral evolution in real time.

Figure 8.2 	Time-domain traces of the MO output after DFT using different fibre configurations. The main MO pulse train at ~20 MHz is 
		marked by green circles, while residual seed pulses at 40 MHz are indicated by red circles. Shorter fibres provide 
		insufficient dispersion, whereas excessively long fibres degrade the temporal contrast. The results highlight the need for 
		seed-pulse modulation and the trade-off between dispersion length and signal quality in DFT measurements.

Figure 8.3 	Wavelength calibration of the DFT signal using 8.6 km SMF-28. (a) Time-domain trace of a mode-locked pulse after passing 
		through the dispersive fibre, captured by a real-time oscilloscope. (b) Optical spectrum of the same pulse measured directly 
		using an OSA. (c) The DFT signal is remapped to the wavelength axis using the calibrated dispersion coefficient and compared 
		with the OSA spectrum, showing good agreement.

Figure 8.4 	Temporal response of the MO under single-pulse seed injection using different modulators. (a) EOM: Due to limited extinction 
		ratio, residual seed pulses are observed outside the gate window, leading to potential multi-pulse triggering. (b) AOM: 
		The seed is well confined within the gate window, enabling cleaner observation of the build-up process.

Figure 8.5 	Real-time temporal evolution of the MO output under steady-state start conditions, recorded with a 5 GHz photodetector. An 
		initial Q-switched spike is followed by pulse narrowing and a visible temporal drift caused by spectral red-shift.

Figure 8.6 	Spectral evolution retrieved via DFT, showing strong broadening during the initial build-up and gradual stabilization of the spectral shape.

Figure 8.7 	Quantitative parameters of the steady-state start process: (a) Pulse energy (log scale) showing relaxation and a subtle 
		secondary transition; (b) sXC parameter indicating steady convergence but with residual fluctuations.

Figure 8.8 	Temporal evolution of the MO output under cold-start conditions, recorded with a 5 GHz photodetector. The early-stage 
		pulses are irregular and noisy, gradually stabilizing into a periodic train.

Figure 8.9 	Spectral evolution captured via DFT during the cold-start build-up. Strong spectral fluctuations, collapses, and 
		red-shifts are observed before the spectrum stabilizes around roundtrip 1500.

Figure 8.10 	Quantitative metrics of the cold-start process: (a) Pulse energy evolution showing bursts followed by gradual convergence; 
		(b) Spectral cross-correlation sXC showing strong early oscillations and eventual stabilization above 0.98 after ~1500 roundtrips.

Figure 8.11 	Simulated spectral evolution of the MO under two start-up conditions. (a) steady-state start: both the preamplifier and main 
		amplifier are fully pumped (5 W), with no seed injection prior to startup. (b) Cold start: both amplifiers are initially unpumped 
		and the seed pulse is injected simultaneously with the activation of the pumps. Each plot shows the evolution of output spectra 
		over 5000 roundtrips. The cold-start case exhibits faster spectral regularization, while the steady-state start leads to broader 
		final spectra but with more fluctuations during the buildup phase.

Figure 8.12	Quantitative comparison of output dynamics under steady-state and cold-start conditions. (a) Simulated pulse energy evolution 
		over 5000 roundtrips. Inset: zoom-in of the last 500 roundtrips (4500-5000), showing that energy in the steady-state case has 
		saturated while the cold-start case continues to grow. (b) Evolution of spectral cross-correlation coefficient sXC within the 
		first 50 roundtrips. (c) Evolution of first-order coherence function g_12^((1)) over the same time window. The cold-start pathway 
		rapidly reaches a coherent state, whereas the steady-state start exhibits a slower and more fluctuation-prone coherence buildup.

Figure 9.1 	Cross-sectional microscope image of the 32-core multi-core fibre (MCF). The cores form a near-square lattice with a pitch of ~28.8 μm 
		and cladding diameter of 241.2 μm. Numerical labels are added to the cores for phase management and mapping to sub-beams generated via SLM.

Figure 9.2 	Schematic diagram of a reflective LCoS SLM. The device consists of a LC layer modulated by individual CMOS electrodes, enabling 
		phase-only control of incident light.

Figure 9.3 	Schematic representation of a transmissive phase-only beam shaping device based on a SLM.

Figure 9.4 	Simulated single-beam offset using linear phase ramps encoded on the SLM. (a-d) Linear phase profiles designed to steer the 
		beam toward four different directions. (e-h) Corresponding far-field intensity distributions obtained from 2D discrete Fourier 
		transform simulations, demonstrating localized beam formation at positions corresponding to MCF core #6, #9, #24, and #27.

Figure 9.5 	Simulation results using the Overlap Method without phase management. (a) Assigned phase values for selected cores (#6, #9, #24, 
		and #27), all set to 0.00π, indicating no phase adjustment between beams. (b) Simulated far-field intensity distribution reveals 
		additional unwanted interference spots due to coherent overlap. (c) Spot energy distribution; the four bars correspond left-to-right 
		to cores #6, #9, #24, and #27. The total efficiency improves perfect uniformity (σp = 0.00%) but limited efficiency (η_p = 63.48%) 
		without phase control.

Figure 9.6 	Comparison of different phase management schemes for generating a 2×2 sub-beam array. (a,d) Spatial phase arrangements corresponding 
		to the four selected target cores (#6, #9, #24, #27), with individual blocks annotated by core number and relative phase (in units 
		of π). (b,e) Simulated far-field intensity patterns under the two phase configurations. (c,f) Corresponding evaluations of power 
		uniformity and total pattern efficiency, denoted as σ_p and η_p, respectively. The four bars correspond left-to-right to cores #6, 
		#9, #24, and #27.

Figure 9.7 	Simulation results for a 4×4 beam array using the Overlap Method. (a,d) Assigned relative phase maps, aligned with the MCF core 
		indices. (b,e) Simulated far-field intensity distributions. (c,f) Statistical evaluation of energy performance using pattern 
		efficiency η_p and uniformity σ_p. Results show that phase control significantly improves both efficiency and uniformity. The 16 
		bars correspond left-to-right to cores #6, #7, #8, #9, #12, #13, #14, #15, #18, #19, #20, #21, #24, #25, #26 and #27.

Figure 9.8 	Simulation results for a full 32-core beam array using the Overlap Method. (a,d) Phase patterns with and without relative phase 
		management. (b,e) Corresponding far-field  intensity distributions. (c,f) Energy analysis confirms that optimized phase assignment 
		suppresses interference and enhances performance. The 32 bars correspond left-to-right to cores from #1 to #32.	

Figure 9.9 	Comparison between the Overlap Method and the Subregion Method for 32-beam generation. (a) Phase profile of the Overlap Method: 
		full-aperture encoding. (b) Phase profile of the Subregion Method: localized encoding with isolated regions. (c) Assigned relative 
		phase map for 32 sub-beams (all set to 0). (d) Simulated far-field intensity under identical optical conditions as the Overlap 
		case, showing significant aperture truncation and incomplete beam formation. The colorbar range was adjusted to enhance the visibility 
		of weaker features near the origin of the focal plane, where strong intensity components are present.

Figure 9.10 	Simulation results of the subregion method using a Gaussian incident beam. (a, d) Phase maps of the 32-beam array without and 
		with phase management, respectively. (b, e) Far-field intensity distributions with the color range adjusted for visualization 
		due to strong central peak. (c, f) Zoomed-in views (0.1 mm × 0.1 mm) showing individual sub-beam contours. (g, h) Statistical 
		analysis of energy uniformity and efficiency. The 32 bars correspond left-to-right to cores from #1 to #32. Notably, each 
		sub-beam exhibits hexagonal or petal-like envelopes with evident Airy sidelobes caused by subregion aperture diffraction.

Figure 9.11 	Incident beam profiles at the SLM plane. (a) Conventional Gaussian beam used in previous simulations. (b) Eighth-order 
		super-Gaussian (flat-top) beam with sharp edge roll-off and uniform center intensity, designed to improve sub-beam uniformity 
		in the subregion method.

Figure 9.12 	Simulation results of the subregion method using a flat-top incident beam. Top row: without phase management; Bottom row: with 
		phase management. (a, d) Phase profiles for the 32-beam array. (b, e) Far-field intensity distributions under uniform color scaling. 
		(c, f) Energy ratio and distribution across all target beams. The 32 bars correspond left-to-right to cores from #1 to #32. The 
		sub-beams display smooth circular contours with suppressed sidelobes. Phase management offers minimal additional benefit in this 
		condition, indicating the intrinsic stability of the flat-top subregion scheme.

Figure 9.13 	Simulation results of subregion-based beam array generation under expanded beam sizes. (a-c) Results for a beam size increased by 
		1.2×; (d-f) results for a 1.4× increase. First column: encoded phase masks on the SLM. The 32 bars correspond left-to-right to cores 
		from #1 to #32. Second column: simulated far-field intensity distributions. Third column: magnified views of individual sub-beam 
		profiles. Rightmost column: quantitative evaluation of uniformity (σ_p) and efficiency (η_p). No phase management is applied. 
		Note: Color scale in the second column is adjusted for visualization due to high-intensity central lobe.

Figure 9.14 	Schematic of the hybrid phase mask design: the SLM plane is divided into four quadrants, each with distinct periodic modulations.

Figure 9.15 	Far-field performance of the hybrid method under Gaussian illumination. (a-c) Results without phase management: (a) assigned phase 
		shifts for 32 target beams, (b) far-field intensity distribution, (c) energy ratio per spot with uniformity σ_p = 1.32% and efficiency 
		η_p = 55.89%. (d-f) Results with phase management: (d) optimized phase shifts, (e) far-field pattern showing improved energy distribution, 
		(f) corresponding histogram with σ_p = 0.80%, η_p = 69.42%. The 32 bars in (c) and (f) correspond left-to-right to cores from #1 to #32. 
		Although phase optimization improves uniformity, sub-beam integrity is degraded and residual sidelobes persist, indicating incomplete 
		spatial decoupling.

Figure 9.16 	Schematic of the experimental setup. A Gaussian beam is collimated, modulated by a reflective SLM, and then coupled into a receiving 
		fibre. A beam splitter is used to monitor the modulated pattern. The SLM is illustrated as a transmissive device for clarity. 
		Camera 1 monitors the modulated far-field pattern, and Camera 2 captures the output from the fibre.

Figure 9.17	Schematic for visualizing the 32-core fibre’s output facet. White light is injected from the output side of the fibre to identify 
		core positions for alignment. The rotation angle of the generated pattern is adjusted accordingly.

Figure 9.18	Optimization of rotation angle and pitch distance for coupling to a 32-core fibre. (a) Captured fibre core image using 
		white-light back-illumination. (b) Simulated beam pattern rotated by 30°; the original unrotated array is shown in the inset. 
		(c) Coupling efficiency P_3 versus rotation angle. (d) Coupling efficiency P_3 versus pitch scaling ratio. Optimal values 
		are 3° and 0.91 (for f_2 = 9.6 mm) and 0.94 (for  f_2  = 40 mm), respectively.

Figure 9.19	Experimental results using the overlap method. (a) Sub-beam array generated on the SLM; the inset shows the target cores to be 
		coupled. The array comprises 12 beams in a 4×4 configuration with omitted corners and large spatial deflection. The central bright 
		spot is the zeroth-order diffraction. (b) Energy distribution of the 12 sub-beams at the generation plane, with calculated standard 
		deviation σ_p  = 2.66% and pattern efficiency η_p  = 84.64%. (c) Coupled output pattern from the 32-core fibre. (d) Energy distribution 
		of the coupled beams, with σ = 2.99% and measured coupling efficiency η = 17.86% (based on P_3  = 6.14 dBm). The 12 bars correspond 
		left-to-right to cores #1, #4, #5, #6, #9, #10, #23, #24, #27, #28, #29 and #32.

Figure 9.20 	Experimental results using the subregion method for coupling into a selected 12-core configuration. (a)SLM-generated sub-beam array, 
		with the target pattern indicated in the inset (four corner beams omitted by design). The eight outer beams exhibit noticeable spatial 
		deviation from intended positions. (b)Energy distribution analysis of the 12 generated sub-beams, with σ_p = 9.14%, η_p  = 83.89%. 
		(c)Output intensity image from the 32-core fibre. Despite contrast adjustment, the outer eight cores show no detectable output, 
		confirming failed coupling. (d)Statistical analysis of coupled output beams, revealing significant energy imbalance with σ = 12.48%, 
		η = 5.22%. The measured coupled power is P_3  = 0.8 dBm. The 12 bars in (b) and (d) correspond left-to-right to cores #1, #4, #5, #6, 
		#9, #10, #23, #24, #27, #28, #29 and #32.

Figure 9.21 	Sub-beam array generated by the hybrid method. A 4×4 beam array (excluding corners) was produced using the hybrid modulation strategy. 
		The inset indicates the corresponding core positions in the 32-core fibre. The zeroth-order diffraction is significantly stronger than 
		the target beams, preventing a meaningful evaluation of pattern efficiency. This strong central spot reflects the poor modulation 
		performance of the hybrid method. As a result, no coupling tests were conducted for this configuration.

Figure 9.22	Experimental demonstration of full 32-core excitation using the overlap method. (a) SLM-generated sub-beam array at the focal plane. 
		The zeroth-order diffraction overlaps with a signal beam, obscuring accurate energy estimation. (b) Statistical energy distribution 
		of the generated pattern. Both η_p and σ_p are omitted due to the overlap. (c) Output from the 32-core fibre showing successful 
		coupling across all cores. (d) Statistical energy distribution of output spots; σ = 1.80%, η = 18.37%. The 32 bars correspond 
		left-to-right to cores from #1 to #32. This result also indicates that future designs should incorporate a global shift to the 
		sub-beam array to avoid interference from the zeroth-order component.




Date of data collection: 28/09/2021 - 28/09/2025

Information about geographic location of data collection:  University of Southampton, U.K.

Licence:CCBY

Related projects:
Engineering and Physical Sciences Research Council (EPSRC); 
InLightenUs Transformative Healthcare 2050 project (EP/T020997/1); 
Transformative Imaging for Quantitative Biology Partnership (EP/V038036/1); 
AirGuide Photonics Programme Grant (EP/P030181/1); 
China Scholarship Council (202106160002)

Date that the file was created: March, 2026