Temporal interaction of hybrid signals in various phases of Eu3+: BiPO4 through photon–phonon dressing

Laser interaction with doped crystals exhibiting photon–photon and photon–phonon coupling has been focused on recently. In pretext, here we report the spectral and temporal profile interaction of two lasers excitation through various phases of Eu3+: BiPO4 crystals. We reveal that spectral-temporal profile interaction of hybrid signals (coexisting fluorescence and spontaneous four-wave mixing) are dressed by nested and cascade processes of two-photons (two-phonon). Such interaction comes from thermal phonon constructive and phase transition phonon destructive dressing. The spectral and temporal (profile) interactions are interrelated and reduced by about 2-times due to two-photon nested dressing in contrast to the interaction through the sum of each laser excitation. In contrast to a single laser, spectral (Fano)-dip interaction reduces by 2-times due to two-photon destructive dressing coupling. Moreover, thermal phonon dressing at 300 K exhibits 3-times more extensive temporal interaction than that at 77 K. The phase transition phonon dressing for a half hexagonal and half low-temperature monoclinic phase is about 1.5-times longer than that of the pure hexagonal phase of Eu3+: BiPO4. These results may help to understand the spectral-temporal relationship in the fields of nonlinear and quantum optics.


Introduction
Rare-earth-doped crystals are exciting candidates for quantum storage applications in terms of atomic coherence. Different coherence time has been demonstrated by using electromagnetically induced transparency (EIT) procedures or photonic entanglement in a crystal [1][2][3][4]. Such strategies, for example, optically addressable nuclear spins in solids, can be used for optical storage [2].
Investigations on photon-photon dressing coupling of double-dark states and splitting of a dark state have been well-thought-out [12,13]. Similarly, inevitable entanglement through different atomic-like systems requires strong spin-phonon coupling to exceed the coherence time of phonon [14,15]. Hence, spin-nanomechanical setup with robust, intrinsic, and tunable magneto-mechanical couplings tolerates the construction of hybrid quantum devices [16,17]. Photon coupling with thermal and phase transition phonons brings up the phenomena of spectral-temporal interaction.
In this paper, we investigate the spectral-temporal profile of dressed hybrid signals based on different phonons vibrational frequencies in five types of crystal lattices. The spectral-temporal profile interaction originates from the pattern of connecting spectrums at different time-gate positions to form a time domain signal. Such interaction of broadband and narrowband excitation is demonstrated at different temperatures. High temperature exhibits more extensive temporal interaction in contrast with low temperature. Further, the relationships among spectral-temporal profile interaction, spectrum (Fano)-dips interaction, and temporal Autler Townes (TAT) splitting interaction are introduced for the different phase transitions.

Experimental setup
Temporal interaction with photon-phonon dressing coupling is studied in five types (different molar ratio represents different phases) Eu 3+ : BiPO 4 crystals with C 1 symmetry (less phonon) and D 2 symmetry (more phonon) [9]. To implement the experiments, samples were held in a cryostat (CFM-102). Figure 1 shows the fine structure of Eu 3+ : BiPO 4 crystals exhibit transition ( 7 F 1 → 5 D 0 ) between levels |k and |l . We used two tunable dye lasers (narrow scan with a 0.04 cm −1 linewidth) pumped by an injection-locked single-mode Nd: YAG laser (continuum power lite DLS 9010, 10 Hz repetition rate, 5 ns pulse width), to generate pumping fields E i (ω i , Δ i ). The frequency detuning is defined as Δ i = Ω kl − ω i , where Ω kl represents the frequency of atomic transition between crystal field splitting levels 5 D 0 and 7 F 1 and ω i = (i − 1, 2) is photon frequency. The photon Rabi frequency is described as G i = μ kl E i / , where μ kl is the dipole moment, the crystal field splitting between different states 5 D 0 and 7 F 1 excited by E i between levels |k and |l . The output out-of-phase fluorescence (FL) signals (E FL1 ) and (E FL2 ) are generated by broadband excitation E 1 and narrowband E 2 , respectively. The term hybrid signal correspond to the coexistence of FL and spontaneous four-wave mixing (SFWM). Hybrid signals can be selected from specific energy levels through boxcar time-gated integrators by controlling time-gate position and time-gate width (integration duration) [18]. Because the decay rates of broadband and narrowband excitations vary with changes in the controlling parameters, a boxcar time-gate position can be used to differentiate them at two photomultiplier tubes (PMT's). The detailed setup conditions are specified by Fan et al [19]. The in-phase SFWM (E S1 ) signals under phase-matched conditions, which (k 1 + k 1 = k S + k AS ) is produced by broadband E 1 and its reflection E 1 , while the second in-phase SFWM (E S2 ) is obtained through narrowband E 2 and its reflection E 2 with (k 2 + k 2 = k S + k AS ). The hybrid signal (coexisting FL and SFWM) in five crystal phases of Eu 3+ : BiPO 4 are collected through PMT's via confocal lenses. The characteristics of the output hybrid signal can be changed by adjusting different parameters such as time-gate position, laser power, detector location, and temperature. Here we pronounce temporal interaction (intensity profile, TAT splitting) as the time domain interaction (resonance or off-resonance) signals of two lasers, which are controlled by thermal phonon and phase transition phonon dressing. Such thermal phonon dressing and phase transition phonon detuning is controlled by temperature and different samples, respectively.
By scanning laser field wavelength and changing boxcar time-gate position, we get the spectral resolved and temporal resolved signals, respectively. Then the spectral-temporal profile interaction of two lasers can be realized by connecting many spectrums at different gate positions. Different frequency phonon is exciting different crystal field splitting levels of 7 F 1 (figures 1(a)-(d)) in the ion Eu 3+ . The photon-phonon coupling appears to be essential in our experiments. Photon excites atomic coherence between 5 D 0 and 7 F 1 can be coupled to phonon excitation atomic coherence of 7 F 1 . Unlike atomic coherence between different states of crystal field splitting of photon excitation, the atomic coherence in the same state of crystal field splitting of phonon excitation is far more difficult to control. Because the photon excitation source is generated by lasers, phonons excitation comes from BiPO 4 crystal lattice vibrations. Different crystal structures determine different vibration frequencies. Broadband excitation couples to more lattice vibration while narrowband excitation is coupled to less lattice vibrations. Photon coupling with thermal phonon and phase transition phonon causes the phenomena of spectral-temporal interaction. High temperatures create more phonon numbers which result in a stronger spectral-temporal profile interaction. The low temperature result in less phonon number, which creates low intensity background and weak profile intensity interaction. However, the phase transition phonon dressing destroys the temporal profile intensity interaction. (f) Stokes/anti-Stokes generation in a two-level system E 1 via SFWM (g) generation of Stokes/anti-Stokes in a three-level system with E 2 dressing. E 2 excitation is similar to (f) and (g). Temporal interaction of hybrid signal considers both E 1 and E 2 excitation.

Basic theory of spectral and temporal interaction
When two lasers are switched on, the density matrix of the accompanying second-order FL via perturbation (2) 11 for G i can be written as Where i = 1, 2 shows the laser E 1 , and E 2 , respectively. The decay rate of the FL signal can be written as shows four dressing terms. Where G p1 , G p1 , Δ p1 , Δ p1 represents phonon1 and phonon2 Rabi frequency and detuning, respectively. The phonon Rabi frequency can be described similarly as G pj = −μ mn E pj / and μ mn is the dipole moment between |m and |n of crystal field energy levels in the same state 7 F 1 . E pj is the phonon field. The phonon detuning Δ pj = Ω mn − ω pj , where Ω mn is the resonant frequency between |m and |n , and ω pj is the frequency of phonon field, which is determined by vibrational frequency of crystal lattice state mode [18]. |G 1 | 2 /(Γ 10 + iΔ i + |G 2 | 2 /(Γ 10 + iΔ i )) represents two laser nested dressing. The G 1 (G 2 ) excite the transition between levels 7 F 1 ( MJ=1 ) → 5 D 0 ( MJ=0 ) in figure 1(a).
In Λ-type three-level system, third-order stokes ρ (3) 10(S) for E i can be written as The decay rate of the Stokes signal can be written as Γ S = Γ 20 + Γ 00 + Γ 20 . The intensity of two laser temporal profile interaction of the measured FL and Stocks signals can be described as Where τ (2) = t CF + τ inter , τ (2) = τ 01 + τ 02 , and τ 01 (G 1 ) and τ 02 (G 2 ) represents the TAT splitting (delay time) for broadband and narrowband excitations, respectively. The τ 0i = t cf + t phot + t phon results from the involvement of crystal field (t cf ), photon dressing (t phot ), and phonon dressing (t phon ) terms. τ inter is related to two lasers' photon-phonon coupling term and t p is the pulse width. Γ (2) FL/S and Γ (2) FL/S denotes the sharp peak and broad shoulder respectively. Equation (3) shows the interaction of the spectral-temporal signal at near time-gate while equation (4) shows the spectral-temporal interaction at far time-gate. The intensity of the spectral-temporal interaction from hybrid signals can be obtained by Where F(t) is the hybrid signal time domain function, which includes the time domain function terms from equations (3) and (4). We demonstrate the relationship between temporal AT splitting and spectral AT splitting in atomic-like media by taking Eu 3+ : BiPO 4 as an example. The spectral AT splitting corresponds to the dressed states |± created by E i which splits the state |i into two dressed states |± . If we set |i as the frequency reference point, then by using Hamiltonian H|G i± = λ ± |G i± , where SAT splitting distance can be written as [20]. For the time-domain signal, the frequency of the input beam E i is fixed at the resonant point (Δ = 0). The distance between two peaks in time domain intensity signal (τ 01 = t cf + t phot + t phon ) or (τ 02 = t cf + t phot + t phon ) is caused by the residual particles in |+ (bright state) transferring to |− (dark state) through a phonon-assisted non-radiative transition determined by phonons. The total TAT splitting interaction depends upon the dressing effect and phonon-assisted non-radiative transition, whereas SAT splitting interaction is caused by the dressing effect only.

Experimental results
The spectral-temporal signals in figures 2-7(a)-(d) can be observed at different boxcar time-gate positions from connecting spectrums, which are demonstrated in a pattern in figures 2-7(e)-(h), with different experimental conditions. Such spectral-temporal profiles for (one laser broadband (or narrowband) excitation (figures 2-7(a) and (c)) and its interaction for two laser excitations (figures 2-7(b) and (d))), corresponding to their temporal profiles in figures 2-7(i) and (k) and figures 2-7(j) and (l), respectively.
The dressing dips intensity interaction is the difference in intensities between dressing dips in figures 2(b) and (d), and the sum of dressing dips intensities originates from E 1, E 2 in figures 2(a) and (c), respectively. The dressing dips interaction is destructive if the intensity of the sum of the dressing dips from the single laser figures 2(a) and (c) is greater than the intensity of dips originated from two lasers destructive dressing figure 2(b). Due to two photons nested destructive dressing  |G 1 | 2 /(Γ 10 + iΔ i + |G 2 | 2 /(Γ 10 + iΔ i )) in the hybrid signal (equation (5)), the dressing dips interaction reduces about 2-times ( figure 2(b)) as compared to the above sum exhibited by broadband ( figure 4(a)) and narrowband (figure 4(c)) laser excitations. Similarly, destructive spectral dips intensity interaction exhibits in figure 2(d) while the increase in the background owing to contribution from E 1 . Such destructive interaction comparison of two lasers is controlled by thermal phonon Rabi frequency (G pT ) in figures 5(b) and (d) and phase transition phonon detuning (Δ pS ) in figures 4(b) and (d).
Since the difference between resonance and non-resonance terms (R (2) 1 − ℵ (2) 1 = R 1 or R (2) 2 − ℵ (2) 2 = R 2 ) represents the strength of temporal profile interaction, so the destructive temporal profile interaction resonance term R 2 1 from figure 2(j1) decreases about 3-times in contrast to the one laser resonance term in figure 2(i1) i.e., R 1 + N 1 = 3R (2) 1 , this is due to R 2 1 suppressed by two lasers destructively dressing. In addition, the difference in R 2 1 (figure 2(j1)) and ℵ (2) 1 (figure 2(j2)) is almost equal to the difference between R (2) 2 (figure 2(l1)) and ℵ (2) 2 (figure 2(l2)), suggesting the strength of the two laser temporal profile interaction is similar in figures 2(j) and (l). Comparing the resonance terms of broadband and narrowband excitations, R 1 + N 1 (figure 2(i1)) is 2.5-times greater than R 2 + N 2 in figure 2(k1). Similarly, about 6-times higher non-resonance exhibits for broadband excitation (figure 2(i2)) than that of narrowband excitation (figure 2(k2)) i.e., N 1 N 2 . Further, we demonstrate TAT splitting for one laser broadband (or narrowband) and its interaction for two laser excitations. The TAT splitting between the sharp peak and broad shoulder (figure 2(i)) for broadband excitation, can be written as τ inter < τ 01 + τ 02 − 2t cf where t phot = t pT + t pS and t pT , t pS represent thermal phonon and phase transition phonon splitting terms, respectively. For narrowband excitation (figure 2(k)) τ 02 = t cf + t phot . In figure 2(i) τ 01 = 10 μs is greater than τ 02 = 6 μs (figure 2(k)) due to broadband excitation including phonon splitting. The destructive profile interaction (figures 2(j) and (l)) is sensitive to photon dressing (t phot ) and phonon dressing (t phon ) while insensitive to crystal field splitting (t cf ). Because of τ inter , the two lasers, TAT splitting (τ (2) ) with destructive nested dressing |G 1 | 2 /|G 2 | 2 is smaller than the sum of TAT splitting without crystal field splitting of each laser i.e., τ inter < τ 01 + τ 02 − 2t cf (equations (3) and (4)). The TAT splitting interaction is much smaller than the observed difference between TAT splitting in figures 2(j) and (l) and the sum of two single laser TAT splitting in figures 2(i) and (k) i.e., τ inter τ 01 + τ 02 . In figure 3, the spectral-temporal profile interaction is studied for the crystal structure (more HP + less LTMP). Different sample crystals structure determines different lattice vibration frequencies of phase transition phonon. According to G pj = −μ mn E pj / with constant Ω mn , ω pj is increased due to change in the crystal phase (figure 3) as compared to figure 2. The medium ω pj (figure 2) and larger ω pj (figure 3) results in Δ pj (off-resonance) and Δ pj (near-resonance), respectively.
In comparison with figures 2 and 3, figure 4 shows destructive spectral-temporal interaction for the pure HP, suggested by more phase transition phonon dressing. Such crystal structure results in the largest vibration of phonon frequency (ω pj ) i.e., Δ pj ∼ = 0 (resonance phase transition phonon dressing) when compared to figures 2 and 3(a). The one laser broadband excitation supports |G 1 | 2 /(Γ 10 + iΔ i + G pT 2 / (Γ 20 + iΔ i − iΔ p1 + G p2 2 /(Γ 23 + iΔ i + iΔ p1 − iΔ pS ))) coupling dressing and exhibits three dressing dips in figure 4(a) due to phonon frequency approaching Δ pj ∼ = 0 in contrast to the single dressing dip in figure 2(e). Here broadband excitation atomic coherence is coupled to thermal phonon and phase transition phonon atomic coherence. As narrowband excitation does not support the phonon dressing, therefore, an increase in ω pj (figure 4(c)) does not exhibit any change, and the results are consistent with figure 2(c). However, the two laser spectral dips intensity interaction in figure 4(b) decreases about 1.33-times due to phonon nested dressing G pT 2 /(Γ 20 + iΔ i − iΔ p1 + G p2 2 /(Γ 23 + iΔ p1 − iΔ pS )). In contrast to figure 2(b). The two laser spectral-temporal profile destructive interaction in figure 4(d) can be explained in a similar fashion as figure 2(d).
Next, we emphasize and suggest that both the resonance and non-resonance terms of the temporal intensity profile interaction are strongly affected by more phase transition phonon dressing. Such interaction resonance term R (2) 1 in figure 4(j) reduced about 1.5 times compared to figure 2(j). The phase transition phonon detuning (Δ pS ∼ = 0) is at resonance in figure 4(l) as compared to figure 2(l), which suppresses the interaction through G pT 2 / G pS 2 dressing in the hybrid signal (equation (5)). Here R (2) 2 in figure 4(l1) is completely overlapped by ℵ (2) 2 ( figure 4(l2)) i.e., R (2) 2 = ℵ (2) 2 . The two lasers temporal profile interaction disappears in figures 4(k) and (l) owing to no difference exhibited between R (2) 2 and the sum of the resonance terms from E 1 , and E 2 . Comparing figures 4(l1) and (l2) to figures 4(k1) and (k2), R (2) 2 (figure 4(l1)) is completely suppressed by the non-resonance term due to the significant contribution of ℵ (2) 2 in figure 4(l2) from R 1 > 0. The difference between R (2) 1 and ℵ (2) 1 in figure 4(j) is enhanced compared to figure 2(j) due to a decrease in ℵ (2) 1 while R (2) 2 − ℵ (2) 2 in figure 4(l) remains almost the same as figure 2(l). Furthermore, phase transition phonon detuning will be gradually increased from figures 2-4. The difference between R (2) 1 and ℵ (2) 1 in figure 4(b) becomes very larger than that of R (2) 2 and ℵ (2) 2 (figure 4(d)) i.e., Due to a decrease in N 1 , the difference between R 1 + N 1 and N 1 in figure 4(i) is enhanced compared to figure 2(i). Owing to R 2 ∼ = N 2 ∼ = 0 in figure 4(k), the R 2 and N 2 suggest reduction of about 7-times and 4-times, respectively, as compared to figure 2(k). From the above discussion, it is exhibited that temporal intensity profile interaction efficiently reduces with enhancement in the phase transition phonon dressing.
Further, we show that more phase transition phonon dressing reduces TAT splitting for one laser (figures 4(i) and (k) and two laser TAT splitting interactions (figures 4(j) and (l). The largest ω pj value influences an increase in t pS which strongly affects the TAT splitting of narrowband excitation in figure 4(k). Since narrowband excitation does not support Δ pj , therefore, τ 02 approaches zero in figure 4(k). τ (2) in figures 4(j) and (l) is equal to τ 01 in figure 4(i). The difference between of τ (2) in figures 4(j) and (l) and the sum of two single laser TAT splitting (figures 4(i) and (k) is also almost equal to zero. Therefore, TAT-splitting interaction (τ inter ) decreases in figures 4(j) and (l) for the pure HP as compared to that of half HP + half LTMP in figures 2(j) and (l)).
The interaction results in figures 2-4 were based on thermal phonon dressing at 300 K. In the following, we decrease the temperature to 77 K in order to study the interaction without thermal phonon dressing in three phase transitions.

Interaction without thermal phonon dressing for three phase transitions
In figure 5, the intensity of spectral-temporal profile for one laser excitation and its interaction for two lasers excitations is dramatically reduced by small thermal phonon dressing. The Rabi frequencies of the thermal phonon dressing is determined by the temperature (thermal phonon number). On the other hand, two laser spectral-temporal profile interaction (figure 5) from the hybrid signal decreases when the temperature is reduced to 77 K (less phonon number) leading to a small Rabi frequency (G pT ∼ = 0) in contrast to 300 K (figure 2).
Further, we exhibit that thermal phonon strongly affect the TAT splitting interaction. The τ (2) in figures 5(j) and (l) disappears at low-temperature as τ 02 ∼ = 0. However, due to no contribution from thermal phonon at 77 K, τ inter reduces about 2-times in figures 5(j) and (l) compared to figures 2(j) and (l).
In figure 6, the phase transition phonon dressing increases due to a change in the crystal structure while keeping the thermal phonon dressing the same as in figure 5. A large value of phonon frequency (ω pj ) i.e., Δ pj (near-resonance) in figure 6 exhibits a minor change in the spectral-temporal profile as compared to figure 5. The spectral signals dip (TAT splitting) from one laser in figures 6(a) and (c), and its intensity interaction (I (2) FL+S ) of two lasers in figures 6(b) and (d) condense more due to a decrease in Δ pS , as compared to figure 5.
Next, the destructive temporal interaction reduces more (figures 6(j) and (l)) due to an increase in the phase transition phonon dressing, and can be explained the same as figures 3(j) and (l). We realize that R (2) 2 = R (2) 1 while ℵ (2) 2 (figure 6(l2)) increases 3-times compared to ℵ (2) 1 (figure 6(j2)) i.e. ℵ (2) 2 = 3ℵ (2) 1 and can be explained the same as figures 5(j2) and (l2). In figure 7, the destructive spectral and temporal interaction is controlled by thermal phonon Rabi frequency and phase transition phonon detuning. In figure 7, the temperature is reduced to 77 K when compared to figure 4 (300 K). Here the sample changed to pure HP. It should be noted that pure HP have high site symmetry than half HP + half LTMP (figure 5). Since, dressing dip number (figures 7(a) and (e)) through single laser should increase due to largest ω pj i.e., Δ pj ∼ = 0, as compared to figures 2(a), (e) and (i). However, a decrease in thermal phonon G pT , destroys the dressing dips in figures 7(a) and (e). In this situation, the phonon dressing ( figure 7) has a small G pT , and largest ω pj (Δ pS ∼ = 0).
Next, we discuss the comparison of spectral and temporal profile interaction at different phonon detuning and temperatures. The two lasers dressing dips intensity interaction is maximum in figures 2(b), (d), (f) and (h) while completely destroying in figures 7(b), (d), (f) and (h). As compared to figures 2(b), (d), (j) and (l) with strong spectral-temporal profile interaction having smaller Δ pS ∼ = 0 and larger G pT , here the spectral-temporal interaction (figures 7(b), (d), (j) and (l)) is completely destroyed by larger Δ pS > 0 and smaller G pT . For the pure hexagonal phase of Eu 3+ : BiPO 4 , the thermal and phase transition phonon destructive dressing G p1 2 /(Γ 20 + iΔ i − iΔ p1 + G p2 2 /(Γ 23 + iΔ p1 − iΔ p2 ))) vanishes the spectral-temporal profile interaction at both 300 K and 77 K. Further, we compare TAT splitting at different phonon detuning and temperatures. Since t pT dominates over t pS , thus Δ pS ∼ = 0 does not bring change in the TAT splitting in figures 7(i) and (k). The TAT splitting in figure 7(i) reduces about 2-time while completely destroying in figure 7(k) as compared to figures 2(i) and (k). Compared to figures 2(i)-(l) with strong TAT splitting interaction owing to larger t pT and smaller t pS , the TAT splitting and its interaction (τ inter ) destroys in figures 7(i)-(l) for the pure HP due to a decrease in t pT .
Based on the above discussions we realized that spectral-temporal intensity profile interaction is depending upon temperature phonon and phase transition phonon. Such interaction is strongest at 300 K and less phase transition phonon dressing, while weakest at 77 K and more phase transition phonon dressing.

Additional two phase transition phonon dressing comparison
Finally, two phase transitions (figure 8) are compared to three phase transitions (figures 2-7) in hybrid signals with photon and phonon dressing. Different phases of a crystal have different lattice vibrational frequencies. A small value of the lattice vibrational frequencies (ω pj ) i.e., Δ p2S 0 (far off-resonance) reduces the phonon dressing than that of figures 2-7. However, the thermal phonon dressing in figures 8(a)-(d) can be explained the same as figures 2-4 and 5-7 respectively. Figure 8(a) shows the FL supremacy at the near time-gate position in the hybrid signal and results in a broad peak. The multi-peaks with three dressing dips in figure 8(b) are exhibited due to |G 1 | 2 /(Γ 10 + iΔ i + G p1 2 /(Γ 20 + iΔ i − iΔ p1 + G p2 2 /(Γ 23 + iΔ i + iΔ p1 − iΔ p2 ))) form equation (1), and can be explained the same as figure 4(a). In figure 8(b), the left dressing dip is produced by |G 1 | 2 , which is further added with two phonon dressing terms on its right produced through G pT 2 /(Γ 20 + iΔ i − iΔ p1 + G p2 2 /(Γ 23 + iΔ p1 − iΔ pS ))). At 77 K, the pure LTMP exhibits a sharp peak with a slight change in the is exhibited due to the high power (7 mW) of the laser as compared to figure 4 and 7 (4 mW).

Conclusions
In summary, the spectral-temporal intensity of the hybrid signals in five phases of Eu 3+ : BiPO 4 are strongly affected by thermal phonon Rabi frequencies and phase transition phonon detuning's. We suggest, the dressing from thermal phonon and phase transition phonon are significantly affected the temporal profile interaction of resonance and non-resonance terms. In the temporal profile intensity interaction, the resonance signal is suppressed by two laser destructive dressing interactions versus broadband excitation detuning. Furthermore, the pure HP shows weak resonance and non-resonance compared to the half HP + half LTMP and more HP + less LTMP samples through narrowband excitation. The resonance and background signals are totally vanished by the phase transition phonon dressing at both high and low temperatures. Lastly, phase transition phonon dressing increases the Fano (dressing)-dip numbers for one laser broadband excitation.