# Tuning the Nonlinear Optical Properties of Quantum Dot by Noise-Anharmonicity Interaction

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method

_{0}and m

^{*}denote the harmonic confinement frequency and the effective mass of the electron, respectively. ${H}_{0\text{}}^{\prime}$ reads:

_{c}=$\frac{eB}{{m}^{*}c}$ where ω

_{c}is the cyclotron frequency. Present calculation uses Landau gauge [A = (By, 0, 0)], where A is the vector potential.

_{anh}may be either even or odd and written as:

_{1}and k

_{2}are the anharmonicity constants.

_{0}. The required trial function $\left[{\psi}_{k}\left(x,y\right)\right]$ was generated by direct multiplication of the harmonic oscillator eigenstates viz. ${\varphi}_{n}\left(px\right)$ and ${\varphi}_{m}\left(qy\right)$ i.e.,

_{nm,k}are the coeffcients of linear combination and $p=\sqrt{\frac{{m}^{*}{\omega}_{0}}{\mathrm{\u045b}}}$ and $q=\sqrt{\frac{{m}^{*}\Omega}{\mathrm{\u045b}}}$. The trial function, thus constructed, leads to the determination of the matrix elements. Afterwards, the Hamiltonian matrix for H

_{0}(see Equation (1)) has been formed and then diagonalized to obtain the energy levels and the normalized eigenstates.

## 3. Results and Discussion

_{0}, where m

_{0}is the mass of free electron, ε = 12.4, n

_{r}= 3.2, ε

_{0}= 8.8542 × 10

^{−12}Fm

^{−1}, τ = 0.14 ps, σ

_{s}= 5.0 × 10

^{24}m

^{−3}, B = 5.0 T, ћω

_{0}= 100.0 meV and ζ = 1.0 × 10

^{−4}. These values appear reasonable for GaAs QD. All the NLO properties have been calculated by following the combination of usual density matrix approach and the iterative process. In subsequent discussions we use two more abbreviations for the brevity of the manuscript viz. odd parity anharmonicity (OPA) and even parity anharmonicity (EPA).

#### 3.1. Total Optical Absorption Coeffcient (TOAC)

_{R}, σ

_{s}, ε

_{0}and n

_{r}are the intensity of the electromagnetic field, magnetic permeability of the system (=1/ε

_{0}c

^{2}, where c is the speed of light in vacuum), real part of permittivity, carrier density, vacuum permittivity and the static component of refractive index, respectively. Γ

_{ij}is the phenomenological relaxation rate arising out of electron-phonon, electron-electron and other collision phenomena. The diagonal matrix element i.e., Γ

_{jj}yields the relaxation rate of state $\u23b8j\u27e9$ and Γ

_{jj}= 1/τ

_{jj}, where τ

_{jj}is the relaxation time of $\u23b8j\u27e9$ -th state. The diagonal matrix element i.e., Γ

_{ij}(= 1/τ

_{ij},i ≠ j) gives the relaxation rate of $\u23b8i\u27e9$-th and $\u23b8j\u27e9$-th states with relaxation time τ

_{ij}. TOAC [$\alpha \left(\nu ,I\right)$] now reads:

^{−8}, 10

^{−5}and 10

^{−2}. With odd anharmonicity and under noise-free state the TOAC peaks display blue-shift and decrease in the peak height with the enhancement of k. Under EPA, the blue-shift is again observed along with an increase in the peak height as k enhances. Therefore, in the absence of noise, both for OPA and EPA, the energy separation increases as k increases. However, the overlap between the concerned eigenstates decreases (increases) with an increase in k with odd (even) anharmonic potential.

^{−5}. Thus, in this case, both with OPA and EPA, we find enhancement of energy interval as k enhances. However, whereas the overlap between the eigenstates declines steadily with an increase in k with OPA, in the presence of EPA, the said overlap minimizes at k ~ 10

^{−5}.

^{−4.8}with MLWN, respectively.

^{−2}, 10

^{−6}and 10

^{−10}. In these diagrams a fixed value of k has been considered (k = 10

^{−8}). Under OPA and with applied ADWN (MLWN) the TOAC peaks reveal red-shift (blue-shift) along with fall in the peak height with an increase in ζ. Such a pattern points to a fall (rise) in the energy gap under applied ADWN (MLWN) and a steady fall in the overlap between the eigenstates as noise strength is increased.

^{−6}. It, therefore, comes out that an enhancement of ζ causes a steady drop in the energy interval while the overlap between the wave functions maximizes around some typical noise strength of ζ ~ 10

^{−6}. Under applied MLWN the TOAC peaks depict blue-shift along with regular decline in the peak height as ζ enhances. The observations indicate that in this case an enhancement of ζ happens to regularly enhance the energy level separations and reduce the aforesaid overlap.

^{−5.7}.

#### 3.2. Total Optical Refractive Index Change (TORIC)

^{−8}, 10

^{−5}and 10

^{−2}. With OPA (EPA) and without noise the TORIC peaks evince blue-shift and fall (rise) in the peak height as k enhances. Thus, under noise-free condition, both for OPA and EPA, the energy separation increases with an increase in k. However, the overlap between the concerned eigenstates decreases (increases) with an increase in k under odd (even) anharmonic potential.

^{−5}. Thus, in this case, both with OPA and EPA the energy separation increases as k enhances. However, whereas the overlap between the eigenfunctions depletes steadily with an increase in k with OPA, under EPA, the said overlap minimizes at k ~ 10

^{−5}.

^{−5}under applied MLWN, respectively.

^{−2}, 10

^{−6}and 10

^{−10}, for fixed value of k = 10

^{−8}. With OPA and under applied ADWN (MLWN) the TORIC peaks display red-shift (blue-shift) coupled with fall in the peak altitude as ζ increases. The said pattern reflects depletion (increase) in the energy separation under applied ADWN (MLWN) and a steadfast decline in the overlap between the relevant state functions as noise strength is increased.

^{−6}. Thus, now, an enhancement of ζ causes a steady fall in the energy interval while the overlap between the wave functions maximizes around some typical noise strength of ζ ~ 10

^{−6}. Under applied MLWN the TORIC peaks depict blue-shift along with regular fall in the peak altitude as ζ increases. The observations indicate that for this particular case an augmentation of ζ happens to persistently augment the energy level separations and diminish the aforesaid overlap.

^{−5}.

#### 3.3. Nonlinear Optical Rectification (NOR)

_{k}= 1/T

_{k}with k = (1, 2) are damping terms associated with the lifetime (longitudinal and transverse, respectively) of the electrons taking part in the transitions.

^{−8}, 10

^{−5}and 10

^{−2}. In the presence of odd anharmonicity and under noise-free state the NOR peaks display blue-shift and enhancement of the peak height with an increase in k. Under EPA, the said blue-shift is re-observed along with non-uniform change of the peak height. The peak altitude maximizes at k ~ 10

^{−5}. Thus, without noise, both for EPA and OPA the energy separation enhances with enhancement of k. It, therefore, comes out that, under OPA, the asymmetric nature of the system undergoes steady increase as k enhances. On the other hand, under EPA, the asymmetry of the system maximizes at k ~ 10

^{−5}.

^{−5}. Thus, resembling the observations under ADWN, in this case also, the parity of the anharmonic potential appears trivial while k changes. Additionally, an enhancement of k gets associated with augmentation of energy level interval and the asymmetric nature of the system maximizes at k ~ 10

^{−5}.

^{−5}under applied MLWN, respectively. However, with even anharmonicity, the aforesaid plots reveal feeble maximization at k ~ 10

^{−4.5}without noise, regular enhancement as k falls under applied ADWN and a noticeable maximization at k ~ 10

^{−5.2}under applied MLWN, respectively.

^{−2}, 10

^{−6}and 10

^{−10}, keeping k fixed at k = 10

^{−6}. Under OPA and with applied ADWN the NOR peaks reveal red-shift as ζ enhances. Added to this, the NOR peak altitude becomes maximum at ζ ~ 10

^{−6}. The pattern reflects a fall in the energy separation as ζ increases. The asymmetric character of the system also becomes maximum at some intermediate ζ. Under applied MLWN the NOR peaks manifest steady blue-shift as ζ increases and the peak altitude reveals maximization at ζ ~ 10

^{−6}. The profiles, therefore, suggest a regular increase of energy separation as ζ increases and generation of extremely large asymmetric nature at ζ ~ 10

^{−6}.

^{−5.7}and settle to the value without noise when ζ becomes negligibly small.

#### 3.4. Second Harmonic Generation (SHG)

_{10}= Γ

_{20}is the off-diagonal relaxation rate. It goes without saying that the peak value of SHG is proportional to the geometric factor (GF)$\left|{M}_{01}\right|\xb7\left|{M}_{12}\right|\xb7\left|{M}_{20}\right|$ of the system. Thus, attainment of large SHG requires small relaxation rate Γ and large GF.

^{−8}, 10

^{−5}and 10

^{−2}. In the presence of both odd and even anharmonicity and without noise the SHG peaks depict blue-shift and the maximization of the peak altitude at k ~ 10

^{−5}. Thus, without noise, the parity of the anharmonicity refrains from affecting the qualitative traits of the SHG profiles over a range of k values.

^{−5}without noise and regular growth with fall of k both under applied ADWN and MLWN.

^{−2}, 10

^{−6}and 10

^{−10}, keeping k fixed at k = 10

^{−3}. With OPA and under applied ADWN (MLWN) the SHG peaks display red-shift (blue-shift) as ζ increases. Additionally, the SHG peak height shows maximization at ζ ~ 10

^{−6}for both under applied ADWN and MLWN. Such a trend suggests a fall (rise) in the energy separation as ζ is increased under applied ADWN (MLWN). However, regardless of mode of application of noise, the asymmetric character of the system becomes maximum at an intermediate strength of ζ ~ 10

^{−6}.

^{−6}.

^{−5.5}. Only for the special combination mentioned above the GF displays steady decline with decrease in the noise strength.

#### 3.5. Third Harmonic Generation (THG)

_{ij}(i ≠ j) = Γ

_{2}= 1/T

_{2}is the off-diagonal relaxation rate with transverse relaxation time T

_{2}. The geometric factor $\left(\left|{M}_{01}\right|\xb7\left|{M}_{12}\right|\xb7\left|{M}_{23}\right|\xb7\left|{M}_{30}\right|\right)$ gives the maximum THG susceptibility (${\chi}_{3\nu ,max}^{\left(3\right)}$) at resonance peaks [39].

^{−8}, 10

^{−5}and 10

^{−2}. In the presence of OPA and under noise-free state the THG peaks evince blue-shift and growth in the peak altitude with enhancement of k. In the presence of EPA, the blue-shift is again observed but the peak altitude now becomes maximum at k ~ 10

^{−5}. Thus, in absence of noise, both for OPA and EPA the energy separation increases as k enhances. However, whereas with OPA the effective extent of overlap of the relevant eigenfunctions grows steadily as k increases, with EPA the said overlap maximizes at k ~ 10

^{−5}.

^{−5}. And with EPA the said blue-shift occurs coupled with monotonic drop in the peak altitude as k enhances. Thus, in the presence of ADWN, both for OPA and EPA, the energy separation augments with enhancement of k. However, whereas with OPA the degree of overlap between the concerned eigenstates maximizes at k ~ 10

^{−5}, with EPA, the said overlap persistently falls as k enhances.

^{−5}with EPA, respectively. Thus, under MLWN, both for OPA and EPA the energy separation augments as k enhances. However, whereas with OPA the extent of overlap between the pertinent eigenfunctions regularly falls as k increases, with EPA the said overlap displays maximization at k ~ 10

^{−5}.

^{−5.2}under applied ADWN and regular rise with fall of k under applied MLWN, respectively. However, under EPA, the said plots divulge feeble maximization at k ~ 10

^{−4.3}and k ~ 10

^{−4}in noise-free state and under MLWN, respectively. Under similar condition and in the presence of ADWN the GF profile reveals a steady increase with a decrease in k.

^{−2}, 10

^{−6}and 10

^{−10}, keeping k fixed at k = 10

^{−4}. With OPA and under applied ADWN (MLWN) the THG peaks exhibit red-shift (blue-shift) as ζ increases. Moreover, both under applied ADWN and MLWN the THG peak altitude undergoes maximization at ζ ~ 10

^{−6}. Such a trend suggests a fall (rise) in the energy separation under applied ADWN (MLWN) as noise strength is increased. However, regardless of the pathway of application of noise, the overlap between the concerned eigenstates maximizes at ζ ~ 10

^{−6}.

^{−6}. The observation reflects depletion (enhancement) in the energy interval under applied ADWN (MLWN) as noise strength is increased. Moreover, under applied ADWN, the degree of overlap between the concerned wave functions enhances regularly as noise strength enhances. However, under applied MLWN, the said overlap maximizes at ζ ~ 10

^{−6}.

^{−5}. Only for the typical combination mentioned above the GF displays steady decline with decrease in the noise strength.

#### 3.6. Electro-Absorption Coeffcient (EAC)

_{1}and υ

_{2}is given by [46]:

_{i}(ψ

_{j}) are the eigenstates and ${\omega}_{ij}=\left({E}_{i}-{E}_{j}\right)/\mathrm{\u045b}$ is the transition frequency. Γ = 1/T

_{2}being the relaxation rate with relaxation time T

_{2}. Current study considers $\nu $

_{1}= 0 and $\nu $

_{2}= −$\nu $ for simplicity. χ

^{(3)}is a complex quantity and its imaginary part is known as the EAC and is given by [46]:

^{−8}, 10

^{−5}and 10

^{−2}. In the presence of both OPA and EPA and without noise the EAC peaks reveal blue-shift and the steady drop of peak height (in absolute sense) as k increases.

^{−5}pursued by blue-shift as k is increased beyond. The peak height depicts steadfast fall (in absolute sense) as k increases.

^{−5}pursued by blue-shift as k is increased further. On the other hand, with even anharmonicity, the EAC peaks initially display red-shift with an increase in k up to k ~ 10

^{−5}pursued by blue-shift as k increases further. However, both with odd and even anharmonicities the EAC peak height monotonically falls (in absolute sense) with an increase in k.

^{−2}, 10

^{−6}and 10

^{−10}at a fixed value of k = 10

^{−4}With OPA and both under applied ADWN and MLWN the EAC peak height decreases (in absolute sense) with an increase in ζ associated with a blue-shift.

^{−6}followed by blue-shift as ζ is increased beyond.

^{−4}. The plots evince persistent decline in the EAC peak value (in absolute sense) with an increase in the noise strength under all conditions.

#### 3.7. DC-Kerr Effect (DCKE)

^{(3)}(see Equation (20)) is called the DCKE and is given by [46]:

^{−8}, 10

^{−5}and 10

^{−2}. In the presence of both OPA and EPA and without noise, the DCKE peaks manifest blue-shift and the regular drop of peak height as k increases.

^{−5}.

^{−5}and then blue-shift as k increases beyond. The peak altitude shows similar trend as with OPA.

^{−5}.

^{−2}, 10

^{−6}and 10

^{−10}, at a fixed value of k = 10

^{−4}. With OPA and both under applied ADWN and MLWN, the DCKE peak reveals blue-shift. However, the DCKE peak height changes in different ways in the presence of ADWN and MLWN. Under ADWN the peak altitude falls regularly as ζ enhances whereas with MLWN the peak altitude minimizes at ζ ~ 10

^{−6}.

^{−6}followed by a blue-shift as ζ increases further. However, under applied MLWN, the DCKE peaks depict uniform blue-shift as ζ increases. The peak altitude, on the other hand, undergoes steady decline with an increase in ζ both under applied ADWN and MLWN.

^{−4}. In compliance with the earlier observations the plot evinces perceptible minimization at ζ ~ 10

^{−5}, only with odd anharmonicity and under applied MLWN. For all other conditions the said plots reveal steady drop as noise strength increases.

_{0}+ n

_{2}I and α = α

_{0}+ α

_{2}I where n, n

_{0}, n

_{2}, α, α

_{0}, α

_{2}and I are total RI, linear RI, nonlinear RI, total AC, linear AC, nonlinear AC and the intensity of electromagnetic wave, respectively. In practice, the expressions of n

_{2}and α

_{2}are substantially modified when we shift from non-absorbing to absorbing medium. This necessitates the estimation of corrections required to the values of n

_{2}and α

_{2}in absorbing materials in comparison with the non-absorbing medium. The above corrections are related to the ratios of linear AC and linear RI and that of imaginary and real parts of χ

^{(3)}. Thus, in view of achieving recognizable refractive nonlinearities and nonlinear absorption effects, the above correction factors (CFs)emerge immensely important [55]. A variation of anharmonic potential of given symmetry under applied noise can be exploited to modulate above CFs quite effectively.

^{(3)}, respectively. Similarly, the CF relevant to nonlinear AC in absorbing and non-absorbing media can be given by [55]:

^{−6}even when anharmonicity is present.

^{−6}even when anharmonicity is present.

^{−4}. Under applied ADWN, and both with odd and even anharmonicities, the CF for RI undergoes monotonic enhancement with a decrease in the noise strength and finally saturates at low noise strength domain. Under applied MLWN, on the other hand, the CF for RI displays minimization at ζ ~ 10

^{−6}in the presence OPA. However, under EPA the CF for RI enhances with weakening of the noise strength and culminates in saturation in the low noise strength regime.

^{−4}. Under the influence of ADWN, and both with OPA and EPA, the CF for AC undergoes steadfast depletion with a drop in the noise strength and ultimately saturates at the low noise strength domain. Under applied MLWN, on the other hand, the CF for AC displays maximization at ζ ~ 10

^{−6.5}in the presence OPA. However, in the presence of EPA, the CF for AC again declines with a reduction in the noise strength and shows saturation in the low noise strength domain.

#### 3.8. Group Index (GI)

_{g}= c/v

_{g}. GI possesses tremendous importance in optical communication and information processing [59]. GI is defined as [59]:

^{−8}, 10

^{−5}and 10

^{−2}. Under a noise-free state, both in the presence of odd and even anharmonicities, the GI peaks exhibit blue-shift. Moreover, in both the cases distinct GI minima are observed over the range of k values. However, the depth of the minima persistently falls (rises) as k increases with odd (even) anharmonicity.

^{−5}.

^{−4.5}under applied MLWN.

^{−5}. Thus, the presence of even anharmonicity brings about more diversities in the features of anomalous dispersion. Furthermore, a suitable combination of applied noise and anharmonicity can modulate the region of anomalous dispersion.

^{−2}, 10

^{−6}and 10

^{−10},keeping k fixed at 10

^{−5}. With OPA and both under applied ADWN and MLWN, the depth of the GI minima decreases monotonically as ζ increases. However, the GI peaks exhibit red-shift (blue-shift) in the presence of ADWN (MLWN) as ζ increases. Such behavior reflects a decrease (increase) in the energy interval under applied ADWN (MLWN) as noise strength is increased. Moreover, irrespective of the mode of application of noise, the extent of anomalous dispersion manifestly diminishes with an increase in the noise strength under odd anharmonicity.

^{−6}indicating the highest extent of anomalous dispersion around this noise strength. However, under applied MLWN the depth of the GI minima steadily falls with an increase in the noise strength, indicating an accompanying decline in the extent of anomalous dispersion in the presence of even anharmonicity.

^{−5}. The profiles manifest that, barring the combination of ADWN and EPA, in all other conditions the depth of the GI minima continually declines with the enhancement of ζ. It is the particular combination referred to above for which the depth of the GI minima maximizes at ζ ~ 10

^{−6}. Thus, it becomes possible to regulate the region of anomalous dispersion by the suitable adjustment of the parity of the anharmonic potential, the noise mode and the value of the noise strength.

#### 3.9. Optical Gain (OG)

_{0}, e, $w$, σ

_{v}, ε, n

_{r}and E are the free electron mass, electronic charge, well width, charge density, dielectric constant of medium, refractive index and the transition energy between VB and CB corresponding to photon energy, respectively. ${M}_{fi}={\psi}_{f}\left|r\right|{\psi}_{i}$ is the transition matrix element with ψ

_{i}and ψ

_{f}as the initial and final wave functions for the optical transition between hole subbands and electron subbands. f

_{c}and f

_{v}are the Fermi-Dirac distribution function of electrons in CB and VB, respectively, given by [65]:

_{nc}and E

_{nv}are the quantized electron and hole energy levels, respectively, and E

_{fc}and E

_{fv}are the electron and hole quasi-Fermi level, respectively.

_{sp}is the spontaneous emission rate given by [62]:

^{−8}, 10

^{−5}and 10

^{−2}. Under a noise-free state, both in the presence of OPA and EPA, the OG peaks display blue-shift along with a regular drop in the OG peak altitude as k enhances.

^{−5}. Under applied MLWN, both with OPA and EPA, the OG peaks delineate blue-shift with steady decline in the peak altitude with an increase in k. Thus, for a given environment (noise-free/under ADWN/under MLWN), the symmetry of the anharmonicity does not qualitatively alter the OG profiles.

^{−5}. The above behavior holds good regardless of the symmetry of the anharmonic potential.

^{−5}. The above behavior is observed both for odd and even anharmonic potentials (Figure 19a). Figure 19b shows that, regardless of the presence of noise and parity of the anharmonicity, the OG peak increases manifestly with J. In all the cases, the OG peaks settle to some steady values for large values of J (the saturation gain). Thus, here the noise mode and the symmetry of the anharmonicity do not qualitatively influence the observed outcome. Figure 19c depicts a prominent rise in band gap as with the enhancement of k without noise and under MLWN. However, under applied ADWN, the band gap undergoes minimizationaround k ~ 10

^{−5}. The above behavior emerges both for odd and even anharmonic potentials.

^{−10}, 10

^{−6}and 10

^{−2}) for ADWN and MLWN, respectively, both with OPA and EPA. In all these diagrams k assumes the fixed value of 10

^{−6}. With OPA and both with ADWN and MLWN the OG peak at first undergoes blue-shift with an increase in ζ up to ζ ~ 10

^{−6}followed by a red-shift as ζ is increased further. Furthermore, the OG peak height also shows maximization (minimization) at ζ ~ 10

^{−6}under applied ADWN (MLWN).

^{−6}. In the presence of OPA the OG peaks display distinct maximization (minimization) at ζ ~ 10

^{−5}under applied ADWN (MLWN). However, with EPA, the said peak values divulge steady rise (fall) as ζ enhances under applied ADWN (MLWN). In all situations, the OG peaks approach their respective noise-free values when the noise strength becomes extremely small.

^{−6}. In the presence of odd anharmonicity J displays distinct maximization (minimization) at ζ ~ 10

^{−5}under applied ADWN (MLWN). However, with EPA, the J values exhibit steady rise (fall) with an increase in ζ under applied ADWN (MLWN). Under all conditions the J values proceed to their noise free values when the noise strength assumes extremely small values. Figure 21b depicts that, independent of the presence of noise and the parity of the anharmonic potential, the OG peak undergoes noticeable enhancement with J and saturate at large value of J (the saturation gain). Thus, here the noise mode and the symmetry of the anharmonicity do not cause any qualitative alteration of the observed outcomes. Figure 21c shows that in the presence of odd anharmonicity the band gap passes through distinct minimization (maximization) at ζ ~ 10

^{−5}under applied ADWN (MLWN). However, with even anharmonicity the band gap exhibits steady decline (growth) with an increase in ζ under applied ADWN (MLWN). In all situations the band gaps approach their noise-free values at vanishingly low values of ζ.

_{v}) both for odd and even anharmonicities without noise, and with ADWN and MLWN, respectively, for three different values of k viz. 10

^{−8}, 10

^{−5}and 10

^{−2}. The DG is defined as the differential coefficient of OG with respect to σ

_{v}. DG is an indicator of the efficacy of the laser to transform the current injected into the flow luminous and transmit OG through carrier injection. An enhanced DG suggests a large modulation speed and low spectral width of emission. DG is also an important tool to determine the modulation of band width of semiconductor laser. Under all conditions the DG profiles reveal maximization more or less around σ

_{v}~3.0 × 10

^{18}cm

^{−3}. Figure 22d shows the plots of DG peak values with the alteration of k in the presence and absence of noise, both with OPA and EPA. The profiles display maximization under applied ADWN (for both OPA and EPA at k ~ 10

^{−5}and k ~ 10

^{−6}, respectively) and under applied MLWN with EPA (at k ~ 10

^{−5.5}). For all other situations the DG peak values delineate steady fall as anharmonicity constant enhances.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**TOAC vs. hυ diagrams: (

**a**) devoid of noise, (

**b**) under ADWN, and (

**c**) under MLWN. In these diagrams the anharmonicity has (i) odd parity and k = 10

^{−8}, (ii) odd parity and k = 10

^{−5}, (iii) odd parity and k = 10

^{−2}, (iv) even parity and k = 10

^{−8}, (v) even parity and k = 10

^{−5}and (vi) even parity and k = 10

^{−2}. (

**d**) Depiction of TOAC peak heights vs. −log(k): (i) devoid of noise and OPA, (ii) devoid of noise and EPA, (iii) with ADWN and OPA, (iv) with ADWN and EPA, (v) with MLWN and OPA and (vi) with MLWN and EPA.

**Figure 2.**TOAC vs. hυ diagrams with (

**a**) OPA and (

**b**) EPA. In these diagrams (i) ADWN and ζ = 10

^{−10}, (ii) ADWN and ζ = 10

^{−6}, (iii) ADWN and ζ = 10

^{−2}, (iv) MLWN and ζ = 10

^{−10}, (v) MLWN and ζ = 10

^{−6}, (vi) MLWN and ζ = 10

^{−2}. (

**c**) Depiction of TOAC peak heights vs. −log(ζ): (i) with ADWN and OPA, (ii) with ADWN and EPA, (iii) with MLWN and OPA and (iv) with MLWN and EPA.

**Figure 3.**TORIC vs. hυ diagrams (

**a**) devoid of noise, (

**b**) under ADWN and (

**c**) under MLWN. In these diagrams the anharmonicity has (i) odd parity and k = 10

^{−8}, (ii) odd parity and k = 10

^{−5}, (iii) odd parity and k = 10

^{−2}, (iv) even parity and k = 10

^{−8}, (v) even parity and k = 10

^{−5}, (vi) even parity and k = 10

^{−2}. (

**d**) Depiction of TORIC peak heights vs. −log(k): (i) devoid of noise and OPA, (ii) devoid of noise and EPA, (iii) with ADWN and OPA, (iv) with ADWN and EPA, (v) with MLWN and OPA and (vi) with MLWN and EPA.

**Figure 4.**TORIC vs. hυ diagrams with (

**a**) OPA and (

**b**) EPA. In these diagrams (i) ADWN and ζ = 10

^{−10}, (ii) ADWN and ζ = 10

^{−6}, (iii) ADWN and ζ = 10

^{−2}, (iv) MLWN and ζ = 10

^{−10}, (v) MLWN and ζ = 10

^{−6}, (vi) MLWN and ζ = 10

^{−2}. (

**c**) Depiction of TOAC peak heights vs. −log(ζ): (i) with ADWN and OPA, (ii) with ADWN and EPA, (iii) with MLWN and OPA and (iv) with MLWN and EPA.

**Figure 5.**NOR vs. hυ diagrams (

**a**) devoid of noise, (

**b**) under ADWN and (

**c**) under MLWN. In these diagrams the anharmonicity has (i) odd parity and k = 10

^{−8}, (ii) odd parity and k = 10

^{−5}, (iii) odd parity and k = 10

^{−2}, (iv) even parity and k = 10

^{−8}, (v) even parity and k = 10

^{−5}, (vi) even parity and k = 10

^{−2}. (

**d**) Depiction of GF for NOR vs. −log(k): (i) devoid of noise and OPA, (ii) devoid of noise and EPA, (iii) with ADWN and OPA, (iv) with ADWN and EPA, (v) with MLWN and OPA and (vi) with MLWN and EPA.

**Figure 6.**NOR vs. hυ diagrams with (

**a**) OPA and (

**b**) EPA. In these diagrams (i) ADWN and ζ = 10

^{−10}, (ii) ADWN and ζ = 10

^{−6}, (iii) ADWN and ζ = 10

^{−2}, (iv) MLWN and ζ = 10

^{−10}, (v) MLWN and ζ = 10

^{−6}, (vi) MLWN and ζ = 10

^{−2}. (

**c**) Depiction of GF for NOR vs. –log(ζ): (i) with ADWN and OPA, (ii) with ADWN and EPA, (iii) with MLWN and OPA and (iv) with MLWN and EPA.

**Figure 7.**SHG vs. hυ diagrams (

**a**) devoid of noise, (

**b**) under ADWN and (

**c**) under MLWN. In these diagrams the anharmonicity has (i) odd parity and k = 10

^{−8}, (ii) odd parity and k = 10

^{−5}, (iii) odd parity and k = 10

^{−2}, (iv) even parity and k = 10

^{−8}, (v) even parity and k = 10

^{−5}, (vi) even parity and k = 10

^{−2}. (

**d**) Depiction of GF for SHG vs. −log(k): (i) devoid of noise and OPA, (ii) devoid of noise and EPA, (iii) with ADWN and OPA, (iv) with ADWN and EPA, (v) with MLWN and OPA and (vi) with MLWN and EPA.

**Figure 8.**SHG vs. hυ diagrams with (

**a**) OPA and (

**b**) EPA. In these diagrams (i) ADWN and ζ = 10

^{−10}, (ii) ADWN and ζ = 10

^{−6}, (iii) ADWN and ζ= 10

^{−2}, (iv) MLWN and ζ = 10

^{−10}, (v) MLWN and ζ = 10

^{−6}, (vi) MLWN and ζ = 10

^{−2}. (

**c**) Depiction of GF for SHG vs. −log(ζ): (i) with ADWN and OPA, (ii) with ADWN and EPA, (iii) with MLWN and OPA and (iv) with MLWN and EPA.

**Figure 9.**THG vs. hυ diagrams (

**a**) devoid of noise, (

**b**) under ADWN and (

**c**) under MLWN. In these diagrams the anharmonicity has (i) odd parity and k = 10

^{−8}, (ii) odd parity and k = 10

^{−5}, (iii) odd parity and k = 10

^{−2}, (iv) even parity and k = 10

^{−8}, (v) even parity and k = 10

^{−5}, (vi) even parity and k = 10

^{−2}. (

**d**) Depiction of GF for THG vs. −log(k): (i) devoid of noise and OPA, (ii) devoid of noise and EPA, (iii) with ADWN and OPA, (iv) with ADWN and EPA, (v) with MLWN and OPA and (vi) with MLWN and EPA.

**Figure 10.**THG vs. hυ diagrams with (

**a**) OPA and (

**b**) EPA. In these diagrams (i) ADWN and ζ = 10

^{−10}, (ii) ADWN and ζ = 10

^{−6}, (iii) ADWN and ζ = 10

^{−2}, (iv) MLWN and ζ = 10

^{−10}, (v) MLWN and ζ = 10

^{−6}, (vi) MLWN and ζ = 10

^{−2}. (

**c**) Depiction of GF for THG vs. −log(ζ): (i) with ADWN and OPA, (ii) with ADWN and EPA, (iii) with MLWN and OPA and (iv) with MLWN and EPA.

**Figure 11.**EAC vs. hυ diagrams (

**a**) devoid of noise, (

**b**) under ADWN and (

**c**) under MLWN. In these diagrams the anharmonicity has (i) odd parity and k = 10

^{−8}, (ii) odd parity and k = 10

^{−5}, (iii) odd parity and k = 10

^{−2}, (iv) even parity and k = 10

^{−8}, (v) even parity and k = 10

^{−5}, (vi) even parity and k = 10

^{−2}. (

**d**) Depiction of EAC minimum peak values vs. −log(k): (i) devoid of noise and OPA, (ii) devoid of noise and EPA, (iii) with ADWN and OPA, (iv) with ADWN and EPA, (v) with MLWN and OPA and (vi) with MLWN and EPA.

**Figure 12.**EAC vs. hυ diagrams with (

**a**) OPA and (

**b**) EPA. In these diagrams (i) ADWN and ζ = 10

^{−10}, (ii) ADWN and ζ = 10

^{−6}, (iii) ADWN and ζ = 10

^{−2}, (iv) MLWN and ζ = 10

^{−10}, (v) MLWN and ζ = 10

^{−6}, (vi) MLWN and ζ = 10

^{−2}. (

**c**) Depiction of EAC peak minima vs. −log(ζ): (i) with ADWN and OPA, (ii) with ADWN and EPA, (iii) with MLWN and OPA and (iv) with MLWN and EPA.

**Figure 13.**DCKE vs. hυ diagrams (

**a**) devoid of noise, (

**b**) under ADWN and (

**c**) under MLWN. In these diagrams the anharmonicity has (i) odd parity and k = 10

^{−8}, (ii) odd parity and k = 10

^{−5}, (iii) odd parity and k = 10

^{−2}, (iv) even parity and k = 10

^{−8}, (v) even parity and k = 10

^{−5}, (vi) even parity and k = 10

^{−2}. (

**d**) Depiction of DCKE peak values vs. −log(k): (i) devoid of noise and OPA, (ii) devoid of noise and EPA, (iii) with ADWN and OPA, (iv) with ADWN and EPA, (v) with MLWN and OPA and (vi) with MLWN and EPA.

**Figure 14.**DCKE vs. hυ diagrams with (

**a**) OPA and (

**b**) EPA. In these diagrams (i) ADWN and ζ = 10

^{−10}, (ii) ADWN and ζ = 10

^{−6}, (iii) ADWN and ζ = 10

^{−2}, (iv) MLWN and ζ = 10

^{−10}, (v) MLWN and ζ = 10

^{−6}, (vi) MLWN and ζ = 10

^{−2}. (

**c**) Depiction of DCKE peak vs. −log(ζ): (i) with ADWN and OPA, (ii) with ADWN and EPA, (iii) with MLWN and OPA and (iv) with MLWN and EPA.

**Figure 15.**Plots of (

**a**) CF for RI vs. −log(k) and (

**b**) CF for AC vs. −log(k): (i) devoid of noise and under OPA, (ii) devoid of noise and under EPA, (iii) with ADWN and under OPA, (iv) with ADWN and under EPA, (v) with MLWN and under OPA and (vi) with MLWN and under EPA. Plots of (

**c**) CF for RI vs. −log(ζ) and (

**d**) CF for AC vs. −log(ζ): (i) with ADWN and under OPA, (ii) with ADWN and under EPA, (iii) with MLWN and under OPA and (iv) with MLWN and under EPA.

**Figure 16.**GI vs. hυ diagrams (

**a**) devoid of noise, (

**b**) under ADWN and (

**c**) under MLWN. In these diagrams the anharmonicity has (i) odd parity and k = 10

^{−8}, (ii) odd parity and k = 10

^{−5}, (iii) odd parity and k = 10

^{−2}, (iv) even parity and k = 10

^{−8}, (v) even parity and k = 10

^{−5}, (vi) even parity and k = 10

^{−2}. (

**d**) Depiction of GI peak values vs. −log(k): (i) devoid of noise and OPA, (ii) devoid of noise and EPA, (iii) with ADWN and OPA, (iv) with ADWN and EPA, (v) with MLWN and OPA and (vi) with MLWN and EPA.

**Figure 17.**GI vs. hυ diagrams with (

**a**) OPA and (

**b**) EPA. In these diagrams (i) ADWN and ζ = 10

^{−10}, (ii) ADWN and ζ = 10

^{−6}, (iii) ADWN and ζ = 10

^{−2}, (iv) MLWN and ζ = 10

^{−10}, (v) MLWN and ζ = 10

^{−6}, (vi) MLWN and ζ = 10

^{−2}. (

**c**) Depiction of GI peak vs. −log(ζ): (i) with ADWN and OPA, (ii) with ADWN and EPA, (iii) with MLWN and OPA and (iv) with MLWN and EPA.

**Figure 18.**OG vs. hυ diagrams (

**a**) devoid of noise, (

**b**) under ADWN and (

**c**) under MLWN. In these diagrams the anharmonicity has (i) odd parity and k = 10

^{−8}, (ii) odd parity and k = 10

^{−5}, (iii) odd parity and k = 10

^{−2}, (iv) even parity and k = 10

^{−8}, (v) even parity and k = 10

^{−5}, (vi) even parity and k = 10

^{−2}. (

**d**) Depiction of OG peak values vs. −log(k): (i) devoid of noise and OPA, (ii) devoid of noise and EPA, (iii) with ADWN and OPA, (iv) with ADWN and EPA, (v) with MLWN and OPA and (vi) with MLWN and EPA.

**Figure 19.**Plots of (

**a**) J vs. −log(k), (

**b**) OG peak vs. J and (

**c**) band gap vs. −log(k): (i) without noise and under OPA, (ii) without noise and under EPA, (iii) with ADWN and under EPA, (iv) with ADWN and under EPA, (v) with MLWN and under OPA and (vi) with MLWN and under EPA.

**Figure 20.**OG vs. hυ diagrams with (

**a**) OPA and (

**b**) EPA. In these diagrams (i) ADWN and ζ = 10

^{−10}, (ii) ADWN and ζ = 10

^{−6}, (iii) ADWN and ζ = 10

^{−2}, (iv) MLWN and ζ = 10

^{−10}, (v) MLWN and ζ = 10

^{−6}, (vi) MLWN and ζ = 10

^{−2}. (

**c**) Depiction of OG peak vs. −log(ζ): (i) with ADWN and OPA, (ii) with ADWN and EPA, (iii) with MLWN and OPA and (iv) with MLWN and EPA.

**Figure 21.**Plots of (

**a**) J vs. −log(ζ), (

**b**) OG peak vs. J and (

**c**) band gap vs. −log(ζ): (i) with ADWN and under OPA, (ii) with ADWN and under EPA, (iii) with MLWN and under OPA and (iv) with MLWN and under EPA.

**Figure 22.**Plots of DG vs. σ

_{v}(

**a**) without noise, (

**b**) with ADWN and (

**c**) with MLWN. In these diagrams (i) OPA and k = 10

^{−8}, (ii) OPA and k = 10

^{−5}, (iii) OPA and k = 10

^{−2}, (iv) EPA and k = 10

^{−8}, (v) EPA and k = 10

^{−5}, (vi) EPA and k = 10

^{−2}. (

**d**) Depiction of DG peak values vs. −log(k): (i) in absence of noise and under OPA, (ii) in absence of noise and under EPA, (iii) with ADWN and under OPA, (iv) with ADWN and under EPA, (v) with MLWN and under OPA and (vi) with MLWN and under EPA.

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**MDPI and ACS Style**

Roy, D.; Arif, S.M.; Datta, S.; Ghosh, M.
Tuning the Nonlinear Optical Properties of Quantum Dot by Noise-Anharmonicity Interaction. *Atoms* **2022**, *10*, 122.
https://doi.org/10.3390/atoms10040122

**AMA Style**

Roy D, Arif SM, Datta S, Ghosh M.
Tuning the Nonlinear Optical Properties of Quantum Dot by Noise-Anharmonicity Interaction. *Atoms*. 2022; 10(4):122.
https://doi.org/10.3390/atoms10040122

**Chicago/Turabian Style**

Roy, Debi, Sk. Md. Arif, Swarnab Datta, and Manas Ghosh.
2022. "Tuning the Nonlinear Optical Properties of Quantum Dot by Noise-Anharmonicity Interaction" *Atoms* 10, no. 4: 122.
https://doi.org/10.3390/atoms10040122