# Errata

### Chapter 3

Page 74. The formula in Problem 3.3 should be
$\alpha_{\rm metal} = V \frac{1-{1\over10} (\varepsilon_{\rm p}-\varepsilon_{\rm m})x^2 + O(x^4)} {\left[\frac{\varepsilon_{\rm m}}{\varepsilon_{\rm p}-\varepsilon_{\rm m}}+{1\over3} \right] - {1\over30} (\varepsilon_{\rm p}+10\varepsilon_{\rm m}) x^2 - i \frac{4\pi^2 \varepsilon_{\rm m}^{3/2}}{3} \frac{V}{\lambda^3} + O(x^4) }$

### Chapter 4

Pages 92-93. Equation (4.38) should be
$\displaystyle \mathbf{E}^{\mathrm{CVB}}_{\varphi}(x,y,z) = E^{\mathrm{HG}}_{01}(x,y,z) \, \hat{\bf y} - E^{\mathrm{HG}}_{10}(x,y,z) \, \hat{\bf x}$
and Fig. 4.10 should be corrected accordingly by changing the labels of the Hermite-Gaussian beams used to obtain the azimuthal cylindrical vector beam. The corrected figure is available at Figure 4.10 (Corrected).
Thanks to the Optical Tweezers group of Sharif University of Technology for finding this mistake!

### Chapter 5

Page 122, Table 5.2. The spherical Hankel functions should be:
$\displaystyle h_0(z) = -i e^{iz} {1 \over z}$
$\displaystyle h_1(z) = - e^{iz} {z+i \over z^2}$
$\displaystyle h_2(z) = i e^{iz} {z^2 + 3iz - 3 \over z^3}$
$\displaystyle h_3(z) = e^{iz} {z^3 +6iz^2 -15z -15i \over z^4}$
Thanks to S. Masoumeh Mousavi for finding this mistake!

Page 125. In Equation (5.76) the second vector spherical harmonic should be
${\bf Z}_{lm}^{(1)}(\hat{\bf r}) = -\frac{i}{\sqrt{l (l+1)}} \; r \hat{\bf r} \times \nabla Y_{lm}(\hat{\bf r})$
Thanks to Bruno Fernando for finding this mistake!

Page 130. Equation (5.82) should be
$\mathbf{E}(r,\hat{\bf r}) = E \sum_{l=0}^\infty \sum_{m=-l}^l A_{lm}^{(1)} {\bf H}_{lm}^{(1)}(k r,\hat{\bf r}) + A_{lm}^{(2)} {\bf H}_{lm}^{(2)}(k r,\hat{\bf r})$

Page 131. Equation (5.89) should be
$W^{(1)}_{+,lm} = W^{(2)}_{+,lm} = i^l \sqrt{4\pi (2l+1)} \delta_{m,1}$
$W^{(1)}_{-,lm} = -W^{(2)}_{-,lm} = i^l \sqrt{4\pi (2l+1)} \delta_{m,-1}$
Thanks to Alessio Caciagli for finding this mistake!

Page 136. Exercise 5.2.23 requires to calculate the \emph{forward} scattering amplitude. ThereEquation (5.105) should be
$\hat{\bf e}_{\rm i} \cdot {\bf f}(\hat{\bf k}_{\rm s}) = - {1 \over 4\pi i k_{\rm m}} ...$
Thanks to Bruno Fernando for finding this mistake!

### Chapter 7

Page 197. Equation (7.18) should be
$\displaystyle {\partial\rho(r,t) \over \partial t} = - {1\over\gamma} {\partial \left[ F(r,t) \rho(r,t) \right] \over \partial r} + D {\partial^2 \rho(r,t) \over \partial r^2}$
Thanks to the Optical Tweezers group of Sharif University of Technology for finding this mistake!

Page 208. Eq. (7.32) should be
${d \over dt}r(t) = {F(t) \over \gamma(r)} + \sqrt{2D(r)} W(t)$
Thanks to Pembe Gizem Ozdil and Gamze Islamoglu from Bogazici University for finding this mistake!

Page 208. After Eq. (7.35), the definition of $\tilde{h}$ should be $\tilde{h} = {\rm Ch}^{-1} \left( \frac{h}{a} \right)$.
Thanks to S. Masoumeh Mousavi for finding this mistake!

### Chapter 8

Page 235. Fig. 8.5 should be corrected by inverting the labels (b) and (c). The corrected figure is available at Figure 4.10 (Corrected).
Thanks to the Optical Tweezers group of Sharif University of Technology for finding this mistake!

### Chapter 9

Page 285. Equation (9.42) should be
$\displaystyle e^{-i2\pi k/N} \check{X}_k = ( 1 - 2\pi f_{{\rm c},x} \Delta t ) \; \check{X}_k + \sqrt{2 D \Delta t} \; \check{W}_{k,x}$
Equation (9.43) should be
$\displaystyle P_k = \frac{|\check{X}_k|^2}{T_{\rm s}} = \frac{D/(2\pi^2 \Delta t)}{f_{{\rm c},x}^2 + f_k^2} |\check{W}_{k,x}|^2$
Equation (9.44) should be
$\displaystyle \langle P_k \rangle> = \frac{D/(2\pi^2)}{f_{{\rm c},x}^2 + f_k^2}$
Thanks to Brian Koss from Thorlabs for finding these mistakes!

Page 292. Equation (9.65) should be
$P(f) = \frac{D/\pi^2}{f^2+f_{\rm c}^2} + \frac{A^2}{2 \left( 1 + {f_{\rm c}^2 \over f_{\rm stage}^2} \right)} \delta(f-f_{\rm stage})$
Thanks to Maria Grazia Donato for finding this mistake!

Page 293. Equation (9.67) should be
$\frac{A^2}{2 \left( 1 + {f_{\rm c}^2 \over f_{\rm stage}^2} \right)}$
Thanks to Maria Grazia Donato for finding this mistake!